Station distribution and quality control for real-time moment tensor inversion at regional distances for the southwestern Iberian Peninsula

Science.gov (United States)

Convers, Jaime; Custodio, Susana

2016-04-01

Rapid assessment of seismological parameters pertinent to the nucleation and rupture of earthquakes are now routinely calculated by local and regional seismic networks. With the increasing number of stations, fast data transmission, and advanced computer power, we can now go beyond accurate magnitude and epicentral locations, to rapid estimations of other higher-order earthquake parameters such as seismic moment tensor. Although an increased number of stations can minimize azimuthal gaps, it also increases computation time, and potentially introduces poor quality data that often leads to a lower the stability of automated inversions. In this presentation, we focus on moment tensor calculations for earthquakes occurring offshore the southwestern Iberian peninsula. The available regional seismic data in this region has a significant azimuthal gap that results from the geographical setting. In this case, increasing the number of data from stations spanning a small area (and at a small azimuthal angle) increases the calculation time without necessarily improving the accuracy of the inversion. Additionally, limited regional data coverage makes it imperative to exclude poor-quality data, as their negative effect on moment tensor inversions is often significant. In our work, we analyze methods to minimize the effects of large azimuthal gaps in a regional station coverage, of potential bias by uneven station distribution, and of poor data quality in moment tensor inversions obtained for earthquakes offshore the southwestern Iberian peninsula. We calculate moment tensors using the KIWI tools, and we implement different configurations of station-weighing, and cross-correlation of neighboring stations, with the aim of automatically estimating and selecting high-quality data, improving the accuracy of results, and reducing the computation time of moment tensor inversions. As the available recent intermediate-size events offshore the Iberian peninsula is limited due to the long

A cut-&-paste strategy for the 3-D inversion of helicopter-borne electromagnetic data - I. 3-D inversion using the explicit Jacobian and a tensor-based formulation

Science.gov (United States)

Scheunert, M.; Ullmann, A.; Afanasjew, M.; Börner, R.-U.; Siemon, B.; Spitzer, K.

2016-06-01

We present an inversion concept for helicopter-borne frequency-domain electromagnetic (HEM) data capable of reconstructing 3-D conductivity structures in the subsurface. Standard interpretation procedures often involve laterally constrained stitched 1-D inversion techniques to create pseudo-3-D models that are largely representative for smoothly varying conductivity distributions in the subsurface. Pronounced lateral conductivity changes may, however, produce significant artifacts that can lead to serious misinterpretation. Still, 3-D inversions of entire survey data sets are numerically very expensive. Our approach is therefore based on a cut-&-paste strategy whereupon the full 3-D inversion needs to be applied only to those parts of the survey where the 1-D inversion actually fails. The introduced 3-D Gauss-Newton inversion scheme exploits information given by a state-of-the-art (laterally constrained) 1-D inversion. For a typical HEM measurement, an explicit representation of the Jacobian matrix is inevitable which is caused by the unique transmitter-receiver relation. We introduce tensor quantities which facilitate the matrix assembly of the forward operator as well as the efficient calculation of the Jacobian. The finite difference forward operator incorporates the displacement currents because they may seriously affect the electromagnetic response at frequencies above 100. Finally, we deliver the proof of concept for the inversion using a synthetic data set with a noise level of up to 5%.

Moment tensor inversion for two micro-earthquakes occurring inside the Haje gas storage facilities, Czech Republic

Czech Academy of Sciences Publication Activity Database

Benetatos, C.; Málek, Jiří; Verga, F.

2013-01-01

Roč. 17, č. 2 (2013), s. 557-577 ISSN 1383-4649 Institutional support: RVO:67985891 Keywords : micro-earthquake * moment-tensor inversion * gas storage * ISOLA Subject RIV: DD - Geochemistry Impact factor: 1.386, year: 2013

Inversion of calcite twin data for paleostress orientations and magnitudes: A new technique tested and calibrated on numerically-generated and natural data

Science.gov (United States)

Parlangeau, Camille; Lacombe, Olivier; Schueller, Sylvie; Daniel, Jean-Marc

2018-01-01

The inversion of calcite twin data is a powerful tool to reconstruct paleostresses sustained by carbonate rocks during their geological history. Following Etchecopar's (1984) pioneering work, this study presents a new technique for the inversion of calcite twin data that reconstructs the 5 parameters of the deviatoric stress tensors from both monophase and polyphase twin datasets. The uncertainties in the parameters of the stress tensors reconstructed by this new technique are evaluated on numerically-generated datasets. The technique not only reliably defines the 5 parameters of the deviatoric stress tensor, but also reliably separates very close superimposed stress tensors (30° of difference in maximum principal stress orientation or switch between σ3 and σ2 axes). The technique is further shown to be robust to sampling bias and to slight variability in the critical resolved shear stress. Due to our still incomplete knowledge of the evolution of the critical resolved shear stress with grain size, our results show that it is recommended to analyze twin data subsets of homogeneous grain size to minimize possible errors, mainly those concerning differential stress values. The methodological uncertainty in principal stress orientations is about ± 10°; it is about ± 0.1 for the stress ratio. For differential stresses, the uncertainty is lower than ± 30%. Applying the technique to vein samples within Mesozoic limestones from the Monte Nero anticline (northern Apennines, Italy) demonstrates its ability to reliably detect and separate tectonically significant paleostress orientations and magnitudes from naturally deformed polyphase samples, hence to fingerprint the regional paleostresses of interest in tectonic studies.

On Inverse Coefficient Heat-Conduction Problems on Reconstruction of Nonlinear Components of the Thermal-Conductivity Tensor of Anisotropic Bodies

Science.gov (United States)

Formalev, V. F.; Kolesnik, S. A.

2017-11-01

The authors are the first to present a closed procedure for numerical solution of inverse coefficient problems of heat conduction in anisotropic materials used as heat-shielding ones in rocket and space equipment. The reconstructed components of the thermal-conductivity tensor depend on temperature (are nonlinear). The procedure includes the formation of experimental data, the implicit gradient-descent method, the economical absolutely stable method of numerical solution of parabolic problems containing mixed derivatives, the parametric identification, construction, and numerical solution of the problem for elements of sensitivity matrices, the development of a quadratic residual functional and regularizing functionals, and also the development of algorithms and software systems. The implicit gradient-descent method permits expanding the quadratic functional in a Taylor series with retention of the linear terms for the increments of the sought functions. This substantially improves the exactness and stability of solution of the inverse problems. Software systems are developed with account taken of the errors in experimental data and disregarding them. On the basis of a priori assumptions of the qualitative behavior of the functional dependences of the components of the thermal-conductivity tensor on temperature, regularizing functionals are constructed by means of which one can reconstruct the components of the thermal-conductivity tensor with an error no higher than the error of the experimental data. Results of the numerical solution of the inverse coefficient problems on reconstruction of nonlinear components of the thermal-conductivity tensor have been obtained and are discussed.

Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

Science.gov (United States)

Sun, Yong; Meng, Zhaohai; Li, Fengting

2018-03-01

Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.

Joint Inversion of Gravity and Gravity Tensor Data Using the Structural Index as Weighting Function Rate Decay

Science.gov (United States)

Ialongo, S.; Cella, F.; Fedi, M.; Florio, G.

2011-12-01

Most geophysical inversion problems are characterized by a number of data considerably higher than the number of the unknown parameters. This corresponds to solve highly underdetermined systems. To get a unique solution, a priori information must be therefore introduced. We here analyze the inversion of the gravity gradient tensor (GGT). Previous approaches to invert jointly or independently more gradient components are by Li (2001) proposing an algorithm using a depth weighting function and Zhdanov et alii (2004), providing a well focused inversion of gradient data. Both the methods give a much-improved solution compared with the minimum length solution, which is invariably shallow and not representative of the true source distribution. For very undetermined problems, this feature is due to the role of the depth weighting matrices used by both the methods. Recently, Cella and Fedi (2011) showed however that for magnetic and gravity data the depth weighting function has to be defined carefully, under a preliminary application of Euler Deconvolution or Depth from Extreme Point methods, yielding the appropriate structural index and then using it as the rate decay of the weighting function. We therefore propose to extend this last approach to invert jointly or independently the GGT tensor using the structural index as weighting function rate decay. In case of a joint inversion, gravity data can be added as well. This multicomponent case is also relevant because the simultaneous use of several components and gravity increase the number of data and reduce the algebraic ambiguity compared to the inversion of a single component. The reduction of such ambiguity was shown in Fedi et al, (2005) decisive to get an improved depth resolution in inverse problems, independently from any form of depth weighting function. The method is demonstrated to synthetic cases and applied to real cases, such as the Vredefort impact area (South Africa), characterized by a complex density

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

International Nuclear Information System (INIS)

Smirnov, Yu.F.; Tolstoi, V.N.; Kharitonov, Yu.I.

1993-01-01

The tree technique for the quantum algebra su q (2) developed in an earlier study is used to construct the q analog of the algebra of irreducible tensor operators. The adjoint action of the algebra su q (2) on irreducible tensor operators is discussed, and the adjoint R matrix is introduced. A set of expressions is obtained for the matrix elements of various irreducible tensor operators and combinations of them. As an application, the recursion relations for the Clebsch-Gordan and Racah coefficients of the algebra su q (2) are derived. 16 refs

Fermionic particles with positron-dependent mass in the presence of inversely quadratic Yukawa potential and tensor interaction

International Nuclear Information System (INIS)

Bahar, M.K.; Yasuk, F.

2013-01-01

Approximate solutions of the Dirac equation with positron-dependent mass are presented for the inversely quadratic Yukawa potential and Coulomb-like tensor interaction by using the asymptotic iteration method. The energy eigenvalues and the corresponding normalized eigenfunctions are obtained in the case of positron-dependent mass and arbitrary spin-orbit quantum number k state and approximation on the spin-orbit coupling term. (author)

3D reconstruction of tensors and vectors

International Nuclear Information System (INIS)

Defrise, Michel; Gullberg, Grant T.

2005-01-01

Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields

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

Science.gov (United States)

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

2016-08-01

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

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

Monte Carlo Volcano Seismic Moment Tensors

Science.gov (United States)

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

2015-12-01

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

Complete algebraic reduction of one-loop tensor Feynman integrals

International Nuclear Information System (INIS)

Fleischer, J.; Riemann, T.

2011-01-01

We set up a new, flexible approach for the tensor reduction of one-loop Feynman integrals. The 5-point tensor integrals up to rank R=5 are expressed by 4-point tensor integrals of rank R-1, such that the appearance of the inverse 5-point Gram determinant is avoided. The 4-point tensor coefficients are represented in terms of 4-point integrals, defined in d dimensions, 4-2ε≤d≤4-2ε+2(R-1), with higher powers of the propagators. They can be further reduced to expressions which stay free of the inverse 4-point Gram determinants but contain higher-dimensional 4-point integrals with only the first power of scalar propagators, plus 3-point tensor coefficients. A direct evaluation of the higher-dimensional 4-point functions would avoid the appearance of inverse powers of the Gram determinants completely. The simplest approach, however, is to apply here dimensional recurrence relations in order to reduce them to the familiar 2- to 4-point functions in generic dimension d=4-2ε, introducing thereby coefficients with inverse 4-point Gram determinants up to power R for tensors of rank R. For small or vanishing Gram determinants--where this reduction is not applicable--we use analytic expansions in positive powers of the Gram determinants. Improving the convergence of the expansions substantially with Pade approximants we close up to the evaluation of the 4-point tensor coefficients for larger Gram determinants. Finally, some relations are discussed which may be useful for analytic simplifications of Feynman diagrams.

Manuel Rocha Medal recipient - A relative moment tensor inversion technique applied to seismicity induced by mining

CSIR Research Space (South Africa)

Linzer, LM

2005-04-01

Full Text Available The primary objective of this study was to develop a robust MTI method to estimate the moment tensors of clusters of seismic events recorded in the underground environment. To achieve this, three 'hybrid' MTI methods were developed by the author...

3D inversion of full gravity gradient tensor data in spherical coordinate system using local north-oriented frame

Science.gov (United States)

Zhang, Yi; Wu, Yulong; Yan, Jianguo; Wang, Haoran; Rodriguez, J. Alexis P.; Qiu, Yue

2018-04-01

In this paper, we propose an inverse method for full gravity gradient tensor data in the spherical coordinate system. As opposed to the traditional gravity inversion in the Cartesian coordinate system, our proposed method takes the curvature of the Earth, the Moon, or other planets into account, using tesseroid bodies to produce gravity gradient effects in forward modeling. We used both synthetic and observed datasets to test the stability and validity of the proposed method. Our results using synthetic gravity data show that our new method predicts the depth of the density anomalous body efficiently and accurately. Using observed gravity data for the Mare Smythii area on the moon, the density distribution of the crust in this area reveals its geological structure. These results validate the proposed method and potential application for large area data inversion of planetary geological structures.[Figure not available: see fulltext.

Source Parameters from Full Moment Tensor Inversions of Potentially Induced Earthquakes in Western Canada

Science.gov (United States)

Wang, R.; Gu, Y. J.; Schultz, R.; Kim, A.; Chen, Y.

2015-12-01

During the past four years, the number of earthquakes with magnitudes greater than three has substantially increased in the southern section of Western Canada Sedimentary Basin (WCSB). While some of these events are likely associated with tectonic forces, especially along the foothills of the Canadian Rockies, a significant fraction occurred in previously quiescent regions and has been linked to waste water disposal or hydraulic fracturing. A proper assessment of the origin and source properties of these 'induced earthquakes' requires careful analyses and modeling of regional broadband data, which steadily improved during the past 8 years due to recent establishments of regional broadband seismic networks such as CRANE, RAVEN and TD. Several earthquakes, especially those close to fracking activities (e.g. Fox creek town, Alberta) are analyzed. Our preliminary full moment tensor inversion results show maximum horizontal compressional orientations (P-axis) along the northeast-southwest orientation, which agree with the regional stress directions from borehole breakout data and the P-axis of historical events. The decomposition of those moment tensors shows evidence of strike-slip mechanism with near vertical fault plane solutions, which are comparable to the focal mechanisms of injection induced earthquakes in Oklahoma. Minimal isotropic components have been observed, while a modest percentage of compensated-linear-vector-dipole (CLVD) components, which have been linked to fluid migraition, may be required to match the waveforms. To further evaluate the non-double-couple components, we compare the outcomes of full, deviatoric and pure double couple (DC) inversions using multiple frequency ranges and phases. Improved location and depth information from a novel grid search greatly assists the identification and classification of earthquakes in potential connection with fluid injection or extraction. Overall, a systematic comparison of the source attributes of

Thermal measurements and inverse techniques

CERN Document Server

Orlande, Helcio RB; Maillet, Denis; Cotta, Renato M

2011-01-01

With its uncommon presentation of instructional material regarding mathematical modeling, measurements, and solution of inverse problems, Thermal Measurements and Inverse Techniques is a one-stop reference for those dealing with various aspects of heat transfer. Progress in mathematical modeling of complex industrial and environmental systems has enabled numerical simulations of most physical phenomena. In addition, recent advances in thermal instrumentation and heat transfer modeling have improved experimental procedures and indirect measurements for heat transfer research of both natural phe

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

Science.gov (United States)

Kim, Jae G; Park, So E; Lee, Soo Y

2014-01-01

In tissue elasticity imaging, measuring the strain tensor components is necessary to solve the inverse problem. However, it is impractical to measure all the tensor components in ultrasound or MRI elastography because of their anisotropic spatial resolution. The objective of this study is to compute 3D strain tensor maps from the 3D CT images of a tissue-mimicking phantom. We took 3D micro-CT images of the phantom twice with applying two different mechanical compressions to it. Applying the 3D image correlation technique to the CT images under different compression, we computed 3D displacement vectors and strain tensors at every pixel. To evaluate the accuracy of the strain tensor maps, we made a 3D FEM model of the phantom, and we computed strain tensor maps through FEM simulation. Experimentally obtained strain tensor maps showed similar patterns to the FEM-simulated ones in visual inspection. The correlation between the strain tensor maps obtained from the experiment and the FEM simulation ranges from 0.03 to 0.93. Even though the strain tensor maps suffer from high level noise, we expect the x-ray strain tensor imaging may find some biomedical applications such as malignant tissue characterization and stress analysis inside the tissues.

A moment-tensor catalog for intermediate magnitude earthquakes in Mexico

Science.gov (United States)

Rodríguez Cardozo, Félix; Hjörleifsdóttir, Vala; Martínez-Peláez, Liliana; Franco, Sara; Iglesias Mendoza, Arturo

2016-04-01

Located among five tectonic plates, Mexico is one of the world's most seismically active regions. The earthquake focal mechanisms provide important information on the active tectonics. A widespread technique for estimating the earthquake magnitud and focal mechanism is the inversion for the moment tensor, obtained by minimizing a misfit function that estimates the difference between synthetic and observed seismograms. An important element in the estimation of the moment tensor is an appropriate velocity model, which allows for the calculation of accurate Green's Functions so that the differences between observed and synthetics seismograms are due to the source of the earthquake rather than the velocity model. However, calculating accurate synthetic seismograms gets progressively more difficult as the magnitude of the earthquakes decreases. Large earthquakes (M>5.0) excite waves of longer periods that interact weakly with lateral heterogeneities in the crust. For these events, using 1D velocity models to compute Greens functions works well and they are well characterized by seismic moment tensors reported in global catalogs (eg. USGS fast moment tensor solutions and GCMT). The opposite occurs for small and intermediate sized events, where the relatively shorter periods excited interact strongly with lateral heterogeneities in the crust and upper mantle. To accurately model the Green's functions for the smaller events in a large heterogeneous area, requires 3D or regionalized 1D models. To obtain a rapid estimate of earthquake magnitude, the National Seismological Survey in Mexico (Servicio Sismológico Nacional, SSN) automatically calculates seismic moment tensors for events in the Mexican Territory (Franco et al., 2002; Nolasco-Carteño, 2006). However, for intermediate-magnitude and small earthquakes the signal-to-noise ratio could is low for many of the seismic stations, and without careful selection and filtering of the data, obtaining a stable focal mechanism

Moment Inversion of the DPRK Nuclear Tests Using Finite-Difference Three-dimensional Strain Green's Tensors

Science.gov (United States)

Bao, X.; Shen, Y.; Wang, N.

2017-12-01

Accurate estimation of the source moment is important for discriminating underground explosions from earthquakes and other seismic sources. In this study, we invert for the full moment tensors of the recent seismic events (since 2016) at the Democratic People's Republic of Korea (PRRK) Punggye-ri test site. We use waveform data from broadband seismic stations located in China, Korea, and Japan in the inversion. Using a non-staggered-grid, finite-difference algorithm, we calculate the strain Green's tensors (SGT) based on one-dimensional (1D) and three-dimensional (3D) Earth models. Taking advantage of the source-receiver reciprocity, a SGT database pre-calculated and stored for the Punggye-ri test site is used in inversion for the source mechanism of each event. With the source locations estimated from cross-correlation using regional Pn and Pn-coda waveforms, we obtain the optimal source mechanism that best fits synthetics to the observed waveforms of both body and surface waves. The moment solutions of the first three events (2016-01-06, 2016-09-09, and 2017-09-03) show dominant isotropic components, as expected from explosions, though there are also notable non-isotropic components. The last event ( 8 minutes after the mb6.3 explosion in 2017) contained mainly implosive component, suggesting a collapse following the explosion. The solutions from the 3D model can better fit observed waveforms than the corresponding solutions from the 1D model. The uncertainty in the resulting moment solution is influenced by heterogeneities not resolved by the Earth model according to the waveform misfit. Using the moment solutions, we predict the peak ground acceleration at the Punggye-ri test site and compare the prediction with corresponding InSAR and other satellite images.

Novel region of interest interrogation technique for diffusion tensor imaging analysis in the canine brain.

Science.gov (United States)

Li, Jonathan Y; Middleton, Dana M; Chen, Steven; White, Leonard; Ellinwood, N Matthew; Dickson, Patricia; Vite, Charles; Bradbury, Allison; Provenzale, James M

2017-08-01

Purpose We describe a novel technique for measuring diffusion tensor imaging metrics in the canine brain. We hypothesized that a standard method for region of interest placement could be developed that is highly reproducible, with less than 10% difference in measurements between raters. Methods Two sets of canine brains (three seven-week-old full-brains and two 17-week-old single hemispheres) were scanned ex-vivo on a 7T small-animal magnetic resonance imaging system. Strict region of interest placement criteria were developed and then used by two raters to independently measure diffusion tensor imaging metrics within four different white-matter regions within each specimen. Average values of fractional anisotropy, radial diffusivity, and the three eigenvalues (λ1, λ2, and λ3) within each region in each specimen overall and within each individual image slice were compared between raters by calculating the percentage difference between raters for each metric. Results The mean percentage difference between raters for all diffusion tensor imaging metrics when pooled by each region and specimen was 1.44% (range: 0.01-5.17%). The mean percentage difference between raters for all diffusion tensor imaging metrics when compared by individual image slice was 2.23% (range: 0.75-4.58%) per hemisphere. Conclusion Our results indicate that the technique described is highly reproducible, even when applied to canine specimens of differing age, morphology, and image resolution. We propose this technique for future studies of diffusion tensor imaging analysis in canine brains and for cross-sectional and longitudinal studies of canine brain models of human central nervous system disease.

Extraction of remanent magnetization from magnetization vector inversions of airborne full tensor magnetic gradiometry data

Science.gov (United States)

Queitsch, M.; Schiffler, M.; Stolz, R.; Meyer, M.; Kukowski, N.

2017-12-01

Measurements of the Earth's magnetic field are one of the most used methods in geophysical exploration. The ambiguity of the method, especially during modeling and inversion of magnetic field data sets, is one of its biggest challenges. Additional directional information, e.g. gathered by gradiometer systems based on Superconducting Quantum Interference Devices (SQUIDs), will positively influence the inversion results and will thus lead to better subsurface magnetization models. This is especially beneficial, regarding the shape and direction of magnetized structures, especially when a significant remanent magnetization of the underlying sources is present. The possibility to separate induced and remanent contributions to the total magnetization may in future also open up advanced ways for geological interpretation of the data, e.g. a first estimation of diagenesis processes. In this study we present the results of airborne full tensor magnetic gradiometry (FTMG) surveys conducted over a dolerite intrusion in central Germany and the results of two magnetization vector inversions (MVI) of the FTMG and a conventional total field anomaly data set. A separation of the two main contributions of the acquired total magnetization will be compared with information of the rock magnetization measured on orientated rock samples. The FTMG inversion results show a much better agreement in direction and strength of both total and remanent magnetization compared to the inversion using only total field anomaly data. To enhance the separation process, the application of additional geophysical methods, i.e. frequency domain electromagnetics (FDEM), in order to gather spatial information of subsurface rock susceptibility will also be discussed. In this approach, we try to extract not only information on subsurface conductivity but also the induced magnetization. Using the total magnetization from the FTMG data and the induced magnetization from the FDEM data, the full separation of

Tucker Tensor analysis of Matern functions in spatial statistics

KAUST Repository

Litvinenko, Alexander

2018-03-09

In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will allow us to consider much larger data sets or finer meshes. Covariance matrices are crucial in spatio-temporal statistical tasks, but are often very expensive to compute and store, especially in 3D. Therefore, we approximate covariance functions by cheap surrogates in a low-rank tensor format. We apply the Tucker and canonical tensor decompositions to a family of Matern- and Slater-type functions with varying parameters and demonstrate numerically that their approximations exhibit exponentially fast convergence. We prove the exponential convergence of the Tucker and canonical approximations in tensor rank parameters. Several statistical operations are performed in this low-rank tensor format, including evaluating the conditional covariance matrix, spatially averaged estimation variance, computing a quadratic form, determinant, trace, loglikelihood, inverse, and Cholesky decomposition of a large covariance matrix. Low-rank tensor approximations reduce the computing and storage costs essentially. For example, the storage cost is reduced from an exponential O(n^d) to a linear scaling O(drn), where d is the spatial dimension, n is the number of mesh points in one direction, and r is the tensor rank. Prerequisites for applicability of the proposed techniques are the assumptions that the data, locations, and measurements lie on a tensor (axes-parallel) grid and that the covariance function depends on a distance, ||x-y||.

Inverse Raman effect: applications and detection techniques

Energy Technology Data Exchange (ETDEWEB)

Hughes, L.J. Jr.

1980-08-01

The processes underlying the inverse Raman effect are qualitatively described by comparing it to the more familiar phenomena of conventional and stimulated Raman scattering. An experession is derived for the inverse Raman absorption coefficient, and its relationship to the stimulated Raman gain is obtained. The power requirements of the two fields are examined qualitatively and quantitatively. The assumption that the inverse Raman absorption coefficient is constant over the interaction length is examined. Advantages of the technique are discussed and a brief survey of reported studies is presented.

Inverse Raman effect: applications and detection techniques

International Nuclear Information System (INIS)

Hughes, L.J. Jr.

1980-08-01

The processes underlying the inverse Raman effect are qualitatively described by comparing it to the more familiar phenomena of conventional and stimulated Raman scattering. An experession is derived for the inverse Raman absorption coefficient, and its relationship to the stimulated Raman gain is obtained. The power requirements of the two fields are examined qualitatively and quantitatively. The assumption that the inverse Raman absorption coefficient is constant over the interaction length is examined. Advantages of the technique are discussed and a brief survey of reported studies is presented

New results for algebraic tensor reduction of Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

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

2012-02-15

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

New results for algebraic tensor reduction of Feynman integrals

International Nuclear Information System (INIS)

Fleischer, Jochem; Yundin, Valery

2012-02-01

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

TensorLy: Tensor Learning in Python

NARCIS (Netherlands)

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.

Analog fault diagnosis by inverse problem technique

KAUST Repository

Ahmed, Rania F.

2011-12-01

A novel algorithm for detecting soft faults in linear analog circuits based on the inverse problem concept is proposed. The proposed approach utilizes optimization techniques with the aid of sensitivity analysis. The main contribution of this work is to apply the inverse problem technique to estimate the actual parameter values of the tested circuit and so, to detect and diagnose single fault in analog circuits. The validation of the algorithm is illustrated through applying it to Sallen-Key second order band pass filter and the results show that the detecting percentage efficiency was 100% and also, the maximum error percentage of estimating the parameter values is 0.7%. This technique can be applied to any other linear circuit and it also can be extended to be applied to non-linear circuits. © 2011 IEEE.

Sparse alignment for robust tensor learning.

Science.gov (United States)

Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming

2014-10-01

Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.

TensorLy: Tensor Learning in Python

OpenAIRE

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \\emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scie...

Seismic moment tensor inversion using 3D velocity model and its application to the 2013 Lushan earthquake sequence

Science.gov (United States)

Zhu, Lupei; Zhou, Xiaofeng

2016-10-01

Source inversion of small-magnitude events such as aftershocks or mine collapses requires use of relatively high frequency seismic waveforms which are strongly affected by small-scale heterogeneities in the crust. In this study, we developed a new inversion method called gCAP3D for determining general moment tensor of a seismic source using Green's functions of 3D models. It inherits the advantageous features of the ;Cut-and-Paste; (CAP) method to break a full seismogram into the Pnl and surface-wave segments and to allow time shift between observed and predicted waveforms. It uses grid search for 5 source parameters (relative strengths of the isotropic and compensated-linear-vector-dipole components and the strike, dip, and rake of the double-couple component) that minimize the waveform misfit. The scalar moment is estimated using the ratio of L2 norms of the data and synthetics. Focal depth can also be determined by repeating the inversion at different depths. We applied gCAP3D to the 2013 Ms 7.0 Lushan earthquake and its aftershocks using a 3D crustal-upper mantle velocity model derived from ambient noise tomography in the region. We first relocated the events using the double-difference method. We then used the finite-differences method and reciprocity principle to calculate Green's functions of the 3D model for 20 permanent broadband seismic stations within 200 km from the source region. We obtained moment tensors of the mainshock and 74 aftershocks ranging from Mw 5.2 to 3.4. The results show that the Lushan earthquake is a reverse faulting at a depth of 13-15 km on a plane dipping 40-47° to N46° W. Most of the aftershocks occurred off the main rupture plane and have similar focal mechanisms to the mainshock's, except in the proximity of the mainshock where the aftershocks' focal mechanisms display some variations.

