Reconstruction of primordial tensor power spectra from B -mode polarization of the cosmic microwave background

NASA Astrophysics Data System (ADS)

Hiramatsu, Takashi; Komatsu, Eiichiro; Hazumi, Masashi; Sasaki, Misao

2018-06-01

Given observations of the B -mode polarization power spectrum of the cosmic microwave background (CMB), we can reconstruct power spectra of primordial tensor modes from the early Universe without assuming their functional form such as a power-law spectrum. The shape of the reconstructed spectra can then be used to probe the origin of tensor modes in a model-independent manner. We use the Fisher matrix to calculate the covariance matrix of tensor power spectra reconstructed in bins. We find that the power spectra are best reconstructed at wave numbers in the vicinity of k ≈6 ×10-4 and 5 ×10-3 Mpc-1 , which correspond to the "reionization bump" at ℓ≲6 and "recombination bump" at ℓ≈80 of the CMB B -mode power spectrum, respectively. The error bar between these two wave numbers is larger because of the lack of the signal between the reionization and recombination bumps. The error bars increase sharply toward smaller (larger) wave numbers because of the cosmic variance (CMB lensing and instrumental noise). To demonstrate the utility of the reconstructed power spectra, we investigate whether we can distinguish between various sources of tensor modes including those from the vacuum metric fluctuation and SU(2) gauge fields during single-field slow-roll inflation, open inflation, and massive gravity inflation. The results depend on the model parameters, but we find that future CMB experiments are sensitive to differences in these models. We make our calculation tool available online.

Geomanetically Induced Currents (GIC) calculation, impact assessment on transmission system and validation using 3-D earth conductivity tensors and GIC measurements.

NASA Astrophysics Data System (ADS)

Sharma, R.; McCalley, J. D.

2016-12-01

Geomagnetic disturbance (GMD) causes the flow of geomagnetically induced currents (GIC) in the power transmission system that may cause large scale power outages and power system equipment damage. In order to plan for defense against GMD, it is necessary to accurately estimate the flow of GICs in the power transmission system. The current calculation as per NERC standards uses the 1-D earth conductivity models that don't reflect the coupling between the geoelectric and geomagnetic field components in the same direction. For accurate estimation of GICs, it is important to have spatially granular 3-D earth conductivity tensors, accurate DC network model of the transmission system and precisely estimated or measured input in the form of geomagnetic or geoelectric field data. Using these models and data the pre event, post event and online planning and assessment can be performed. The pre, post and online planning can be done by calculating GIC, analyzing voltage stability margin, identifying protection system vulnerabilities and estimating heating in transmission equipment. In order to perform the above mentioned tasks, an established GIC calculation and analysis procedure is needed that uses improved geophysical and DC network models obtained by model parameter tuning. The issue is addressed by performing the following tasks; 1) Geomagnetic field data and improved 3-D earth conductivity tensors are used to plot the geoelectric field map of a given area. The obtained geoelectric field map then serves as an input to the PSS/E platform, where through DC circuit analysis the GIC flows are calculated. 2) The computed GIC is evaluated against GIC measurements in order to fine tune the geophysical and DC network model parameters for any mismatch in the calculated and measured GIC. 3) The GIC calculation procedure is then adapted for a one in 100 year storm, in order to assess the impact of the worst case GMD on the power system. 4) Using the transformer models, the voltage stability margin would be analyzed for various real and synthetic geomagnetic or geoelectric field inputs, by calculating the reactive power absorbed by the transformers during an event. All four steps will help the electric utilities and planners to make use of better and accurate estimation techniques for GIC calculation, and impact assessment for future GMD events.

Measurement of Systematic Error Effects for a Sensitive Storage Ring EDM Polarimeter

NASA Astrophysics Data System (ADS)

Imig, Astrid; Stephenson, Edward

2009-10-01

The Storage Ring EDM Collaboration was using the Cooler Synchrotron (COSY) and the EDDA detector at the Forschungszentrum J"ulich to explore systematic errors in very sensitive storage-ring polarization measurements. Polarized deuterons of 235 MeV were used. The analyzer target was a block of 17 mm thick carbon placed close to the beam so that white noise applied to upstream electrostatic plates increases the vertical phase space of the beam, allowing deuterons to strike the front face of the block. For a detector acceptance that covers laboratory angles larger than 9 ^o, the efficiency for particles to scatter into the polarimeter detectors was about 0.1% (all directions) and the vector analyzing power was about 0.2. Measurements were made of the sensitivity of the polarization measurement to beam position and angle. Both vector and tensor asymmetries were measured using beams with both vector and tensor polarization. Effects were seen that depend upon both the beam geometry and the data rate in the detectors.

Performance of tensor decomposition-based modal identification under nonstationary vibration

NASA Astrophysics Data System (ADS)

Friesen, P.; Sadhu, A.

2017-03-01

Health monitoring of civil engineering structures is of paramount importance when they are subjected to natural hazards or extreme climatic events like earthquake, strong wind gusts or man-made excitations. Most of the traditional modal identification methods are reliant on stationarity assumption of the vibration response and posed difficulty while analyzing nonstationary vibration (e.g. earthquake or human-induced vibration). Recently tensor decomposition based methods are emerged as powerful and yet generic blind (i.e. without requiring a knowledge of input characteristics) signal decomposition tool for structural modal identification. In this paper, a tensor decomposition based system identification method is further explored to estimate modal parameters using nonstationary vibration generated due to either earthquake or pedestrian induced excitation in a structure. The effects of lag parameters and sensor densities on tensor decomposition are studied with respect to the extent of nonstationarity of the responses characterized by the stationary duration and peak ground acceleration of the earthquake. A suite of more than 1400 earthquakes is used to investigate the performance of the proposed method under a wide variety of ground motions utilizing both complete and partial measurements of a high-rise building model. Apart from the earthquake, human-induced nonstationary vibration of a real-life pedestrian bridge is also used to verify the accuracy of the proposed method.

Genten: Software for Generalized Tensor Decompositions v. 1.0.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phipps, Eric T.; Kolda, Tamara G.; Dunlavy, Daniel

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.

Multivariate Tensor-based Morphometry on Surfaces: Application to Mapping Ventricular Abnormalities in HIV/AIDS

PubMed Central

Wang, Yalin; Zhang, Jie; Gutman, Boris; Chan, Tony F.; Becker, James T.; Aizenstein, Howard J.; Lopez, Oscar L.; Tamburo, Robert J.; Toga, Arthur W.; Thompson, Paul M.

2010-01-01

Here we developed a new method, called multivariate tensor-based surface morphometry (TBM), and applied it to study lateral ventricular surface differences associated with HIV/AIDS. Using concepts from differential geometry and the theory of differential forms, we created mathematical structures known as holomorphic one-forms, to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain. The new meshing approach also provides a natural way to register anatomical surfaces across subjects, and improves on prior methods as it handles surfaces that branch and join at complex 3D junctions. To analyze anatomical differences, we computed new statistics from the Riemannian surface metrics - these retain multivariate information on local surface geometry. We applied this framework to analyze lateral ventricular surface morphometry in 3D MRI data from 11 subjects with HIV/AIDS and 8 healthy controls. Our method detected a 3D profile of surface abnormalities even in this small sample. Multivariate statistics on the local tensors gave better effect sizes for detecting group differences, relative to other TBM-based methods including analysis of the Jacobian determinant, the largest and smallest eigenvalues of the surface metric, and the pair of eigenvalues of the Jacobian matrix. The resulting analysis pipeline may improve the power of surface-based morphometry studies of the brain. PMID:19900560

Constraints on the cosmological parameters from BICEP2, Planck, and WMAP

NASA Astrophysics Data System (ADS)

Cheng, Cheng; Huang, Qing-Guo

2014-11-01

In this paper we constrain the cosmological parameters, in particular the tilt of tensor power spectrum, by adopting Background Imaging of Cosmic Extragalactic Polarization (B2), Planck released in 2013 and Wilkinson Microwaves Anisotropy Probe 9-year Polarization data. We find that a blue tilted tensor power spectrum is preferred at more than confidence level if the data from B2 are assumed to be totally interpreted as the relic gravitational waves, but a scale-invariant tensor power spectrum is consistent with the data once the polarized dust is taken into account. The recent Planck 353 GHz HFI dust polarization data imply that the B2 data are perfectly consistent with there being no gravitational wave signal.

Diffusion weighted imaging for the differentiation of breast tumors: From apparent diffusion coefficient to high order diffusion tensor imaging.

PubMed

Teruel, Jose R; Goa, Pål E; Sjøbakk, Torill E; Østlie, Agnes; Fjøsne, Hans E; Bathen, Tone F

2016-05-01

To compare "standard" diffusion weighted imaging, and diffusion tensor imaging (DTI) of 2(nd) and 4(th) -order for the differentiation of malignant and benign breast lesions. Seventy-one patients were imaged at 3 Tesla with a 16-channel breast coil. A diffusion weighted MRI sequence including b = 0 and b = 700 in 30 directions was obtained for all patients. The image data were fitted to three different diffusion models: isotropic model - apparent diffusion coefficient (ADC), 2(nd) -order tensor model (the standard model used for DTI) and a 4(th) -order tensor model, with increased degrees of freedom to describe anisotropy. The ability of the fitted parameters in the different models to differentiate between malignant and benign tumors was analyzed. Seventy-two breast lesions were analyzed, out of which 38 corresponded to malignant and 34 to benign tumors. ADC (using any model) presented the highest discriminative ability of malignant from benign tumors with a receiver operating characteristic area under the curve (AUC) of 0.968, and sensitivity and specificity of 94.1% and 94.7% respectively for a 1.33 × 10(-3) mm(2) /s cutoff. Anisotropy measurements presented high statistical significance between malignant and benign tumors (P < 0.001), but with lower discriminative ability of malignant from benign tumors than ADC (AUC of 0.896 and 0.897 for fractional anisotropy and generalized anisotropy respectively). Statistical significant difference was found between generalized anisotropy and fractional anisotropy for cancers (P < 0.001) but not for benign lesions (P = 0.87). While anisotropy parameters have the potential to provide additional value for breast applications as demonstrated in this study, ADC exhibited the highest differentiation power between malignant and benign breast tumors. © 2015 Wiley Periodicals, Inc.

Steps to reconcile inflationary tensor and scalar spectra

NASA Astrophysics Data System (ADS)

Miranda, Vinícius; Hu, Wayne; Adshead, Peter

2014-05-01

The recent BICEP2 B-mode polarization determination of an inflationary tensor-scalar ratio r=0.2-0.05+0.07 is in tension with simple scale-free models of inflation due to a lack of a corresponding low multipole excess in the temperature power spectrum which places a limit of r0.002<0.11 (95% C.L.) on such models. Single-field inflationary models that reconcile these two observations, even those where the tilt runs substantially, introduce a scale into the scalar power spectrum. To cancel the tensor excess, and simultaneously remove the excess already present without tensors, ideally the model should introduce this scale as a relatively sharp transition in the tensor-scalar ratio around the horizon at recombination. We consider models which generate such a step in this quantity and find that they can improve the joint fit to the temperature and polarization data by up to 2ΔlnL≈-14 without changing cosmological parameters. Precision E-mode polarization measurements should be able to test this explanation.

Inflationary tensor fossils in large-scale structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimastrogiovanni, Emanuela; Fasiello, Matteo; Jeong, Donghui

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

Investigation of the Three-Nucleon System Dynamics in the Deuteron-Proton Breakup Reaction

NASA Astrophysics Data System (ADS)

Ciepał, I.; Kłos, B.; Kistryn, St.; Stephan, E.; Biegun, A.; Bodek, K.; Deltuva, A.; Epelbaum, E.; Eslami-Kalantari, M.; Fonseca, A. C.; Golak, J.; Jha, V.; Kalantar-Nayestanaki, N.; Kamada, H.; Khatri, G.; Kirillov, Da.; Kirillov, Di.; Kliczewski, St.; Kozela, A.; Kravcikova, M.; Machner, H.; Magiera, A.; Martinska, G.; Messchendorp, J.; Nogga, A.; Parol, W.; Ramazani-Moghaddam-Arani, A.; Roy, B. J.; Sakai, H.; Sekiguchi, K.; Sitnik, I.; Siudak, R.; Skibiński, R.; Sworst, R.; Urban, J.; Witała, H.; Zejma, J.

2014-08-01

Precise and large sets of cross section, vector A x , A y and tensor A xx , A xy , A yy analyzing power data for the 1 H( d, pp) n breakup reactions were measured at 100 and 130 MeV deuteron beam energies with the SALAD and BINA detectors at KVI and the Germanium Wall setup at FZ-Jülich. Results are compared with various theoretical approaches which model the three-nucleon system dynamics. The cross section data reveal a sizable three-nucleon force (3NF) and Coulomb force influence. In case of the analyzing powers very low sensitivity to these effects was found and the data are well describe by 2N models only. For A xy at 130 MeV, serious disagreements were observed when 3NF models are included in the calculations.

Development of the Tensoral Computer Language

NASA Technical Reports Server (NTRS)

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.

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

NASA Astrophysics Data System (ADS)

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.

Frustrated Magnetism of Dipolar Molecules on a Square Optical Lattice: Prediction of a Quantum Paramagnetic Ground State

NASA Astrophysics Data System (ADS)

Zou, Haiyuan; Zhao, Erhai; Liu, W. Vincent

2017-08-01

Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1 /2 dipolar Heisenberg model with competing anisotropic, long-range exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the J1-J2 model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the Néel, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by an unbiased variational ansatz based on tensor network states and a tensor renormalization group.

Correlation Between Fracture Network Properties and Stress Variability in Geological Media

NASA Astrophysics Data System (ADS)

Lei, Qinghua; Gao, Ke

2018-05-01

We quantitatively investigate the stress variability in fractured geological media under tectonic stresses. The fracture systems studied include synthetic fracture networks following power law length scaling and natural fracture patterns based on outcrop mapping. The stress field is derived from a finite-discrete element model, and its variability is analyzed using a set of mathematical formulations that honor the tensorial nature of stress data. We show that local stress perturbation, quantified by the Euclidean distance of a local stress tensor to the mean stress tensor, has a positive, linear correlation with local fracture intensity, defined as the total fracture length per unit area within a local sampling window. We also evaluate the stress dispersion of the entire stress field using the effective variance, that is, a scalar-valued measure of the overall stress variability. The results show that a well-connected fracture system under a critically stressed state exhibits strong local and global stress variabilities.

Fast multipole method using Cartesian tensor in beam dynamic simulation

DOE PAGES

Zhang, He; Huang, He; Li, Rui; ...

2017-03-06

Here, the fast multipole method (FMM) using traceless totally symmetric Cartesian tensor to calculate the Coulomb interaction between charged particles will be presented. The Cartesian tensor-based FMM can be generalized to treat other non-oscillating interactions with the help of the differential algebra or the truncated power series algebra. Issues on implementation of the FMM in beam dynamic simulations are also discussed.

Molecular Eigensolution Symmetry Analysis and Fine Structure

PubMed Central

Harter, William G.; Mitchell, Justin C.

2013-01-01

Spectra of high-symmetry molecules contain fine and superfine level cluster structure related to J-tunneling between hills and valleys on rovibronic energy surfaces (RES). Such graphic visualizations help disentangle multi-level dynamics, selection rules, and state mixing effects including widespread violation of nuclear spin symmetry species. A review of RES analysis compares it to that of potential energy surfaces (PES) used in Born–Oppenheimer approximations. Both take advantage of adiabatic coupling in order to visualize Hamiltonian eigensolutions. RES of symmetric and D2 asymmetric top rank-2-tensor Hamiltonians are compared with Oh spherical top rank-4-tensor fine-structure clusters of 6-fold and 8-fold tunneling multiplets. Then extreme 12-fold and 24-fold multiplets are analyzed by RES plots of higher rank tensor Hamiltonians. Such extreme clustering is rare in fundamental bands but prevalent in hot bands, and analysis of its superfine structure requires more efficient labeling and a more powerful group theory. This is introduced using elementary examples involving two groups of order-6 (C6 and D3~C3v), then applied to families of Oh clusters in SF6 spectra and to extreme clusters. PMID:23344041

Symmetry breaking in tensor models

NASA Astrophysics Data System (ADS)

Benedetti, Dario; Gurau, Razvan

2015-11-01

In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical point corresponds to a phase transition in the tensor model associated to a breaking of the unitary symmetry. We analyze the model in the two phases and prove that, in a double scaling limit, the symmetric phase corresponds to a theory of infinitely refined random surfaces, while the broken phase corresponds to a theory of infinitely refined random nodal surfaces. At leading order in the double scaling limit planar surfaces dominate in the symmetric phase, and planar nodal surfaces dominate in the broken phase.

Diffusion tensor analysis with invariant gradients and rotation tangents.

PubMed

Kindlmann, Gordon; Ennis, Daniel B; Whitaker, Ross T; Westin, Carl-Fredrik

2007-11-01

Guided by empirically established connections between clinically important tissue properties and diffusion tensor parameters, we introduce a framework for decomposing variations in diffusion tensors into changes in shape and orientation. Tensor shape and orientation both have three degrees-of-freedom, spanned by invariant gradients and rotation tangents, respectively. As an initial demonstration of the framework, we create a tunable measure of tensor difference that can selectively respond to shape and orientation. Second, to analyze the spatial gradient in a tensor volume (a third-order tensor), our framework generates edge strength measures that can discriminate between different neuroanatomical boundaries, as well as creating a novel detector of white matter tracts that are adjacent yet distinctly oriented. Finally, we apply the framework to decompose the fourth-order diffusion covariance tensor into individual and aggregate measures of shape and orientation covariance, including a direct approximation for the variance of tensor invariants such as fractional anisotropy.

Effective field theory of statistical anisotropies for primordial bispectrum and gravitational waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rostami, Tahereh; Karami, Asieh; Firouzjahi, Hassan, E-mail: t.rostami@ipm.ir, E-mail: karami@ipm.ir, E-mail: firouz@ipm.ir

2017-06-01

We present the effective field theory studies of primordial statistical anisotropies in models of anisotropic inflation. The general action in unitary gauge is presented to calculate the leading interactions between the gauge field fluctuations, the curvature perturbations and the tensor perturbations. The anisotropies in scalar power spectrum and bispectrum are calculated and the dependence of these anisotropies to EFT couplings are presented. In addition, we calculate the statistical anisotropy in tensor power spectrum and the scalar-tensor cross correlation. Our EFT approach incorporates anisotropies generated in models with non-trivial speed for the gauge field fluctuations and sound speed for scalar perturbationsmore » such as in DBI inflation.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bolis, Nadia; Albrecht, Andreas; Holman, R.

We consider the effects of entanglement in the initial quantum state of scalar and tensor fluctuations during inflation. We allow the gauge-invariant scalar and tensor fluctuations to be entangled in the initial state and compute modifications to the various cosmological power spectra. We compute the angular power spectra (C{sub l}’s) for some specific cases of our entangled state and discuss what signals one might expect to find in CMB data. This entanglement also can break rotational invariance, allowing for the possibility that some of the large scale anomalies in the CMB power spectrum might be explained by this mechanism.

Anisotropic tensor power spectrum at interferometer scales induced by tensor squeezed non-Gaussianity

NASA Astrophysics Data System (ADS)

Ricciardone, Angelo; Tasinato, Gianmassimo

2018-02-01

We develop a scenario of inflation with spontaneously broken time and space diffeomorphisms, with distinctive features for the primordial tensor modes. Inflationary tensor fluctuations are not conserved outside the horizon, and can acquire a mass during the inflationary epoch. They can evade the Higuchi bound around de Sitter space, thanks to interactions with the fields driving expansion. Correspondingly, the primordial stochastic gravitational wave background (SGWB) is characterised by a tuneable scale dependence, and can be detectable at interferometer scales. In this set-up, tensor non-Gaussianity can be parametrically enhanced in the squeezed limit. This induces a coupling between long and short tensor modes, leading to a specific quadrupolar anisotropy in the primordial SGWB spectrum, which can be used to build estimators for tensor non-Gaussianity. We analyse how our inflationary system can be tested with interferometers, also discussing how an interferometer can be sensitive to a primordial anisotropic SGWB.

The TT, TB, EB and BB correlations in anisotropic inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Xingang; Emami, Razieh; Firouzjahi, Hassan

2014-08-01

The ongoing and future experiments will measure the B-mode from different sky coverage and frequency bands, with the potential to reveal non-trivial features in polarization map. In this work we study the TT, TB, EB and BB correlations associated with the B-mode polarization of CMB map in models of charged anisotropic inflation. The model contains a chaotic-type large field complex inflaton which is charged under the U(1) gauge field. We calculate the statistical anisotropies generated in the power spectra of the curvature perturbation, the tensor perturbation and their cross-correlation. It is shown that the asymmetry in tensor power spectrum ismore » a very sensitive probe of the gauge coupling. While the level of statistical anisotropy in temperature power spectrum can be small and satisfy the observational bounds, the interactions from the gauge coupling can induce large directional dependence in tensor modes. This will leave interesting anisotropic fingerprints in various correlations involving the B-mode polarization such as the TB cross-correlation which may be detected in upcoming Planck polarization data. In addition, the TT correlation receives an anisotropic contribution from the tensor sector which naturally decays after l ∼> 100. We expect that the mechanism of using tensor sector to induce asymmetry at low l to be generic which can also be applied to address other low l CMB anomalies.« less

Anisotropy tensor of the potential model of steady creep

NASA Astrophysics Data System (ADS)

Annin, B. D.; Ostrosablin, N. I.

2014-01-01

The Kelvin approach describing the structure of the generalized Hooke's law is used to analyze the potential model of anisotropic creep of materials. The creep equations of incompressible transversely isotropic, orthotropic materials and those with cubic symmetry are considered. The eigen coefficients of anisotropy and eigen tensors for the anisotropy tensors of these materials are determined.