Relativistic New Yukawa-Like Potential and Tensor Coupling

International Nuclear Information System (INIS)

Ikhdair, S.M.; Hamzavi, M.

2012-01-01

We approximately solve the Dirac equation for a new suggested generalized inversely quadratic Yukawa potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number κ. In the framework of the spin and pseudo spin (p-spin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions, in closed form, by using the parametric Nikiforov-Uvarov method. The numerical results show that the Coulomb-like tensor interaction, -T/r, removes degeneracies between spin and p-spin state doublets. The Dirac solutions in the presence of exact spin symmetry are reduced to Schroedinger solutions for Yukawa and inversely quadratic Yukawa potentials. (author)

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

Virtual Seismometers for Induced Seismicity Monitoring and Full Moment Tensor Inversion

Science.gov (United States)

Morency, C.; Matzel, E.

2016-12-01

Induced seismicity is associated with subsurface fluid injection, and puts at risk efforts to develop geologic carbon sequestration and enhanced geothermal systems. We are developing methods to monitor the microseismically active zone so that we can ultimately identify faults at risk of slipping. The virtual seismometer method (VSM) is an interferometric technique that is very sensitive to the source parameters (location, mechanism and magnitude) and to the Earth structure in the source region. VSM works by virtually placing seismometers inside a micro events cloud, where we can focus on properties directly between induced micro events, and effectively replacing each earthquake with a virtual seismometer recording all the others. Here, we show that the cross-correlated signals from seismic wavefields triggered by two events and recorded at the surface are a combination of the strain field between these two sources times a moment tensor. Based on this relationship, we demonstrate how we can use these measured cross-correlated signals to invert for full moment tensor. The advantage of VSM is to allow to considerably reduce the modeled numerical domain to the region directly around the micro events cloud, which lowers computational cost, permits to reach higher frequency resolution, and suppresses the impact of the Earth structural model uncertainties outside the micro events cloud. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

A complete algebraic reduction of one-loop tensor Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Fleischer, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2010-09-15

Guided by the need to eliminate inverse Gram determinants (){sub 5} from tensorial 5-point functions and sub-Gram determinants (){sub 4} from tensorial 4-point functions, we set up a new and very efficient approach for the tensor reduction of Feynman integrals. We eliminate all Gram determinants for one-loop 5-point integrals up to tensors of rank R=5 by reducing their tensor coefficients to higherdimensional 4-point tensor coefficients. These in turn are reduced to expressions which are free of inverse powers of (){sub 4}, but depend on higher-dimensional integrals I{sub 4}{sup (d)} with d{<=}2R. Their expression in terms of scalar integrals defined in the generic dimension, I{sub 4}; I{sub 3}; I{sub 2}; I{sub 1}, however, introduces coefficients [1=(){sub 4}]{sup R} for tensors of rank R. For small or vanishing (){sub 4}, an efficient expansion is found so that a stable numerical evaluation of massive and massless Feynman integrals at arbitrary values of the Gram determinants is made possible. Finally, some relations are mentioned which may be useful for analytic simplifications of the original Feynman diagrams. (orig.)

A new validation technique for estimations of body segment inertia tensors: Principal axes of inertia do matter.

Science.gov (United States)

Rossi, Marcel M; Alderson, Jacqueline; El-Sallam, Amar; Dowling, James; Reinbolt, Jeffrey; Donnelly, Cyril J

2016-12-08

The aims of this study were to: (i) establish a new criterion method to validate inertia tensor estimates by setting the experimental angular velocity data of an airborne objects as ground truth against simulations run with the estimated tensors, and (ii) test the sensitivity of the simulations to changes in the inertia tensor components. A rigid steel cylinder was covered with reflective kinematic markers and projected through a calibrated motion capture volume. Simulations of the airborne motion were run with two models, using inertia tensor estimated with geometric formula or the compound pendulum technique. The deviation angles between experimental (ground truth) and simulated angular velocity vectors and the root mean squared deviation angle were computed for every simulation. Monte Carlo analyses were performed to assess the sensitivity of simulations to changes in magnitude of principal moments of inertia within ±10% and to changes in orientation of principal axes of inertia within ±10° (of the geometric-based inertia tensor). Root mean squared deviation angles ranged between 2.9° and 4.3° for the inertia tensor estimated geometrically, and between 11.7° and 15.2° for the compound pendulum values. Errors up to 10% in magnitude of principal moments of inertia yielded root mean squared deviation angles ranging between 3.2° and 6.6°, and between 5.5° and 7.9° when lumped with errors of 10° in principal axes of inertia orientation. The proposed technique can effectively validate inertia tensors from novel estimation methods of body segment inertial parameter. Principal axes of inertia orientation should not be neglected when modelling human/animal mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.

Frequency sensitive moment tensor inversion for light to moderate magnitude earthquakes in eastern Africa

Science.gov (United States)

Barth, A.; Wenzel, F.; Giardini, D.

2007-08-01

We provide a procedure for the routine determination of moment tensors from earthquakes with magnitudes as low as M W 4.4 using data recorded by only a few permanent seismic stations at regional to teleseismic distances. Waveforms are inverted for automatically determined frequency pass-bands that depend on source-receiver locations as well as the earthquake magnitude. Inversion results are stable against small variations in the frequency band and provide low data variances, i.e., a good fit between observed and modelled waveform traces. The total frequency band used for our procedure ranges from 10 mHz to 29 mHz (periods of 35 s to 100 s). This enables us to determine focal mechanisms for earthquakes that were not derived previously by routine procedures of CMT or other agencies. As a case study, we determine focal mechanism solutions of 38 light to moderate magnitude earthquakes in eastern Africa between 1995 and 2002.

A one-dimensional seismic model for Uturuncu volcano, Bolivia, and its impact on full moment tensor inversions

KAUST Repository

Shen, Weisen; Alvizuri, Celso; Lin, Fan-Chi; Tape, Carl

2016-01-01

Using receiver functions, Rayleigh wave phase velocity dispersion determined from ambient noise and teleseismic earthquakes, and Rayleigh wave horizontal to vertical ground motion amplitude ratios from earthquakes observed across the PLUTONS seismic array, we construct a one-dimensional (1-D) S-wave velocity (Vs) seismic model with uncertainties for Uturuncu volcano, Bolivia, located in the central Andes and overlying the eastward-subducting Nazca plate. We find a fast upper crustal lid placed upon a low-velocity zone (LVZ) in the mid-crust. By incorporating all three types of measurements with complimentary sensitivity, we also explore the average density and Vp/Vs (ratio of P-wave to S-wave velocity) structures beneath the young silicic volcanic field. We observe slightly higher Vp/Vs and a decrease in density near the LVZ, which implies a dacitic source of the partially molten magma body. We exploit the impact of the 1-D model on full moment tensor inversion for the two largest local earthquakes recorded (both magnitude ∼3), demonstrating that the 1-D model influences the waveform fits and the estimated source type for the full moment tensor. Our 1-D model can serve as a robust starting point for future efforts to determine a three-dimensional velocity model for Uturuncu volcano.

A one-dimensional seismic model for Uturuncu volcano, Bolivia, and its impact on full moment tensor inversions

KAUST Repository

Shen, Weisen

2016-11-24

Using receiver functions, Rayleigh wave phase velocity dispersion determined from ambient noise and teleseismic earthquakes, and Rayleigh wave horizontal to vertical ground motion amplitude ratios from earthquakes observed across the PLUTONS seismic array, we construct a one-dimensional (1-D) S-wave velocity (Vs) seismic model with uncertainties for Uturuncu volcano, Bolivia, located in the central Andes and overlying the eastward-subducting Nazca plate. We find a fast upper crustal lid placed upon a low-velocity zone (LVZ) in the mid-crust. By incorporating all three types of measurements with complimentary sensitivity, we also explore the average density and Vp/Vs (ratio of P-wave to S-wave velocity) structures beneath the young silicic volcanic field. We observe slightly higher Vp/Vs and a decrease in density near the LVZ, which implies a dacitic source of the partially molten magma body. We exploit the impact of the 1-D model on full moment tensor inversion for the two largest local earthquakes recorded (both magnitude ∼3), demonstrating that the 1-D model influences the waveform fits and the estimated source type for the full moment tensor. Our 1-D model can serve as a robust starting point for future efforts to determine a three-dimensional velocity model for Uturuncu volcano.

Estimation of Uncertainties of Full Moment Tensors

Science.gov (United States)

2017-10-06

For our moment tensor inversions, we use the ‘cut-and-paste’ ( CAP ) code of Zhu and Helmberger (1996) and Zhu and Ben-Zion (2013), with some...modifications. For the misfit function we use an L1 norm Silwal and Tape (2016), and we incorporate the number of misfitting polarities into the waveform... norm of the eigenvalue triple provides the magnitude of the moment tensor, leaving two free parameters to define the source type. In the same year

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

Science.gov (United States)

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

2017-08-01

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

Tensor completion for PDEs with uncertain coefficients and Bayesian Update

KAUST Repository

Litvinenko, Alexander

2017-03-05

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

Tensor completion for PDEs with uncertain coefficients and Bayesian Update

KAUST Repository

Litvinenko, Alexander

2017-01-01

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

Magnetic resonance separation imaging using a divided inversion recovery technique (DIRT).

Science.gov (United States)

Goldfarb, James W

2010-04-01

The divided inversion recovery technique is an MRI separation method based on tissue T(1) relaxation differences. When tissue T(1) relaxation times are longer than the time between inversion pulses in a segmented inversion recovery pulse sequence, longitudinal magnetization does not pass through the null point. Prior to additional inversion pulses, longitudinal magnetization may have an opposite polarity. Spatial displacement of tissues in inversion recovery balanced steady-state free-precession imaging has been shown to be due to this magnetization phase change resulting from incomplete magnetization recovery. In this paper, it is shown how this phase change can be used to provide image separation. A pulse sequence parameter, the time between inversion pulses (T180), can be adjusted to provide water-fat or fluid separation. Example water-fat and fluid separation images of the head, heart, and abdomen are presented. The water-fat separation performance was investigated by comparing image intensities in short-axis divided inversion recovery technique images of the heart. Fat, blood, and fluid signal was suppressed to the background noise level. Additionally, the separation performance was not affected by main magnetic field inhomogeneities.

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

Science.gov (United States)

Iwasaki, Tohru; Furukawa, Tetsuo

2016-05-01

In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.

The tensor product in Wadler's analysis of lists

DEFF Research Database (Denmark)

Nielson, Flemming; Nielson, Hanne Riis

1992-01-01

We consider abstract interpretation (in particular strictness analysis) for pairs and lists. We begin by reviewing the well-known fact that the best known description of a pair of elements is obtained using the tensor product rather than the cartesian product. We next present a generalisation...... of Wadler's strictness analysis for lists using the notion of open set. Finally, we illustrate the intimate connection between the case analysis implicit in Wadler's strictness analysis and the precision that the tensor product allows for modelling the inverse cons operation....

Efficient Tensor Strategy for Recommendation

Directory of Open Access Journals (Sweden)

Aboagye Emelia Opoku

2017-07-01

Full Text Available The era of big data has witnessed the explosion of tensor datasets, and large scale Probabilistic Tensor Factorization (PTF analysis is important to accommodate such increasing trend of data. Sparsity, and Cold-Start are some of the inherent problems of recommender systems in the era of big data. This paper proposes a novel Sentiment-Based Probabilistic Tensor Analysis technique senti-PTF to address the problems. The propose framework first applies a Natural Language Processing technique to perform sentiment analysis taking advantage of the huge sums of textual data generated available from the social media which are predominantly left untouched. Although some current studies do employ review texts, many of them do not consider how sentiments in reviews influence recommendation algorithm for prediction. There is therefore this big data text analytics gap whose modeling is computationally expensive. From our experiments, our novel machine learning sentiment-based tensor analysis is computationally less expensive, and addresses the cold-start problem, for optimal recommendation prediction.

The tensor product in Wadler's analysis of lists

DEFF Research Database (Denmark)

Nielson, Flemming; Nielson, Hanne Riis

1994-01-01

We consider abstract interpretation (in particular strictness analysis) for pairs and lists. We begin by reviewing the well-known fact that the best known description of a pair of elements is obtained using the tensor product rather than the cartesian product. We next present a generalisation...... of Wadler's strictness analysis for lists (1987) using the notion of open set. Finally, we illustrate the intimate connection between the case analysis implicit in Wadler's strictness analysis and the precision that the tensor product allows for modelling the inverse cons operation...

New Techniques for Deep Learning with Geospatial Data using TensorFlow, Earth Engine, and Google Cloud Platform

Science.gov (United States)

Hancher, M.

2017-12-01

Recent years have seen promising results from many research teams applying deep learning techniques to geospatial data processing. In that same timeframe, TensorFlow has emerged as the most popular framework for deep learning in general, and Google has assembled petabytes of Earth observation data from a wide variety of sources and made them available in analysis-ready form in the cloud through Google Earth Engine. Nevertheless, developing and applying deep learning to geospatial data at scale has been somewhat cumbersome to date. We present a new set of tools and techniques that simplify this process. Our approach combines the strengths of several underlying tools: TensorFlow for its expressive deep learning framework; Earth Engine for data management, preprocessing, postprocessing, and visualization; and other tools in Google Cloud Platform to train TensorFlow models at scale, perform additional custom parallel data processing, and drive the entire process from a single familiar Python development environment. These tools can be used to easily apply standard deep neural networks, convolutional neural networks, and other custom model architectures to a variety of geospatial data structures. We discuss our experiences applying these and related tools to a range of machine learning problems, including classic problems like cloud detection, building detection, land cover classification, as well as more novel problems like illegal fishing detection. Our improved tools will make it easier for geospatial data scientists to apply modern deep learning techniques to their own problems, and will also make it easier for machine learning researchers to advance the state of the art of those techniques.

On the computation of the demagnetization tensor field for an arbitrary particle shape using a Fourier space approach

International Nuclear Information System (INIS)

Beleggia, M.; Graef, M. de

2003-01-01

A method is presented to compute the demagnetization tensor field for uniformly magnetized particles of arbitrary shape. By means of a Fourier space approach it is possible to compute analytically the Fourier representation of the demagnetization tensor field for a given shape. Then, specifying the direction of the uniform magnetization, the demagnetizing field and the magnetostatic energy associated with the particle can be evaluated. In some particular cases, the real space representation is computable analytically. In general, a numerical inverse fast Fourier transform is required to perform the inversion. As an example, the demagnetization tensor field for the tetrahedron will be given

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.)

Multiple M2-branes and the embedding tensor

NARCIS (Netherlands)

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

2008-01-01

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

Anisotropy and phonon modes from analysis of the dielectric function tensor and the inverse dielectric function tensor of monoclinic yttrium orthosilicate

Science.gov (United States)

Mock, A.; Korlacki, R.; Knight, S.; Schubert, M.

2018-04-01

We determine the frequency dependence of the four independent Cartesian tensor elements of the dielectric function for monoclinic symmetry Y2SiO5 using generalized spectroscopic ellipsometry from 40-1200 cm-1. Three different crystal cuts, each perpendicular to a principle axis, are investigated. We apply our recently described augmentation of lattice anharmonicity onto the eigendielectric displacement vector summation approach [A. Mock et al., Phys. Rev. B 95, 165202 (2017), 10.1103/PhysRevB.95.165202], and we present and demonstrate the application of an eigendielectric displacement loss vector summation approach with anharmonic broadening. We obtain an excellent match between all measured and model-calculated dielectric function tensor elements and all dielectric loss function tensor elements. We obtain 23 Au and 22 Bu symmetry long-wavelength active transverse and longitudinal optical mode parameters including their eigenvector orientation within the monoclinic lattice. We perform density functional theory calculations and obtain 23 Au symmetry and 22 Bu transverse and longitudinal optical mode parameters and their orientation within the monoclinic lattice. We compare our results from ellipsometry and density functional theory and find excellent agreement. We also determine the static and above reststrahlen spectral range dielectric tensor values and find a recently derived generalization of the Lyddane-Sachs-Teller relation for polar phonons in monoclinic symmetry materials satisfied [M. Schubert, Phys Rev. Lett. 117, 215502 (2016), 10.1103/PhysRevLett.117.215502].

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

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

Science.gov (United States)

Dibb, Russell; Liu, Chunlei

2017-06-01

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

A conditioning technique for matrix inversion for Wilson fermions

International Nuclear Information System (INIS)

DeGrand, T.A.

1988-01-01

I report a simple technique for conditioning conjugate gradient or conjugate residue matrix inversion as applied to the lattice gauge theory problem of computing the propagator of Wilson fermions. One form of the technique provides about a factor of three speedup over an unconditioned algorithm while running at the same speed as an unconditioned algorithm. I illustrate the method as it is applied to a conjugate residue algorithm. (orig.)

Reduction method for one-loop tensor 5- and 6-point integrals revisited

International Nuclear Information System (INIS)

Diakonidis, Theodoros

2009-01-01

A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for the cancellation of leading inverse Gram determinants. The resulting compact formulae allow both for a study of analytical properties and for efficient numerical programming. Here some special numerical examples are presented. (orig.)

Reduction method for one-loop tensor 5- and 6-point integrals revisited

Energy Technology Data Exchange (ETDEWEB)

Diakonidis, Theodoros [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2009-01-15

A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for the cancellation of leading inverse Gram determinants. The resulting compact formulae allow both for a study of analytical properties and for efficient numerical programming. Here some special numerical examples are presented. (orig.)

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

2018-01-01

textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

2017-01-01

textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in

Tensor rank is not multiplicative under the tensor product

OpenAIRE

Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

2017-01-01

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...

Tensor surgery and tensor rank

NARCIS (Netherlands)

M. Christandl (Matthias); J. Zuiddam (Jeroen)

2018-01-01

textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices

Tensor surgery and tensor rank

NARCIS (Netherlands)

M. Christandl (Matthias); J. Zuiddam (Jeroen)

2016-01-01

textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new

Tensor rank is not multiplicative under the tensor product

DEFF Research Database (Denmark)

Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

2018-01-01

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection b...

On improving the efficiency of tensor voting

OpenAIRE

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

2011-01-01

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor v...

Bayesian ISOLA: new tool for automated centroid moment tensor inversion

Czech Academy of Sciences Publication Activity Database

Vackář, J.; Burjánek, Jan; Gallovič, F.; Zahradník, J.; Clinton, J.

2017-01-01

Roč. 210, č. 2 (2017), s. 693-705 ISSN 0956-540X Institutional support: RVO:67985530 Keywords : inverse theory * waveform inversion * computational seismology * earthquake source observations * seismic noise Subject RIV: DC - Siesmology, Volcanology, Earth Structure OBOR OECD: Volcanology Impact factor: 2.414, year: 2016

Tensor Factorization for Low-Rank Tensor Completion.

Science.gov (United States)

Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao

2018-03-01

Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.

A Review of Tensors and Tensor Signal Processing

Science.gov (United States)

Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.

Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

Science.gov (United States)

Shi, Peidong; Angus, Doug; Nowacki, Andy; Yuan, Sanyi; Wang, Yanyan

2018-03-01

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green's function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.

Compartmentalization of the Coso East Flank geothermal field imaged by 3-D full-tensor MT inversion

Science.gov (United States)

Lindsey, Nathaniel J.; Kaven, Joern; Davatzes, Nicholas C.; Newman, Gregory A.

2017-01-01

Previous magnetotelluric (MT) studies of the high-temperature Coso geothermal system in California identified a subvertical feature of low resistivity (2–5 Ohm m) and appreciable lateral extent (>1 km) in the producing zone of the East Flank field. However, these models could not reproduce gross 3-D effects in the recorded data. We perform 3-D full-tensor inversion and retrieve a resistivity model that out-performs previous 2-D and 3-D off-diagonal models in terms of its fit to the complete 3-D MT data set as well as the degree of modelling bias. Inclusion of secondary Zxx and Zyy data components leads to a robust east-dip (60†) to the previously identified conductive East Flank reservoir feature, which correlates strongly with recently mapped surface faults, downhole well temperatures, 3-D seismic reflection data, and local microseismicity. We perform synthetic forward modelling to test the best-fit dip of this conductor using the response at a nearby MT station. We interpret the dipping conductor as a fractured and fluidized compartment, which is structurally controlled by an unmapped blind East Flank fault zone.

Solving Inverse Kinematics – A New Approach to the Extended Jacobian Technique

Directory of Open Access Journals (Sweden)

M. Šoch

2005-01-01

Full Text Available This paper presents a brief summary of current numerical algorithms for solving the Inverse Kinematics problem. Then a new approach based on the Extended Jacobian technique is compared with the current Jacobian Inversion method. The presented method is intended for use in the field of computer graphics for animation of articulated structures. 

Tensor-GMRES method for large sparse systems of nonlinear equations

Science.gov (United States)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

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

Joint Tensor Feature Analysis For Visual Object Recognition.

Science.gov (United States)

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

2015-11-01

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

Interferogram analysis using the Abel inversion technique

International Nuclear Information System (INIS)

Yusof Munajat; Mohamad Kadim Suaidi

2000-01-01

High speed and high resolution optical detection system were used to capture the image of acoustic waves propagation. The freeze image in the form of interferogram was analysed to calculate the transient pressure profile of the acoustic waves. The interferogram analysis was based on the fringe shift and the application of the Abel inversion technique. An easier approach was made by mean of using MathCAD program as a tool in the programming; yet powerful enough to make such calculation, plotting and transfer of file. (Author)

Tensor network method for reversible classical computation

Science.gov (United States)

Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.

2018-03-01

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

The Topology of Symmetric Tensor Fields

Science.gov (United States)

Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

1997-01-01

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

A highly efficient Shannon wavelet inverse Fourier technique for pricing European options

NARCIS (Netherlands)

L. Ortiz Gracia (Luis); C.W. Oosterlee (Cornelis)

2016-01-01

htmlabstractIn the search for robust, accurate, and highly efficient financial option valuation techniques, we here present the SWIFT method (Shannon wavelets inverse Fourier technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of

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.)

Towards real-time regional earthquake simulation I: real-time moment tensor monitoring (RMT) for regional events in Taiwan

Science.gov (United States)

Lee, Shiann-Jong; Liang, Wen-Tzong; Cheng, Hui-Wen; Tu, Feng-Shan; Ma, Kuo-Fong; Tsuruoka, Hiroshi; Kawakatsu, Hitoshi; Huang, Bor-Shouh; Liu, Chun-Chi

2014-01-01

We have developed a real-time moment tensor monitoring system (RMT) which takes advantage of a grid-based moment tensor inversion technique and real-time broad-band seismic recordings to automatically monitor earthquake activities in the vicinity of Taiwan. The centroid moment tensor (CMT) inversion technique and a grid search scheme are applied to obtain the information of earthquake source parameters, including the event origin time, hypocentral location, moment magnitude and focal mechanism. All of these source parameters can be determined simultaneously within 117 s after the occurrence of an earthquake. The monitoring area involves the entire Taiwan Island and the offshore region, which covers the area of 119.3°E to 123.0°E and 21.0°N to 26.0°N, with a depth from 6 to 136 km. A 3-D grid system is implemented in the monitoring area with a uniform horizontal interval of 0.1° and a vertical interval of 10 km. The inversion procedure is based on a 1-D Green's function database calculated by the frequency-wavenumber (fk) method. We compare our results with the Central Weather Bureau (CWB) catalogue data for earthquakes occurred between 2010 and 2012. The average differences between event origin time and hypocentral location are less than 2 s and 10 km, respectively. The focal mechanisms determined by RMT are also comparable with the Broadband Array in Taiwan for Seismology (BATS) CMT solutions. These results indicate that the RMT system is realizable and efficient to monitor local seismic activities. In addition, the time needed to obtain all the point source parameters is reduced substantially compared to routine earthquake reports. By connecting RMT with a real-time online earthquake simulation (ROS) system, all the source parameters will be forwarded to the ROS to make the real-time earthquake simulation feasible. The RMT has operated offline (2010-2011) and online (since January 2012 to present) at the Institute of Earth Sciences (IES), Academia Sinica

One-dimensional nonlinear inverse heat conduction technique

International Nuclear Information System (INIS)

Hills, R.G.; Hensel, E.C. Jr.

1986-01-01

The one-dimensional nonlinear problem of heat conduction is considered. A noniterative space-marching finite-difference algorithm is developed to estimate the surface temperature and heat flux from temperature measurements at subsurface locations. The trade-off between resolution and variance of the estimates of the surface conditions is discussed quantitatively. The inverse algorithm is stabilized through the use of digital filters applied recursively. The effect of the filters on the resolution and variance of the surface estimates is quantified. Results are presented which indicate that the technique is capable of handling noisy measurement data

A Highly Efficient Shannon Wavelet Inverse Fourier Technique for Pricing European Options

NARCIS (Netherlands)

Ortiz-Gracia, Luis; Oosterlee, C.W.

2016-01-01

In the search for robust, accurate, and highly efficient financial option valuation techniques, we here present the SWIFT method (Shannon wavelets inverse Fourier technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of sharp quantitative error

Tensor gauge condition and tensor field decomposition

Science.gov (United States)

Zhu, Ben-Chao; Chen, Xiang-Song

2015-10-01

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

Full paleostress tensor reconstruction: case study of the Panasqueira Mine, Portugal.

Science.gov (United States)

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.

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

Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.

Science.gov (United States)

Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene

2016-03-01

Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.

Three-dimensional magnetotelluric inversion in practice—the electrical conductivity structure of the San Andreas Fault in Central California

Science.gov (United States)

Tietze, Kristina; Ritter, Oliver

2013-10-01

3-D inversion techniques have become a widely used tool in magnetotelluric (MT) data interpretation. However, with real data sets, many of the controlling factors for the outcome of 3-D inversion are little explored, such as alignment of the coordinate system, handling and influence of data errors and model regularization. Here we present 3-D inversion results of 169 MT sites from the central San Andreas Fault in California. Previous extensive 2-D inversion and 3-D forward modelling of the data set revealed significant along-strike variation of the electrical conductivity structure. 3-D inversion can recover these features but only if the inversion parameters are tuned in accordance with the particularities of the data set. Based on synthetic 3-D data we explore the model space and test the impacts of a wide range of inversion settings. The tests showed that the recovery of a pronounced regional 2-D structure in inversion of the complete impedance tensor depends on the coordinate system. As interdependencies between data components are not considered in standard 3-D MT inversion codes, 2-D subsurface structures can vanish if data are not aligned with the regional strike direction. A priori models and data weighting, that is, how strongly individual components of the impedance tensor and/or vertical magnetic field transfer functions dominate the solution, are crucial controls for the outcome of 3-D inversion. If deviations from a prior model are heavily penalized, regularization is prone to result in erroneous and misleading 3-D inversion models, particularly in the presence of strong conductivity contrasts. A `good' overall rms misfit is often meaningless or misleading as a huge range of 3-D inversion results exist, all with similarly `acceptable' misfits but producing significantly differing images of the conductivity structures. Reliable and meaningful 3-D inversion models can only be recovered if data misfit is assessed systematically in the frequency

Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI

Science.gov (United States)

Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.

2015-01-01

Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085

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

Science.gov (United States)

Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gérard

2012-08-01

We prove a closed-form solution to tensor voting (CFTV): Given a point set in any dimensions, our closed-form solution provides an exact, continuous, and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway.

-Dimensional Fractional Lagrange's Inversion Theorem

Directory of Open Access Journals (Sweden)

F. A. Abd El-Salam

2013-01-01

Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.

One-loop tensor Feynman integral reduction with signed minors

International Nuclear Information System (INIS)

Fleischer, J.; Yundin, V.

2011-12-01

We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically in a systematic way. The final expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions. (orig.)

One-loop tensor Feynman integral reduction with signed minors

Energy Technology Data Exchange (ETDEWEB)

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

2011-12-15

We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically in a systematic way. The final expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions. (orig.)