An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolda, Tamara G.; Mayo, Jackson R.

2014-12-11

Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson, and Zhang [J. Math. Anal. Appl., 350 (2009), pp. 416--422]. Given mth-order, n-dimensional real-valued symmetric tensorsmore » $${\\mathscr{A}}$$ and $$\\boldsymbol{\\mathscr{B}}$$, the goal is to find $$\\lambda \\in \\mathbb{R}$$ and $$\\mathbf{x} \\in \\mathbb{R}^{n}, \\mathbf{x} \

Killing(-Yano) tensors in string theory

NASA Astrophysics Data System (ADS)

Chervonyi, Yuri; Lunin, Oleg

2015-09-01

We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors encode the symmetries beyond isometries, which lead to insights into dynamics of particles and fields on a given geometry by providing a set of conserved quantities. By analyzing the eigenvalues of the Killing tensor, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing tensors in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) tensors under string dualities, and find the unique modification of the Killing-Yano equation consistent with these symmetries. These results are used to construct the explicit form of the Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.

Gravitational waves from inflation

NASA Astrophysics Data System (ADS)

Guzzetti, M. C.; Bartolo, N.; Liguori, M.; Matarrese, S.

2016-09-01

The production of a stochastic background of gravitational waves is a fundamental prediction of any cosmological inflationary model. The features of such a signal encode unique information about the physics of the Early Universe and beyond, thus representing an exciting, powerful window on the origin and evolution of the Universe. We review the main mechanisms of gravitational-wave production, ranging from quantum fluctuations of the gravitational field to other mechanisms that can take place during or after inflation. These include e.g. gravitational waves generated as a consequence of extra particle production during inflation, or during the (p)reheating phase. Gravitational waves produced in inflation scenarios based on modified gravity theories and second-order gravitational waves are also considered. For each analyzed case, the expected power spectrum is given. We discuss the discriminating power among different models, associated with the validity/violation of the standard consistency relation between tensor-to-scalar ratio r and tensor spectral index nT. In light of the prospects for (directly/indirectly) detecting primordial gravitational waves, we give the expected present-day gravitational radiation spectral energy-density, highlighting the main characteristics imprinted by the cosmic thermal history, and we outline the signatures left by gravitational waves on the Cosmic Microwave Background and some imprints in the Large-Scale Structure of the Universe. Finally, current bounds and prospects of detection for inflationary gravitational waves are summarized.

TNSPackage: A Fortran2003 library designed for tensor network state methods

NASA Astrophysics Data System (ADS)

Dong, Shao-Jun; Liu, Wen-Yuan; Wang, Chao; Han, Yongjian; Guo, G.-C.; He, Lixin

2018-07-01

Recently, the tensor network states (TNS) methods have proven to be very powerful tools to investigate the strongly correlated many-particle physics in one and two dimensions. The implementation of TNS methods depends heavily on the operations of tensors, including contraction, permutation, reshaping tensors, SVD and so on. Unfortunately, the most popular computer languages for scientific computation, such as Fortran and C/C++ do not have a standard library for such operations, and therefore make the coding of TNS very tedious. We develop a Fortran2003 package that includes all kinds of basic tensor operations designed for TNS. It is user-friendly and flexible for different forms of TNS, and therefore greatly simplifies the coding work for the TNS methods.

In situ observations of the scale-size of plasma turbulence in the asteroid belt /1.6-3 astronomical units/

NASA Technical Reports Server (NTRS)

Intriligator, D. S.

1975-01-01

Pioneer 10 observations from the Ames Research Center Plasma Analyzer experiment between 1 and 3 AU in 1972 have been used to estimate the power spectra of the streaming speed of solar wind protons. A power-law spectrum is obtained in the 10,000 to 0.001 Hz frequency range which is similar to that obtained for the solar wind proton number density and streaming speed at 1 AU in 1965 December and 1966 January. The power spectra indicate that significant turbulence on the scale of about 1,000,000 km or more is present throughout this range of heliocentric distances, implying the importance of the role of large-scale turbulence between 1 and 3 AU. The power spectra also present qualitatively information concerning the cosmic-ray diffusion tensor at these extended distances.

DBI in the Sky

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alishahiha, M

2004-04-19

We analyze the spectrum of density perturbations generated in models of the recently discovered ''D-cceleration'' mechanism of inflation. In this scenario, strong coupling quantum field theoretic effects sum to provide a DBI-like action for the inflaton. We show that the model has a strict lower bound on the non-Gaussianity of the CMBR power spectrum at an observable level, and is thus falsifiable. This in particular observationally distinguishes this mechanism from traditional slow roll inflation generated by weakly interacting scalar fields. The model also favors a large observable tensor component to the CMBR spectrum.

Null conformal Killing-Yano tensors and Birkhoff theorem

NASA Astrophysics Data System (ADS)

Ferrando, Joan Josep; Sáez, Juan Antonio

2016-04-01

We study the space-times admitting a null conformal Killing-Yano tensor whose divergence defines a Killing vector. We analyze the similarities and differences with the recently studied non null case (Ferrando and Sáez in Gen Relativ Gravit 47:1911, 2015). The results by Barnes concerning the Birkhoff theorem for the case of null orbits are analyzed and generalized.

The Twist Tensor Nuclear Norm for Video Completion.

PubMed

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.

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

NASA Astrophysics Data System (ADS)

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.

A Review of Tensors and Tensor Signal Processing

NASA Astrophysics Data System (ADS)

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.

Dark neutrino interactions make gravitational waves blue

NASA Astrophysics Data System (ADS)

Ghosh, Subhajit; Khatri, Rishi; Roy, Tuhin S.

2018-03-01

New interactions of neutrinos can stop them from free-streaming in the early Universe even after the weak decoupling epoch. This results in the enhancement of the primordial gravitational wave amplitude on small scales compared to the standard Λ CDM prediction. In this paper, we calculate the effect of dark matter neutrino interactions in CMB tensor B -modes spectrum. We show that the effect of new neutrino interactions generates a scale- or ℓ-dependent imprint in the CMB B -modes power spectrum at ℓ≳100 . In the event that primordial B -modes are detected by future experiments, a departure from scale invariance, with a blue spectrum, may not necessarily mean failure of simple inflationary models but instead may be a sign of nonstandard interactions of relativistic particles. New interactions of neutrinos also induce a phase shift in the CMB B -mode power spectrum which cannot be mimicked by simple modifications of the primordial tensor power spectrum. There is rich information hidden in the CMB B -modes spectrum beyond just the tensor-to-scalar ratio.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Yi; Xue, Wei, E-mail: yw366@cam.ac.uk, E-mail: wei.xue@sissa.it

We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmology predicts blue tensor spectrum with highly Gaussian fluctuations. If further experimentsmore » do confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test between inflation and alternatives.« less

A gravitational energy–momentum and the thermodynamic description of gravity

NASA Astrophysics Data System (ADS)

Acquaviva, G.; Kofroň, D.; Scholtz, M.

2018-05-01

A proposal for the gravitational energy–momentum tensor, known in the literature as the square root of Bel–Robinson tensor (SQBR), is analyzed in detail. Being constructed exclusively from the Weyl part of the Riemann tensor, such tensor encapsulates the geometric properties of free gravitational fields in terms of optical scalars of null congruences: making use of the general decomposition of any energy–momentum tensor, we explore the thermodynamic interpretation of such geometric quantities. While the matter energy–momentum is identically conserved due to Einstein’s field equations, the SQBR is not necessarily conserved and dissipative terms could arise in its vacuum continuity equation. We discuss the possible physical interpretations of such mathematical properties.

Scale Properties of Anisotropic and Isotropic Turbulence in the Urban Surface Layer

NASA Astrophysics Data System (ADS)

Liu, Hao; Yuan, Renmin; Mei, Jie; Sun, Jianning; Liu, Qi; Wang, Yu

2017-11-01

The scale properties of anisotropic and isotropic turbulence in the urban surface layer are investigated. A dimensionless anisotropic tensor is introduced and the turbulent tensor anisotropic coefficient, defined as C, where C = 3d3 + 1 (d3 is the minimum eigenvalue of the tensor) is used to characterize the turbulence anisotropy or isotropy. Turbulence is isotropic when C ≈ 1, and anisotropic when C ≪ 1. Three-dimensional velocity data collected using a sonic anemometer are analyzed to obtain the anisotropic characteristics of atmospheric turbulence in the urban surface layer, and the tensor anisotropic coefficient of turbulent eddies at different spatial scales calculated. The analysis shows that C is strongly dependent on atmospheric stability ξ = (z-zd)/L_{{it{MO}}}, where z is the measurement height, zd is the displacement height, and L_{{it{MO}}} is the Obukhov length. The turbulence at a specific scale in unstable conditions (i.e., ξ < 0) is closer to isotropic than that at the same scale under stable conditions. The maximum isotropic scale of turbulence is determined based on the characteristics of the power spectrum in three directions. Turbulence does not behave isotropically when the eddy scale is greater than the maximum isotropic scale, whereas it is horizontally isotropic at relatively large scales. The maximum isotropic scale of turbulence is compared to the outer scale of temperature, which is obtained by fitting the temperature fluctuation spectrum using the von Karman turbulent model. The results show that the outer scale of temperature is greater than the maximum isotropic scale of turbulence.

General theories of linear gravitational perturbations to a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Tattersall, Oliver J.; Ferreira, Pedro G.; Lagos, Macarena

2018-02-01

We use the covariant formulation proposed by Tattersall, Lagos, and Ferreira [Phys. Rev. D 96, 064011 (2017), 10.1103/PhysRevD.96.064011] to analyze the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasinormal modes of perturbed black holes may be affected by modifications to general relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyze odd parity (axial) and even parity (polar) perturbations simultaneously in a straightforward manner.

Dynamical analysis for a scalar-tensor model with kinetic and nonminimal couplings

NASA Astrophysics Data System (ADS)

Granda, L. N.; Jimenez, D. F.

We study the autonomous system for a scalar-tensor model of dark energy with nonminimal coupling to curvature and nonminimal kinetic coupling to the Einstein tensor. The critical points describe important stable asymptotic scenarios including quintessence, phantom and de Sitter attractor solutions. Two functional forms for the coupling functions and the scalar potential were considered: power-law and exponential functions of the scalar field. For power-law couplings, the restrictions on stable quintessence and phantom solutions lead to asymptotic freedom regime for the gravitational interaction. For the exponential functions, the stable quintessence, phantom or de Sitter solutions allow asymptotic behaviors where the effective Newtonian coupling can reach either the asymptotic freedom regime or constant value. The phantom solutions could be realized without appealing to ghost degrees of freedom. Transient inflationary and radiation dominated phases can also be described.

Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics.

PubMed

Greene, Samuel M; Batista, Victor S

2017-09-12

We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S 1 /S 2 interconversion dynamics of pyrazine after UV photoexcitation to the S 2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.

Investigations of Few-Nucleon System Dynamics in Medium Energy Domain

NASA Astrophysics Data System (ADS)

Ciepał, I.; Kłos, B.; Kistryn, St.; Stephan, E.; Biegun, A.; Bodek, K.; Deltuva, A.; Epelbaum, E.; Eslami-Kalantari, M.; Fonseca, A. C.; Golak, J.; Jha, V.; Kalantar-Nayestanaki, N.; Kamada, H.; Khatri, G.; Kirillov, Da.; Kirillov, Di.; Kliczewski, St.; Kozela, A.; Kravcikova, M.; Machner, H.; Magiera, A.; Martinska, G.; Messchendorp, J.; Nogga, A.; Parol, W.; Ramazani-Moghaddam-Arani, A.; Roy, B. J.; Sakai, H.; Sekiguchi, K.; Sitnik, I.; Siudak, R.; Skibiński, R.; Sworst, R.; Urban, J.; Witała, H.; Wrońska, A.; Zejma, J.

2013-08-01

Precise and large set of cross sections, vector A x , A y and tensor A xx , A xy , A yy analyzing powers for the 1 H( d, pp) n breakup reactions were measured at 100 and 130 MeV deuteron beam energies with the use of the SALAD and BINA detectors at KVI and Germanium Wall setup at FZ-Jülich. Results are compared with various theoretical approaches which model the three-nucleon (3N) system dynamics. The calculations are based on different two-nucleon (2N) potentials which can be combined with models of the three-nucleon force (3NF) and other pieces of the dynamics can also be included like the Coulomb interaction and relativistic effects. The cross sections data reveal seizable 3NF and Coulomb force influence. In case of analyzing powers very low sensitivity to the effects was found and the data are well describe by 2N models only. At 130 MeV for A xy serious disagreements appear when 3NF models are included into calculations.

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

NASA Astrophysics Data System (ADS)

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.

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

NASA Astrophysics Data System (ADS)

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

2018-07-01

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.

Obtaining orthotropic elasticity tensor using entries zeroing method.

NASA Astrophysics Data System (ADS)

Gierlach, Bartosz; Danek, Tomasz

2017-04-01

A generally anisotropic elasticity tensor obtained from measurements can be represented by a tensor belonging to one of eight material symmetry classes. Knowledge of symmetry class and orientation is helpful for describing physical properties of a medium. For each non-trivial symmetry class except isotropic this problem is nonlinear. A common method of obtaining effective tensor is a choosing its non-trivial symmetry class and minimizing Frobenius norm between measured and effective tensor in the same coordinate system. Global optimization algorithm has to be used to determine the best rotation of a tensor. In this contribution, we propose a new approach to obtain optimal tensor, with the assumption that it is orthotropic (or at least has a similar shape to the orthotropic one). In orthotropic form tensor 24 out of 36 entries are zeros. The idea is to minimize the sum of squared entries which are supposed to be equal to zero through rotation calculated with optimization algorithm - in this case Particle Swarm Optimization (PSO) algorithm. Quaternions were used to parametrize rotations in 3D space to improve computational efficiency. In order to avoid a choice of local minima we apply PSO several times and only if we obtain similar results for the third time we consider it as a correct value and finish computations. To analyze obtained results Monte-Carlo method was used. After thousands of single runs of PSO optimization, we obtained values of quaternion parts and plot them. Points concentrate in several points of the graph following the regular pattern. It suggests the existence of more complex symmetry in the analyzed tensor. Then thousands of realizations of generally anisotropic tensor were generated - each tensor entry was replaced with a random value drawn from normal distribution having a mean equal to measured tensor entry and standard deviation of the measurement. Each of these tensors was subject of PSO based optimization delivering quaternion for optimal rotation. Computations were parallelized with OpenMP to decrease computational time what enables different tensors to be processed by different threads. As a result the distributions of rotated tensor entries values were obtained. For the entries which were to be zeroed we can observe almost normal distributions having mean equal to zero or sum of two normal distributions having inverse means. Non-zero entries represent different distributions with two or three maxima. Analysis of obtained results shows that described method produces consistent values of quaternions used to rotate tensors. Despite of less complex target function in a process of optimization in comparison to common approach, entries zeroing method provides results which can be applied to obtain an orthotropic tensor with good reliability. Modification of the method can produce also a tool for obtaining effective tensors belonging to another symmetry classes. This research was supported by the Polish National Science Center under contract No. DEC-2013/11/B/ST10/0472.

Contribution of the polarization moments of different rank to the integral CPT signal

NASA Astrophysics Data System (ADS)

Taskova, E.; Alipieva, E.; Todorov, G.

2016-01-01

In the present work we investigate the relation of the polarization moments having different ranks with the tensor components which form the observable integral CPT signal, in the presence of a stray magnetic field. A numerical experiment with parameters close to the real ones is performed, using a program based on the irreducible tensor operator formalism1. The integral fluorescent signal is calculated for the non-polarized fluorescence at different laser power excitation. Detailed analysis of the numerical solutions for all tensor components which describe population and alignment allows visualizing the dynamics of their behavior in dependence on the experimental geometry and laboratory magnetic field B'. The dependence of population f00, longitudinal f02 and transverse f22 alignment in the presence of transverse magnetic field is investigated. The shape and sign of the resonance change with laser power.

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

NASA Astrophysics Data System (ADS)

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.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Durrer, Ruth; Tansella, Vittorio, E-mail: ruth.durrer@unige.ch, E-mail: vittorio.tansella@unige.ch

We derive the contribution to relativistic galaxy number count fluctuations from vector and tensor perturbations within linear perturbation theory. Our result is consistent with the the relativistic corrections to number counts due to scalar perturbation, where the Bardeen potentials are replaced with line-of-sight projection of vector and tensor quantities. Since vector and tensor perturbations do not lead to density fluctuations the standard density term in the number counts is absent. We apply our results to vector perturbations which are induced from scalar perturbations at second order and give numerical estimates of their contributions to the power spectrum of relativistic galaxymore » number counts.« less

Constant-roll tachyon inflation and observational constraints

NASA Astrophysics Data System (ADS)

Gao, Qing; Gong, Yungui; Fei, Qin

2018-05-01

For the constant-roll tachyon inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts and the tensor to scalar ratio to the first order of epsilon1 by using the method of Bessel function approximation. The derived ns-r results are compared with the observations, we find that only the constant-roll inflation with ηH being a constant is consistent with the observations and observations constrain the constant-roll inflation to be slow-roll inflation. The tachyon potential is also reconstructed for the constant-roll inflation which is consistent with the observations.

Inflation in Einstein-Cartan theory with energy-momentum tensor with spin

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Bradas, James C.; Smalley, Larry L.

1988-01-01

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic (Bianchi Type I) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley (RS) improved energy-momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density.

Lambda-universe in scalar-tensor gravity

NASA Astrophysics Data System (ADS)

Berman, Marcelo Samuel

2009-09-01

We present a lambda-Universe, in scalar-tensor gravity, reviewing Berman and Trevisan’s inflationary case (Berman and Trevisan in Int. J. Theor. Phys., 2009) and then we find a solution for an accelerating power-law scale-factor. The negativity of cosmic pressure implies acceleration of the expansion, even with Λ<0. The cosmological term, and the coupling “constant”, are in fact, time-varying.

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, He; Luo, Li -Shi; Li, Rui

To compute the non-oscillating mutual interaction for a systems with N points, the fast multipole method (FMM) has an efficiency that scales linearly with the number of points. Specifically, for Coulomb interaction, FMM can be constructed using either the spherical harmonic functions or the totally symmetric Cartesian tensors. In this paper, we will present that the effciency of the Cartesian tensor-based FMM for the Coulomb interaction can be significantly improved by implementing the traces of the Cartesian tensors in calculation to reduce the independent elements of the n-th rank totally symmetric Cartesian tensor from (n + 1)(n + 2)=2 tomore » 2n + 1. The computation complexity for the operations in FMM are analyzed and expressed as polynomials of the highest rank of the Cartesian tensors. For most operations, the complexity is reduced by one order. Numerical examples regarding the convergence and the effciency of the new algorithm are demonstrated. As a result, a reduction of computation time up to 50% has been observed for a moderate number of points and rank of tensors.« less

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

DOE PAGES

Huang, He; Luo, Li -Shi; Li, Rui; ...

2018-05-17

To compute the non-oscillating mutual interaction for a systems with N points, the fast multipole method (FMM) has an efficiency that scales linearly with the number of points. Specifically, for Coulomb interaction, FMM can be constructed using either the spherical harmonic functions or the totally symmetric Cartesian tensors. In this paper, we will present that the effciency of the Cartesian tensor-based FMM for the Coulomb interaction can be significantly improved by implementing the traces of the Cartesian tensors in calculation to reduce the independent elements of the n-th rank totally symmetric Cartesian tensor from (n + 1)(n + 2)=2 tomore » 2n + 1. The computation complexity for the operations in FMM are analyzed and expressed as polynomials of the highest rank of the Cartesian tensors. For most operations, the complexity is reduced by one order. Numerical examples regarding the convergence and the effciency of the new algorithm are demonstrated. As a result, a reduction of computation time up to 50% has been observed for a moderate number of points and rank of tensors.« less

The role of tensor force in heavy-ion fusion dynamics

NASA Astrophysics Data System (ADS)

Guo, Lu; Simenel, Cédric; Shi, Long; Yu, Chong

2018-07-01

The tensor force is implemented into the time-dependent Hartree-Fock (TDHF) theory so that both exotic and stable collision partners, as well as their dynamics in heavy-ion fusion, can be described microscopically. The role of tensor force on fusion dynamics is systematically investigated for 40Ca +40Ca , 40Ca +48Ca , 48Ca +48Ca , 48Ca +56Ni , and 56Ni +56Ni reactions which vary by the total number of spin-unsaturated magic numbers in target and projectile. A notable effect on fusion barriers and cross sections is observed by the inclusion of tensor force. The origin of this effect is analyzed. The influence of isoscalar and isovector tensor terms is investigated with the TIJ forces. These effects of tensor force in fusion dynamics are essentially attributed to the shift of low-lying vibration states of colliding partners and nucleon transfer in the asymmetric reactions. Our calculations of above-barrier fusion cross sections also show that tensor force does not significantly affect the dynamical dissipation at near-barrier energies.

Induced vacuum energy-momentum tensor in the background of a cosmic string

NASA Astrophysics Data System (ADS)

Sitenko, Yu A.; Vlasii, N. D.

2012-05-01

A massive scalar field is quantized in the background of a cosmic string which is generalized to a static flux-carrying codimension-2 brane in the locally flat multidimensional spacetime. We find that the finite energy-momentum tensor is induced in the vacuum. The dependence of the tensor components on the brane flux and tension, as well as on the coupling to the spacetime curvature scalar, is comprehensively analyzed. The tensor components are holomorphic functions of space dimension, decreasing exponentially with the distance from the brane. The case of the massless quantized scalar field is also considered, and the relevance of Bernoulli’s polynomials of even order for this case is discussed.

Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

NASA Astrophysics Data System (ADS)

Mukherjee, Suvodip; Das, Santanu; Joy, Minu; Souradeep, Tarun

2015-01-01

Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass meff for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation νt and change in spectral index for scalar perturbation νst to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r<0.1 or r<0.01) for a scalar spectral index of ns=0.96 by having a non-zero value of effective mass of the inflaton field m2eff/H2. The analysis with WP + Planck likelihood shows a non-zero detection of m2eff/H2 with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m2eff/H2 = -0.0237 ± 0.0135 which is consistent with zero.

Evidence for Bouncing Evolution Before Inflation After BICEP2

NASA Astrophysics Data System (ADS)

Xia, Jun-Qing; Cai, Yi-Fu; Li, Hong; Zhang, Xinmin

2014-06-01

The BICEP2 Collaboration reports a detection of primordial cosmic microwave background (CMB) B mode with a tensor-to-scalar ratio r =0.20-0.05+0.07 (68% C.L.). However, this result disagrees with the recent Planck limit r<0.11 (95% C.L.) on constraining inflation models. In this Letter we consider an inflationary cosmology with a preceding nonsingular bounce, which gives rise to observable signatures on primordial perturbations. One interesting phenomenon is that both the primordial scalar and tensor modes can have a step feature on their power spectra, which nicely cancels the tensor excess power on the CMB temperature power spectrum. By performing a global analysis, we obtain the 68% C.L. constraints on the parameters of the model from the Planck+WP and BICEP2 data together: the jump scale log10(kB/Mpc-1)=-2.4±0.2 and the spectrum amplitude ratio of bounce to inflation rB≡Pm/As=0.71±0.09. Our result reveals that the bounce inflation scenario can simultaneously explain the Planck and BICEP2 observations better than the standard cold dark matter model with a cosmological constant, and can be verified by future CMB polarization measurements.

Parallel Flux Tensor Analysis for Efficient Moving Object Detection

DTIC Science & Technology

2011-07-01

computing as well as parallelization to enable real time performance in analyzing complex video [3, 4 ]. There are a number of challenging computer vision... 4 . TITLE AND SUBTITLE Parallel Flux Tensor Analysis for Efficient Moving Object Detection 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT...We use the trace of the flux tensor matrix, referred to as Tr JF , that is defined below, Tr JF = ∫ Ω W (x− y)(I2xt(y) + I2yt(y) + I2tt(y))dy ( 4 ) as

Tensor scale: An analytic approach with efficient computation and applications☆

PubMed Central

Xu, Ziyue; Saha, Punam K.; Dasgupta, Soura

2015-01-01

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods. PMID:26236148

Separability of black holes in string theory

NASA Astrophysics Data System (ADS)

Keeler, Cynthia; Larsen, Finn

2012-10-01

We analyze the origin of separability for rotating black holes in string theory, considering both massless and massive geodesic equations as well as the corresponding wave equations. We construct a conformal Killing-Stackel tensor for a general class of black holes with four independent charges, then identify two-charge configurations where enhancement to an exact Killing-Stackel tensor is possible. We show that further enhancement to a conserved Killing-Yano tensor is possible only for the special case of Kerr-Newman black holes. We construct natural null congruences for all these black holes and use the results to show that only the Kerr-Newman black holes are algebraically special in the sense of Petrov. Modifying the asymptotic behavior by the subtraction procedure that induces an exact SL(2)2 also preserves only the conformal Killing-Stackel tensor. Similarly, we find that a rotating Kaluza-Klein black hole possesses a conformal Killing-Stackel tensor but has no further enhancements.

A defect in holographic interpretations of tensor networks

NASA Astrophysics Data System (ADS)

Czech, Bartlomiej; Nguyen, Phuc H.; Swaminathan, Sivaramakrishnan

2017-03-01

We initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain tensors require updating. On the other hand, even identical tensors can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating tensor updates to turning on non-normalizable modes in the bulk. In passing, we also clarify and complement existing arguments in support of the theory of minimal updates, propose a novel ansatz called rayed MERA that applies to a class of generalized interface CFTs, and analyze the kinematic spaces of the thin wall and AdS3-Janus geometries.

Conditional Spectral Analysis of Replicated Multiple Time Series with Application to Nocturnal Physiology.

PubMed

Krafty, Robert T; Rosen, Ori; Stoffer, David S; Buysse, Daniel J; Hall, Martica H

2017-01-01

This article considers the problem of analyzing associations between power spectra of multiple time series and cross-sectional outcomes when data are observed from multiple subjects. The motivating application comes from sleep medicine, where researchers are able to non-invasively record physiological time series signals during sleep. The frequency patterns of these signals, which can be quantified through the power spectrum, contain interpretable information about biological processes. An important problem in sleep research is drawing connections between power spectra of time series signals and clinical characteristics; these connections are key to understanding biological pathways through which sleep affects, and can be treated to improve, health. Such analyses are challenging as they must overcome the complicated structure of a power spectrum from multiple time series as a complex positive-definite matrix-valued function. This article proposes a new approach to such analyses based on a tensor-product spline model of Cholesky components of outcome-dependent power spectra. The approach exibly models power spectra as nonparametric functions of frequency and outcome while preserving geometric constraints. Formulated in a fully Bayesian framework, a Whittle likelihood based Markov chain Monte Carlo (MCMC) algorithm is developed for automated model fitting and for conducting inference on associations between outcomes and spectral measures. The method is used to analyze data from a study of sleep in older adults and uncovers new insights into how stress and arousal are connected to the amount of time one spends in bed.

A tensor analysis to evaluate the effect of high-pull headgear on Class II malocclusions.

PubMed

Ngan, P; Scheick, J; Florman, M

1993-03-01

The inaccuracies inherent in cephalometric analysis of treatment effects are well known. The objective of this article is to present a more reliable research tool in the analysis of cephalometric data. Bookstein introduced a dilation function by means of a homogeneous deformation tensor as a method of describing changes in cephalometric data. His article gave an analytic description of the deformation tensor that permits the rapid and highly accurate calculation of it on a desktop computer. The first part of this article describes the underlying ideas and mathematics. The second part uses the tensor analysis to analyze the cephalometric results of a group of patients treated with high-pull activator (HPA) to demonstrate the application of this research tool. Eight patients with Class II skeletal open bite malocclusions in the mixed dentition were treated with HPA. A control sample consisting of eight untreated children with Class II who were obtained from The Ohio State University Growth Study was used as a comparison group. Lateral cephalograms taken before and at the completion of treatment were traced, digitized, and analyzed with the conventional method and tensor analysis. The results showed that HPA had little or no effect on maxillary skeletal structures. However, reduction in growth rate was found with the skeletal triangle S-N-A, indicating a posterior tipping and torquing of the maxillary incisors. The treatment also induced additional deformation on the mandible in a downward and slightly forward direction. Together with the results from the conventional cephalometric analysis, HPA seemed to provide the vertical and rotational control of the maxilla during orthopedic Class II treatment by inhibiting the downward and forward eruptive path of the upper posterior teeth. The newly designed computer software permits rapid analysis of cephalometric data with the tensor analysis on a desktop computer. This tool may be useful in analyzing growth changes for research data.

Correcting power and p-value calculations for bias in diffusion tensor imaging.

PubMed

Lauzon, Carolyn B; Landman, Bennett A

2013-07-01

Diffusion tensor imaging (DTI) provides quantitative parametric maps sensitive to tissue microarchitecture (e.g., fractional anisotropy, FA). These maps are estimated through computational processes and subject to random distortions including variance and bias. Traditional statistical procedures commonly used for study planning (including power analyses and p-value/alpha-rate thresholds) specifically model variability, but neglect potential impacts of bias. Herein, we quantitatively investigate the impacts of bias in DTI on hypothesis test properties (power and alpha-rate) using a two-sided hypothesis testing framework. We present theoretical evaluation of bias on hypothesis test properties, evaluate the bias estimation technique SIMEX for DTI hypothesis testing using simulated data, and evaluate the impacts of bias on spatially varying power and alpha rates in an empirical study of 21 subjects. Bias is shown to inflame alpha rates, distort the power curve, and cause significant power loss even in empirical settings where the expected difference in bias between groups is zero. These adverse effects can be attenuated by properly accounting for bias in the calculation of power and p-values. Copyright © 2013 Elsevier Inc. All rights reserved.

Protein Structure Determination from Pseudocontact Shifts Using ROSETTA

PubMed Central

Schmitz, Christophe; Vernon, Robert; Otting, Gottfried; Baker, David; Huber, Thomas

2013-01-01

Paramagnetic metal ions generate pseudocontact shifts (PCSs) in nuclear magnetic resonance spectra that are manifested as easily measurable changes in chemical shifts. Metals can be incorporated into proteins through metal binding tags, and PCS data constitute powerful long-range restraints on the positions of nuclear spins relative to the coordinate system of the magnetic susceptibility anisotropy tensor (Δχ-tensor) of the metal ion. We show that three-dimensional structures of proteins can reliably be determined using PCS data from a single metal binding site combined with backbone chemical shifts. The program PCS-ROSETTA automatically determines the Δχ-tensor and metal position from the PCS data during the structure calculations, without any prior knowledge of the protein structure. The program can determine structures accurately for proteins of up to 150 residues, offering a powerful new approach to protein structure determination that relies exclusively on readily measurable backbone chemical shifts and easily discriminates between correctly and incorrectly folded conformations. PMID:22285518

Forecasting sensitivity on tilt of power spectrum of primordial gravitational waves after Planck satellite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Qing-Guo; Wang, Sai; Zhao, Wen, E-mail: huangqg@itp.ac.cn, E-mail: wangsai@itp.ac.cn, E-mail: wzhao7@ustc.edu.cn

2015-10-01

By taking into account the contamination of foreground radiations, we employ the Fisher matrix to forecast the future sensitivity on the tilt of power spectrum of primordial tensor perturbations for several ground-based (AdvACT, CLASS, Keck/BICEP3, Simons Array, SPT-3G), balloon-borne (EBEX, Spider) and satellite (CMBPol, COrE, LiteBIRD) experiments of B-mode polarizations. For the fiducial model n{sub t}=0, our results show that the satellite experiments give good sensitivity on the tensor tilt n{sub t} to the level σ{sub n{sub t}}∼<0.1 for r∼>2×10{sup −3}, while the ground-based and balloon-borne experiments give worse sensitivity. By considering the BICEP2/Keck Array and Planck (BKP) constraint onmore » the tensor-to-scalar ratio r, we see that it is impossible for these experiments to test the consistency relation n{sub t}=−r/8 in the canonical single-field slow-roll inflation models.« less

Forward modeling and inversion of tensor CSAMT in 3D anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Tao; Wang, Kun-Peng; Tan, Han-Dong

2017-12-01

Tensor controlled-source audio-frequency magnetotellurics (CSAMT) can yield information about electric and magnetic fields owing to its multi-transmitter configuration compared with the common scalar CSAMT. The most current theories, numerical simulations, and inversion of tensor CSAMT are based on far-field measurements and the assumption that underground media have isotropic resistivity. We adopt a three-dimensional (3D) staggered-grid finite difference numerical simulation method to analyze the resistivity in axial anisotropic and isotropic media. We further adopt the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method to perform 3D tensor CSAMT axial anisotropic inversion. The inversion results suggest that when the underground structure is anisotropic, the isotropic inversion will introduce errors to the interpretation.