Mean magnetic susceptibility regularized susceptibility tensor imaging (MMSR-STI) for estimating orientations of white matter fibers in human brain.

Science.gov (United States)

Li, Xu; van Zijl, Peter C M

2014-09-01

An increasing number of studies show that magnetic susceptibility in white matter fibers is anisotropic and may be described by a tensor. However, the limited head rotation possible for in vivo human studies leads to an ill-conditioned inverse problem in susceptibility tensor imaging (STI). Here we suggest the combined use of limiting the susceptibility anisotropy to white matter and imposing morphology constraints on the mean magnetic susceptibility (MMS) for regularizing the STI inverse problem. The proposed MMS regularized STI (MMSR-STI) method was tested using computer simulations and in vivo human data collected at 3T. The fiber orientation estimated from both the STI and MMSR-STI methods was compared to that from diffusion tensor imaging (DTI). Computer simulations show that the MMSR-STI method provides a more accurate estimation of the susceptibility tensor than the conventional STI approach. Similarly, in vivo data show that use of the MMSR-STI method leads to a smaller difference between the fiber orientation estimated from STI and DTI for most selected white matter fibers. The proposed regularization strategy for STI can improve estimation of the susceptibility tensor in white matter. © 2014 Wiley Periodicals, Inc.

Diffusion tensor imaging of the human skeletal muscle: contributions and applications

International Nuclear Information System (INIS)

Neji, Radhouene

2010-01-01

In this thesis, we present several techniques for the processing of diffusion tensor images. They span a wide range of tasks such as estimation and regularization, clustering and segmentation, as well as registration. The variational framework proposed for recovering a tensor field from noisy diffusion weighted images exploits the fact that diffusion data represent populations of fibers and therefore each tensor can be reconstructed using a weighted combination of tensors lying in its neighborhood. The segmentation approach operates both at the voxel and the fiber tract levels. It is based on the use of Mercer kernels over Gaussian diffusion probabilities to model tensor similarity and spatial interactions, allowing the definition of fiber metrics that combine information from spatial localization and diffusion tensors. Several clustering techniques can be subsequently used to segment tensor fields and fiber tractographies. Moreover, we show how to develop supervised extensions of these algorithms. The registration algorithm uses probability kernels in order to match moving and target images. The deformation consistency is assessed using the distortion induced in the distances between neighboring probabilities. Discrete optimization is used to seek an optimum of the defined objective function. The experimental validation is done over a dataset of manually segmented diffusion images of the lower leg muscle for healthy and diseased subjects. The results of the techniques developed throughout this thesis are promising. (author)

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

Science.gov (United States)

Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian

The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.

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

NARCIS (Netherlands)

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

2008-01-01

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

Genten: Software for Generalized Tensor Decompositions v. 1.0.0

Energy Technology Data Exchange (ETDEWEB)

2017-06-22

Tensors, or multidimensional arrays, are a powerful mathematical means of describing multiway data. This software provides computational means for decomposing or approximating a given tensor in terms of smaller tensors of lower dimension, focusing on decomposition of large, sparse tensors. These techniques have applications in many scientific areas, including signal processing, linear algebra, computer vision, numerical analysis, data mining, graph analysis, neuroscience and more. The software is designed to take advantage of parallelism present emerging computer architectures such has multi-core CPUs, many-core accelerators such as the Intel Xeon Phi, and computation-oriented GPUs to enable efficient processing of large tensors.

Motion Detection in Ultrasound Image-Sequences Using Tensor Voting

Science.gov (United States)

Inba, Masafumi; Yanagida, Hirotaka; Tamura, Yasutaka

2008-05-01

Motion detection in ultrasound image sequences using tensor voting is described. We have been developing an ultrasound imaging system adopting a combination of coded excitation and synthetic aperture focusing techniques. In our method, frame rate of the system at distance of 150 mm reaches 5000 frame/s. Sparse array and short duration coded ultrasound signals are used for high-speed data acquisition. However, many artifacts appear in the reconstructed image sequences because of the incompleteness of the transmitted code. To reduce the artifacts, we have examined the application of tensor voting to the imaging method which adopts both coded excitation and synthetic aperture techniques. In this study, the basis of applying tensor voting and the motion detection method to ultrasound images is derived. It was confirmed that velocity detection and feature enhancement are possible using tensor voting in the time and space of simulated ultrasound three-dimensional image sequences.

On improving the efficiency of tensor voting.

Science.gov (United States)

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

2011-11-01

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.

A technique for measurement of vector and tensor polarization in solid spin one polarized targets

International Nuclear Information System (INIS)

Kielhorn, W.F.

1991-06-01

Vector and tensor polarizations are explicitly defined and used to characterize the polarization states of spin one polarized targets, and a technique for extracting these polarizations from nuclear magnetic resonance (NMR) data is developed. This technique is independent of assumptions about spin temperature, but assumes the target's crystal structure induces a quadrupole interaction with the spin one particles. Analysis of the NMR signals involves a computer curve fitting algorithm implemented with a fast Fourier transform method which speeds and simplifies curve fitting algorithms used previously. For accurate curve fitting, the NMR electronic circuit must be modeled by the fitting algorithm. Details of a circuit, its model, and data collected from this circuit are given for a solid deuterated ammonia target. 37 refs., 19 figs., 3 tabs

Mantle conductivity obtained by 3-D inversion of magnetic satellite data

DEFF Research Database (Denmark)

Kuvshinov, A.; Olsen, Nils

distributed geomagnetic observatories. Due to the high computational load of a 3-D inversion (requiring thousands of forward calculations), a comprehensive numerical framework is developed to increase the efficiency of the inversion.In particular, we take an advantage of specific features of the IE approach...... and perform the most consuming-time part of the IE forward simulations (the calculation of electric and magnetic tensor Green’s functions) only once. Approximate calculation of the data sensitivities also gives essential speed up of the inversion. We validate our inversion scheme using synthetic induction...

Measurement of third-order nonlinear susceptibility tensor in InP using extended Z-scan technique with elliptical polarization

Science.gov (United States)

Oishi, Masaki; Shinozaki, Tomohisa; Hara, Hikaru; Yamamoto, Kazunuki; Matsusue, Toshio; Bando, Hiroyuki

2018-05-01

The elliptical polarization dependence of the two-photon absorption coefficient β in InP has been measured by the extended Z-scan technique for thick materials in the wavelength range from 1640 to 1800 nm. The analytical formula of the Z-scan technique has been extended with consideration of multiple reflections. The Z-scan results have been fitted very well by the formula and β has been evaluated accurately. The three independent elements of the third-order nonlinear susceptibility tensor in InP have also been determined accurately from the elliptical polarization dependence of β.

Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique

Science.gov (United States)

Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi

2013-09-01

According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.

Diffusion tensor image registration using hybrid connectivity and tensor features.

Science.gov (United States)

Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang

2014-07-01

Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.

Tensor representation techniques for full configuration interaction: A Fock space approach using the canonical product format.

Science.gov (United States)

Böhm, Karl-Heinz; Auer, Alexander A; Espig, Mike

2016-06-28

In this proof-of-principle study, we apply tensor decomposition techniques to the Full Configuration Interaction (FCI) wavefunction in order to approximate the wavefunction parameters efficiently and to reduce the overall computational effort. For this purpose, the wavefunction ansatz is formulated in an occupation number vector representation that ensures antisymmetry. If the canonical product format tensor decomposition is then applied, the Hamiltonian and the wavefunction can be cast into a multilinear product form. As a consequence, the number of wavefunction parameters does not scale to the power of the number of particles (or orbitals) but depends on the rank of the approximation and linearly on the number of particles. The degree of approximation can be controlled by a single threshold for the rank reduction procedure required in the algorithm. We demonstrate that using this approximation, the FCI Hamiltonian matrix can be stored with N(5) scaling. The error of the approximation that is introduced is below Millihartree for a threshold of ϵ = 10(-4) and no convergence problems are observed solving the FCI equations iteratively in the new format. While promising conceptually, all effort of the algorithm is shifted to the required rank reduction procedure after the contraction of the Hamiltonian with the coefficient tensor. At the current state, this crucial step is the bottleneck of our approach and even for an optimistic estimate, the algorithm scales beyond N(10) and future work has to be directed towards reduction-free algorithms.

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

Science.gov (United States)

Li, Wei; Liu, Chunlei

2013-10-01

Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.

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 for physics

CERN Document Server

Hess, Siegfried

2015-01-01

This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics,  at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to  tensors of any rank, at graduate level.  Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...

Software tool for resolution of inverse problems using artificial intelligence techniques: an application in neutron spectrometry

International Nuclear Information System (INIS)

Castaneda M, V. H.; Martinez B, M. R.; Solis S, L. O.; Castaneda M, R.; Leon P, A. A.; Hernandez P, C. F.; Espinoza G, J. G.; Ortiz R, J. M.; Vega C, H. R.; Mendez, R.; Gallego, E.; Sousa L, M. A.

2016-10-01

The Taguchi methodology has proved to be highly efficient to solve inverse problems, in which the values of some parameters of the model must be obtained from the observed data. There are intrinsic mathematical characteristics that make a problem known as inverse. Inverse problems appear in many branches of science, engineering and mathematics. To solve this type of problem, researches have used different techniques. Recently, the use of techniques based on Artificial Intelligence technology is being explored by researches. This paper presents the use of a software tool based on artificial neural networks of generalized regression in the solution of inverse problems with application in high energy physics, specifically in the solution of the problem of neutron spectrometry. To solve this problem we use a software tool developed in the Mat Lab programming environment, which employs a friendly user interface, intuitive and easy to use for the user. This computational tool solves the inverse problem involved in the reconstruction of the neutron spectrum based on measurements made with a Bonner spheres spectrometric system. Introducing this information, the neural network is able to reconstruct the neutron spectrum with high performance and generalization capability. The tool allows that the end user does not require great training or technical knowledge in development and/or use of software, so it facilitates the use of the program for the resolution of inverse problems that are in several areas of knowledge. The techniques of Artificial Intelligence present singular veracity to solve inverse problems, given the characteristics of artificial neural networks and their network topology, therefore, the tool developed has been very useful, since the results generated by the Artificial Neural Network require few time in comparison to other techniques and are correct results comparing them with the actual data of the experiment. (Author)

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...

A technique for measurement of vector and tensor polarization in solid spin one polarized targets

Energy Technology Data Exchange (ETDEWEB)

Kielhorn, W.F.

1991-06-01

Vector and tensor polarizations are explicitly defined and used to characterize the polarization states of spin one polarized targets, and a technique for extracting these polarizations from nuclear magnetic resonance (NMR) data is developed. This technique is independent of assumptions about spin temperature, but assumes the target's crystal structure induces a quadrupole interaction with the spin one particles. Analysis of the NMR signals involves a computer curve fitting algorithm implemented with a fast Fourier transform method which speeds and simplifies curve fitting algorithms used previously. For accurate curve fitting, the NMR electronic circuit must be modeled by the fitting algorithm. Details of a circuit, its model, and data collected from this circuit are given for a solid deuterated ammonia target. 37 refs., 19 figs., 3 tabs.

Effect of cocaine on structural changes in brain: MRI volumetry using tensor-based morphometry.

Science.gov (United States)

Narayana, Ponnada A; Datta, Sushmita; Tao, Guozhi; Steinberg, Joel L; Moeller, F Gerard

2010-10-01

Magnetic resonance imaging (MRI) was performed in cocaine-dependent subjects to determine the structural changes in brain compared to non-drug using controls. Cocaine-dependent subjects and controls were carefully screened to rule out brain pathology of undetermined origin. Magnetic resonance images were analyzed using tensor-based morphometry (TBM) and voxel-based morphometry (VBM) without and with modulation to adjust for volume changes during normalization. For TBM analysis, unbiased atlases were generated using two different inverse consistent and diffeomorphic nonlinear registration techniques. Two different control groups were used for generating unbiased atlases. Independent of the nonlinear registration technique and normal cohorts used for creating the unbiased atlases, our analysis failed to detect any statistically significant effect of cocaine on brain volumes. These results show that cocaine-dependent subjects do not show differences in regional brain volumes compared to non-drug using controls. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

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

Science.gov (United States)

Gurau, Razvan

2018-06-01

It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.

Determining the metallicity of the solar envelope using seismic inversion techniques

Science.gov (United States)

Buldgen, G.; Salmon, S. J. A. J.; Noels, A.; Scuflaire, R.; Dupret, M. A.; Reese, D. R.

2017-11-01

The solar metallicity issue is a long-lasting problem of astrophysics, impacting multiple fields and still subject to debate and uncertainties. While spectroscopy has mostly been used to determine the solar heavy elements abundance, helioseismologists attempted providing a seismic determination of the metallicity in the solar convective envelope. However, the puzzle remains since two independent groups provided two radically different values for this crucial astrophysical parameter. We aim at providing an independent seismic measurement of the solar metallicity in the convective envelope. Our main goal is to help provide new information to break the current stalemate amongst seismic determinations of the solar heavy element abundance. We start by presenting the kernels, the inversion technique and the target function of the inversion we have developed. We then test our approach in multiple hare-and-hounds exercises to assess its reliability and accuracy. We then apply our technique to solar data using calibrated solar models and determine an interval of seismic measurements for the solar metallicity. We show that our inversion can indeed be used to estimate the solar metallicity thanks to our hare-and-hounds exercises. However, we also show that further dependencies in the physical ingredients of solar models lead to a low accuracy. Nevertheless, using various physical ingredients for our solar models, we determine metallicity values between 0.008 and 0.014.

A robust spatial filtering technique for multisource localization and geoacoustic inversion.

Science.gov (United States)

Stotts, S A

2005-07-01

Geoacoustic inversion and source localization using beamformed data from a ship of opportunity has been demonstrated with a bottom-mounted array. An alternative approach, which lies within a class referred to as spatial filtering, transforms element level data into beam data, applies a bearing filter, and transforms back to element level data prior to performing inversions. Automation of this filtering approach is facilitated for broadband applications by restricting the inverse transform to the degrees of freedom of the array, i.e., the effective number of elements, for frequencies near or below the design frequency. A procedure is described for nonuniformly spaced elements that guarantees filter stability well above the design frequency. Monitoring energy conservation with respect to filter output confirms filter stability. Filter performance with both uniformly spaced and nonuniformly spaced array elements is discussed. Vertical (range and depth) and horizontal (range and bearing) ambiguity surfaces are constructed to examine filter performance. Examples that demonstrate this filtering technique with both synthetic data and real data are presented along with comparisons to inversion results using beamformed data. Examinations of cost functions calculated within a simulated annealing algorithm reveal the efficacy of the approach.

Review of diffusion tensor imaging and its application in children

Energy Technology Data Exchange (ETDEWEB)

Vorona, Gregory A. [Children' s Hospital of Richmond at Virginia Commonwealth University, Department of Radiology, Richmond, VA (United States); Berman, Jeffrey I. [Children' s Hospital of Philadelphia, Department of Radiology, Philadelphia, PA (United States)

2015-09-15

Diffusion MRI is an imaging technique that uses the random motion of water to probe tissue microstructure. Diffusion tensor imaging (DTI) can quantitatively depict the organization and connectivity of white matter. Given the non-invasiveness of the technique, DTI has become a widely used tool for researchers and clinicians to examine the white matter of children. This review covers the basics of diffusion-weighted imaging and diffusion tensor imaging and discusses examples of their clinical application in children. (orig.)

Homogenization and implementation of a 3D regional velocity model in Mexico for its application in moment tensor inversion of intermediate-magnitude earthquakes

Science.gov (United States)

Rodríguez Cardozo, Félix; Hjörleifsdóttir, Vala; Caló, Marco

2017-04-01

Moment tensor inversions for intermediate and small earthquakes (M. < 4.5) are challenging as they principally excite relatively short period seismic waves that interact strongly with local heterogeneities. Incorporating detailed regional 3D velocity models permits obtaining realistic synthetic seismograms and recover the seismic source parameters these smaller events. Two 3D regional velocity models have recently been developed for Mexico, using surface waves and seismic noise tomography (Spica et al., 2016; Gaite et al., 2015), which could be used to model the waveforms of intermediate magnitud earthquakes in this region. Such models are parameterized as layered velocity profiles and for some of the profiles, the velocity difference between two layers are considerable. The "jump" in velocities between two layers is inconvenient for some methods and algorithms that calculate synthetic waveforms, in particular for the method that we are using, the spectral element method (SPECFEM3D GLOBE, Komatitsch y Tromp, 2000), when the mesh does not follow the layer boundaries. In order to make the velocity models more easily implementec in SPECFEM3D GLOBE it is neccesary to apply a homogenization algorithm (Capdeville et al., 2015) such that the (now anisotropic) layer velocities are smoothly varying with depth. In this work, we apply a homogenization algorithm to the regional velocity models in México for implementing them in SPECFEM3D GLOBE, calculate synthetic waveforms for intermediate-magnitude earthquakes in México and invert them for the seismic moment tensor.

Eigenvector of gravity gradient tensor for estimating fault dips considering fault type

Science.gov (United States)

Kusumoto, Shigekazu

2017-12-01

The dips of boundaries in faults and caldera walls play an important role in understanding their formation mechanisms. The fault dip is a particularly important parameter in numerical simulations for hazard map creation as the fault dip affects estimations of the area of disaster occurrence. In this study, I introduce a technique for estimating the fault dip using the eigenvector of the observed or calculated gravity gradient tensor on a profile and investigating its properties through numerical simulations. From numerical simulations, it was found that the maximum eigenvector of the tensor points to the high-density causative body, and the dip of the maximum eigenvector closely follows the dip of the normal fault. It was also found that the minimum eigenvector of the tensor points to the low-density causative body and that the dip of the minimum eigenvector closely follows the dip of the reverse fault. It was shown that the eigenvector of the gravity gradient tensor for estimating fault dips is determined by fault type. As an application of this technique, I estimated the dip of the Kurehayama Fault located in Toyama, Japan, and obtained a result that corresponded to conventional fault dip estimations by geology and geomorphology. Because the gravity gradient tensor is required for this analysis, I present a technique that estimates the gravity gradient tensor from the gravity anomaly on a profile.

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

Science.gov (United States)

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

2014-01-01

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

Trimming and procrastination as inversion techniques

Science.gov (United States)

Backus, George E.

1996-12-01

By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.

Coupled channels Marchenko inversion for nucleon-nucleon potentials

International Nuclear Information System (INIS)

Kohlhoff, H.; Geramb, H.V. von

1994-01-01

Marchenko inversion is used to determine local energy independent but channel dependent potential matrices from optimum sets of experimental phase shifts. 3 SD 1 and 3 PF 2 channels of nucleon-nucleon systems contain in their off-diagonal potential matrices explicitly the tensor force for T = 0 and 1 isospin. We obtain, together with single channels, complete sets of quantitative nucleon-nucleon potential results which are ready for application in nuclear structure and reaction analyses. The historic coupled channels inversion result of Newton and Fulton is revisited. (orig.)

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

Science.gov (United States)

Li, Xutao; Ng, Michael K; Cong, Gao; Ye, Yunming; Wu, Qingyao

2017-08-01

With the advancement of data acquisition techniques, tensor (multidimensional data) objects are increasingly accumulated and generated, for example, multichannel electroencephalographies, multiview images, and videos. In these applications, the tensor objects are usually nonnegative, since the physical signals are recorded. As the dimensionality of tensor objects is often very high, a dimension reduction technique becomes an important research topic of tensor data. From the perspective of geometry, high-dimensional objects often reside in a low-dimensional submanifold of the ambient space. In this paper, we propose a new approach to perform the dimension reduction for nonnegative tensor objects. Our idea is to use nonnegative Tucker decomposition (NTD) to obtain a set of core tensors of smaller sizes by finding a common set of projection matrices for tensor objects. To preserve geometric information in tensor data, we employ a manifold regularization term for the core tensors constructed in the Tucker decomposition. An algorithm called manifold regularization NTD (MR-NTD) is developed to solve the common projection matrices and core tensors in an alternating least squares manner. The convergence of the proposed algorithm is shown, and the computational complexity of the proposed method scales linearly with respect to the number of tensor objects and the size of the tensor objects, respectively. These theoretical results show that the proposed algorithm can be efficient. Extensive experimental results have been provided to further demonstrate the effectiveness and efficiency of the proposed MR-NTD algorithm.

Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction

Science.gov (United States)

Song, Chenchen; Martínez, Todd J.

2017-01-01

In the first paper of the series [Paper I, C. Song and T. J. Martinez, J. Chem. Phys. 144, 174111 (2016)], we showed how tensor-hypercontracted (THC) SOS-MP2 could be accelerated by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs). This reduced the formal scaling of the SOS-MP2 energy calculation to cubic with respect to system size. The computational bottleneck then becomes the THC metric matrix inversion, which scales cubically with a large prefactor. In this work, the local THC approximation is proposed to reduce the computational cost of inverting the THC metric matrix to linear scaling with respect to molecular size. By doing so, we have removed the primary bottleneck to THC-SOS-MP2 calculations on large molecules with O(1000) atoms. The errors introduced by the local THC approximation are less than 0.6 kcal/mol for molecules with up to 200 atoms and 3300 basis functions. Together with the graphical processing unit techniques and locality-exploiting approaches introduced in previous work, the scaled opposite spin MP2 (SOS-MP2) calculations exhibit O(N2.5) scaling in practice up to 10 000 basis functions. The new algorithms make it feasible to carry out SOS-MP2 calculations on small proteins like ubiquitin (1231 atoms/10 294 atomic basis functions) on a single node in less than a day.

Evaluation of glymphatic system activity with the diffusion MR technique: diffusion tensor image analysis along the perivascular space (DTI-ALPS) in Alzheimer’s disease cases

OpenAIRE

Taoka, Toshiaki; Masutani, Yoshitaka; Kawai, Hisashi; Nakane, Toshiki; Matsuoka, Kiwamu; Yasuno, Fumihiko; Kishimoto, Toshifumi; Naganawa, Shinji

2017-01-01

Purpose: The activity of the glymphatic system is impaired in animal models of Alzheimer’s disease (AD). We evaluated the activity of the human glymphatic system in cases of AD with a diffusion-based technique called diffusion tensor image analysis along the perivascular space (DTI-ALPS). Materials and methods: Diffusion tensor images were acquired to calculate diffusivities in the x, y, and z axes of the plane of the lateral ventricle body in 31 patients. We evaluated the diffusivity along t...

Retinal Vessel Segmentation via Structure Tensor Coloring and Anisotropy Enhancement

Directory of Open Access Journals (Sweden)

Mehmet Nergiz

2017-11-01

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

Full paleostress tensor reconstruction using quartz veins of Panasqueira Mine, central Portugal; part I: Paleopressure determination

Science.gov (United 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.

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

Science.gov (United States)

Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S

2017-05-01

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order- k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k }. We derive general inequalities between the l p -norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm ( p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations.

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.

A comparative study of surface waves inversion techniques at strong motion recording sites in Greece

Science.gov (United States)

Panagiotis C. Pelekis,; Savvaidis, Alexandros; Kayen, Robert E.; Vlachakis, Vasileios S.; Athanasopoulos, George A.

2015-01-01

Surface wave method was used for the estimation of Vs vs depth profile at 10 strong motion stations in Greece. The dispersion data were obtained by SASW method, utilizing a pair of electromechanical harmonic-wave source (shakers) or a random source (drop weight). In this study, three inversion techniques were used a) a recently proposed Simplified Inversion Method (SIM), b) an inversion technique based on a neighborhood algorithm (NA) which allows the incorporation of a priori information regarding the subsurface structure parameters, and c) Occam's inversion algorithm. For each site constant value of Poisson's ratio was assumed (ν=0.4) since the objective of the current study is the comparison of the three inversion schemes regardless the uncertainties resulting due to the lack of geotechnical data. A penalty function was introduced to quantify the deviations of the derived Vs profiles. The Vs models are compared as of Vs(z), Vs30 and EC8 soil category, in order to show the insignificance of the existing variations. The comparison results showed that the average variation of SIM profiles is 9% and 4.9% comparing with NA and Occam's profiles respectively whilst the average difference of Vs30 values obtained from SIM is 7.4% and 5.0% compared with NA and Occam's.

Evaluation of inverse modeling techniques for pinpointing water leakages at building constructions

NARCIS (Netherlands)

Schijndel, van A.W.M.

2015-01-01

The location and nature of the moisture leakages are sometimes difficult to detect. Moreover, the relation between observed inside surface moisture patterns and where the moisture enters the construction is often not clear. The objective of this paper is to investigate inverse modeling techniques as

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

OpenAIRE

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

2016-01-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor tra...

Tensor eigenvalues and their applications

CERN Document Server

Qi, Liqun; Chen, Yannan

2018-01-01

This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

Detection of Cavities by Inverse Heat Conduction Boundary Element Method Using Minimal Energy Technique

International Nuclear Information System (INIS)

Choi, C. Y.

1997-01-01

A geometrical inverse heat conduction problem is solved for the infrared scanning cavity detection by the boundary element method using minimal energy technique. By minimizing the kinetic energy of temperature field, boundary element equations are converted to the quadratic programming problem. A hypothetical inner boundary is defined such that the actual cavity is located interior to the domain. Temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error of surface temperature obtained by infrared scanning, and then boundary element analysis is performed for the position of an unknown boundary (cavity). Cavity detection algorithm is provided, and the effects of minimal energy technique on the inverse solution method are investigated by means of numerical analysis

Tensor Transpose and Its Properties

OpenAIRE

Pan, Ran

2014-01-01

Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.

White matter injury in newborns with congenital heart disease: a diffusion tensor imaging study.

Science.gov (United States)

Mulkey, Sarah B; Ou, Xiawei; Ramakrishnaiah, Raghu H; Glasier, Charles M; Swearingen, Christopher J; Melguizo, Maria S; Yap, Vivien L; Schmitz, Michael L; Bhutta, Adnan T

2014-09-01

Brain injury is observed on cranial magnetic resonance imaging preoperatively in up to 50% of newborns with congenital heart disease. Newer imaging techniques such as diffusion tensor imaging provide sensitive measures of the white matter integrity. The objective of this study was to evaluate the diffusion tensor imaging analysis technique of tract-based spatial statistics in newborns with congenital heart disease. Term newborns with congenital heart disease who would require surgery at less than 1 month of age were prospectively enrolled (n = 19). Infants underwent preoperative and postoperative brain magnetic resonance imaging with diffusion tensor imaging. Tract-based spatial statistics, an objective whole-brain diffusion tensor imaging analysis technique, was used to determine differences in white matter fractional anisotropy between infant groups. Term control infants were also compared with congenital heart disease infants. Postmenstrual age was equivalent between congenital heart disease infant groups and between congenital heart disease and control infants. Ten infants had preoperative brain injury, either infarct or white matter injury, by conventional brain magnetic resonance imaging. The technique of tract-based spatial statistics showed significantly lower fractional anisotropy (P tensor imaging analysis technique that may have better sensitivity in detecting white matter injury compared with conventional brain magnetic resonance imaging in term newborns with congenital heart disease. Copyright © 2014 Elsevier Inc. All rights reserved.

Active tectonics in Central Italy: Constraint from surface wave tomography and source moment tensor inversion

International Nuclear Information System (INIS)

Chimera, G.; Aoudia, A.; Panza, G.F.; Sarao, A.

2002-06-01

We make a multiscale investigation of the lithosphere-asthenosphere structure and of the active tectonics along a stripe from the Tyrrhenian to the Adriatic coast, with emphasis on the Umbria-Marche area, by means of surface-wave tomography and inversion experiments for structure and seismic moment tensor retrieval. The data include: a large number of new local and regional group velocity measurements sampling the Umbria-Marche Apennines and the Adria margin respectively; new and published phase velocity measurements sampling Italy and surroundings; deep seismic soundings which, crossing the whole Peninsula from the Tyrrhenian to the Adriatic coasts, go through the Umbria-Marche area. The local group velocity maps cover the area reactivated by the 1997-1998 Umbria-Marche earthquake sequence. These maps suggest an intimate relation between the lateral variations and distribution of the active fault systems and related sedimentary basins. Such relation is confirmed by the non-linear inversion of the local dispersion curves. To image the structure of the lithosphere-asthenosphere system from the Tyrrhenian to the Adriatic coast, we fix the upper crust parameters consistently with our Umbria-Marche models and with pertinent deep seismic sounding data and invert the regional long period dispersion measurements. At a local scale, in the Umbria-Marche area, the retrieved models for the upper crust reveal the importance of the inherited compressional tectonics on the ongoing extensional deformation and related seismic activity. The lateral and in-depth structural changes in the upper crust are likely controlling fault segmentation and seismogenesis. Source inversion studies of the large crustal events of the 1997 earthquake sequence show the dominance of normal faulting mechanisms, whereas selected aftershocks between the fault segments reveal that the prevailing deformation at the step-over is of strike-slip faulting type and may control the lateral fault extent. At the

Stress tensor fluctuations in de Sitter spacetime

Energy Technology Data Exchange (ETDEWEB)

Pérez-Nadal, Guillem; Verdaguer, Enric [Departament de Física Fonamental and Institut de Ciències del Cosmos, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain); Roura, Albert, E-mail: guillem@ffn.ub.es, E-mail: albert.roura@aei.mpg.de, E-mail: enric.verdaguer@ub.edu [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm (Germany)

2010-05-01

The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m{sup 2}/H{sup 2}. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.

Tensors, differential forms, and variational principles

CERN Document Server

Lovelock, David

1989-01-01

Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments.

Diffusion tensor imaging and tractography in clinical neuro sciences

International Nuclear Information System (INIS)

Zarei, M.; Johansen-Berg, H.; Matthews, P.M.

2003-01-01

Rapidly evolving MR technology has allowed better understanding of structure and function of the human brain. Diffusion weighted MRI was developed two decades ago and it is now well established in diagnosis of acute ischaemia in patients with stroke. Diffusion tensor MRI uses the same principles but takes a step further allowing US to measure magnitude of the diffusion along different directions. This lead to the development of diffusion tensor tractography, a technique by which major neural pathways in the living brain can be visualized. There is a growing interest in exploring possible use of these techniques in clinical neurology and psychiatry. This article aims to review the principles of this technique and recent discoveries which may help US to better understand neurological and psychiatric disorders

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

International Nuclear Information System (INIS)

Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian

2016-01-01

Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions. (paper)

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

Science.gov (United States)

Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian

2016-05-01

Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.

Partitioned Alternating Least Squares Technique for Canonical Polyadic Tensor Decomposition

Czech Academy of Sciences Publication Activity Database

Tichavský, Petr; Phan, A. H.; Cichocki, A.

2016-01-01

Roč. 23, č. 7 (2016), s. 993-997 ISSN 1070-9908 R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : canonical polyadic decomposition * PARAFAC * tensor decomposition Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.528, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/tichavsky-0460710.pdf

SQUIDs and inverse problem techniques in nondestructive evaluation of metals

CERN Document Server

Bruno, A C

2001-01-01

Superconducting Quantum Interference Devices coupled to gradiometers were used to defect flaws in metals. We detected flaws in aluminium samples carrying current, measuring fields at lift-off distances up to one order of magnitude larger than the size of the flaw. Configured as a susceptometer we detected surface-braking flaws in steel samples, measuring the distortion on the applied magnetic field. We also used spatial filtering techniques to enhance the visualization of the magnetic field due to the flaws. In order to assess its severity, we used the generalized inverse method and singular value decomposition to reconstruct small spherical inclusions in steel. In addition, finite elements and optimization techniques were used to image complex shaped flaws.

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

OpenAIRE

Chen, Lin; Friedland, Shmuel

2017-01-01

We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.

Multi-mode technique for the determination of the biaxial Y{sub 2}SiO{sub 5} permittivity tensor from 300 to 6 K

Energy Technology Data Exchange (ETDEWEB)

Carvalho, N. C., E-mail: natalia.docarmocarvalho@research.uwa.edu.au; Le Floch, J-M.; Tobar, M. E. [School of Physics, The University of Western Australia, Crawley 6009 (Australia); ARC Centre of Excellence for Engineered Quantum Systems (EQuS), 35 Stirling Hwy, Crawley 6009 (Australia); Krupka, J. [Instytut Mikroelektroniki i Optoelektroniki PW, Koszykowa 75, 00-662 Warsaw (Poland)

2015-05-11

The Y{sub 2}SiO{sub 5} (YSO) crystal is a dielectric material with biaxial anisotropy with known values of refractive index at optical frequencies. It is a well-known rare-earth (RE) host material for optical research and more recently has shown promising performance for quantum-engineered devices. In this paper, we report the first microwave characterization of the real permittivity tensor of a bulk YSO sample, as well as an investigation of the temperature dependence of the tensor components from 296 K down to 6 K. Estimated uncertainties were below 0.26%, limited by the precision of machining the cylindrical dielectric. Also, the electrical Q-factors of a few electromagnetic modes were recorded as a way to provide some information about the crystal losses over the temperature range. To solve the tensor components necessary for a biaxial crystal, we developed the multi-mode technique, which uses simultaneous measurement of low order whispering gallery modes. Knowledge of the permittivity tensor offers important data, essential for the design of technologies involving YSO, such as microwave coupling to electron and hyperfine transitions in RE doped samples at low temperatures.

Recovery of material parameters of soft hyperelastic tissue by an inverse spectral technique

KAUST Repository

Gou, Kun; Joshi, Sunnie; Walton, Jay R.

2012-01-01

An inverse spectral method is developed for recovering a spatially inhomogeneous shear modulus for soft tissue. The study is motivated by a novel use of the intravascular ultrasound technique to image arteries. The arterial wall is idealized as a

Analyses of Effects of Cutting Parameters on Cutting Edge Temperature Using Inverse Heat Conduction Technique

Directory of Open Access Journals (Sweden)

Marcelo Ribeiro dos Santos

2014-01-01

Full Text Available During machining energy is transformed into heat due to plastic deformation of the workpiece surface and friction between tool and workpiece. High temperatures are generated in the region of the cutting edge, which have a very important influence on wear rate of the cutting tool and on tool life. This work proposes the estimation of heat flux at the chip-tool interface using inverse techniques. Factors which influence the temperature distribution at the AISI M32C high speed steel tool rake face during machining of a ABNT 12L14 steel workpiece were also investigated. The temperature distribution was predicted using finite volume elements. A transient 3D numerical code using irregular and nonstaggered mesh was developed to solve the nonlinear heat diffusion equation. To validate the software, experimental tests were made. The inverse problem was solved using the function specification method. Heat fluxes at the tool-workpiece interface were estimated using inverse problems techniques and experimental temperatures. Tests were performed to study the effect of cutting parameters on cutting edge temperature. The results were compared with those of the tool-work thermocouple technique and a fair agreement was obtained.

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

Science.gov (United States)

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

2017-05-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

Bowen-York tensors

International Nuclear Information System (INIS)

Beig, Robert; Krammer, Werner

2004-01-01

For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York

Comparative evaluation of entero-anastomosis by inversion techniques with different suturing materials in bovine [Water buffalo

Energy Technology Data Exchange (ETDEWEB)

Gupta, S. C.P.; Khan, A. A.; Dass, L. L.; Sahay, P. N.; Jha, G. J.

1985-07-01

Single layer end-to-end inverted and everted techniques of entero-anastomosis were evaluated in sixteen male buffalo calves using silk and catgut sutures. All the animals of everting group showed areas of adhesion grossly, whereas it was only in three animals of inverting group. Histological evidences revealed a more uniform healing pattern in inversion group and radiography suggested comparatively greater degree of stenosis, but without functional impairment of intestinal lumen, than everting anastomosis. Connective tissue proliferation and mononuclear cell infiltrations were very minimal with silk suture whereas these were pronounced with catgut, irrespective of anastomotic technique. Thus inversion technique of anastomosis accomplished by single layer suturing with silk thread was ideal for enteroanastomosis in cattle.

Inverse kinetics technique for reactor shutdown measurement: an experimental assessment. [AGR

Energy Technology Data Exchange (ETDEWEB)

Lewis, T. A.; McDonald, D.

1975-09-15

It is proposed to use the Inverse Kinetics Technique to measure the subcritical reactivity as a function of time during the testing of the nitrogen injection systems on AGRs. A description is given of an experimental assessment of the technique by investigating known transients created by control rod movements on a small experimental reactor, (2m high, 1m radius). Spatial effects were observed close to the moving rods but otherwise derived reactivities were independent of detector position and agreed well with the existing calibrations. This prompted the suggestion that data from installed reactor instrumentation could be used to calibrate CAGR control rods.

Measurement of mean rotation and strain-rate tensors by using stereoscopic PIV

DEFF Research Database (Denmark)

Özcan, Oktay; Meyer, Knud Erik; Larsen, Poul Scheel

2005-01-01

A technique is described for measuring the mean velocity gradient (rate-of-displacement) tensor by using a conventional stereoscopic particle image velocimetry (SPIV) system. Planar measurement of the mean vorticity vector, rate-of-rotation and rate-of-strain tensors and the production of turbule...

Fourth meeting entitled “Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data”

CERN Document Server

Vilanova, Anna; Burgeth, Bernhard; Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data

2014-01-01

Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and...

Atomic-batched tensor decomposed two-electron repulsion integrals

Science.gov (United States)

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

2017-04-01

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

Recovery of material parameters of soft hyperelastic tissue by an inverse spectral technique

KAUST Repository

Gou, Kun

2012-07-01

An inverse spectral method is developed for recovering a spatially inhomogeneous shear modulus for soft tissue. The study is motivated by a novel use of the intravascular ultrasound technique to image arteries. The arterial wall is idealized as a nonlinear isotropic cylindrical hyperelastic body. A boundary value problem is formulated for the response of the arterial wall within a specific class of quasistatic deformations reflective of the response due to imposed blood pressure. Subsequently, a boundary value problem is developed via an asymptotic construction modeling intravascular ultrasound interrogation which generates small amplitude, high frequency time harmonic vibrations superimposed on the static finite deformation. This leads to a system of second order ordinary Sturm-Liouville boundary value problems that are then employed to reconstruct the shear modulus through a nonlinear inverse spectral technique. Numerical examples are demonstrated to show the viability of the method. © 2012 Elsevier Ltd. All rights reserved.

Utility of natural generalised inverse technique in the interpretation of dyke structures

Digital Repository Service at National Institute of Oceanography (India)

Rao, M.M.M.; Murty, T.V.R.; Rao, P.R.; Lakshminarayana, S.; Subrahmanyam, A.S.; Murthy, K.S.R.

environs along the central west coast of India: analysis using EOF, J. Geophys.Res.,91(1986) 8523 -8526. 9 Marquardt D W, An algorithm for least-squares estimation of non-linear parameters, J. Soc. Indust. Appl. Math, 11 (1963) 431-441. INDIAN J. MAR... technique in reconstruction of gravity anomalies due to a fault, Indian J. Pure. Appl. Math., 34 (2003) 31-47. 16 Ramana Murty T V, Somayajulu Y K & Murty C S, Reconstruction of sound speed profile through natural generalised inverse technique, Indian J...

Comments on "A Closed-Form Solution to Tensor Voting: Theory and Applications".

Science.gov (United States)

Maggiori, Emmanuel; Lotito, Pablo; Manterola, Hugo Luis; del Fresno, Mariana

2014-12-01

We comment on a paper that describes a closed-form formulation to Tensor Voting, a technique to perceptually group clouds of points, usually applied to infer features in images. The authors proved an analytic solution to the technique, a highly relevant contribution considering that the original formulation required numerical integration, a time-consuming task. Their work constitutes the first closed-form expression for the Tensor Voting framework. In this work we first observe that the proposed formulation leads to unexpected results which do not satisfy the constraints for a Tensor Voting output, hence they cannot be interpreted. Given that the closed-form expression is said to be an analytic equivalent solution, unexpected outputs should not be encountered unless there are flaws in the proof. We analyzed the underlying math to find which were the causes of these unexpected results. In this commentary we show that their proposal does not in fact provide a proper analytic solution to Tensor Voting and we indicate the flaws in the proof.

Harmonic d-tensors

Energy Technology Data Exchange (ETDEWEB)

Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)

2016-07-01

Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.

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

Science.gov (United States)

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

2015-09-01

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

Current density tensors

Science.gov (United States)

Lazzeretti, Paolo

2018-04-01

It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

Comments on "A closed-form solution to Tensor voting: theory and applications"

OpenAIRE

Maggiori, Emmanuel; Lotito, Pablo Andres; Manterola, Hugo Luis; del Fresno, Mariana

2017-01-01

We comment on a paper that describes a closed-form formulation to Tensor Voting, a technique to perceptually group clouds of points, usually applied to infer features in images. The authors proved an analytic solution to the technique, a highly relevant contribution considering that the original formulation required numerical integration, a time-consuming task. Their work constitutes the first closed-form expression for the Tensor Voting framework. In this work we first observe that the propo...

Susceptibility Tensor Imaging (STI) of the Brain

Science.gov (United States)

Li, Wei; Liu, Chunlei; Duong, Timothy Q.; van Zijl, Peter C.M.; Li, Xu

2016-01-01

Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility (MMS) and magnetic susceptibility anisotropy (MSA) can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping (QSM) to remove such dependence. Similar to diffusion tensor imaging (DTI), STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of susceptibility anisotropy in brain white matter is myelin. Another unique feature of susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. PMID:27120169

3D structure tensor analysis of light microscopy data for validating diffusion MRI.

Science.gov (United States)

Khan, Ahmad Raza; Cornea, Anda; Leigland, Lindsey A; Kohama, Steven G; Jespersen, Sune Nørhøj; Kroenke, Christopher D

2015-05-01

Diffusion magnetic resonance imaging (d-MRI) is a powerful non-invasive and non-destructive technique for characterizing brain tissue on the microscopic scale. However, the lack of validation of d-MRI by independent experimental means poses an obstacle to accurate interpretation of data acquired using this method. Recently, structure tensor analysis has been applied to light microscopy images, and this technique holds promise to be a powerful validation strategy for d-MRI. Advantages of this approach include its similarity to d-MRI in terms of averaging the effects of a large number of cellular structures, and its simplicity, which enables it to be implemented in a high-throughput manner. However, a drawback of previous implementations of this technique arises from it being restricted to 2D. As a result, structure tensor analyses have been limited to tissue sectioned in a direction orthogonal to the direction of interest. Here we describe the analytical framework for extending structure tensor analysis to 3D, and utilize the results to analyze serial image "stacks" acquired with confocal microscopy of rhesus macaque hippocampal tissue. Implementation of 3D structure tensor procedures requires removal of sources of anisotropy introduced in tissue preparation and confocal imaging. This is accomplished with image processing steps to mitigate the effects of anisotropic tissue shrinkage, and the effects of anisotropy in the point spread function (PSF). In order to address the latter confound, we describe procedures for measuring the dependence of PSF anisotropy on distance from the microscope objective within tissue. Prior to microscopy, ex vivo d-MRI measurements performed on the hippocampal tissue revealed three regions of tissue with mutually orthogonal directions of least restricted diffusion that correspond to CA1, alveus and inferior longitudinal fasciculus. We demonstrate the ability of 3D structure tensor analysis to identify structure tensor orientations that

Comparative interpretations of renormalization inversion technique for reconstructing unknown emissions from measured atmospheric concentrations

Science.gov (United States)

Singh, Sarvesh Kumar; Kumar, Pramod; Rani, Raj; Turbelin, Grégory

2017-04-01

The study highlights a theoretical comparison and various interpretations of a recent inversion technique, called renormalization, developed for the reconstruction of unknown tracer emissions from their measured concentrations. The comparative interpretations are presented in relation to the other inversion techniques based on principle of regularization, Bayesian, minimum norm, maximum entropy on mean, and model resolution optimization. It is shown that the renormalization technique can be interpreted in a similar manner to other techniques, with a practical choice of a priori information and error statistics, while eliminating the need of additional constraints. The study shows that the proposed weight matrix and weighted Gram matrix offer a suitable deterministic choice to the background error and measurement covariance matrices, respectively, in the absence of statistical knowledge about background and measurement errors. The technique is advantageous since it (i) utilizes weights representing a priori information apparent to the monitoring network, (ii) avoids dependence on background source estimates, (iii) improves on alternative choices for the error statistics, (iv) overcomes the colocalization problem in a natural manner, and (v) provides an optimally resolved source reconstruction. A comparative illustration of source retrieval is made by using the real measurements from a continuous point release conducted in Fusion Field Trials, Dugway Proving Ground, Utah.

Inversion of Love wave phase velocity using smoothness-constrained least-squares technique; Heikatsuka seiyakutsuki saisho jijoho ni yoru love ha iso sokudo no inversion

Energy Technology Data Exchange (ETDEWEB)

Kawamura, S [Nippon Geophysical Prospecting Co. Ltd., Tokyo (Japan)

1996-10-01

Smoothness-constrained least-squares technique with ABIC minimization was applied to the inversion of phase velocity of surface waves during geophysical exploration, to confirm its usefulness. Since this study aimed mainly at the applicability of the technique, Love wave was used which is easier to treat theoretically than Rayleigh wave. Stable successive approximation solutions could be obtained by the repeated improvement of velocity model of S-wave, and an objective model with high reliability could be determined. While, for the inversion with simple minimization of the residuals squares sum, stable solutions could be obtained by the repeated improvement, but the judgment of convergence was very hard due to the smoothness-constraint, which might make the obtained model in a state of over-fitting. In this study, Love wave was used to examine the applicability of the smoothness-constrained least-squares technique with ABIC minimization. Applicability of this to Rayleigh wave will be investigated. 8 refs.

Partition-based Collaborative Tensor Factorization for POI Recommendation

Institute of Scientific and Technical Information of China (English)

Wenjing Luan; Guanjun Liu; Changjun Jiang; Liang Qi

2017-01-01

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

TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow

OpenAIRE

Hafner, Danijar; Davidson, James; Vanhoucke, Vincent

2017-01-01

We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel witho...

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

Science.gov (United States)

Rütten, Markus; Chong, Min S

2006-01-01

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

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

OpenAIRE

SASAKURA, NAOKI

2010-01-01

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...

Source-Type Identification Analysis Using Regional Seismic Moment Tensors

Science.gov (United States)

Chiang, A.; Dreger, D. S.; Ford, S. R.; Walter, W. R.

2012-12-01

Waveform inversion to determine the seismic moment tensor is a standard approach in determining the source mechanism of natural and manmade seismicity, and may be used to identify, or discriminate different types of seismic sources. The successful applications of the regional moment tensor method at the Nevada Test Site (NTS) and the 2006 and 2009 North Korean nuclear tests (Ford et al., 2009a, 2009b, 2010) show that the method is robust and capable for source-type discrimination at regional distances. The well-separated populations of explosions, earthquakes and collapses on a Hudson et al., (1989) source-type diagram enables source-type discrimination; however the question remains whether or not the separation of events is universal in other regions, where we have limited station coverage and knowledge of Earth structure. Ford et al., (2012) have shown that combining regional waveform data and P-wave first motions removes the CLVD-isotropic tradeoff and uniquely discriminating the 2009 North Korean test as an explosion. Therefore, including additional constraints from regional and teleseismic P-wave first motions enables source-type discrimination at regions with limited station coverage. We present moment tensor analysis of earthquakes and explosions (M6) from Lop Nor and Semipalatinsk test sites for station paths crossing Kazakhstan and Western China. We also present analyses of smaller events from industrial sites. In these sparse coverage situations we combine regional long-period waveforms, and high-frequency P-wave polarity from the same stations, as well as from teleseismic arrays to constrain the source type. Discrimination capability with respect to velocity model and station coverage is examined, and additionally we investigate the velocity model dependence of vanishing free-surface traction effects on seismic moment tensor inversion of shallow sources and recovery of explosive scalar moment. Our synthetic data tests indicate that biases in scalar

The gauge-invariant canonical energy-momentum tensor

Science.gov (United States)

Lorcé, Cédric

2016-03-01

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

The gauge-invariant canonical energy-momentum tensor

International Nuclear Information System (INIS)

Lorce, C.

2016-01-01

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

Susceptibility tensor imaging (STI) of the brain.

Science.gov (United States)

Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu

2017-04-01

Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Time integration of tensor trains

OpenAIRE

Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart

2014-01-01

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formul...

Measuring the complex permittivity tensor of uniaxial biological materials with coplanar waveguide transmission line

Science.gov (United States)

A simple and accurate technique is described for measuring the uniaxial permittivity tensor of biological materials with a coplanar waveguide transmission-line configuration. Permittivity tensor results are presented for several chicken and beef fresh meat samples at 2.45 GHz....

Tensor spaces and exterior algebra

CERN Document Server

Yokonuma, Takeo

1992-01-01

This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

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

NARCIS (Netherlands)

Akkerman, Erik M.

2010-01-01

Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional

Integrated intensities in inverse time-of-flight technique

International Nuclear Information System (INIS)

Dorner, Bruno

2006-01-01

In traditional data analysis a model function, convoluted with the resolution, is fitted to the measured data. In case that integrated intensities of signals are of main interest, one can use an approach which does not require a model function for the signal nor detailed knowledge of the resolution. For inverse TOF technique, this approach consists of two steps: (i) Normalisation of the measured spectrum with the help of a monitor, with 1/k sensitivity, which is positioned in front of the sample. This means at the same time a conversion of the data from time of flight to energy transfer. (ii) A Jacobian [I. Waller, P.O. Froeman, Ark. Phys. 4 (1952) 183] transforms data collected at constant scattering angle into data as if measured at constant momentum transfer Q. This Jacobian works correctly for signals which have a constant width at different Q along the trajectory of constant scattering angle. The approach has been tested on spectra of Compton scattering with neutrons, having epithermal energies, obtained on the inverse TOF spectrometer VESUVIO/ISIS. In this case the width of the signal is increasing proportional to Q and in consequence the application of the Jacobian leads to integrated intensities slightly too high. The resulting integrated intensities agree very well with results derived in the traditional way. Thus this completely different approach confirms the observation that signals from recoil by H-atoms at large momentum transfers are weaker than expected

Seismic moment tensor for anisotropic media: implication for Non-double-couple earthquakes

Science.gov (United States)

Cai, X.; Chen, X.; Chen, Y.; Cai, M.

2008-12-01

It is often found that the inversion results of seismic moment tensor from real seismic recorded data show the trace of seismic moment tensor M is not zero, a phenomenon called non-double-couple earthquake sources mechanism. Recently we have derived the analytical expressions of M in transversely isotropic media with the titled axis of symmetry and the results shows even only pure shear-motion of fault can lead to the implosive components determined by several combined anisotropic elastic constants. Many non-double-couple earthquakes from observations often appear in volcanic and geothermal areas (Julian, 1998), where there exist a mount of stress-aligned fluid-saturated parallel vertical micro-cracks identical to transversely isotropic media (Crampin, 2008), this stress-aligned crack will modify the seismic moment tensor. In another word, non-double-couple earthquakes don't mean to have a seismic failure movement perpendicular to the fault plane, while traditional research of seismic moment tensor focus on the case of isotropy, which cannot provide correct interpretation of seismic source mechanism. Reference: Julian, B.R., Miller, A.D. and Foulger, G.R., 1998. Non-double-couple earthquakes,1. Theory, Rev. Geophys., 36, 525¨C549. Crampin,S., Peacock,S., 2008, A review of the current understanding of seismic shear-wave splitting in the Earth's crust and common fallacies in interpretation, wave motion, 45,675-722

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.)

Inverse anisotropic diffusion from power density measurements in two dimensions

International Nuclear Information System (INIS)

Monard, François; Bal, Guillaume

2012-01-01

This paper concerns the reconstruction of an anisotropic diffusion tensor γ = (γ ij ) 1⩽i,j⩽2 from knowledge of internal functionals of the form γ∇u i · ∇u j with u i for 1 ⩽ i ⩽ I solutions of the elliptic equation ∇ · γ∇u i = 0 on a two-dimensional bounded domain with appropriate boundary conditions. We show that for I = 4 and appropriately chosen boundary conditions, γ may uniquely and stably be reconstructed from such internal functionals, which appear in coupled-physics inverse problems involving the ultrasound modulation of electrical or optical coefficients. Explicit reconstruction procedures for the diffusion tensor are presented and implemented numerically. (paper)

Tensor structure for Nori motives

OpenAIRE

Barbieri-Viale, Luca; Huber, Annette; Prest, Mike

2018-01-01

We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.

Uncertainty estimates of a GRACE inversion modelling technique over Greenland using a simulation

Science.gov (United States)

Bonin, Jennifer; Chambers, Don

2013-07-01

The low spatial resolution of GRACE causes leakage, where signals in one location spread out into nearby regions. Because of this leakage, using simple techniques such as basin averages may result in an incorrect estimate of the true mass change in a region. A fairly simple least squares inversion technique can be used to more specifically localize mass changes into a pre-determined set of basins of uniform internal mass distribution. However, the accuracy of these higher resolution basin mass amplitudes has not been determined, nor is it known how the distribution of the chosen basins affects the results. We use a simple `truth' model over Greenland as an example case, to estimate the uncertainties of this inversion method and expose those design parameters which may result in an incorrect high-resolution mass distribution. We determine that an appropriate level of smoothing (300-400 km) and process noise (0.30 cm2 of water) gets the best results. The trends of the Greenland internal basins and Iceland can be reasonably estimated with this method, with average systematic errors of 3.5 cm yr-1 per basin. The largest mass losses found from GRACE RL04 occur in the coastal northwest (-19.9 and -33.0 cm yr-1) and southeast (-24.2 and -27.9 cm yr-1), with small mass gains (+1.4 to +7.7 cm yr-1) found across the northern interior. Acceleration of mass change is measurable at the 95 per cent confidence level in four northwestern basins, but not elsewhere in Greenland. Due to an insufficiently detailed distribution of basins across internal Canada, the trend estimates of Baffin and Ellesmere Islands are expected to be incorrect due to systematic errors caused by the inversion technique.

Combined rock-physical modelling and seismic inversion techniques for characterisation of stacked sandstone reservoir

NARCIS (Netherlands)

Justiniano, A.; Jaya, Y.; Diephuis, G.; Veenhof, R.; Pringle, T.

2015-01-01

The objective of the study is to characterise the Triassic massive stacked sandstone deposits of the Main Buntsandstein Subgroup at Block Q16 located in the West Netherlands Basin. The characterisation was carried out through combining rock-physics modelling and seismic inversion techniques. The

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

OpenAIRE

Loveridge, Lee C.

2004-01-01

Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

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

Science.gov (United States)

Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M

2008-01-01

This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.

Airborne full tensor magnetic gradiometry surveys in the Thuringian basin, Germany

Science.gov (United States)

Queitsch, M.; Schiffler, M.; Goepel, A.; Stolz, R.; Meyer, M.; Meyer, H.; Kukowski, N.

2013-12-01

In this contribution we introduce a newly developed fully operational full tensor magnetic gradiometer (FTMG) instrument based on Superconducting Quantum Interference Devices (SQUIDs) and show example data acquired in 2012 within the framework of the INFLUINS (Integrated Fluid Dynamics in Sedimentary basins) project. This multidisciplinary project aims for a better understanding of movements and interaction between shallow and deep fluids in the Thuringian Basin in the center of Germany. In contrast to mapping total magnetic field intensity (TMI) in conventional airborne magnetic surveys for industrial exploration of mineral deposits and sedimentary basins, our instrument measures all components of the magnetic field gradient tensor using highly sensitive SQUID gradiometers. This significantly constrains the solutions of the inverse problem. Furthermore, information on the ratio between induced and remanent magnetization is obtained. Special care has been taken to reduce motion noise while acquiring data in airborne operation. Therefore, the sensors are mounted in a nonmagnetic and aerodynamically shaped bird made of fiberglas with a high drag tail which stabilizes the bird even at low velocities. The system is towed by a helicopter and kept at 30m above ground during data acquisition. Additionally, the system in the bird incorporates an inertial unit for geo-referencing and enhanced motion noise compensation, a radar altimeter for topographic correction and a GPS system for high precision positioning. Advanced data processing techniques using reference magnetometer and inertial unit data result in a very low system noise of less than 60 pT/m peak to peak in airborne operation. To show the performance of the system we present example results from survey areas within the Thuringian basin and along its bordering highlands. The mapped gradient tensor components show a high correlation to existing geologic maps. Furthermore, the measured gradient components indicate

Development of the Tensoral Computer Language

Science.gov (United States)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

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

Science.gov (United States)

Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben

2017-08-02

It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.