Tensor distribution function

NASA Astrophysics Data System (ADS)

Leow, Alex D.; Zhu, Siwei

2008-03-01

Diffusion weighted MR imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitizing gradients along a minimum of 6 directions, second-order tensors (represetnted by 3-by-3 positive definiite matrices) can be computed to model dominant diffusion processes. However, it has been shown that conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g. crossing fiber tracts. More recently, High Angular Resolution Diffusion Imaging (HARDI) seeks to address this issue by employing more than 6 gradient directions. To account for fiber crossing when analyzing HARDI data, several methodologies have been introduced. For example, q-ball imaging was proposed to approximate Orientation Diffusion Function (ODF). Similarly, the PAS method seeks to reslove the angular structure of displacement probability functions using the maximum entropy principle. Alternatively, deconvolution methods extract multiple fiber tracts by computing fiber orientations using a pre-specified single fiber response function. In this study, we introduce Tensor Distribution Function (TDF), a probability function defined on the space of symmetric and positive definite matrices. Using calculus of variations, we solve for the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, ODF can easily be computed by analytical integration of the resulting displacement probability function. Moreover, principle fiber directions can also be directly derived from the TDF.

On the running of the spectral index to all orders: a new model-dependent approach to constrain inflationary models

NASA Astrophysics Data System (ADS)

Zarei, Moslem

2016-06-01

In conventional model-independent approaches, the power spectrum of primordial perturbations is characterized by such free parameters as the spectral index, its running, the running of running, and the tensor-to-scalar ratio. In this work we show that, at least for simple inflationary potentials, one can find the primordial scalar and tensor power spectra exactly by resumming over all the running terms. In this model-dependent method, we expand the power spectra about the pivot scale to find the series terms as functions of the e-folding number for some single field models of inflation. Interestingly, for the viable models studied here, one can sum over all the terms and evaluate the exact form of the power spectra. This in turn gives more accurate parametrization of the specific models studied in this work. We finally compare our results with recent cosmic microwave background data to find that our new power spectra are in good agreement with the data.

Observing the inflation potential. [in models of cosmological inflation

NASA Technical Reports Server (NTRS)

Copeland, Edmund J.; Kolb, Edward W.; Liddle, Andrew R.; Lidsey, James E.

1993-01-01

We show how observations of the density perturbation (scalar) spectrum and the gravitational wave (tensor) spectrum allow a reconstruction of the potential responsible for cosmological inflation. A complete functional reconstruction or a perturbative approximation about a single scale are possible; the suitability of each approach depends on the data available. Consistency equations between the scalar and tensor spectra are derived, which provide a powerful signal of inflation.

Studies of the Three-Nucleon System Dynamics in the Deuteron-Proton Breakup Reaction

NASA Astrophysics Data System (ADS)

Ciepał, I.; Kłos, B.; Stephan, E.; Kistryn, St.; Biegun, A.; Bodek, K.; Deltuva, A.; Epelbaum, E.; Eslami-Kalantari, M.; Fonseca, A. C.; Golak, J.; Jha, V.; Kalantar-Nayestanaki, N.; Kamada, H.; Khatri, G.; Kirillov, Da.; Kirillov, Di.; Kliczewski, St.; Kozela, A.; Kravcikova, M.; Machner, H.; Magiera, A.; Martinska, G.; Messchendorp, J.; Nogga, A.; Parol, W.; Ramazani-Moghaddam-Arani, A.; Roy, B. J.; Sakai, H.; Sekiguchi, K.; Sitnik, I.; Siudak, R.; Skibiński, R.; Sworst, R.; Urban, J.; Witała, H.; Zejma, J.

2014-03-01

One of the most important goals of modern nuclear physics is to contruct nuclear force model which properly describes the experimental data. To develop and test predictions of current models the breakup 1H(overrightarrow d, pp)n reaction was investigated experimentally at 100 and 130 MeV deuteron beam energies. Rich set of data for cross section, vector and tensor analyzing powers was obtained with the use of the SALAD and BINA detectors at KVI and Germanium Wall setup at FZ-Jülich. Results are compared with various theoretical approaches which describe the three-nucleon (3N) system dynamics. For correct description of the cross section data both, three-nucleon force (3NF) and Coulomb force, have to be included into calculations and influence of those ingredients is seizable at specific parts of the phase space. In case of the vector analyzing powers very low sensitivity to any effects beyond nucleon-nucleon interaction was found. At 130 MeV, the Axy data are not correctly described when 3NF models are included into calculations.

Using tensor-based morphometry to detect structural brain abnormalities in rats with adolescent intermittent alcohol exposure

NASA Astrophysics Data System (ADS)

Paniagua, Beatriz; Ehlers, Cindy; Crews, Fulton; Budin, Francois; Larson, Garrett; Styner, Martin; Oguz, Ipek

2011-03-01

Understanding the effects of adolescent binge drinking that persist into adulthood is a crucial public health issue. Adolescent intermittent ethanol exposure (AIE) is an animal model that can be used to investigate these effects in rodents. In this work, we investigate the application of a particular image analysis technique, tensor-based morphometry, for detecting anatomical differences between AIE and control rats using Diffusion Tensor Imaging (DTI). Deformation field analysis is a popular method for detecting volumetric changes analyzing Jacobian determinants calculated on deformation fields. Recent studies showed that computing deformation field metrics on the full deformation tensor, often referred to as tensor-based morphometry (TBM), increases the sensitivity to anatomical differences. In this paper we conduct a comprehensive TBM study for precisely locating differences between control and AIE rats. Using a DTI RARE sequence designed for minimal geometric distortion, 12-directional images were acquired postmortem for control and AIE rats (n=9). After preprocessing, average images for the two groups were constructed using an unbiased atlas building approach. We non-rigidly register the two atlases using Large Deformation Diffeomorphic Metric Mapping, and analyze the resulting deformation field using TBM. In particular, we evaluate the tensor determinant, geodesic anisotropy, and deformation direction vector (DDV) on the deformation field to detect structural differences. This yields data on the local amount of growth, shrinkage and the directionality of deformation between the groups. We show that TBM can thus be used to measure group morphological differences between rat populations, demonstrating the potential of the proposed framework.

Monitoring the refinement of crystal structures with {sup 15}N solid-state NMR shift tensor data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalakewich, Keyton; Eloranta, Harriet; Harper, James K.

The {sup 15}N chemical shift tensor is shown to be extremely sensitive to lattice structure and a powerful metric for monitoring density functional theory refinements of crystal structures. These refinements include lattice effects and are applied here to five crystal structures. All structures improve based on a better agreement between experimental and calculated {sup 15}N tensors, with an average improvement of 47.0 ppm. Structural improvement is further indicated by a decrease in forces on the atoms by 2–3 orders of magnitude and a greater similarity in atom positions to neutron diffraction structures. These refinements change bond lengths by more thanmore » the diffraction errors including adjustments to X–Y and X–H bonds (X, Y = C, N, and O) of 0.028 ± 0.002 Å and 0.144 ± 0.036 Å, respectively. The acquisition of {sup 15}N tensors at natural abundance is challenging and this limitation is overcome by improved {sup 1}H decoupling in the FIREMAT method. This decoupling dramatically narrows linewidths, improves signal-to-noise by up to 317%, and significantly improves the accuracy of measured tensors. A total of 39 tensors are measured with shifts distributed over a range of more than 400 ppm. Overall, experimental {sup 15}N tensors are at least 5 times more sensitive to crystal structure than {sup 13}C tensors due to nitrogen’s greater polarizability and larger range of chemical shifts.« less

Spatial and Temporal Variations in the Moment Tensor Solutions of the 2008 Wenchuan Earthquake Aftershocks and Their Tectonic Implications

NASA Astrophysics Data System (ADS)

Lin, X.; Dreger, D.; Ge, H.; Xu, P.; Wu, M.; Chiang, A.; Zhao, G.; Yuan, H.

2018-03-01

Following the mainshock of the 2008 M8 Wenchuan Earthquake, there were more than 300 ML ≥ 4.0 aftershocks that occurred between 12 May 2008 and 8 September 2010. We analyzed the broadband waveforms for these events and found 160 events with sufficient signal-to-noise levels to invert for seismic moment tensors. Considering the length of the activated fault and the distances to the recording stations, four velocity models were employed to account for variability in crustal structure. The moment tensor solutions show considerable variations with a mixture of mainly reverse and strike-slip mechanisms and a small number of normal events and ambiguous events. We analyzed the spatial and temporal distribution of the aftershocks and their mechanism types to characterize the structure and the deformation occurring in the Longmen Shan fold and thrust belt. Our results suggest that the stress is very complex at the Longmen Shan fault zone. The moment tensors have both a spatial segmentation with two major categories of the moment tensor of thrust and strike slip; and a temporal pattern that the majority of the aftershocks gradually migrated to thrust-type events. The variability of aftershock mechanisms is a strong indication of significant tectonic release and stress reorganization that activated numerous small faults in the system.

The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations

NASA Astrophysics Data System (ADS)

Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.

2018-04-01

The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.

Multiway modeling and analysis in stem cell systems biology

PubMed Central

2008-01-01

Background Systems biology refers to multidisciplinary approaches designed to uncover emergent properties of biological systems. Stem cells are an attractive target for this analysis, due to their broad therapeutic potential. A central theme of systems biology is the use of computational modeling to reconstruct complex systems from a wealth of reductionist, molecular data (e.g., gene/protein expression, signal transduction activity, metabolic activity, etc.). A number of deterministic, probabilistic, and statistical learning models are used to understand sophisticated cellular behaviors such as protein expression during cellular differentiation and the activity of signaling networks. However, many of these models are bimodal i.e., they only consider row-column relationships. In contrast, multiway modeling techniques (also known as tensor models) can analyze multimodal data, which capture much more information about complex behaviors such as cell differentiation. In particular, tensors can be very powerful tools for modeling the dynamic activity of biological networks over time. Here, we review the application of systems biology to stem cells and illustrate application of tensor analysis to model collagen-induced osteogenic differentiation of human mesenchymal stem cells. Results We applied Tucker1, Tucker3, and Parallel Factor Analysis (PARAFAC) models to identify protein/gene expression patterns during extracellular matrix-induced osteogenic differentiation of human mesenchymal stem cells. In one case, we organized our data into a tensor of type protein/gene locus link × gene ontology category × osteogenic stimulant, and found that our cells expressed two distinct, stimulus-dependent sets of functionally related genes as they underwent osteogenic differentiation. In a second case, we organized DNA microarray data in a three-way tensor of gene IDs × osteogenic stimulus × replicates, and found that application of tensile strain to a collagen I substrate accelerated the osteogenic differentiation induced by a static collagen I substrate. Conclusion Our results suggest gene- and protein-level models whereby stem cells undergo transdifferentiation to osteoblasts, and lay the foundation for mechanistic, hypothesis-driven studies. Our analysis methods are applicable to a wide range of stem cell differentiation models. PMID:18625054

Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

PubMed

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.