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

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

International Nuclear Information System (INIS)

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

2014-01-01

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

Tensor integrand reduction via Laurent expansion

Energy Technology Data Exchange (ETDEWEB)

Hirschi, Valentin [SLAC, National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025-7090 (United States); Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom)

2016-06-09

We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MADLOOP, which is part of the public MADGRAPH5{sub A}MC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CUTTOOLS, SAMURAI, IREGI, PJFRY++ and GOLEM95. We find that Ninja outperforms traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool GOLEM95 which is however more limited and slower than Ninja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.

Inverse Function: Pre-Service Teachers' Techniques and Meanings

Science.gov (United States)

Paoletti, Teo; Stevens, Irma E.; Hobson, Natalie L. F.; Moore, Kevin C.; LaForest, Kevin R.

2018-01-01

Researchers have argued teachers and students are not developing connected meanings for function inverse, thus calling for a closer examination of teachers' and students' inverse function meanings. Responding to this call, we characterize 25 pre-service teachers' inverse function meanings as inferred from our analysis of clinical interviews. After…

Categorical Tensor Network States

Directory of Open Access Journals (Sweden)

Jacob D. Biamonte

2011-12-01

Full Text Available We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state |ψ〉, we present a new and general method to factor |ψ〉 into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.

Distance Adaptive Tensor Discriminative Geometry Preserving Projection for Face Recognition

Directory of Open Access Journals (Sweden)

Ziqiang Wang

2012-09-01

Full Text Available There is a growing interest in dimensionality reduction techniques for face recognition, however, the traditional dimensionality reduction algorithms often transform the input face image data into vectors before embedding. Such vectorization often ignores the underlying data structure and leads to higher computational complexity. To effectively cope with these problems, a novel dimensionality reduction algorithm termed distance adaptive tensor discriminative geometry preserving projection (DATDGPP is proposed in this paper. The key idea of DATDGPP is as follows: first, the face image data are directly encoded in high-order tensor structure so that the relationships among the face image data can be preserved; second, the data-adaptive tensor distance is adopted to model the correlation among different coordinates of tensor data; third, the transformation matrix which can preserve discrimination and local geometry information is obtained by an iteration algorithm. Experimental results on three face databases show that the proposed algorithm outperforms other representative dimensionality reduction algorithms.

Tensor Permutation Matrices in Finite Dimensions

OpenAIRE

Christian, Rakotonirina

2005-01-01

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...

Tensor Completion for Estimating Missing Values in Visual Data

KAUST Repository

Liu, Ji

2012-01-25

In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependant relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between Fa

Tensor Completion for Estimating Missing Values in Visual Data

KAUST Repository

Liu, Ji; Musialski, Przemyslaw; Wonka, Peter; Ye, Jieping

2012-01-01

In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependant relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between Fa

Tensor completion for estimating missing values in visual data.

Science.gov (United States)

Liu, Ji; Musialski, Przemyslaw; Wonka, Peter; Ye, Jieping

2013-01-01

In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependent relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between FaLRTC an

Source-jerk analysis using a semi-explicit inverse kinetic technique

International Nuclear Information System (INIS)

Spriggs, G.D.; Pederson, R.A.

1985-01-01

A method is proposed for measuring the effective reproduction factor, k, in subcritical systems. The method uses the transient response of a subcritical system to the sudden removal of an extraneous neutron source (i.e., a source jerk). The response is analyzed using an inverse kinetic technique that least-squares fits the exact analytical solution corresponding to a source-jerk transient as derived from the point-reactor model. It has been found that the technique can provide an accurate means of measuring k in systems that are close to critical (i.e., 0.95 < k < 1.0). As a system becomes more subcritical (i.e., k << 1.0) spatial effects can introduce significant biases depending on the source and detector positions. However, methods are available that can correct for these biases and, hence, can allow measuring subcriticality in systems with k as low as 0.5. 12 refs., 3 figs

Source-jerk analysis using a semi-explicit inverse kinetic technique

International Nuclear Information System (INIS)

Spriggs, G.D.; Pederson, R.A.

1985-01-01

A method is proposed for measuring the effective reproduction factor, k, in subcritical systems. The method uses the transient responses of a subcritical system to the sudden removal of an extraneous neutron source (i.e., a source jerk). The response is analyzed using an inverse kinetic technique that least-squares fits the exact analytical solution corresponding to a source-jerk transient as derived from the point-reactor model. It has been found that the technique can provide an accurate means of measuring k in systems that are close to critical (i.e., 0.95 < k < 1.0). As a system becomes more subcritical (i.e., k << 1.0) spatial effects can introduce significant biases depending on the source and detector positions. However, methods are available that can correct for these biases and, hence, can allow measuring subcriticality in systems with k as low as 0.5

Theoretical assessment of the full-moment-tensor resolvability for receiver arrays used in microseismic monitoring

Czech Academy of Sciences Publication Activity Database

Staněk, František; Eisner, Leo; Vesnaver, A.

2017-01-01

Roč. 14, č. 2 (2017), s. 235-240 ISSN 1214-9705 Grant - others:AV ČR(CZ) CNR-16-17 Program:Bilaterální spolupráce Institutional support: RVO:67985891 Keywords : microseismic monitoring * source mechanism * moment tensor * inversion Subject RIV: DC - Siesmology, Volcanology, Earth Structure OBOR OECD: 1.7 Other natural sciences Impact factor: 0.699, year: 2016

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...

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)

Morphometric study of tensor of vastus intermedius in South Indian population.

Science.gov (United States)

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.

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....

An EM System With Dramatic Multi-Axis Transmitter and Tensor Gradiometer Receiver

Science.gov (United States)

2011-06-01

Thus, the main difference between the spatial behavior of target anomalies measured with a magnetometer and those we measured with an EM system is in...current efforts include the development of tensor magnetic gradiometers based on triaxial fluxgate technology by the USGS (Snyder & Bracken, Development...Superconducting gradiometer/ Magnetometer Arrays and a Novel Signal Processing Technique. IEEE Trans. on Magnetics, MAG-11(2), 701-707. EM Tensor Gradiometer

An EM System with Dynamic Multi-Axis Transmitter and Tensor Gradiometer Receiver

Science.gov (United States)

2011-06-01

main difference between the spatial behavior of target anomalies measured with a magnetometer and those we measured with an EM system is in the nature...environmental and UXO applications, current efforts include the development of tensor magnetic gradiometers based on triaxial fluxgate technology by the USGS...Superconducting gradiometer/ Magnetometer Arrays and a Novel Signal Processing Technique. IEEE Trans. on Magnetics, MAG-11(2), 701-707. EM Tensor

Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

Science.gov (United States)

Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej

2015-09-01

CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.

Simultaneous tensor decomposition and completion using factor priors.

Science.gov (United States)

Chen, Yi-Lei; Hsu, Chiou-Ting; Liao, Hong-Yuan Mark

2014-03-01

The success of research on matrix completion is evident in a variety of real-world applications. Tensor completion, which is a high-order extension of matrix completion, has also generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called simultaneous tensor decomposition and completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. By exploiting this auxiliary information, our method leverages two classic schemes and accurately estimates the model factors and missing entries. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.

Monograph On Tensor Notations

Science.gov (United States)

Sirlin, Samuel W.

1993-01-01

Eight-page report describes systems of notation used most commonly to represent tensors of various ranks, with emphasis on tensors in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial tensor, vector, dyadic, and matrix notations, and relationships among them described.

Moment-tensor solutions estimated using optimal filter theory: Global seismicity, 2001

Science.gov (United States)

Sipkin, S.A.; Bufe, C.G.; Zirbes, M.D.

2003-01-01

This paper is the 12th in a series published yearly containing moment-tensor solutions computed at the US Geological Survey using an algorithm based on the theory of optimal filter design (Sipkin, 1982 and Sipkin, 1986b). An inversion has been attempted for all earthquakes with a magnitude, mb or MS, of 5.5 or greater. Previous listings include solutions for earthquakes that occurred from 1981 to 2000 (Sipkin, 1986b; Sipkin and Needham, 1989, Sipkin and Needham, 1991, Sipkin and Needham, 1992, Sipkin and Needham, 1993, Sipkin and Needham, 1994a and Sipkin and Needham, 1994b; Sipkin and Zirbes, 1996 and Sipkin and Zirbes, 1997; Sipkin et al., 1998, Sipkin et al., 1999, Sipkin et al., 2000a, Sipkin et al., 2000b and Sipkin et al., 2002).The entire USGS moment-tensor catalog can be obtained via anonymous FTP at ftp://ghtftp.cr.usgs.gov. After logging on, change directory to “momten”. This directory contains two compressed ASCII files that contain the finalized solutions, “mt.lis.Z” and “fmech.lis.Z”. “mt.lis.Z” contains the elements of the moment tensors along with detailed event information; “fmech.lis.Z” contains the decompositions into the principal axes and best double-couples. The fast moment-tensor solutions for more recent events that have not yet been finalized and added to the catalog, are gathered by month in the files “jan01.lis.Z”, etc. “fmech.doc.Z” describes the various fields.

Applying inversion techniques to derive source currents and geoelectric fields for geomagnetically induced current calculations

Directory of Open Access Journals (Sweden)

J. S. de Villiers

2014-10-01

Full Text Available This research focuses on the inversion of geomagnetic variation field measurement to obtain source currents in the ionosphere. During a geomagnetic disturbance, the ionospheric currents create magnetic field variations that induce geoelectric fields, which drive geomagnetically induced currents (GIC in power systems. These GIC may disturb the operation of power systems and cause damage to grounded power transformers. The geoelectric fields at any location of interest can be determined from the source currents in the ionosphere through a solution of the forward problem. Line currents running east–west along given surface position are postulated to exist at a certain height above the Earth's surface. This physical arrangement results in the fields on the ground having the magnetic north and down components, and the electric east component. Ionospheric currents are modelled by inverting Fourier integrals (over the wavenumber of elementary geomagnetic fields using the Levenberg–Marquardt technique. The output parameters of the inversion model are the current strength, height and surface position of the ionospheric current system. A ground conductivity structure with five layers from Quebec, Canada, based on the Layered-Earth model is used to obtain the complex skin depth at a given angular frequency. This paper presents preliminary and inversion results based on these structures and simulated geomagnetic fields. The results show some interesting features in the frequency domain. Model parameters obtained through inversion are within 2% of simulated values. This technique has applications for modelling the currents of electrojets at the equator and auroral regions, as well as currents in the magnetosphere.

Cartesian tensors an introduction

CERN Document Server

Temple, G

2004-01-01

This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t

The metric theory of tensor products Grothendieck's resume revisited

CERN Document Server

Diestel, Joe; Swart, Johan; Swarte, Johannes Laurentius; Diestel, Joseph

2008-01-01

Grothendieck's Resumé is a landmark in functional analysis. Despite having appeared more than a half century ago, its techniques and results are still not widely known nor appreciated. This is due, no doubt, to the fact that Grothendieck included practically no proofs, and the presentation is based on the theory of the very abstract notion of tensor products. This book aims at providing the details of Grothendieck's constructions and laying bare how the important classes of operators are a consequence of the abstract operations on tensor norms. Particular attention is paid to how the classical

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.

Stress-energy tensor near a charged, rotating, evaporating black hole

International Nuclear Information System (INIS)

Hiscock, W.A.

1977-01-01

The recently developed two-dimensional stress-energy regularization techniques are applied to the two-dimensional analog of the Reissner-Nordstroem family of black-hole metrics. The calculated stress-energy tensor in all cases contains the thermal radiation discovered by Hawking. Implications for the evolution of the interior of a charged black hole are considered. The calculated stress-energy tensor is found to diverge on the inner, Cauchy, horizon. Thus the effect of quantum mechanics is to cause the Cauchy horizon to become singular. The stress-energy tensor is also calculated for the ''most reasonable'' two-dimensional analog of the Kerr-Newman family of black-hole metrics. Although the analysis is not as rigorous as in the Reissner-Nordstroem case, it appears that the correct value for the Hawking radiation also appears in this model

Inverse photoemission

International Nuclear Information System (INIS)

Namatame, Hirofumi; Taniguchi, Masaki

1994-01-01

Photoelectron spectroscopy is regarded as the most powerful means since it can measure almost perfectly the occupied electron state. On the other hand, inverse photoelectron spectroscopy is the technique for measuring unoccupied electron state by using the inverse process of photoelectron spectroscopy, and in principle, the similar experiment to photoelectron spectroscopy becomes feasible. The development of the experimental technology for inverse photoelectron spectroscopy has been carried out energetically by many research groups so far. At present, the heightening of resolution of inverse photoelectron spectroscopy, the development of inverse photoelectron spectroscope in which light energy is variable and so on are carried out. But the inverse photoelectron spectroscope for vacuum ultraviolet region is not on the market. In this report, the principle of inverse photoelectron spectroscopy and the present state of the spectroscope are described, and the direction of the development hereafter is groped. As the experimental equipment, electron guns, light detectors and so on are explained. As the examples of the experiment, the inverse photoelectron spectroscopy of semimagnetic semiconductors and resonance inverse photoelectron spectroscopy are reported. (K.I.)

A technique for increasing the accuracy of the numerical inversion of the Laplace transform with applications

Science.gov (United States)

Berger, B. S.; Duangudom, S.

1973-01-01

A technique is introduced which extends the range of useful approximation of numerical inversion techniques to many cycles of an oscillatory function without requiring either the evaluation of the image function for many values of s or the computation of higher-order terms. The technique consists in reducing a given initial value problem defined over some interval into a sequence of initial value problems defined over a set of subintervals. Several numerical examples demonstrate the utility of the method.

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

Energy Technology Data Exchange (ETDEWEB)

Krtous, Pavel [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Kubiznak, David [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Page, Don N. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada); Frolov, Valeri P. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada)

2007-02-15

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 {<=} j {<=} k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

International Nuclear Information System (INIS)

Krtous, Pavel; Kubiznak, David; Page, Don N.; Frolov, Valeri P.

2007-01-01

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 ≤ j ≤ k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

Science.gov (United States)

Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

2017-07-01

The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied to a model suffering the notorious quantum Monte Carlo sign problem—the orbital eg model with spatially highly anisotropic orbital interactions. Coarse graining of the tensor network along the inverse temperature β yields a numerically tractable 2D tensor network representing the Gibbs state. Its bond dimension D —limiting the amount of entanglement—is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of Tc, and give the critical exponents within 1 % of the 2D Ising universality class.

A high performance data parallel tensor contraction framework: Application to coupled electro-mechanics

Science.gov (United States)

Poya, Roman; Gil, Antonio J.; Ortigosa, Rogelio

2017-07-01

The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.

Tensor-based spatiotemporal saliency detection

Science.gov (United States)

Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen

2018-03-01

This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.

On Adapting the Tensor Voting Framework to Robust Color Image Denoising

Science.gov (United States)

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Julià, Carme

This paper presents an adaptation of the tensor voting framework for color image denoising, while preserving edges. Tensors are used in order to encode the CIELAB color channels, the uniformity and the edginess of image pixels. A specific voting process is proposed in order to propagate color from a pixel to its neighbors by considering the distance between pixels, the perceptual color difference (by using an optimized version of CIEDE2000), a uniformity measurement and the likelihood of the pixels being impulse noise. The original colors are corrected with those encoded by the tensors obtained after the voting process. Peak to noise ratios and visual inspection show that the proposed methodology has a better performance than state-of-the-art techniques.

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 J₂ 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 J₂ 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.

A Tensor-Product-Kernel Framework for Multiscale Neural Activity Decoding and Control

Science.gov (United States)

Li, Lin; Brockmeier, Austin J.; Choi, John S.; Francis, Joseph T.; Sanchez, Justin C.; Príncipe, José C.

2014-01-01

Brain machine interfaces (BMIs) have attracted intense attention as a promising technology for directly interfacing computers or prostheses with the brain's motor and sensory areas, thereby bypassing the body. The availability of multiscale neural recordings including spike trains and local field potentials (LFPs) brings potential opportunities to enhance computational modeling by enriching the characterization of the neural system state. However, heterogeneity on data type (spike timing versus continuous amplitude signals) and spatiotemporal scale complicates the model integration of multiscale neural activity. In this paper, we propose a tensor-product-kernel-based framework to integrate the multiscale activity and exploit the complementary information available in multiscale neural activity. This provides a common mathematical framework for incorporating signals from different domains. The approach is applied to the problem of neural decoding and control. For neural decoding, the framework is able to identify the nonlinear functional relationship between the multiscale neural responses and the stimuli using general purpose kernel adaptive filtering. In a sensory stimulation experiment, the tensor-product-kernel decoder outperforms decoders that use only a single neural data type. In addition, an adaptive inverse controller for delivering electrical microstimulation patterns that utilizes the tensor-product kernel achieves promising results in emulating the responses to natural stimulation. PMID:24829569

Generalized dielectric permittivity tensor

International Nuclear Information System (INIS)

Borzdov, G.N.; Barkovskii, L.M.; Fedorov, F.I.

1986-01-01

The authors deal with the question of what is to be done with the formalism of the electrodynamics of dispersive media based on the introduction of dielectric-permittivity tensors for purely harmonic fields when Voigt waves and waves of more general form exist. An attempt is made to broaden and generalize the formalism to take into account dispersion of waves of the given type. In dispersive media, the polarization, magnetization, and conduction current-density vectors of point and time are determined by the values of the electromagnetic field vectors in the vicinity of this point (spatial dispersion) in the preceding instants of time (time dispersion). The dielectric-permittivity tensor and other tensors of electrodynamic parameters of the medium are introduced in terms of a set of evolution operators and not the set of harmonic function. It is noted that a magnetic-permeability tensor and an elastic-modulus tensor may be introduced for an acoustic field in dispersive anisotropic media with coupling equations of general form

Tensor analysis for physicists

CERN Document Server

Schouten, J A

1989-01-01

This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...

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

International Nuclear Information System (INIS)

Huf, P A; Carminati, J

2015-01-01

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

A gEUD-based inverse planning technique for HDR prostate brachytherapy: Feasibility study

Energy Technology Data Exchange (ETDEWEB)

Giantsoudi, D. [Department of Radiological Sciences, University of Texas Health Sciences Center, San Antonio, Texas 78229 (United States); Department of Radiation Oncology, Francis H. Burr Proton Therapy Center, Boston, Massachusetts 02114 (United States); Baltas, D. [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, 63069 Offenbach (Germany); Nuclear and Particle Physics Section, Physics Department, University of Athens, 15701 Athens (Greece); Karabis, A. [Pi-Medical Ltd., Athens 10676 (Greece); Mavroidis, P. [Department of Radiological Sciences, University of Texas Health Sciences Center, San Antonio, Texas 78299 and Department of Medical Radiation Physics, Karolinska Institutet and Stockholm University, 17176 (Sweden); Zamboglou, N.; Tselis, N. [Strahlenklinik, Klinikum Offenbach GmbH, 63069 Offenbach (Germany); Shi, C. [St. Vincent' s Medical Center, 2800 Main Street, Bridgeport, Connecticut 06606 (United States); Papanikolaou, N. [Department of Radiological Sciences, University of Texas Health Sciences Center, San Antonio, Texas 78299 (United States)

2013-04-15

Purpose: The purpose of this work was to study the feasibility of a new inverse planning technique based on the generalized equivalent uniform dose for image-guided high dose rate (HDR) prostate cancer brachytherapy in comparison to conventional dose-volume based optimization. Methods: The quality of 12 clinical HDR brachytherapy implants for prostate utilizing HIPO (Hybrid Inverse Planning Optimization) is compared with alternative plans, which were produced through inverse planning using the generalized equivalent uniform dose (gEUD). All the common dose-volume indices for the prostate and the organs at risk were considered together with radiobiological measures. The clinical effectiveness of the different dose distributions was investigated by comparing dose volume histogram and gEUD evaluators. Results: Our results demonstrate the feasibility of gEUD-based inverse planning in HDR brachytherapy implants for prostate. A statistically significant decrease in D{sub 10} or/and final gEUD values for the organs at risk (urethra, bladder, and rectum) was found while improving dose homogeneity or dose conformity of the target volume. Conclusions: Following the promising results of gEUD-based optimization in intensity modulated radiation therapy treatment optimization, as reported in the literature, the implementation of a similar model in HDR brachytherapy treatment plan optimization is suggested by this study. The potential of improved sparing of organs at risk was shown for various gEUD-based optimization parameter protocols, which indicates the ability of this method to adapt to the user's preferences.

Unique characterization of the Bel-Robinson tensor

International Nuclear Information System (INIS)

Bergqvist, G; Lankinen, P

2004-01-01

We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors

Tensor decomposition in electronic structure calculations on 3D Cartesian grids

International Nuclear Information System (INIS)

Khoromskij, B.N.; Khoromskaia, V.; Chinnamsetty, S.R.; Flad, H.-J.

2009-01-01

In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform nxnxn grid. Combined with the Richardson extrapolation, our approach exhibits O(h 3 ) convergence in the grid-size h=O(n -1 ). Moreover, this requires O(3rn+r 3 ) storage, where r denotes the Tucker rank of the electron density with r=O(logn), almost uniformly in n. For example, calculations of the Coulomb matrix and the Hartree-Fock energy for the CH 4 molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10 -6 hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.

Tensor Product of Polygonal Cell Complexes

OpenAIRE

Chien, Yu-Yen

2017-01-01

We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.

Mean template for tensor-based morphometry using deformation tensors.

Science.gov (United States)

Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M

2007-01-01

Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.

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.

Diffusion tensor trace mapping in normal adult brain using single-shot EPI technique: A methodological study of the aging brain

International Nuclear Information System (INIS)

Chen, Z.G.; Hindmarsh, T.; Li, T.Q.

2001-01-01

Purpose: To quantify age-related changes of the average diffusion coefficient value in normal adult brain using orientation-independent diffusion tensor trace mapping and to address the methodological influences on diffusion quantification. Material and Methods: Fifty-four normal subjects (aged 20-79 years) were studied on a 1.5-T whole-body MR medical unit using a diffusion-weighted single-shot echo-planar imaging technique. Orientation-independent diffusion tensor trace maps were constructed for each subject using diffusion-weighted MR measurements in four different directions using a tetrahedral gradient combination pattern. The global average (including cerebral spinal fluid) and the tissue average of diffusion coefficients in adult brains were determined by analyzing the diffusion coefficient distribution histogram for the entire brain. Methodological influences on the measured diffusion coefficient were also investigated by comparing the results obtained using different experimental settings. Results: Both global and tissue averages of the diffusion coefficient are significantly correlated with age (p<0.03). The global average of the diffusion coefficient increases 3% per decade after the age of 40, whereas the increase in the tissue average of diffusion coefficient is about 1% per decade. Experimental settings for self-diffusion measurements, such as data acquisition methods and number of b-values, can slightly influence the statistical distribution histogram of the diffusion tensor trace and its average value. Conclusion: Increased average diffusion coefficient in adult brains with aging are consistent with findings regarding structural changes in the brain that have been associated with aging. The study also demonstrates that it is desirable to use the same experimental parameters for diffusion coefficient quantification when comparing between different subjects and groups of interest

A forward model and conjugate gradient inversion technique for low-frequency ultrasonic imaging.

Science.gov (United States)

van Dongen, Koen W A; Wright, William M D

2006-10-01

Emerging methods of hyperthermia cancer treatment require noninvasive temperature monitoring, and ultrasonic techniques show promise in this regard. Various tomographic algorithms are available that reconstruct sound speed or contrast profiles, which can be related to temperature distribution. The requirement of a high enough frequency for adequate spatial resolution and a low enough frequency for adequate tissue penetration is a difficult compromise. In this study, the feasibility of using low frequency ultrasound for imaging and temperature monitoring was investigated. The transient probing wave field had a bandwidth spanning the frequency range 2.5-320.5 kHz. The results from a forward model which computed the propagation and scattering of low-frequency acoustic pressure and velocity wave fields were used to compare three imaging methods formulated within the Born approximation, representing two main types of reconstruction. The first uses Fourier techniques to reconstruct sound-speed profiles from projection or Radon data based on optical ray theory, seen as an asymptotical limit for comparison. The second uses backpropagation and conjugate gradient inversion methods based on acoustical wave theory. The results show that the accuracy in localization was 2.5 mm or better when using low frequencies and the conjugate gradient inversion scheme, which could be used for temperature monitoring.

Tensor Train Neighborhood Preserving Embedding

Science.gov (United States)

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2018-05-01

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.

Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem

Directory of Open Access Journals (Sweden)

Xuqing Zhang

2013-01-01

Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.

Applications of tensor (multiway array) factorizations and decompositions in data mining

DEFF Research Database (Denmark)

Mørup, Morten

2011-01-01

Tensor (multiway array) factorization and decomposition has become an important tool for data mining. Fueled by the computational power of modern computer researchers can now analyze large-scale tensorial structured data that only a few years ago would have been impossible. Tensor factorizations...... have several advantages over two-way matrix factorizations including uniqueness of the optimal solution and component identification even when most of the data is missing. Furthermore, multiway decomposition techniques explicitly exploit the multiway structure that is lost when collapsing some...... of the modes of the tensor in order to analyze the data by regular matrix factorization approaches. Multiway decomposition is being applied to new fields every year and there is no doubt that the future will bring many exciting new applications. The aim of this overview is to introduce the basic concepts...

Joint 1D inversion of TEM and MT data and 3D inversion of MT data in the Hengill area, SW Iceland

Energy Technology Data Exchange (ETDEWEB)

Arnason, Knutur; Eysteinsson, Hjalmar; Hersir, Gylfi Pall [ISOR-Iceland GeoSurvey, Grensasvegi 9, 108 Reykjavik (Iceland)

2010-03-15

An extensive study of the resistivity structure of the Hengill area in SW Iceland was carried out by the combined use of TEM and MT soundings. Joint inversion of the collected data can correct for static shifts in the MT data, which can be severe due to large near-surface resistivity contrasts. Joint 1D inversion of 148 TEM/MT sounding pairs and a 3D inversion of a 60 sounding subset of the MT data were performed. The 3D inversion was based on full MT impedance tensors previously corrected for static shift. Both inversion approaches gave qualitatively similar results, and revealed a shallow resistivity layer reflecting conductive alteration minerals at temperatures of 100-240 C. They also delineated a deep conductor at 3-10 km depth. The reason for this deep-seated high conductivity is not fully understood. The distribution of the deep conductors correlates with a positive residual Bouguer gravity anomaly, and with transform tectonics inferred from seismicity. One model of the Hengill that is consistent with the well temperature data and the deep conductor that does not attenuate S-waves, is a group of hot, solidified, but still ductile magmatic intrusions that are closely associated with the heat source for the geothermal system. (author)

Random SU(2) invariant tensors

Science.gov (United States)

Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei

2018-04-01

SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n  =  4. In this paper, we show that for n  >  4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.

Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group

Science.gov (United States)

Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

2018-05-01

We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42 - complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.

Spherical Tensor Calculus for Local Adaptive Filtering

Science.gov (United States)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Improved tensor multiplets

International Nuclear Information System (INIS)

Wit, B. de; Rocek, M.

1982-01-01

We construct a conformally invariant theory of the N = 1 supersymmetric tensor gauge multiplet and discuss the situation in N = 2. We show that our results give rise to the recently proposed variant of Poincare supergravity, and provide the complete tensor calculus for the theory. Finally, we argue that this theory cannot be quantized sensibly. (orig.)

The evolution of tensor polarization

International Nuclear Information System (INIS)

Huang, H.; Lee, S.Y.; Ratner, L.

1993-01-01

By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake

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

CERN Document Server

Itskov, Mikhail

2015-01-01

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

Diffusion tensor tractography of the mammillothalamic tract in the human brain using a high spatial resolution DTI technique.

Science.gov (United States)

Kamali, Arash; Zhang, Caroline C; Riascos, Roy F; Tandon, Nitin; Bonafante-Mejia, Eliana E; Patel, Rajan; Lincoln, John A; Rabiei, Pejman; Ocasio, Laura; Younes, Kyan; Hasan, Khader M

2018-03-27

The mammillary bodies as part of the hypothalamic nuclei are in the central limbic circuitry of the human brain. The mammillary bodies are shown to be directly or indirectly connected to the amygdala, hippocampus, and thalami as the major gray matter structures of the human limbic system. Although it is not primarily considered as part of the human limbic system, the thalamus is shown to be involved in many limbic functions of the human brain. The major direct connection of the thalami with the hypothalamic nuclei is known to be through the mammillothalamic tract. Given the crucial role of the mammillothalamic tracts in memory functions, diffusion tensor imaging may be helpful in better visualizing the surgical anatomy of this pathway noninvasively. This study aimed to investigate the utility of high spatial resolution diffusion tensor tractography for mapping the trajectory of the mammillothalamic tract in the human brain. Fifteen healthy adults were studied after obtaining written informed consent. We used high spatial resolution diffusion tensor imaging data at 3.0 T. We delineated, for the first time, the detailed trajectory of the mammillothalamic tract of the human brain using deterministic diffusion tensor tractography.

Tensor Calculus: Unlearning Vector Calculus

Science.gov (United States)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Lagrangian analysis of vector and tensor fields: Algorithmic foundations and applications in medical imaging and computational fluid dynamics

OpenAIRE

Ding, Zi'ang

2016-01-01

Both vector and tensor fields are important mathematical tools used to describe the physics of many phenomena in science and engineering. Effective vector and tensor field visualization techniques are therefore needed to interpret and analyze the corresponding data and achieve new insight into the considered problem. This dissertation is concerned with the extraction of important structural properties from vector and tensor datasets. Specifically, we present a unified approach for the charact...

Elastic full waveform inversion based on the homogenization method: theoretical framework and 2-D numerical illustrations

Science.gov (United States)

Capdeville, Yann; Métivier, Ludovic

2018-05-01

Seismic imaging is an efficient tool to investigate the Earth interior. Many of the different imaging techniques currently used, including the so-called full waveform inversion (FWI), are based on limited frequency band data. Such data are not sensitive to the true earth model, but to a smooth version of it. This smooth version can be related to the true model by the homogenization technique. Homogenization for wave propagation in deterministic media with no scale separation, such as geological media, has been recently developed. With such an asymptotic theory, it is possible to compute an effective medium valid for a given frequency band such that effective waveforms and true waveforms are the same up to a controlled error. In this work we make the link between limited frequency band inversion, mainly FWI, and homogenization. We establish the relation between a true model and an FWI result model. This relation is important for a proper interpretation of FWI images. We numerically illustrate, in the 2-D case, that an FWI result is at best the homogenized version of the true model. Moreover, it appears that the homogenized FWI model is quite independent of the FWI parametrization, as long as it has enough degrees of freedom. In particular, inverting for the full elastic tensor is, in each of our tests, always a good choice. We show how the homogenization can help to understand FWI behaviour and help to improve its robustness and convergence by efficiently constraining the solution space of the inverse problem.

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....

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

Time-Dependent Moment Tensors of the First Four Source Physics Experiments (SPE) Explosions

Science.gov (United States)

Yang, X.

2015-12-01

We use mainly vertical-component geophone data within 2 km from the epicenter to invert for time-dependent moment tensors of the first four SPE explosions: SPE-1, SPE-2, SPE-3 and SPE-4Prime. We employ a one-dimensional (1D) velocity model developed from P- and Rg-wave travel times for Green's function calculations. The attenuation structure of the model is developed from P- and Rg-wave amplitudes. We select data for the inversion based on the criterion that they show consistent travel times and amplitude behavior as those predicted by the 1D model. Due to limited azimuthal coverage of the sources and the mostly vertical-component-only nature of the dataset, only long-period, diagonal components of the moment tensors are well constrained. Nevertheless, the moment tensors, particularly their isotropic components, provide reasonable estimates of the long-period source amplitudes as well as estimates of corner frequencies, albeit with larger uncertainties. The estimated corner frequencies, however, are consistent with estimates from ratios of seismogram spectra from different explosions. These long-period source amplitudes and corner frequencies cannot be fit by classical P-wave explosion source models. The results motivate the development of new P-wave source models suitable for these chemical explosions. To that end, we fit inverted moment-tensor spectra by modifying the classical explosion model using regressions of estimated source parameters. Although the number of data points used in the regression is small, the approach suggests a way for the new-model development when more data are collected.

A new Weyl-like tensor of geometric origin

Science.gov (United States)

Vishwakarma, Ram Gopal

2018-04-01

A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.

Verification of the helioseismology travel-time measurement technique and the inversion procedure for sound speed using artificial data

Energy Technology Data Exchange (ETDEWEB)

Parchevsky, K. V.; Zhao, J.; Hartlep, T.; Kosovichev, A. G., E-mail: akosovichev@solar.stanford.edu [Stanford University, HEPL, Stanford, CA 94305 (United States)

2014-04-10

We performed three-dimensional numerical simulations of the solar surface acoustic wave field for the quiet Sun and for three models with different localized sound-speed perturbations in the interior with deep, shallow, and two-layer structures. We used the simulated data generated by two solar acoustics codes that employ the same standard solar model as a background model, but utilize different integration techniques and different models of stochastic wave excitation. Acoustic travel times were measured using a time-distance helioseismology technique, and compared with predictions from ray theory frequently used for helioseismic travel-time inversions. It is found that the measured travel-time shifts agree well with the helioseismic theory for sound-speed perturbations, and for the measurement procedure with and without phase-speed filtering of the oscillation signals. This testing verifies the whole measuring-filtering-inversion procedure for static sound-speed anomalies with small amplitude inside the Sun outside regions of strong magnetic field. It is shown that the phase-speed filtering, frequently used to extract specific wave packets and improve the signal-to-noise ratio, does not introduce significant systematic errors. Results of the sound-speed inversion procedure show good agreement with the perturbation models in all cases. Due to its smoothing nature, the inversion procedure may overestimate sound-speed variations in regions with sharp gradients of the sound-speed profile.

Verification of the helioseismology travel-time measurement technique and the inversion procedure for sound speed using artificial data

International Nuclear Information System (INIS)

Parchevsky, K. V.; Zhao, J.; Hartlep, T.; Kosovichev, A. G.

2014-01-01

We performed three-dimensional numerical simulations of the solar surface acoustic wave field for the quiet Sun and for three models with different localized sound-speed perturbations in the interior with deep, shallow, and two-layer structures. We used the simulated data generated by two solar acoustics codes that employ the same standard solar model as a background model, but utilize different integration techniques and different models of stochastic wave excitation. Acoustic travel times were measured using a time-distance helioseismology technique, and compared with predictions from ray theory frequently used for helioseismic travel-time inversions. It is found that the measured travel-time shifts agree well with the helioseismic theory for sound-speed perturbations, and for the measurement procedure with and without phase-speed filtering of the oscillation signals. This testing verifies the whole measuring-filtering-inversion procedure for static sound-speed anomalies with small amplitude inside the Sun outside regions of strong magnetic field. It is shown that the phase-speed filtering, frequently used to extract specific wave packets and improve the signal-to-noise ratio, does not introduce significant systematic errors. Results of the sound-speed inversion procedure show good agreement with the perturbation models in all cases. Due to its smoothing nature, the inversion procedure may overestimate sound-speed variations in regions with sharp gradients of the sound-speed profile.

Tensor calculus for physics a concise guide

CERN Document Server

Neuenschwander, Dwight E

2015-01-01

Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...

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...

An efficient method for tensor voting using steerable filters

NARCIS (Netherlands)

Franken, E.M.; Almsick, van M.A.; Rongen, P.M.J.; Florack, L.M.J.; Haar Romenij, ter B.M.; Leonardis, A.; Bischof, H; Pinz, A.

2006-01-01

In many image analysis applications there is a need to extract curves in noisy images. To achieve a more robust extraction, one can exploit correlations of oriented features over a spatial context in the image. Tensor voting is an existing technique to extract features in this way. In this paper, we

Tensor norms and operator ideals

CERN Document Server

Defant, A; Floret, K

1992-01-01

The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer

A 2D forward and inverse code for streaming potential problems

Science.gov (United States)

Soueid Ahmed, A.; Jardani, A.; Revil, A.

2013-12-01

The self-potential method corresponds to the passive measurement of the electrical field in response to the occurrence of natural sources of current in the ground. One of these sources corresponds to the streaming current associated with the flow of the groundwater. We can therefore apply the self- potential method to recover non-intrusively some information regarding the groundwater flow. We first solve the forward problem starting with the solution of the groundwater flow problem, then computing the source current density, and finally solving a Poisson equation for the electrical potential. We use the finite-element method to solve the relevant partial differential equations. In order to reduce the number of (petrophysical) model parameters required to solve the forward problem, we introduced an effective charge density tensor of the pore water, which can be determined directly from the permeability tensor for neutral pore waters. The second aspect of our work concerns the inversion of the self-potential data using Tikhonov regularization with smoothness and weighting depth constraints. This approach accounts for the distribution of the electrical resistivity, which can be independently and approximately determined from electrical resistivity tomography. A numerical code, SP2DINV, has been implemented in Matlab to perform both the forward and inverse modeling. Three synthetic case studies are discussed.

Shape anisotropy: tensor distance to anisotropy measure

Science.gov (United States)

Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S.

2011-03-01

Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.

Stereoscopic Visualization of Diffusion Tensor Imaging Data: A Comparative Survey of Visualization Techniques

International Nuclear Information System (INIS)

Raslan, O.; Debnam, J.M.; Ketonen, L.; Kumar, A.J.; Schellingerhout, D.; Wang, J.

2013-01-01

Diffusion tensor imaging (DTI) data has traditionally been displayed as a gray scale functional anisotropy map (GSFM) or color coded orientation map (CCOM). These methods use black and white or color with intensity values to map the complex multidimensional DTI data to a two-dimensional image. Alternative visualization techniques, such as V m ax maps utilize enhanced graphical representation of the principal eigenvector by means of a headless arrow on regular non stereoscopic (VM) or stereoscopic display (VMS). A survey of clinical utility of patients with intracranial neoplasms was carried out by 8 neuro radiologists using traditional and nontraditional methods of DTI display. Pairwise comparison studies of 5 intracranial neoplasms were performed with a structured questionnaire comparing GSFM, CCOM, VM, and VMS. Six of 8 neuro radiologists favored V m ax maps over traditional methods of display (GSFM and CCOM). When comparing the stereoscopic (VMS) and the non-stereoscopic (VM) modes, 4 favored VMS, 2 favored VM, and 2 had no preference. In conclusion, processing and visualizing DTI data stereoscopically is technically feasible. An initial survey of users indicated that V m ax based display methodology with or without stereoscopic visualization seems to be preferred over traditional methods to display DTI data.

Tensors and their applications

CERN Document Server

Islam, Nazrul

2006-01-01

About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces

Tensor Completion Algorithms in Big Data Analytics

OpenAIRE

Song, Qingquan; Ge, Hancheng; Caverlee, James; Hu, Xia

2017-01-01

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data an...

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.

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

Directory of Open Access Journals (Sweden)

Gernot Reishofer

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

Reciprocal mass tensor : a general form

International Nuclear Information System (INIS)

Roy, C.L.

1978-01-01

Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)

A new deteriorated energy-momentum tensor

International Nuclear Information System (INIS)

Duff, M.J.

1982-01-01

The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)

Antisymmetric tensor generalizations of affine vector fields.

Science.gov (United States)

Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro

2016-02-01

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.

(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

The Riemann-Lovelock Curvature Tensor

OpenAIRE

Kastor, David

2012-01-01

In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D

The Physical Interpretation of the Lanczos Tensor

OpenAIRE

Roberts, Mark D.

1999-01-01

The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...

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

Science.gov (United States)

Cyganek, Boguslaw; Smolka, Bogdan

2015-02-01

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

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

Science.gov (United States)

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

2012-01-01

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

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

Science.gov (United States)

Alam, Meheboob; Saha, Saikat

2014-11-01

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

Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows

NARCIS (Netherlands)

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

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

Tensor decompositions for the analysis of atomic resolution electron energy loss spectra

Energy Technology Data Exchange (ETDEWEB)

Spiegelberg, Jakob; Rusz, Ján [Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala (Sweden); Pelckmans, Kristiaan [Department of Information Technology, Uppsala University, Box 337, S-751 05 Uppsala (Sweden)

2017-04-15

A selection of tensor decomposition techniques is presented for the detection of weak signals in electron energy loss spectroscopy (EELS) data. The focus of the analysis lies on the correct representation of the simulated spatial structure. An analysis scheme for EEL spectra combining two-dimensional and n-way decomposition methods is proposed. In particular, the performance of robust principal component analysis (ROBPCA), Tucker Decompositions using orthogonality constraints (Multilinear Singular Value Decomposition (MLSVD)) and Tucker decomposition without imposed constraints, canonical polyadic decomposition (CPD) and block term decompositions (BTD) on synthetic as well as experimental data is examined. - Highlights: • A scheme for compression and analysis of EELS or EDX data is proposed. • Several tensor decomposition techniques are presented for BSS on hyperspectral data. • Robust PCA and MLSVD are discussed for denoising of raw data.

A Tensor Statistical Model for Quantifying Dynamic Functional Connectivity.

Science.gov (United States)

Zhu, Yingying; Zhu, Xiaofeng; Kim, Minjeong; Yan, Jin; Wu, Guorong

2017-06-01

Functional connectivity (FC) has been widely investigated in many imaging-based neuroscience and clinical studies. Since functional Magnetic Resonance Image (MRI) signal is just an indirect reflection of brain activity, it is difficult to accurately quantify the FC strength only based on signal correlation. To address this limitation, we propose a learning-based tensor model to derive high sensitivity and specificity connectome biomarkers at the individual level from resting-state fMRI images. First, we propose a learning-based approach to estimate the intrinsic functional connectivity. In addition to the low level region-to-region signal correlation, latent module-to-module connection is also estimated and used to provide high level heuristics for measuring connectivity strength. Furthermore, sparsity constraint is employed to automatically remove the spurious connections, thus alleviating the issue of searching for optimal threshold. Second, we integrate our learning-based approach with the sliding-window technique to further reveal the dynamics of functional connectivity. Specifically, we stack the functional connectivity matrix within each sliding window and form a 3D tensor where the third dimension denotes for time. Then we obtain dynamic functional connectivity (dFC) for each individual subject by simultaneously estimating the within-sliding-window functional connectivity and characterizing the across-sliding-window temporal dynamics. Third, in order to enhance the robustness of the connectome patterns extracted from dFC, we extend the individual-based 3D tensors to a population-based 4D tensor (with the fourth dimension stands for the training subjects) and learn the statistics of connectome patterns via 4D tensor analysis. Since our 4D tensor model jointly (1) optimizes dFC for each training subject and (2) captures the principle connectome patterns, our statistical model gains more statistical power of representing new subject than current state

Tensor voting for robust color edge detection

OpenAIRE

Moreno, Rodrigo; García, Miguel Ángel; Puig, Domenec

2014-01-01

The final publication is available at Springer via http://dx.doi.org/10.1007/978-94-007-7584-8_9 This chapter proposes two robust color edge detection methods based on tensor voting. The first method is a direct adaptation of the classical tensor voting to color images where tensors are initialized with either the gradient or the local color structure tensor. The second method is based on an extension of tensor voting in which the encoding and voting processes are specifically tailored to ...

The modified inverse hockey stick technique for adjuvant irradiation after mastectomy

International Nuclear Information System (INIS)

Kukolowicz, P.; Selerski, B.; Kuszewski, T.; Wieczorek, A.

2004-01-01

To present the technique of irradiation of post-mastectomy patients used in the Holycross Cancer Centre in Kielce.The paper presents a detailed description of the technique which is referred to as the 'modified inverse hockey stick technique (MIHS)'. The dosimetric characteristic of dose distribution for the MIHS technique is presented basing on dose distributions calculated for 40 patients. The measurements used to evaluate dose distribution included standard deviation of the dose in the Planning Target Volume (PTV) and the percentage of the PTV volume receiving a dose larger than 110% and smaller than 90%; the lung volume received at least 20 Gy (LV20) and the heart volume received at least 30 Gy (HV30). The distribution of the electron beam energy is also presented. The standard deviation of the dose in the PTV was approx. 10% in a majority of patients. About 12% of the PTV volume received a dose more than 10% smaller than intended and about 10% of the PTV volume received a dose more than 10% greater than intended. For patients irradiated on the left side of the chest wall the LV20 was always lesser than 25% and for patients irradiated on the right side of the chest wall - always less than 35%, except for one patient, in whom it reached 37%. The HV30 was always below 8%. The MIHS technique is a safe and reliable modality. The main advantages of the technique include very convenient and easily repeated positioning of the patient and small doses applied to the organs at risk. The individually calculated bolus plays an important role in diminishing the dose to the lung and heart. The disadvantages of the technique include poor dose homogeneity within the PTV and long matching lines of the electron and photon beams. (author)

Fast Bayesian optimal experimental design for seismic source inversion

KAUST Repository

Long, Quan

2015-07-01

We develop a fast method for optimally designing experiments in the context of statistical seismic source inversion. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by elastodynamic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the "true" parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem. © 2015 Elsevier B.V.

Fast Bayesian Optimal Experimental Design for Seismic Source Inversion

KAUST Repository

Long, Quan

2016-01-06

We develop a fast method for optimally designing experiments [1] in the context of statistical seismic source inversion [2]. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by the elastic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the true parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.

Fast Bayesian Optimal Experimental Design for Seismic Source Inversion

KAUST Repository

Long, Quan; Motamed, Mohammad; Tempone, Raul

2016-01-01

We develop a fast method for optimally designing experiments [1] in the context of statistical seismic source inversion [2]. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by the elastic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the true parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.

Should I use TensorFlow

OpenAIRE

Schrimpf, Martin

2016-01-01

Google's Machine Learning framework TensorFlow was open-sourced in November 2015 [1] and has since built a growing community around it. TensorFlow is supposed to be flexible for research purposes while also allowing its models to be deployed productively. This work is aimed towards people with experience in Machine Learning considering whether they should use TensorFlow in their environment. Several aspects of the framework important for such a decision are examined, such as the heterogenity,...

Dictionary-Based Tensor Canonical Polyadic Decomposition

Science.gov (United States)

Cohen, Jeremy Emile; Gillis, Nicolas

2018-04-01

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.

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...

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

Efficient computation of the elastography inverse problem by combining variational mesh adaption and a clustering technique

International Nuclear Information System (INIS)

Arnold, Alexander; Bruhns, Otto T; Reichling, Stefan; Mosler, Joern

2010-01-01

This paper is concerned with an efficient implementation suitable for the elastography inverse problem. More precisely, the novel algorithm allows us to compute the unknown stiffness distribution in soft tissue by means of the measured displacement field by considerably reducing the numerical cost compared to previous approaches. This is realized by combining and further elaborating variational mesh adaption with a clustering technique similar to those known from digital image compression. Within the variational mesh adaption, the underlying finite element discretization is only locally refined if this leads to a considerable improvement of the numerical solution. Additionally, the numerical complexity is reduced by the aforementioned clustering technique, in which the parameters describing the stiffness of the respective soft tissue are sorted according to a predefined number of intervals. By doing so, the number of unknowns associated with the elastography inverse problem can be chosen explicitly. A positive side effect of this method is the reduction of artificial noise in the data (smoothing of the solution). The performance and the rate of convergence of the resulting numerical formulation are critically analyzed by numerical examples.

Detecting the Community Structure and Activity Patterns of Temporal Networks: A Non-Negative Tensor Factorization Approach

Science.gov (United States)

Gauvin, Laetitia; Panisson, André; Cattuto, Ciro

2014-01-01

The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule. PMID:24497935

Tensor veli palatini electromyography for monitoring Eustachian tube rehabilitation in otitis media.

Science.gov (United States)

Picciotti, P M; Della Marca, G; D'Alatri, L; Lucidi, D; Rigante, M; Scarano, E

2017-05-01

The pathogenesis of otitis media is related to Eustachian tube dysfunction. The tensor veli palatini muscle actively opens the Eustachian tube and promotes middle-ear ventilation. This study describes a technique for paratubal electromyography that uses a surface, non-invasive electrode able to record tensor veli palatini muscle activity during swallowing. Twenty otitis media patients and 10 healthy patients underwent tensor veli palatini electromyography. Activity of this muscle before and after Eustachian tube rehabilitation was also assessed. In 78.5 per cent of patients, the electromyography duration phase and/or amplitude were reduced in the affected side. The muscle action potential was impaired in all patients who underwent Eustachian tube rehabilitation. This study confirmed that Eustachian tube muscle dysfunction has a role in otitis media pathogenesis and showed that muscle activity increases after Eustachian tube rehabilitation therapy.

Non-contrast MRA using an inflow-enhanced, inversion recovery SSFP technique in pediatric abdominal imaging

International Nuclear Information System (INIS)

Serai, Suraj; Towbin, Alexander J.; Podberesky, Daniel J.

2012-01-01

Abdominal contrast-enhanced MR angiography (CE-MRA) is routinely performed in children. CE-MRA is challenging in children because of patient motion, difficulty in obtaining intravenous access, and the inability of young patients to perform a breath-hold during imaging. The combination of pediatric-specific difficulties in imaging and the safety concerns regarding the risk of gadolinium-based contrast agents in patients with impaired renal function has renewed interest in the use of non-contrast (NC) MRA techniques. At our institution, we have optimized 3-D NC-MRA techniques for abdominal imaging. The purpose of this work is to demonstrate the utility of an inflow-enhanced, inversion recovery balanced steady-state free precession-based (b-SSFP) NC-MRA technique. (orig.)

Symmetric energy-momentum tensor in Maxwell, Yang-Mills, and Proca theories obtained using only Noether's theorem

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)

Resistivity Image from 2D Inversion of Magnetotelluric Data in the Northern Cascadia Subduction Zone (United States)

Science.gov (United States)

Gultom, F. B.; Niasari, S. W.; Hartantyo, E.

2018-04-01

Cascadia Subduction Zone (CSZ) lies between Pacific margin and North America plate. The purpose of this research is to identify the CSZ along Oregon, Idaho, Wyoming from conductivity (σ) contrast in the subsurface by using the magnetotelluric (MT) method. MT is an electromagnetic method that use frequency between 10-4 Hz and 104 Hz. We obtained the MT data from the EarthScope USArray in the form of EDI-File (five components of the electromagnetic field). We analyzed the MT data using phase tensor and modeled the data using 2D inversion. From the phase tensor analysis, the 3D data dominated the eastern regions. Global data misfit is 6,88, where WYI18 (close to Yellowstone) contributes misfit of 29,3. This means that the model response does not fit the data, which implies the data is not fully 2D. The 2D inversion results are found high resistivity anomalies (more than 500 ohm.m) at shallow depth beneath Oregon and Wyoming, which coresspond to high density anomalies. This high resistivity anomalies might correspond to the north American plate. Thus, it can be concluded that 2D inversion model can be used for most 3D MT data to illustrate the resistivity distribution in the Cascadia Subduction Zone.

Forward modeling. Route to electromagnetic inversion

Energy Technology Data Exchange (ETDEWEB)

Groom, R; Walker, P [PetRos EiKon Incorporated, Ontario (Canada)

1996-05-01

Inversion of electromagnetic data is a topical subject in the literature, and much time has been devoted to understanding the convergence properties of various inverse methods. The relative lack of success of electromagnetic inversion techniques is partly attributable to the difficulties in the kernel forward modeling software. These difficulties come in two broad classes: (1) Completeness and robustness, and (2) convergence, execution time and model simplicity. If such problems exist in the forward modeling kernel, it was demonstrated that inversion can fail to generate reasonable results. It was suggested that classical inversion techniques, which are based on minimizing a norm of the error between data and the simulated data, will only be successful when these difficulties in forward modeling kernels are properly dealt with. 4 refs., 5 figs.

Objective mapping of observed sub-surface mesoscale cold core eddy in the Bay of Bengal by stochastic inverse technique with tomographically simulated travel times

Digital Repository Service at National Institute of Oceanography (India)

Murty, T.V.R.; Rao, M.M.M.; Sadhuram, Y.; Sridevi, B.; Maneesha, K.; SujithKumar, S.; Prasanna, P.L.; Murthy, K.S.R.

of Bengal during south-west monsoon season and explore possibility to reconstruct the acoustic profile of the eddy by Stochastic Inverse Technique. A simulation experiment on forward and inverse problems for observed sound velocity perturbation field has...

Electromagnetic modelling, inversion and data-processing techniques for GPR: ongoing activities in Working Group 3 of COST Action TU1208

Science.gov (United States)

Pajewski, Lara; Giannopoulos, Antonis; van der Kruk, Jan

2015-04-01

This work aims at presenting the ongoing research activities carried out in Working Group 3 (WG3) 'EM methods for near-field scattering problems by buried structures; data processing techniques' of the COST (European COoperation in Science and Technology) Action TU1208 'Civil Engineering Applications of Ground Penetrating Radar' (www.GPRadar.eu). The principal goal of the COST Action TU1208 is to exchange and increase scientific-technical knowledge and experience of GPR techniques in civil engineering, simultaneously promoting throughout Europe the effective use of this safe and non-destructive technique in the monitoring of infrastructures and structures. WG3 is structured in four Projects. Project 3.1 deals with 'Electromagnetic modelling for GPR applications.' Project 3.2 is concerned with 'Inversion and imaging techniques for GPR applications.' The topic of Project 3.3 is the 'Development of intrinsic models for describing near-field antenna effects, including antenna-medium coupling, for improved radar data processing using full-wave inversion.' Project 3.4 focuses on 'Advanced GPR data-processing algorithms.' Electromagnetic modeling tools that are being developed and improved include the Finite-Difference Time-Domain (FDTD) technique and the spectral domain Cylindrical-Wave Approach (CWA). One of the well-known freeware and versatile FDTD simulators is GprMax that enables an improved realistic representation of the soil/material hosting the sought structures and of the GPR antennas. Here, input/output tools are being developed to ease the definition of scenarios and the visualisation of numerical results. The CWA expresses the field scattered by subsurface two-dimensional targets with arbitrary cross-section as a sum of cylindrical waves. In this way, the interaction is taken into account of multiple scattered fields within the medium hosting the sought targets. Recently, the method has been extended to deal with through-the-wall scenarios. One of the

The Einstein tensor characterizing some Riemann spaces

International Nuclear Information System (INIS)

Rahman, M.S.

1993-07-01

A formal definition of the Einstein tensor is given. Mention is made of how this tensor plays a role of expressing certain conditions in a precise form. The cases of reducing the Einstein tensor to a zero tensor are studied on its merit. A lucid account of results, formulated as theorems, on Einstein symmetric and Einstein recurrent spaces is then presented. (author). 5 refs

Volume illustration of muscle from diffusion tensor images.

Science.gov (United States)

Chen, Wei; Yan, Zhicheng; Zhang, Song; Crow, John Allen; Ebert, David S; McLaughlin, Ronald M; Mullins, Katie B; Cooper, Robert; Ding, Zi'ang; Liao, Jun

2009-01-01

Medical illustration has demonstrated its effectiveness to depict salient anatomical features while hiding the irrelevant details. Current solutions are ineffective for visualizing fibrous structures such as muscle, because typical datasets (CT or MRI) do not contain directional details. In this paper, we introduce a new muscle illustration approach that leverages diffusion tensor imaging (DTI) data and example-based texture synthesis techniques. Beginning with a volumetric diffusion tensor image, we reformulate it into a scalar field and an auxiliary guidance vector field to represent the structure and orientation of a muscle bundle. A muscle mask derived from the input diffusion tensor image is used to classify the muscle structure. The guidance vector field is further refined to remove noise and clarify structure. To simulate the internal appearance of the muscle, we propose a new two-dimensional example based solid texture synthesis algorithm that builds a solid texture constrained by the guidance vector field. Illustrating the constructed scalar field and solid texture efficiently highlights the global appearance of the muscle as well as the local shape and structure of the muscle fibers in an illustrative fashion. We have applied the proposed approach to five example datasets (four pig hearts and a pig leg), demonstrating plausible illustration and expressiveness.

Combining boundary-based methods with tensor-based morphometry in the measurement of longitudinal brain change.

Science.gov (United States)

Fletcher, Evan; Knaack, Alexander; Singh, Baljeet; Lloyd, Evan; Wu, Evan; Carmichael, Owen; DeCarli, Charles

2013-02-01

Tensor-based morphometry is a powerful tool for automatically computing longitudinal change in brain structure. Because of bias in images and in the algorithm itself, however, a penalty term and inverse consistency are needed to control the over-reporting of nonbiological change. These may force a tradeoff between the intrinsic sensitivity and specificity, potentially leading to an under-reporting of authentic biological change with time. We propose a new method incorporating prior information about tissue boundaries (where biological change is likely to exist) that aims to keep the robustness and specificity contributed by the penalty term and inverse consistency while maintaining localization and sensitivity. Results indicate that this method has improved sensitivity without increased noise. Thus it will have enhanced power to detect differences within normal aging and along the spectrum of cognitive impairment.

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

Transposes, L-Eigenvalues and Invariants of Third Order Tensors

OpenAIRE

Qi, Liqun

2017-01-01

Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t...

An introduction to visualization of diffusion tensor imaging and its applications

NARCIS (Netherlands)

Vilanova, A.; Zhang, S.; Kindlmann, G.; Laidlaw, D.H.; Weickert, J.; Hagen, H.

2005-01-01

Summary. Water diffusion is anisotropic in organized tissues such as white matter and muscle. Diffusion tensor imaging (DTI), a non-invasive MR technique, measures water self-diffusion rates and thus gives an indication of the underlying tissue microstructure. The diffusion rate is often expressed

Graded tensor calculus

International Nuclear Information System (INIS)

Scheunert, M.

1982-10-01

We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)

A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge

International Nuclear Information System (INIS)

Davis, Paul

2006-01-01

In this paper, we study the recently discovered family of higher dimensional Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse metric is additively separable after multiplication by a simple function. This allows us to separate the Hamilton-Jacobi equation, showing that geodesic motion is integrable on this background. The separation of the Hamilton-Jacobi equation is intimately linked to the existence of an irreducible Killing tensor, which provides an extra constant of motion. We also demonstrate that the Klein-Gordon equation for this background is separable

Real-time MR diffusion tensor and Q-ball imaging using Kalman filtering

International Nuclear Information System (INIS)

Poupon, C.; Roche, A.; Dubois, J.; Mangin, J.F.; Poupon, F.

2008-01-01

Diffusion magnetic resonance imaging (dMRI) has become an established research tool for the investigation of tissue structure and orientation. In this paper, we present a method for real-time processing of diffusion tensor and Q-ball imaging. The basic idea is to use Kalman filtering framework to fit either the linear tensor or Q-ball model. Because the Kalman filter is designed to be an incremental algorithm, it naturally enables updating the model estimate after the acquisition of any new diffusion-weighted volume. Processing diffusion models and maps during ongoing scans provides a new useful tool for clinicians, especially when it is not possible to predict how long a subject may remain still in the magnet. First, we introduce the general linear models corresponding to the two diffusion tensor and analytical Q-ball models of interest. Then, we present the Kalman filtering framework and we focus on the optimization of the diffusion orientation sets in order to speed up the convergence of the online processing. Last, we give some results on a healthy volunteer for the online tensor and the Q-ball model, and we make some comparisons with the conventional offline techniques used in the literature. We could achieve full real-time for diffusion tensor imaging and deferred time for Q-ball imaging, using a single workstation. (authors)

(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

Robust estimation of adaptive tensors of curvature by tensor voting.

Science.gov (United States)

Tong, Wai-Shun; Tang, Chi-Keung

2005-03-01

Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.

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

Glyph-Based Comparative Visualization for Diffusion Tensor Fields.

Science.gov (United States)

Zhang, Changgong; Schultz, Thomas; Lawonn, Kai; Eisemann, Elmar; Vilanova, Anna

2016-01-01

Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.

Tensoral for post-processing users and simulation authors

Science.gov (United States)

Dresselhaus, Eliot

1993-01-01

The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.

Computer-Aided Numerical Inversion of Laplace Transform

Directory of Open Access Journals (Sweden)

Umesh Kumar

2000-01-01

Full Text Available This paper explores the technique for the computer aided numerical inversion of Laplace transform. The inversion technique is based on the properties of a family of three parameter exponential probability density functions. The only limitation in the technique is the word length of the computer being used. The Laplace transform has been used extensively in the frequency domain solution of linear, lumped time invariant networks but its application to the time domain has been limited, mainly because of the difficulty in finding the necessary poles and residues. The numerical inversion technique mentioned above does away with the poles and residues but uses precomputed numbers to find the time response. This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

Science.gov (United States)

Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.

2018-05-01

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

Applications of tensor functions in creep mechanics

International Nuclear Information System (INIS)

Betten, J.

1991-01-01

Within this contribution a short survey is given of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The mechanical behaviour of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behaviour. This paper presents certain principles, methods, and recent successfull applications of tensor functions in solid mechanics. The rules for specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are also discussed. Furthermore, it is very important that the scalar coefficients in constitutive and evolutional equations are determined as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use are discussed. (orig./RHM)

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.)

Sodium ion conducting polymer electrolyte membrane prepared by phase inversion technique

Science.gov (United States)

Harshlata, Mishra, Kuldeep; Rai, D. K.

2018-04-01

A mechanically stable porous polymer membrane of Poly(vinylidene fluoride-hexafluoropropylene) has been prepared by phase inversion technique using steam as a non-solvent. The membrane possesses semicrystalline network with enhanced amorphicity as observed by X-ray diffraction. The membrane has been soaked in an electrolyte solution of 0.5M NaPF6 in Ethylene Carbonate/Propylene Carbonate (1:1) to obtain the gel polymer electrolyte. The porosity and electrolyte uptake of the membrane have been found to be 67% and 220% respectively. The room temperature ionic conductivity of the membrane has been obtained as ˜ 0.3 mS cm-1. The conductivity follows Arrhenius behavior with temperature and gives activation energy as 0.8 eV. The membrane has been found to possess significantly large electrochemical stability window of 5.0 V.

The role of diffusion tensor imaging in brain tumor surgery : A review of the literature

NARCIS (Netherlands)

Potgieser, Adriaan R. E.; Wagemakers, Michiel; van Hulzen, Arjen L. J.; de Jong, Bauke M.; Hoving, Eelco W.; Groen, Rob J. M.

Diffusion tensor imaging (DTI) is a recent technique that utilizes diffusion of water molecules to make assumptions about white matter tract architecture of the brain. Early on, neurosurgeons recognized its potential value in neurosurgical planning, as it is the only technique that offers the

On Lovelock analogs of the Riemann tensor

Science.gov (United States)

Camanho, Xián O.; Dadhich, Naresh

2016-03-01

It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.

The simplicial Ricci tensor

International Nuclear Information System (INIS)

Alsing, Paul M; McDonald, Jonathan R; Miller, Warner A

2011-01-01

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area-an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

The simplicial Ricci tensor

Science.gov (United States)

Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.

2011-08-01

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

Beyond Low Rank: A Data-Adaptive Tensor Completion Method

OpenAIRE

Zhang, Lei; Wei, Wei; Shi, Qinfeng; Shen, Chunhua; Hengel, Anton van den; Zhang, Yanning

2017-01-01

Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor data which only approximately fulfils the low-rank requirement. To address these two issues, we develop a data-adaptive tensor completion model which explicitly represents both the low-rank and non-low-rank structures in a latent tensor. Representing the no...

Algorithm for polarimetry data inversion, consistent with other measuring techniques in tokamak plasma

International Nuclear Information System (INIS)

Kravtsov, Y.A.; Kravtsov, Y.A.; Chrzanowski, J.; Mazon, D.

2011-01-01

New procedure for plasma polarimetry data inversion is suggested, which fits two parameter knowledge-based plasma model to the measured parameters (azimuthal and ellipticity angles) of the polarization ellipse. The knowledge-based model is supposed to use the magnetic field and electron density profiles, obtained from magnetic measurements and LIDAR data on the Thomson scattering. In distinction to traditional polarimetry, polarization evolution along the ray is determined on the basis of angular variables technique (AVT). The paper contains a few examples of numerical solutions of these equations, which are applicable in conditions, when Faraday and Cotton-Mouton effects are simultaneously strong. (authors)

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.

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.

Application of a numerical Laplace transform inversion technique to a problem in reactor dynamics

International Nuclear Information System (INIS)

Ganapol, B.D.; Sumini, M.

1990-01-01

A newly developed numerical technique for the Laplace transform inversion is applied to a classical time-dependent problem of reactor physics. The dynamic behaviour of a multiplying system has been analyzed through a continuous slowing down model, taking into account a finite slowing down time, the presence of several groups of neutron precursors and simplifying the spatial analysis using the space asymptotic approximation. The results presented, show complete agreement with analytical ones previously obtained and allow a deeper understanding of the model features. (author)

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)

Energy-momentum tensor in scalar QED

International Nuclear Information System (INIS)

Joglekar, S.D.; Misra, A.

1988-01-01

We consider the renormalization of the energy-momentum tensor in scalar quantum electrodynamics. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be obtained from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/). .AE

Calculus of tensors and differential forms

CERN Document Server

Sinha, Rajnikant

2014-01-01

Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.

Trace anomaly of the stress-energy tensor for massless vector particles propagating in a general background metric

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

Linearized inversion of two components seismic data; Inversion linearisee de donnees sismiques a deux composantes

Energy Technology Data Exchange (ETDEWEB)

Lebrun, D.

1997-05-22

The aim of the dissertation is the linearized inversion of multicomponent seismic data for 3D elastic horizontally stratified media, using Born approximation. A Jacobian matrix is constructed; it will be used to model seismic data from elastic parameters. The inversion technique, relying on single value decomposition (SVD) of the Jacobian matrix, is described. Next, the resolution of inverted elastic parameters is quantitatively studies. A first use of the technique is shown in the frame of an evaluation of a sea bottom acquisition (synthetic data). Finally, a real data set acquired with conventional marine technique is inverted. (author) 70 refs.

Tensor Galileons and gravity

Energy Technology Data Exchange (ETDEWEB)

Chatzistavrakidis, Athanasios [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Khoo, Fech Scen [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Schupp, Peter [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany)

2017-03-13

The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

Algebraic and computational aspects of real tensor ranks

CERN Document Server

Sakata, Toshio; Miyazaki, Mitsuhiro

2016-01-01

This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...

Decomposition of a symmetric second-order tensor

Science.gov (United States)

Heras, José A.

2018-05-01

In the three-dimensional space there are different definitions for the dot and cross products of a vector with a second-order tensor. In this paper we show how these products can uniquely be defined for the case of symmetric tensors. We then decompose a symmetric second-order tensor into its ‘dot’ part, which involves the dot product, and the ‘cross’ part, which involves the cross product. For some physical applications, this decomposition can be interpreted as one in which the dot part identifies with the ‘parallel’ part of the tensor and the cross part identifies with the ‘perpendicular’ part. This decomposition of a symmetric second-order tensor may be suitable for undergraduate courses of vector calculus, mechanics and electrodynamics.

1+1+2 gravitational perturbations on LRS class II spacetimes: decoupling gravito-electromagnetic tensor harmonic amplitudes

International Nuclear Information System (INIS)

Burston, R B

2008-01-01

This is the first in a series of papers which considers gauge-invariant and covariant gravitational perturbations on arbitrary vacuum locally rotationally symmetric (LRS) class II spacetimes. Ultimately, we derive four decoupled equations governing four specific combinations of the gravito-electromagnetic (GEM) 2-tensor harmonic amplitudes. We use the gauge-invariant and covariant 1+1+2 formalism which Clarkson and Barrett (2003 Class. Quantum Grav. 20 3855) developed for analysis of vacuum Schwarzschild perturbations. In particular we focus on the first-order 1+1+2 GEM system and use linear algebra techniques suitable for exploiting its structure. Consequently, we express the GEM system new 1+1+2 complex form by choosing new complex GEM tensors, which is conducive to decoupling. We then show how to derive a gauge-invariant and covariant decoupled equation governing a newly defined complex GEM 2-tensor. Finally, the GEM 2-tensor is expanded in terms of arbitrary tensor harmonics and linear algebra is used once again to decouple the system further into four real decoupled equations

Efficient Low Rank Tensor Ring Completion

OpenAIRE

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2017-01-01

Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. In this paper, we propose a spectral initialization for the tensor ring completion algorithm and ana...

Evidence of tensor correlations in the nuclear many-body system using a modern NN potential

International Nuclear Information System (INIS)

Fiase, J.O.; Nkoma, J.S.; Sharmaand, L.K.; Hosaka, A.

2003-01-01

In this paper we show evidence of the importance of tensor correlations in the nuclear many-body system by calculating the effective two-body nuclear matrix elements in the frame work of the Lowest-Order Constrained Variational (LOCV) technique with two-body correlation functions using the Reid93 potential. We have achieved this by switching on and off the strength of the tensor correlations, α k . We have found that in order to obtain reasonable agreement with earlier calculations based on the G-matrix theory, we must turn on the strength of the tensor correlations especially in the triplet even (TE) and tensor even (TNE) channels to take the value of approximately, 0.05. As an application, we have estimated the value of the Landau - Migdal parameter, g' NN which we found to be g' NN = 0.65. This compares favorably with the G-matrix calculated value of g' NN = 0.54. (author)

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.

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.

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

Conformal field theories and tensor categories. Proceedings

International Nuclear Information System (INIS)

Bai, Chengming; Fuchs, Juergen; Huang, Yi-Zhi; Kong, Liang; Runkel, Ingo; Schweigert, Christoph

2014-01-01

First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

Loop optimization for tensor network renormalization

Science.gov (United States)

Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

Comparison of three IMRT inverse planning techniques that allow for partial esophagus sparing in patients receiving thoracic radiation therapy for lung cancer

International Nuclear Information System (INIS)

Xiao Ying; Werner-Wasik, Maria; Michalski, D.; Houser, C.; Bednarz, G.; Curran, W.; Galvin, James

2004-01-01

The purpose of this study is to compare 3 intensity-modulated radiation therapy (IMRT) inverse treatment planning techniques as applied to locally-advanced lung cancer. This study evaluates whether sufficient radiotherapy (RT) dose is given for durable control of tumors while sparing a portion of the esophagus, and whether large number of segments and monitor units are required. We selected 5 cases of locally-advanced lung cancer with large central tumor, abutting the esophagus. To ensure that no more than half of the esophagus circumference at any level received the specified dose limit, it was divided into disk-like sections and dose limits were imposed on each. Two sets of dose objectives were specified for tumor and other critical structures for standard dose RT and for dose escalation RT. Plans were generated using an aperture-based inverse planning (ABIP) technique with the Cimmino algorithm for optimization. Beamlet-based inverse treatment planning was carried out with a commercial simulated annealing package (CORVUS) and with an in-house system that used the Cimmino projection algorithm (CIMM). For 3 of the 5 cases, results met all of the constraints from the 3 techniques for the 2 sets of dose objectives. The CORVUS system without delivery efficiency consideration required the most segments and monitor units. The CIMM system reduced the number while the ABIP techniques showed a further reduction, although for one of the cases, a solution was not readily obtained using the ABIP technique for dose escalation objectives

The Twist Tensor Nuclear Norm for Video Completion.

Science.gov (United States)

Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui

2017-12-01

In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.

Simultaneous multislice echo planar imaging with blipped controlled aliasing in parallel imaging results in higher acceleration: a promising technique for accelerated diffusion tensor imaging of skeletal muscle

OpenAIRE

Filli, Lukas; Piccirelli, Marco; Kenkel, David; Guggenberger, Roman; Andreisek, Gustav; Beck, Thomas; Runge, Val M; Boss, Andreas

2015-01-01

PURPOSE The aim of this study was to investigate the feasibility of accelerated diffusion tensor imaging (DTI) of skeletal muscle using echo planar imaging (EPI) applying simultaneous multislice excitation with a blipped controlled aliasing in parallel imaging results in higher acceleration unaliasing technique. MATERIALS AND METHODS After federal ethics board approval, the lower leg muscles of 8 healthy volunteers (mean [SD] age, 29.4 [2.9] years) were examined in a clinical 3-T magnetic ...

Nanostructured Double Hydrophobic Poly(Styrene-b-Methyl Methacrylate) Block Copolymer Membrane Manufactured Via Phase Inversion Technique

KAUST Repository

Karunakaran, Madhavan; Shevate, Rahul; Peinemann, Klaus-Viktor

2016-01-01

In this paper, we demonstrate the formation of nanostructured double hydrophobic poly(styrene-b-methyl methacrylate) (PS-b-PMMA) block copolymer membranes via state-of-the-art phase inversion technique. The nanostructured membrane morphologies are tuned by different solvent and block copolymer compositions. The membrane morphology has been investigated using FESEM, AFM and TEM. Morphological investigation shows the formation of both cylindrical and lamellar structures on the top surface of the block copolymer membranes. The PS-b-PMMA having an equal block length (PS160K-b-PMMA160K) exhibits both cylindrical and lamellar structures on the top layer of the asymmetric membrane. All membranes fabricated from PS160K-b-PMMA160K shows an incomplete pore formation in both cylindrical and lamellar morphologies during the phase inversion process. However, PS-b-PMMA (PS135K-b-PMMA19.5K) block copolymer having a short PMMA block allowed us to produce open pore structures with ordered hexagonal cylindrical pores during the phase inversion process. The resulting PS-b-PMMA nanostructured block copolymer membranes have pure water flux from 105-820 l/m2.h.bar and 95% retention of PEG50K

Nanostructured Double Hydrophobic Poly(Styrene-b-Methyl Methacrylate) Block Copolymer Membrane Manufactured Via Phase Inversion Technique

KAUST Repository

Karunakaran, Madhavan

2016-03-11

In this paper, we demonstrate the formation of nanostructured double hydrophobic poly(styrene-b-methyl methacrylate) (PS-b-PMMA) block copolymer membranes via state-of-the-art phase inversion technique. The nanostructured membrane morphologies are tuned by different solvent and block copolymer compositions. The membrane morphology has been investigated using FESEM, AFM and TEM. Morphological investigation shows the formation of both cylindrical and lamellar structures on the top surface of the block copolymer membranes. The PS-b-PMMA having an equal block length (PS160K-b-PMMA160K) exhibits both cylindrical and lamellar structures on the top layer of the asymmetric membrane. All membranes fabricated from PS160K-b-PMMA160K shows an incomplete pore formation in both cylindrical and lamellar morphologies during the phase inversion process. However, PS-b-PMMA (PS135K-b-PMMA19.5K) block copolymer having a short PMMA block allowed us to produce open pore structures with ordered hexagonal cylindrical pores during the phase inversion process. The resulting PS-b-PMMA nanostructured block copolymer membranes have pure water flux from 105-820 l/m2.h.bar and 95% retention of PEG50K

Off-shell N = 2 tensor supermultiplets

International Nuclear Information System (INIS)

Wit, Bernard de; Saueressig, Frank

2006-01-01

A multiplet calculus is presented for an arbitrary number n of N = 2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkaehler or quaternion-Kaehler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kaehler manifolds with two commuting isometries is given

Symmetric energy-momentum tensor in Maxwell, Yang-Mills, and Proca theories obtained using only Noether's theorem

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)

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

OpenAIRE

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

2008-01-01

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

Tensors, relativity, and cosmology

CERN Document Server

Dalarsson, Mirjana

2015-01-01

Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...

Tucker tensor analysis of Matern functions in spatial statistics

KAUST Repository

Litvinenko, Alexander

2018-04-20

Low-rank Tucker tensor methods in spatial statistics 1. Motivation: improve statistical models 2. Motivation: disadvantages of matrices 3. Tools: Tucker tensor format 4. Tensor approximation of Matern covariance function via FFT 5. Typical statistical operations in Tucker tensor format 6. Numerical experiments

Three-dimensional inversion of multisource array electromagnetic data

Science.gov (United States)

Tartaras, Efthimios

Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM

A new recoil distance technique using low energy coulomb excitation in inverse kinematics

Energy Technology Data Exchange (ETDEWEB)

Rother, W., E-mail: wolfram.rother@googlemail.com [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, D-50937 Koeln (Germany); Dewald, A.; Pascovici, G.; Fransen, C.; Friessner, G.; Hackstein, M. [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, D-50937 Koeln (Germany); Ilie, G. [Wright Nuclear Structure Laboratory, Yale University, New Haven, CT 06520 (United States); National Institute of Physics and Nuclear Engineering, P.O. Box MG-6, Bucharest-Magurele (Romania); Iwasaki, H. [National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); Jolie, J. [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, D-50937 Koeln (Germany); Melon, B. [Dipartimento di Fisica, Universita di Firenze and INFN Sezione di Firenze, Sesto Fiorentino (Firenze) I-50019 (Italy); Petkov, P. [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, D-50937 Koeln (Germany); INRNE-BAS, Sofia (Bulgaria); Pfeiffer, M. [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, D-50937 Koeln (Germany); Pissulla, Th. [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, D-50937 Koeln (Germany); Bundesumweltministerium, Robert-Schuman-Platz 3, D - 53175 Bonn (Germany); Zell, K.-O. [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, D-50937 Koeln (Germany); Jakobsson, U.; Julin, R.; Jones, P.; Ketelhut, S.; Nieminen, P.; Peura, P. [Department of Physics, University of Jyvaeskylae, P.O. Box 35, FI-40014 (Finland); and others

2011-10-21

We report on the first experiment combining the Recoil Distance Doppler Shift technique and multistep Coulomb excitation in inverse kinematics at beam energies of 3-10 A MeV. The setup involves a standard plunger device equipped with a degrader foil instead of the normally used stopper foil. An array of particle detectors is positioned at forward angles to detect target-like recoil nuclei which are used as a trigger to discriminate against excitations in the degrader foil. The method has been successfully applied to measure lifetimes in {sup 128}Xe and is suited to be a useful tool for experiments with radioactive ion beams.

Renormalized energy-momentum tensor of λΦ4 theory in curved ...

Indian Academy of Sciences (India)

Divergenceless expression for the energy-momentum tensor of scalar field is obtained using the momentum cut-off regularization technique. We consider a scalar field with quartic self-coupling in a spatially flat (3+1)-dimensional Robertson–Walker space-time, having arbitrary mass and coupled to gravity. As special cases ...

Surface tensor estimation from linear sections

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....

Surface tensor estimation from linear sections

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

2015-01-01

From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....

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

Science.gov (United States)

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

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

Evaluation of glymphatic system activity with the diffusion MR technique: diffusion tensor image analysis along the perivascular space (DTI-ALPS) in Alzheimer's disease cases.

Science.gov (United States)

Taoka, Toshiaki; Masutani, Yoshitaka; Kawai, Hisashi; Nakane, Toshiki; Matsuoka, Kiwamu; Yasuno, Fumihiko; Kishimoto, Toshifumi; Naganawa, Shinji

2017-04-01

The activity of the glymphatic system is impaired in animal models of Alzheimer's disease (AD). We evaluated the activity of the human glymphatic system in cases of AD with a diffusion-based technique called diffusion tensor image analysis along the perivascular space (DTI-ALPS). Diffusion tensor images were acquired to calculate diffusivities in the x, y, and z axes of the plane of the lateral ventricle body in 31 patients. We evaluated the diffusivity along the perivascular spaces as well as projection fibers and association fibers separately, to acquire an index for diffusivity along the perivascular space (ALPS-index) and correlated them with the mini mental state examinations (MMSE) score. We found a significant negative correlation between diffusivity along the projection fibers and association fibers. We also observed a significant positive correlation between diffusivity along perivascular spaces shown as ALPS-index and the MMSE score, indicating lower water diffusivity along the perivascular space in relation to AD severity. Activity of the glymphatic system may be evaluated with diffusion images. Lower diffusivity along the perivascular space on DTI-APLS seems to reflect impairment of the glymphatic system. This method may be useful for evaluating the activity of the glymphatic system.

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.)

Moment tensor and location of seismic events in the 2017 DPRK test

Science.gov (United States)

Wei, S.; Shi, Q.; Chen, Q. F.; Wang, T.

2017-12-01

The main seismic event in the 2017 DPRK test was followed by a secondary event about eight minutes later. We conducted waveform analysis on the regional broadband waveform data to better constrain the moment tensor and location of these two events, to further understand their relations. In the first place, we applied the generalized Cut-And-Paste (gCAP) method to the regional data to invert the full moment tensor solutions of the two events. Our long period (0.02-0.08 Hz for Pnl, 0.02-0.055 Hz for surface waves) inversions show that the main event was composed of large positive ISO component ( 90% of the total moment) and has a moment magnitude of 5.4. In contrast, the second event shows large negative ISO component ( 50% of the total moment) with a moment magnitude of 4.5. Although there are trade-offs between the CLVD and the ISO component for the second event, chiefly caused by the coda waves from the first event, the result is more robust if we force a small CVLD component in the inversion. We also relocated the epicenter of the second event using P-wave first arrival picks, relative to the location of the first event, which has been accurately determined from the high-resolution geodetic data. The calibration from the first event allows us to precisely locate the second event, which shows an almost identical location to the first event. After a polarity correction, their high-frequency ( 0.25 - 0.9 Hz) regional surface waves also display high similarity, supporting the similar location but opposite ISO polarity of the two events. Our results suggest that the second event was likely to be caused by the collapsing after the main event, in agreement with the surface displacement derived from geodetic observation and modeling results.

Tensor-based Dictionary Learning for Spectral CT Reconstruction

Science.gov (United States)

Zhang, Yanbo; Wang, Ge

2016-01-01

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

Tensor-Based Dictionary Learning for Spectral CT Reconstruction.

Science.gov (United States)

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

2017-01-01

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

Probabilistic inversion for chicken processing lines

International Nuclear Information System (INIS)

Cooke, Roger M.; Nauta, Maarten; Havelaar, Arie H.; Fels, Ine van der

2006-01-01

We discuss an application of probabilistic inversion techniques to a model of campylobacter transmission in chicken processing lines. Such techniques are indicated when we wish to quantify a model which is new and perhaps unfamiliar to the expert community. In this case there are no measurements for estimating model parameters, and experts are typically unable to give a considered judgment. In such cases, experts are asked to quantify their uncertainty regarding variables which can be predicted by the model. The experts' distributions (after combination) are then pulled back onto the parameter space of the model, a process termed 'probabilistic inversion'. This study illustrates two such techniques, iterative proportional fitting (IPF) and PARmeter fitting for uncertain models (PARFUM). In addition, we illustrate how expert judgement on predicted observable quantities in combination with probabilistic inversion may be used for model validation and/or model criticism

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

Science.gov (United States)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

Science.gov (United States)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Optimal Inversion Parameters for Full Waveform Inversion using OBS Data Set

Science.gov (United States)

Kim, S.; Chung, W.; Shin, S.; Kim, D.; Lee, D.

2017-12-01

In recent years, full Waveform Inversion (FWI) has been the most researched technique in seismic data processing. It uses the residuals between observed and modeled data as an objective function; thereafter, the final subsurface velocity model is generated through a series of iterations meant to minimize the residuals.Research on FWI has expanded from acoustic media to elastic media. In acoustic media, the subsurface property is defined by P-velocity; however, in elastic media, properties are defined by multiple parameters, such as P-velocity, S-velocity, and density. Further, the elastic media can also be defined by Lamé constants, density or impedance PI, SI; consequently, research is being carried out to ascertain the optimal parameters.From results of advanced exploration equipment and Ocean Bottom Seismic (OBS) survey, it is now possible to obtain multi-component seismic data. However, to perform FWI on these data and generate an accurate subsurface model, it is important to determine optimal inversion parameters among (Vp, Vs, ρ), (λ, μ, ρ), and (PI, SI) in elastic media. In this study, staggered grid finite difference method was applied to simulate OBS survey. As in inversion, l2-norm was set as objective function. Further, the accurate computation of gradient direction was performed using the back-propagation technique and its scaling was done using the Pseudo-hessian matrix.In acoustic media, only Vp is used as the inversion parameter. In contrast, various sets of parameters, such as (Vp, Vs, ρ) and (λ, μ, ρ) can be used to define inversion in elastic media. Therefore, it is important to ascertain the parameter that gives the most accurate result for inversion with OBS data set.In this study, we generated Vp and Vs subsurface models by using (λ, μ, ρ) and (Vp, Vs, ρ) as inversion parameters in every iteration, and compared the final two FWI results.This research was supported by the Basic Research Project(17-3312) of the Korea Institute of

Time-reversal and Bayesian inversion

Science.gov (United States)

Debski, Wojciech

2017-04-01

Probabilistic inversion technique is superior to the classical optimization-based approach in all but one aspects. It requires quite exhaustive computations which prohibit its use in huge size inverse problems like global seismic tomography or waveform inversion to name a few. The advantages of the approach are, however, so appealing that there is an ongoing continuous afford to make the large inverse task as mentioned above manageable with the probabilistic inverse approach. One of the perspective possibility to achieve this goal relays on exploring the internal symmetry of the seismological modeling problems in hand - a time reversal and reciprocity invariance. This two basic properties of the elastic wave equation when incorporating into the probabilistic inversion schemata open a new horizons for Bayesian inversion. In this presentation we discuss the time reversal symmetry property, its mathematical aspects and propose how to combine it with the probabilistic inverse theory into a compact, fast inversion algorithm. We illustrate the proposed idea with the newly developed location algorithm TRMLOC and discuss its efficiency when applied to mining induced seismic data.

Typesafe Abstractions for Tensor Operations

OpenAIRE

Chen, Tongfei

2017-01-01

We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural layers such as convolution or recurrent neural networks. This abstraction could lay the foundation of future typesafe deep learning frameworks that runs on Scala/JVM.

Tensor network state correspondence and holography

Science.gov (United States)

Singh, Sukhwinder

2018-01-01

In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.

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

Concatenated image completion via tensor augmentation and completion

OpenAIRE

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

2016-01-01

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

General projective relativity and the vector-tensor gravitational field

International Nuclear Information System (INIS)

Arcidiacono, G.

1986-01-01

In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation

Tensor harmonic analysis on homogenous space

International Nuclear Information System (INIS)

Wrobel, G.

1997-01-01

The Hilbert space of tensor functions on a homogenous space with the compact stability group is considered. The functions are decomposed onto a sum of tensor plane waves (defined in the text), components of which are transformed by irreducible representations of the appropriate transformation group. The orthogonality relation and the completeness relation for tensor plane waves are found. The decomposition constitutes a unitary transformation, which allows to obtain the Parseval equality. The Fourier components can be calculated by means of the Fourier transformation, the form of which is given explicitly. (author)

Applications of multiscale waveform inversion to marine data using a flooding technique and dynamic early-arrival windows

KAUST Repository

Boonyasiriwat, Chaiwoot

2010-11-01

A recently developed time-domain multiscale waveform tomography (MWT) method is applied to synthetic and field marine data. Although the MWT method was already applied to synthetic data, the synthetic data application leads to a development of a hybrid method between waveform tomography and the salt flooding technique commonly use in subsalt imaging. This hybrid method can overcome a convergence problem encountered by inversion with a traveltime velocity tomogram and successfully provides an accurate and highly resolved velocity tomogram for the 2D SEG/EAGE salt model. In the application of MWT to the field data, the inversion process is carried out using a multiscale method with a dynamic early-arrival muting window to mitigate the local minima problem of waveform tomography and elastic effects. With the modified MWT method, reasonably accurate results as verified by comparison of migration images and common image gathers were obtained. The hybrid method with the salt flooding technique is not used in this field data example because there is no salt in the subsurface according to our interpretation. However, we believe it is applicable to field data applications. © 2010 Society of Exploration Geophysicists.

Inverse Kinematics of a Serial Robot

Directory of Open Access Journals (Sweden)

Amici Cinzia

2016-01-01

Full Text Available This work describes a technique to treat the inverse kinematics of a serial manipulator. The inverse kinematics is obtained through the numerical inversion of the Jacobian matrix, that represents the equation of motion of the manipulator. The inversion is affected by numerical errors and, in different conditions, due to the numerical nature of the solver, it does not converge to a reasonable solution. Thus a soft computing approach is adopted to mix different traditional methods to obtain an increment of algorithmic convergence.

Tensor estimation for double-pulsed diffusional kurtosis imaging.

Science.gov (United States)

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

2017-07-01

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

Tensor network decompositions in the presence of a global symmetry

International Nuclear Information System (INIS)

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

2010-01-01

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

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

Science.gov (United States)

Marin Quintero, Maider J.

2013-01-01

The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…

Fully probabilistic seismic source inversion – Part 1: Efficient parameterisation

Directory of Open Access Journals (Sweden)

S. C. Stähler

2014-11-01

Full Text Available Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters themselves but also estimates of their uncertainties are of great practical importance. Probabilistic source inversion (Bayesian inference is very adapted to this challenge, provided that the parameter space can be chosen small enough to make Bayesian sampling computationally feasible. We propose a framework for PRobabilistic Inference of Seismic source Mechanisms (PRISM that parameterises and samples earthquake depth, moment tensor, and source time function efficiently by using information from previous non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 source time functions (STFs by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits propagating these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible.

Measurement of rotation and strain-rate tensors by using stereoscopic PIV

DEFF Research Database (Denmark)

Özcan, O.; Meyer, Knud Erik; Larsen, Poul Scheel

2004-01-01

A simple technique is described for measuring the mean rate-of-displacement (velocity gradient) tensor in a plane by using a conventional stereoscopic PIV system. The technique involves taking PIV data in two or three closely-spaced parallel planes at different times. All components of the mean...... are presented to show the applicability of the proposed technique. The PIV cameras and light sheet optics shown in Fig. 1a are mounted on the same traverse mechanism in order to displace the measurement plane accurately. Data obtained in constant-y and -z planes are presented. Fig. 1b shows a contour plot...

A review of anisotropic conductivity models of brain white matter based on diffusion tensor imaging.

Science.gov (United States)

Wu, Zhanxiong; Liu, Yang; Hong, Ming; Yu, Xiaohui

2018-06-01

The conductivity of brain tissues is not only essential for electromagnetic source estimation (ESI), but also a key reflector of the brain functional changes. Different from the other brain tissues, the conductivity of whiter matter (WM) is highly anisotropic and a tensor is needed to describe it. The traditional electrical property imaging methods, such as electrical impedance tomography (EIT) and magnetic resonance electrical impedance tomography (MREIT), usually fail to image the anisotropic conductivity tensor of WM with high spatial resolution. The diffusion tensor imaging (DTI) is a newly developed technique that can fulfill this purpose. This paper reviews the existing anisotropic conductivity models of WM based on the DTI and discusses their advantages and disadvantages, as well as identifies opportunities for future research on this subject. It is crucial to obtain the linear conversion coefficient between the eigenvalues of anisotropic conductivity tensor and diffusion tensor, since they share the same eigenvectors. We conclude that the electrochemical model is suitable for ESI analysis because the conversion coefficient can be directly obtained from the concentration of ions in extracellular liquid and that the volume fraction model is appropriate to study the influence of WM structural changes on electrical conductivity. Graphical abstract ᅟ.

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.)

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...

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

A Joint Method of Envelope Inversion Combined with Hybrid-domain Full Waveform Inversion

Science.gov (United States)

CUI, C.; Hou, W.

2017-12-01

Full waveform inversion (FWI) aims to construct high-precision subsurface models by fully using the information in seismic records, including amplitude, travel time, phase and so on. However, high non-linearity and the absence of low frequency information in seismic data lead to the well-known cycle skipping problem and make inversion easily fall into local minima. In addition, those 3D inversion methods that are based on acoustic approximation ignore the elastic effects in real seismic field, and make inversion harder. As a result, the accuracy of final inversion results highly relies on the quality of initial model. In order to improve stability and quality of inversion results, multi-scale inversion that reconstructs subsurface model from low to high frequency are applied. But, the absence of very low frequencies (time domain and inversion in the frequency domain. To accelerate the inversion, we adopt CPU/GPU heterogeneous computing techniques. There were two levels of parallelism. In the first level, the inversion tasks are decomposed and assigned to each computation node by shot number. In the second level, GPU multithreaded programming is used for the computation tasks in each node, including forward modeling, envelope extraction, DFT (discrete Fourier transform) calculation and gradients calculation. Numerical tests demonstrated that the combined envelope inversion + hybrid-domain FWI could obtain much faithful and accurate result than conventional hybrid-domain FWI. The CPU/GPU heterogeneous parallel computation could improve the performance speed.

Inverse Optimization and Forecasting Techniques Applied to Decision-making in Electricity Markets

DEFF Research Database (Denmark)

Saez Gallego, Javier

patterns that the load traditionally exhibited. On the other hand, this thesis is motivated by the decision-making processes of market players. In response to these challenges, this thesis provides mathematical models for decision-making under uncertainty in electricity markets. Demand-side bidding refers......This thesis deals with the development of new mathematical models that support the decision-making processes of market players. It addresses the problems of demand-side bidding, price-responsive load forecasting and reserve determination. From a methodological point of view, we investigate a novel...... approach to model the response of aggregate price-responsive load as a constrained optimization model, whose parameters are estimated from data by using inverse optimization techniques. The problems tackled in this dissertation are motivated, on one hand, by the increasing penetration of renewable energy...

Effects of tensor forces in nuclei

International Nuclear Information System (INIS)

Tanihata, Isao

2013-01-01

Recent studies of nuclei far from the stability line have revealed drastic changes in nuclear orbitals and reported the appearance of new magic numbers and the disappearance of magic numbers observed at the stability line. One of the important reasons for such changes is considered to be because of the effect of tensor forces on nuclear structure. Although the role of tensor forces in binding very light nuclei such as deuterons and 4 He has been known, direct experimental evidence for the effect on nuclear structure is scarce. In this paper, I review known effects of tensor forces in nuclei and then discuss the recently raised question of s–p wave mixing in a halo nucleus of 11 Li. Following these reviews, the development of a new experiment to see the high-momentum components due to the tensor forces is discussed and some of the new data are presented. (paper)

Predicting patterns of glioma recurrence using diffusion tensor imaging

International Nuclear Information System (INIS)

Price, Stephen J.; Pickard, John D.; Jena, Rajesh; Burnet, Neil G.; Carpenter, T.A.; Gillard, Jonathan H.

2007-01-01

Although multimodality therapy for high-grade gliomas is making some improvement in outcome, most patients will still die from their disease within a short time. We need tools that allow treatments to be tailored to an individual. In this study we used diffusion tensor imaging (DTI), a technique sensitive to subtle disruption of white-matter tracts due to tumour infiltration, to see if it can be used to predict patterns of glioma recurrence. In this study we imaged 26 patients with gliomas using DTI. Patients were imaged after 2 years or on symptomatic tumour recurrence. The diffusion tensor was split into its isotropic (p) and anisotropic (q) components, and these were plotted on T 2 -weighted images to show the pattern of DTI abnormality. This was compared to the pattern of recurrence. Three DTI patterns could be identified: (a) a diffuse pattern of abnormality where p exceeded q in all directions and was associated with diffuse increase in tumour size; (b) a localised pattern of abnormality where the tumour recurred in one particular direction; and (c) a pattern of minimal abnormality seen in some patients with or without evidence of recurrence. Diffusion tensor imaging is able to predict patterns of tumour recurrence and may allow better individualisation of tumour management and stratification for randomised controlled trials. (orig.)

Predicting patterns of glioma recurrence using diffusion tensor imaging

Energy Technology Data Exchange (ETDEWEB)

Price, Stephen J.; Pickard, John D. [University of Cambridge and Cambridge University Hospitals NHS Foundation Trust, Addenbrooke' s Hospital, Academic Neurosurgery Unit (United Kingdom); University of Cambridge and Cambridge University Hospitals NHS Foundation Trust, Addenbrooke' s Hospital, Wolfson Brain Imaging Centre, Department of Clinical Neurosciences (United Kingdom); Jena, Rajesh; Burnet, Neil G. [University of Cambridge and Cambridge University Hospitals NHS Foundation Trust, Addenbrooke' s Hospital, University Department of Oncology (United Kingdom); Carpenter, T.A. [University of Cambridge and Cambridge University Hospitals NHS Foundation Trust, Addenbrooke' s Hospital, Wolfson Brain Imaging Centre, Department of Clinical Neurosciences (United Kingdom); Gillard, Jonathan H. [University of Cambridge and Cambridge University Hospitals NHS Foundation Trust, Addenbrooke' s Hospital, University Department of Radiology (United Kingdom)

2007-07-15

Although multimodality therapy for high-grade gliomas is making some improvement in outcome, most patients will still die from their disease within a short time. We need tools that allow treatments to be tailored to an individual. In this study we used diffusion tensor imaging (DTI), a technique sensitive to subtle disruption of white-matter tracts due to tumour infiltration, to see if it can be used to predict patterns of glioma recurrence. In this study we imaged 26 patients with gliomas using DTI. Patients were imaged after 2 years or on symptomatic tumour recurrence. The diffusion tensor was split into its isotropic (p) and anisotropic (q) components, and these were plotted on T{sub 2}-weighted images to show the pattern of DTI abnormality. This was compared to the pattern of recurrence. Three DTI patterns could be identified: (a) a diffuse pattern of abnormality where p exceeded q in all directions and was associated with diffuse increase in tumour size; (b) a localised pattern of abnormality where the tumour recurred in one particular direction; and (c) a pattern of minimal abnormality seen in some patients with or without evidence of recurrence. Diffusion tensor imaging is able to predict patterns of tumour recurrence and may allow better individualisation of tumour management and stratification for randomised controlled trials. (orig.)

Toroidal Dielectric Tensor-Operator for Arbitrary Aspect-Ratio and Wave Frequency an Anisotropic-Resistivity MHD Formulation

International Nuclear Information System (INIS)

Komoshvili, K.; Cuperman, S.

1998-01-01

Motivated by the recently increased interest in small aspect ratio tokamaks, we have derived a 2(1/2)D dielectric tensor-operator which can properly describe the plasma response to r.f. waves, under conditions prevailing in the pre-heated stages of arbitrary aspect ratio, axisymmetric toroidal fusion devices. The derived dielectric tensor elements are based on a two-fluid, weakly collisional plasma description, with the Hall term included. They are characterized by the following features: (i) They are cast in a form evidencing the dielectric (non-operator) and operator contributions - the latter being due to the toroidal structure of the V-operators present in Maxwell's equations, on the background of equilibrium currents and pressure gradients; (ii) They are not subject to any I imitation on the (relative) magnitude of the toroidal effects - no expansion in the inverse aspect ratio parameter is used for their derivation; (iii) They include anisotropic - parallel and perpendicular to the magnetic field - contributions to the plasma resistivity; (iv) They are not Iimited by any restriction on the (relative) value of the wave frequency. The explicit, physically transparent formulation of the dielectric tensor is intended for the numerical solution of the full (E ll ≠ 0) wave equation and subsequently, evaluation of the Alfven wave current drive in small aspect ratio tokamaks

Spectral Tensor-Train Decomposition

DEFF Research Database (Denmark)

Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.

2016-01-01

The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT...... adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online (http://pypi.python.org/pypi/TensorToolbox/)....

Reduction of CSF flow artifact in fast fluid attenuated inversion recovery MR imaging. Study of excitation width in 180deg inversion pulse

International Nuclear Information System (INIS)

Tsuchihashi, Toshio; Yoshizawa, Satoshi; Maki, Toshio; Kitagawa, Matsuo; Suzuki, Ken; Fujita, Isao

1998-01-01

A technique that increases slice thickness so that it becomes wider than the excitation width of the 180deg inversion pulse and in which TR is partitioned twice has been investigated with regard to fast FLAIR. This is a technique that reduces the flow artifact of CSF. It is thought that, with this technique, the flow artifact is reduced because the CSF that flows onto the slice reaches the null point. The cross talk effect of the 180deg inversion pulse appears as a high CSF signal. As a result, the number of slices needs to be partitioned two or three times before imaging. Thus the imaging time is doubled or tripled. Considering the cross talk effect of the 180deg inversion pulse and the imaging time needed for this technique, the optimal imaging technique would be one that uses an inversion pulse that is four times slice thickness plus slice space and for which the number of slices is partitioned twice. Furthermore, the null point of CSF was dependent on dividing TR in half. (author)

Scalable Tensor Factorizations with Missing Data

DEFF Research Database (Denmark)

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

2010-01-01

of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP...... is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram...

Scalable tensor factorizations for incomplete data

DEFF Research Database (Denmark)

Acar, Evrim; Dunlavy, Daniel M.; KOlda, Tamara G.

2011-01-01

to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP...... experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 × 1000 × 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP...

Adaptive stochastic Galerkin FEM with hierarchical tensor representations

KAUST Repository

Eigel, Martin

2016-01-08

PDE with stochastic data usually lead to very high-dimensional algebraic problems which easily become unfeasible for numerical computations because of the dense coupling structure of the discretised stochastic operator. Recently, an adaptive stochastic Galerkin FEM based on a residual a posteriori error estimator was presented and the convergence of the adaptive algorithm was shown. While this approach leads to a drastic reduction of the complexity of the problem due to the iterative discovery of the sparsity of the solution, the problem size and structure is still rather limited. To allow for larger and more general problems, we exploit the tensor structure of the parametric problem by representing operator and solution iterates in the tensor train (TT) format. The (successive) compression carried out with these representations can be seen as a generalisation of some other model reduction techniques, e.g. the reduced basis method. We show that this approach facilitates the efficient computation of different error indicators related to the computational mesh, the active polynomial chaos index set, and the TT rank. In particular, the curse of dimension is avoided.

Relevance vector machine technique for the inverse scattering problem

International Nuclear Information System (INIS)

Wang Fang-Fang; Zhang Ye-Rong

2012-01-01

A novel method based on the relevance vector machine (RVM) for the inverse scattering problem is presented in this paper. The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered. The nonlinearity is embodied in the relation between the scattered field and the target property, which can be obtained through the RVM training process. Besides, rather than utilizing regularization, the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output. Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy, convergence, robustness, generalization, and improved performance in terms of sparse property in comparison with the support vector machine (SVM) based approach. (general)

Full moment tensor retrieval and fluid dynamics in volcanic areas: The case of phlegraean field (south Italy)

International Nuclear Information System (INIS)

Campus, P.; Cespuglio, G.

1994-04-01

When studying seismicity in volcanic areas it is appropriate to treat the seismic source in a form a priori not restricted to a double couple, since its mechanism may reflect not only small scale tectonics but also fluid dynamics. The monitoring of fluid dynamics can be therefore attempted from the retrieval of the rupture processes. It is not possible to use standard methods, based on the distribution of polarities of first arrivals to determine the non double-couple components of the seismic source. The new method presented here is based on the wave form inversion of the dominant part of the seismograms, where the signal to noise ratio is very large and allows the inversion of the full seismic moment tensor. The results of a pilot study in the Phlegraean Fields (South Italy) are presented. 13 refs, 10 figs, 4 tabs

Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

Science.gov (United States)

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

2017-10-12

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

The tensor bi-spectrum in a matter bounce

Energy Technology Data Exchange (ETDEWEB)

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

2015-11-01

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

Endoscopic Anatomy of the Tensor Fold and Anterior Attic.

Science.gov (United States)

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

2018-02-01

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

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)

Gauge theories, duality relations and the tensor hierarchy

International Nuclear Information System (INIS)

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

2009-01-01

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

Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo

Science.gov (United States)

Bui-Thanh, T.; Girolami, M.

2014-11-01

We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint

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....

Global seismic inversion as the next standard step in the processing sequence

Energy Technology Data Exchange (ETDEWEB)

Maver, Kim G.; Hansen, Lars S.; Jepsen, Anne-Marie; Rasmussen, Klaus B.

1998-12-31

Seismic inversion of post stack seismic data has until recently been regarded as a reservoir oriented method since the standard inversion techniques rely on extensive well control and a detailed user derived input model. Most seismic inversion techniques further requires a stable wavelet. As a consequence seismic inversion is mainly utilised in mature areas focusing of specific zones only after the seismic data has been interpreted and is well understood. By using an advanced 3-D global technique, seismic inversion is presented as the next standard step in the processing sequence. The technique is robust towards noise within the seismic data, utilizes a time variant wavelet, and derives a low frequency model utilizing the stacking velocities and only limited well control. 4 figs.

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.)

Reconstruction of the arcuate fasciculus for surgical planning in the setting of peritumoral edema using two-tensor unscented Kalman filter tractography.

Science.gov (United States)

Chen, Zhenrui; Tie, Yanmei; Olubiyi, Olutayo; Rigolo, Laura; Mehrtash, Alireza; Norton, Isaiah; Pasternak, Ofer; Rathi, Yogesh; Golby, Alexandra J; O'Donnell, Lauren J

2015-01-01

Diffusion imaging tractography is increasingly used to trace critical fiber tracts in brain tumor patients to reduce the risk of post-operative neurological deficit. However, the effects of peritumoral edema pose a challenge to conventional tractography using the standard diffusion tensor model. The aim of this study was to present a novel technique using a two-tensor unscented Kalman filter (UKF) algorithm to track the arcuate fasciculus (AF) in brain tumor patients with peritumoral edema. Ten right-handed patients with left-sided brain tumors in the vicinity of language-related cortex and evidence of significant peritumoral edema were retrospectively selected for the study. All patients underwent 3-Tesla magnetic resonance imaging (MRI) including a diffusion-weighted dataset with 31 directions. Fiber tractography was performed using both single-tensor streamline and two-tensor UKF tractography. A two-regions-of-interest approach was applied to perform the delineation of the AF. Results from the two different tractography algorithms were compared visually and quantitatively. Using single-tensor streamline tractography, the AF appeared disrupted in four patients and contained few fibers in the remaining six patients. Two-tensor UKF tractography delineated an AF that traversed edematous brain areas in all patients. The volume of the AF was significantly larger on two-tensor UKF than on single-tensor streamline tractography (p tensor UKF tractography provides the ability to trace a larger volume AF than single-tensor streamline tractography in the setting of peritumoral edema in brain tumor patients.

Oil encapsulation in core-shell alginate capsules by inverse gelation II: comparison between dripping techniques using W/O or O/W emulsions.

Science.gov (United States)

Martins, Evandro; Poncelet, Denis; Rodrigues, Ramila Cristiane; Renard, Denis

2017-09-01

In the first part of this article, it was described an innovative method of oil encapsulation from dripping-inverse gelation using water-in-oil (W/O) emulsions. It was noticed that the method of oil encapsulation was quite different depending on the emulsion type (W/O or oil-in-water (O/W)) used and that the emulsion structure (W/O or O/W) had a high impact on the dripping technique and the capsules characteristics. The objective of this article was to elucidate the differences between the dripping techniques using both emulsions and compare the capsule properties (mechanical resistance and release of actives). The oil encapsulation using O/W emulsions was easier to perform and did not require the use of emulsion destabilisers. However, capsules produced from W/O emulsions were more resistant to compression and showed the slower release of actives over time. The findings detailed here widened the knowledge of the inverse gelation and gave opportunities to develop new techniques of oil encapsulation.

Visualizing Dataflow Graphs of Deep Learning Models in TensorFlow.

Science.gov (United States)

Wongsuphasawat, Kanit; Smilkov, Daniel; Wexler, James; Wilson, Jimbo; Mane, Dandelion; Fritz, Doug; Krishnan, Dilip; Viegas, Fernanda B; Wattenberg, Martin

2018-01-01

We present a design study of the TensorFlow Graph Visualizer, part of the TensorFlow machine intelligence platform. This tool helps users understand complex machine learning architectures by visualizing their underlying dataflow graphs. The tool works by applying a series of graph transformations that enable standard layout techniques to produce a legible interactive diagram. To declutter the graph, we decouple non-critical nodes from the layout. To provide an overview, we build a clustered graph using the hierarchical structure annotated in the source code. To support exploration of nested structure on demand, we perform edge bundling to enable stable and responsive cluster expansion. Finally, we detect and highlight repeated structures to emphasize a model's modular composition. To demonstrate the utility of the visualizer, we describe example usage scenarios and report user feedback. Overall, users find the visualizer useful for understanding, debugging, and sharing the structures of their models.

Intersections, ideals, and inversion

International Nuclear Information System (INIS)

Vasco, D.W.

1998-01-01

Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly one dimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons

Intersections, ideals, and inversion

Energy Technology Data Exchange (ETDEWEB)

Vasco, D.W.

1998-10-01

Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly onedimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons.

Prescribed curvature tensor in locally conformally flat manifolds

Science.gov (United States)

Pina, Romildo; Pieterzack, Mauricio

2018-01-01

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

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.

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

OpenAIRE

Hadjesfandiari, Ali R.

2013-01-01

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

Determination of the plastic deformation and residual stress tensor distribution using surface and bulk intrinsic magnetic properties

International Nuclear Information System (INIS)

Hristoforou, E.; Svec, P. Sr.

2015-01-01

We have developed an unique method to provide the stress calibration curve in steels: performing flaw-less welding in the under examination steel, we obtained to determine the level of the local plastic deformation and the residual stress tensors. These properties where measured using both the X-ray and the neutron diffraction techniques, concerning their surface and bulk stresses type II (intra-grain stresses) respectively, as well as the stress tensor type III by using the electron diffraction technique. Measuring the distribution of these residual stresses along the length of a welded sample or structure, resulted in determining the local stresses from the compressive to tensile yield point. Local measurement of the intrinsic surface and bulk magnetic property tensors allowed for the un-hysteretic correlation. The dependence of these local magnetic tensors with the above mentioned local stress tensors, resulting in a unique and almost un-hysteretic stress calibration curve of each grade of steel. This calibration integrated the steel's mechanical and thermal history, as well as the phase transformations and the presence of precipitations occurring during the welding process.Additionally to that, preliminary results in different grade of steels reveal the existence of a universal law concerning the dependence of magnetic and magnetostrictive properties of steels on their plastic deformation and residual stress state, as they have been accumulated due to their mechanical and thermal fatigue and history. This universality is based on the unique dependence of the intrinsic magnetic properties of steels normalized with a certain magnetoelastic factor, upon the plastic deformation or residual stress state, which, in terms, is normalized with their yield point of stress. (authors)

Tensor products of higher almost split sequences

OpenAIRE

Pasquali, Andrea

2015-01-01

We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama gave a precise criterion for when the tensor product of an $n$-representation finite algebra and an $m$-representation finite algebra is $(n+m)$-representation finite. In this case we give a complete description of the higher almost split sequences over the tensor product by expressing every higher almost split sequence as the mapping cone of a suit...

Reducing surgical levels by paraspinal mapping and diffusion tensor imaging techniques in lumbar spinal stenosis

OpenAIRE

Chen, Hua-Biao; Wan, Qi; Xu, Qi-Feng; Chen, Yi; Bai, Bo

2016-01-01

Background Correlating symptoms and physical examination findings with surgical levels based on common imaging results is not reliable. In patients who have no concordance between radiological and clinical symptoms, the surgical levels determined by conventional magnetic resonance imaging (MRI) and neurogenic examination (NE) may lead to a more extensive surgery and significant complications. We aimed to confirm that whether the use of diffusion tensor imaging (DTI) and paraspinal mapping (PM...

The 'gravitating' tensor in the dualistic theory

International Nuclear Information System (INIS)

Mahanta, M.N.

1989-01-01