Vacuum polarization of the quantized massive fields in Friedman-Robertson-Walker spacetime

NASA Astrophysics Data System (ADS)

Matyjasek, Jerzy; Sadurski, Paweł; Telecka, Małgorzata

2014-04-01

The stress-energy tensor of the quantized massive fields in a spatially open, flat, and closed Friedman-Robertson-Walker universe is constructed using the adiabatic regularization (for the scalar field) and the Schwinger-DeWitt approach (for the scalar, spinor, and vector fields). It is shown that the stress-energy tensor calculated in the sixth adiabatic order coincides with the result obtained from the regularized effective action, constructed from the heat kernel coefficient a3. The behavior of the tensor is examined in the power-law cosmological models, and the semiclassical Einstein field equations are solved exactly in a few physically interesting cases, such as the generalized Starobinsky models.

The 1/ N Expansion of Tensor Models Beyond Perturbation Theory

NASA Astrophysics Data System (ADS)

Gurau, Razvan

2014-09-01

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/ N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/ N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.

Tensor non-Gaussianity from axion-gauge-fields dynamics: parameter search

NASA Astrophysics Data System (ADS)

Agrawal, Aniket; Fujita, Tomohiro; Komatsu, Eiichiro

2018-06-01

We calculate the bispectrum of scale-invariant tensor modes sourced by spectator SU(2) gauge fields during inflation in a model containing a scalar inflaton, a pseudoscalar axion and SU(2) gauge fields. A large bispectrum is generated in this model at tree-level as the gauge fields contain a tensor degree of freedom, and its production is dominated by self-coupling of the gauge fields. This is a unique feature of non-Abelian gauge theory. The shape of the tensor bispectrum is approximately an equilateral shape for 3lesssim mQlesssim 4, where mQ is an effective dimensionless mass of the SU(2) field normalised by the Hubble expansion rate during inflation. The amplitude of non-Gaussianity of the tensor modes, characterised by the ratio Bh/P2h, is inversely proportional to the energy density fraction of the gauge field. This ratio can be much greater than unity, whereas the ratio from the vacuum fluctuation of the metric is of order unity. The bispectrum is effective at constraining large mQ regions of the parameter space, whereas the power spectrum constrains small mQ regions.

An optimization approach for fitting canonical tensor decompositions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methodsmore » have also been recommended; existing NLS methods are accurate but slow. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and further show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient-based optimization methods are much more accurate than ALS and orders of magnitude faster than NLS.« less

Experimental determination of the carboxylate oxygen electric-field-gradient and chemical shielding tensors in L-alanine and L-phenylalanine

NASA Astrophysics Data System (ADS)

Yamada, Kazuhiko; Asanuma, Miwako; Honda, Hisashi; Nemoto, Takahiro; Yamazaki, Toshio; Hirota, Hiroshi

2007-10-01

We report a solid-state 17O NMR study of the 17O electric-field-gradient (EFG) and chemical shielding (CS) tensors for each carboxylate group in polycrystalline L-alanine and L-phenylalanine. The magic angle spinning (MAS) and stationary 17O NMR spectra of these compounds were obtained at 9.4, 14.1, and 16.4 T. Analyzes of these 17O NMR spectra yielded reliable experimental NMR parameters including 17O CS tensor components, 17O quadrupole coupling parameters, and the relative orientations between the 17O CS and EFG tensors. The extensive quantum chemical calculations at both the restricted Hartree-Fock and density-functional theories were carried out with various basis sets to evaluate the quality of quantum chemical calculations for the 17O NMR tensors in L-alanine. For 17O CS tensors, the calculations at the B3LYP/D95 ∗∗ level could reasonably reproduce 17O CS tensors, but they still showed some discrepancies in the δ11 components by approximately 36 ppm. For 17O EFG calculations, it was advantageous to use calibrated Q value to give acceptable CQ values. The calculated results also demonstrated that not only complete intermolecular hydrogen-bonding networks to target oxygen in L-alanine, but also intermolecular interactions around the NH3+ group were significant to reproduce the 17O NMR tensors.

Permutation on hybrid natural inflation

NASA Astrophysics Data System (ADS)

Carone, Christopher D.; Erlich, Joshua; Ramos, Raymundo; Sher, Marc

2014-09-01

We analyze a model of hybrid natural inflation based on the smallest non-Abelian discrete group S3. Leading invariant terms in the scalar potential have an accidental global symmetry that is spontaneously broken, providing a pseudo-Goldstone boson that is identified as the inflaton. The S3 symmetry restricts both the form of the inflaton potential and the couplings of the inflaton field to the waterfall fields responsible for the end of inflation. We identify viable points in the model parameter space. Although the power in tensor modes is small in most of the parameter space of the model, we identify parameter choices that yield potentially observable values of r without super-Planckian initial values of the inflaton field.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klima, Matej; Kucharik, MIlan; Shashkov, Mikhail Jurievich

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.more » We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J 2 invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J 2 invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.« less

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

PubMed

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.

Modeling the evolution of lithium-ion particle contact distributions using a fabric tensor approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stershic, A. J.; Simunovic, S.; Nanda, J.

2015-08-25

Electrode microstructure and processing can strongly influence lithium-ion battery performance such as capacity retention, power, and rate. Battery electrodes are multi-phase composite structures wherein conductive diluents and binder bond active material to a current collector. The structure and response of this composite network during repeated electrochemical cycling directly affects battery performance characteristics. We propose the fabric tensor formalism for describing the structure and evolution of the electrode microstructure. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Fabric tensor analysis is applied to experimental data-sets for positivemore » electrode made of lithium nickel manganese cobalt oxide, captured by X-ray tomography for several compositions and consolidation pressures. We show that fabric tensors capture the evolution of inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode. The fabric tensor analysis is also applied to Discrete Element Method (DEM) simulations of electrode microstructures using spherical particles with size distributions from the tomography. Furthermore, these results do not follow the experimental trends, which indicates that the particle size distribution alone is not a sufficient measure for the electrode microstructures in DEM simulations.« less

Finite temperature behavior of the CPT-even and parity-even electrodynamics of the standard model extension

DOE Office of Scientific and Technical Information (OSTI.GOV)

Casana, Rodolfo; Ferreira, Manoel M. Jr; Rodrigues, Josberg S.

2009-10-15

In this work, we examine the finite temperature properties of the CPT-even and Lorentz-invariance-violating (LIV) electrodynamics of the standard model extension, represented by the term W{sub {alpha}}{sub {nu}}{sub {rho}}{sub {phi}}F{sup {alpha}}{sup {nu}}F{sup {rho}}{sup {phi}}. We begin analyzing the Hamiltonian structure following the Dirac's procedure for constrained systems and construct a well-defined and gauge invariant partition function in the functional integral formalism. Next, we specialize for the nonbirefringent coefficients of the tensor W{sub {alpha}}{sub {nu}}{sub {rho}}{sub {phi}}. In the sequel, the partition function is explicitly carried out for the parity-even sector of the tensor W{sub {alpha}}{sub {nu}}{sub {rho}}{sub {phi}}. The modifiedmore » partition function is a power of the Maxwell's partition function. It is observed that the LIV coefficients induce an anisotropy in the black body angular energy density distribution. The Planck's radiation law, however, retains its frequency dependence and the Stefan-Boltzmann law keeps the usual form, except for a change in the Stefan-Boltzmann constant by a factor containing the LIV contributions.« less

Three dimensional topography correction applied to magnetotelluric data from Sikkim Himalayas

NASA Astrophysics Data System (ADS)

Kumar, Sushil; Patro, Prasanta K.; Chaudhary, B. S.

2018-06-01

Magnetotelluric (MT) method is one of the powerful tools to investigate the deep crustal image of mountainous regions such as Himalayas. Topographic variations due to irregular surface terrain distort the resistivity curves and hence may not give accurate interpretation of magnetotelluric data. The two-dimensional (2-D) topographic effects in Transverse Magnetic (TM) mode is only galvanic whereas inductive in Transverse Electric (TE) mode, thus TM mode responses is much more important than TE mode responses in 2-D. In three-dimensional (3-D), the topography effect is both galvanic and inductive in each element of impedance tensor and hence the interpretation is complicated. In the present work, we investigate the effects of three-dimensional (3-D) topography for a hill model. This paper presents the impedance tensor correction algorithm to reduce the topographic effects in MT data. The distortion caused by surface topography effectively decreases by using homogeneous background resistivity in impedance correction method. In this study, we analyze the response of ramp, distance from topographic edges, conductive and resistive dykes. The new correction method is applied to the real data from Sikkim Himalayas, which brought out the true nature of the basement in this region.

A complex fermionic tensor model in d dimensions

NASA Astrophysics Data System (ADS)

Prakash, Shiroman; Sinha, Ritam

2018-02-01

In this note, we study a melonic tensor model in d dimensions based on three-index Dirac fermions with a four-fermion interaction. Summing the melonic diagrams at strong coupling allows one to define a formal large- N saddle point in arbitrary d and calculate the spectrum of scalar bilinear singlet operators. For d = 2 - ɛ the theory is an infrared fixed point, which we find has a purely real spectrum that we determine numerically for arbitrary d < 2, and analytically as a power series in ɛ. The theory appears to be weakly interacting when ɛ is small, suggesting that fermionic tensor models in 1-dimension can be studied in an ɛ expansion. For d > 2, the spectrum can still be calculated using the saddle point equations, which may define a formal large- N ultraviolet fixed point analogous to the Gross-Neveu model in d > 2. For 2 < d < 6, we find that the spectrum contains at least one complex scalar eigenvalue (similar to the complex eigenvalue present in the bosonic tensor model recently studied by Giombi, Klebanov and Tarnopolsky) which indicates that the theory is unstable. We also find that the fixed point is weakly-interacting when d = 6 (or more generally d = 4 n + 2) and has a real spectrum for 6 < d < 6 .14 which we present as a power series in ɛ in 6 + ɛ dimensions.

On synthetic gravitational waves from multi-field inflation

NASA Astrophysics Data System (ADS)

Ozsoy, Ogan

2018-04-01

We revisit the possibility of producing observable tensor modes through a continuous particle production process during inflation. Particularly, we focus on the multi-field realization of inflation where a spectator pseudoscalar σ induces a significant amplification of the U(1) gauge fields through the coupling propto σFμνtilde Fμν. In this model, both the scalar σ and the Abelian gauge fields are gravitationally coupled to the inflaton sector, therefore they can only affect the primordial scalar and tensor fluctuations through their mixing with gravitational fluctuations. Recent studies on this scenario show that the sourced contributions to the scalar correlators can be dangerously large to invalidate a large tensor power spectrum through the particle production mechanism. In this paper, we re-examine these recent claims by explicitly calculating the dominant contribution to the scalar power and bispectrum. Particularly, we show that once the current limits from CMB data are taken into account, it is still possible to generate a signal as large as r ≈ 10‑3 and the limitations on the model building are more relaxed than what was considered before.

Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Suvodip; Das, Santanu; Souradeep, Tarun

2015-01-01

Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass m{sub eff} for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independentmore » parameters, namely spectral index for tensor perturbation ν{sub t} and change in spectral index for scalar perturbation ν{sub st} to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r<0.1 or r<0.01) for a scalar spectral index of n{sub s}=0.96 by having a non-zero value of effective mass of the inflaton field m{sup 2}{sub eff}/H{sup 2}. The analysis with WP + Planck likelihood shows a non-zero detection of m{sup 2}{sub eff}/H{sup 2} with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m{sup 2}{sub eff}/H{sup 2} = −0.0237 ± 0.0135 which is consistent with zero.« less

Low temperature EPR investigation of Co2+ ion doped into rutile TiO2 single crystal: Experiments and simulations

NASA Astrophysics Data System (ADS)

Zerentürk, A.; Açıkgöz, M.; Kazan, S.; Yıldız, F.; Aktaş, B.

2017-02-01

In this paper, we present the results of X-band EPR spectra of Co2+ ion doped rutile (TiO2) which is one of the most promising memristor material. We obtained the angular variation of spectra in three mutually perpendicular planes at liquid helium (7-13 K) temperatures. Since the impurity ions have ½ effective spin and 7/2 nuclear spin, a relatively simple spin Hamiltonian containing only electronic Zeeman and hyperfine terms was utilized. Two different methods were used in theoretical analysis. Firstly, a linear regression analysis of spectra based on perturbation theory was studied. However, this approach is not sufficient for analyzing Co+2 spectra and leads to complex eigenvectors for G and A tensors due to large anisotropy of eigenvalues. Therefore, all spectra were analyzed again with exact diagonalization of spin Hamiltonian and the high accuracy eigenvalues and eigenvectors of G and A tensors were obtained by taking into account the effect of small sample misalignment from the exact crystallographic planes due to experimental conditions. Our results show that eigen-axes of g and A tensors are parallel to crystallographic directions. Hence, our EPR experiments proves that Co2+ ions substitute for Ti4+ ions in lattice. The obtained principal values of g tensor are gx=2.110(6), gy=5.890(2), gz=3.725(7) and principal values of hyperfine tensor are Ax=42.4, Ay=152.7, Az=26 (in 10-4/cm).

Q-space trajectory imaging for multidimensional diffusion MRI of the human brain

PubMed Central

Westin, Carl-Fredrik; Knutsson, Hans; Pasternak, Ofer; Szczepankiewicz, Filip; Özarslan, Evren; van Westen, Danielle; Mattisson, Cecilia; Bogren, Mats; O’Donnell, Lauren; Kubicki, Marek; Topgaard, Daniel; Nilsson, Markus

2016-01-01

This work describes a new diffusion MR framework for imaging and modeling of microstructure that we call q-space trajectory imaging (QTI). The QTI framework consists of two parts: encoding and modeling. First we propose q-space trajectory encoding, which uses time-varying gradients to probe a trajectory in q-space, in contrast to traditional pulsed field gradient sequences that attempt to probe a point in q-space. Then we propose a microstructure model, the diffusion tensor distribution (DTD) model, which takes advantage of additional information provided by QTI to estimate a distributional model over diffusion tensors. We show that the QTI framework enables microstructure modeling that is not possible with the traditional pulsed gradient encoding as introduced by Stejskal and Tanner. In our analysis of QTI, we find that the well-known scalar b-value naturally extends to a tensor-valued entity, i.e., a diffusion measurement tensor, which we call the b-tensor. We show that b-tensors of rank 2 or 3 enable estimation of the mean and covariance of the DTD model in terms of a second order tensor (the diffusion tensor) and a fourth order tensor. The QTI framework has been designed to improve discrimination of the sizes, shapes, and orientations of diffusion microenvironments within tissue. We derive rotationally invariant scalar quantities describing intuitive microstructural features including size, shape, and orientation coherence measures. To demonstrate the feasibility of QTI on a clinical scanner, we performed a small pilot study comparing a group of five healthy controls with five patients with schizophrenia. The parameter maps derived from QTI were compared between the groups, and 9 out of the 14 parameters investigated showed differences between groups. The ability to measure and model the distribution of diffusion tensors, rather than a quantity that has already been averaged within a voxel, has the potential to provide a powerful paradigm for the study of complex tissue architecture. PMID:26923372

Exploring extra dimensions through inflationary tensor modes

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Birkhoff theorem and conformal Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Ferrando, Joan Josep; Sáez, Juan Antonio

2015-06-01

We analyze the main geometric conditions imposed by the hypothesis of the Jebsen-Birkhoff theorem. We show that the result (existence of an additional Killing vector) does not necessarily require a three-dimensional isometry group on two-dimensional orbits but only the existence of a conformal Killing-Yano tensor. In this approach the (additional) isometry appears as the known invariant Killing vector that the -metrics admit.

Heterotic reduction of Courant algebroid connections and Einstein-Hilbert actions

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Vysoký, Jan

2016-08-01

We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein-Hilbert type of actions known from supergravity. In particular, we carefully analyze the process of the reduction for the generalized metric, connection, curvature tensor and the scalar curvature.

Yield Scaling of Frequency Domain Moment Tensors from Contained Chemical Explosions Detonated in Granite

NASA Astrophysics Data System (ADS)

MacPhail, M. D.; Stump, B. W.; Zhou, R.

2017-12-01

The Source Phenomenology Experiment (SPE - Arizona) was a series of nine, contained and partially contained chemical explosions within the porphyry granite at the Morenci Copper mine in Arizona. Its purpose was to detonate, record and analyze seismic waveforms from these single-fired explosions. Ground motion data from the SPE is analyzed in this study to assess the uniqueness of the time domain moment tensor source representation and its ability to quantify containment and yield scaling. Green's functions were computed for each of the explosions based on a 1D velocity model developed for the SPE. The Green's functions for the sixteen, near-source stations focused on observations from 37 to 680 m. This study analyzes the three deepest, fully contained explosions with a depth of burial of 30 m and yields of 0.77e-3, 3.08e-3 and 6.17e-3 kt. Inversions are conducted within the frequency domain and moment tensors are decomposed into deviatoric and isotropic components to evaluate the effects of containment and yield on the resulting source representation. Isotropic moments are compared to those for other contained explosions as reported by Denny and Johnson, 1991, and are in good agreement with their scaling results. The explosions in this study have isotropic moments of 1.2e12, 3.1e12 and 6.1e13 n*m. Isotropic and Mzz moment tensor spectra are compared to Mueller-Murphy, Denny-Johnson and revised Heard-Ackerman (HA) models and suggest that the larger explosions fit the HA model better. Secondary source effects resulting from free surface interactions including the effects of spallation contribute to the resulting moment tensors which include a CLVD component. Hudson diagrams, using frequency domain moment tensor data, are computed as a tool to assess how these containment scenarios affect the source representation. Our analysis suggests that, within our band of interest (2-20 Hz), as the frequency increases, the source representation becomes more explosion like, peaking at around 20 Hz. These results guide additional analysis of the observational data and the practical resolution of physical phenomenology accompanying underground explosions.

White matter degeneration in schizophrenia: a comparative diffusion tensor analysis

NASA Astrophysics Data System (ADS)

Ingalhalikar, Madhura A.; Andreasen, Nancy C.; Kim, Jinsuh; Alexander, Andrew L.; Magnotta, Vincent A.

2010-03-01

Schizophrenia is a serious and disabling mental disorder. Diffusion tensor imaging (DTI) studies performed on schizophrenia have demonstrated white matter degeneration either due to loss of myelination or deterioration of fiber tracts although the areas where the changes occur are variable across studies. Most of the population based studies analyze the changes in schizophrenia using scalar indices computed from the diffusion tensor such as fractional anisotropy (FA) and relative anisotropy (RA). The scalar measures may not capture the complete information from the diffusion tensor. In this paper we have applied the RADTI method on a group of 9 controls and 9 patients with schizophrenia. The RADTI method converts the tensors to log-Euclidean space where a linear regression model is applied and hypothesis testing is performed between the control and patient groups. Results show that there is a significant difference in the anisotropy between patients and controls especially in the parts of forceps minor, superior corona radiata, anterior limb of internal capsule and genu of corpus callosum. To check if the tensor analysis gives a better idea of the changes in anisotropy, we compared the results with voxelwise FA analysis as well as voxelwise geodesic anisotropy (GA) analysis.

Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description

PubMed Central

SHETTY, ANIL N.; CHIANG, SHARON; MALETIC-SAVATIC, MIRJANA; KASPRIAN, GREGOR; VANNUCCI, MARINA; LEE, WESLEY

2016-01-01

In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain. PMID:27441031

DOE Office of Scientific and Technical Information (OSTI.GOV)

Casadio, Roberto; Orlandi, Alessio; Kühnel, Florian, E-mail: casadio@bo.infn.it, E-mail: florian.kuhnel@fysik.su.se, E-mail: aorlandi@bo.infn.it

Following a new quantum cosmological model proposed by Dvali and Gomez, we quantitatively investigate possible modifications to the Hubble parameter and following corrections to the cosmic microwave background spectrum. In this model, scalar and tensor perturbations are generated by the quantum depletion of the background inflaton and graviton condensate respectively. We show how the inflaton mass affects the power spectra and the tensor-to-scalar ratio. Masses approaching the Planck scale would lead to strong deviations, while standard spectra are recovered for an inflaton mass much smaller than the Planck mass.

Energy-momentum tensors in linearized Einstein's theory and massive gravity: The question of uniqueness

NASA Astrophysics Data System (ADS)

Bičák, Jiří; Schmidt, Josef

2016-01-01

The question of the uniqueness of energy-momentum tensors in the linearized general relativity and in the linear massive gravity is analyzed without using variational techniques. We start from a natural ansatz for the form of the tensor (for example, that it is a linear combination of the terms quadratic in the first derivatives), and require it to be conserved as a consequence of field equations. In the case of the linear gravity in a general gauge we find a four-parametric system of conserved second-rank tensors which contains a unique symmetric tensor. This turns out to be the linearized Landau-Lifshitz pseudotensor employed often in full general relativity. We elucidate the relation of the four-parametric system to the expression proposed recently by Butcher et al. "on physical grounds" in harmonic gauge, and we show that the results coincide in the case of high-frequency waves in vacuum after a suitable averaging. In the massive gravity we show how one can arrive at the expression which coincides with the "generalized linear symmetric Landau-Lifshitz" tensor. However, there exists another uniquely given simpler symmetric tensor which can be obtained by adding the divergence of a suitable superpotential to the canonical energy-momentum tensor following from the Fierz-Pauli action. In contrast to the symmetric tensor derived by the Belinfante procedure which involves the second derivatives of the field variables, this expression contains only the field and its first derivatives. It is simpler than the generalized Landau-Lifshitz tensor but both yield the same total quantities since they differ by the divergence of a superpotential. We also discuss the role of the gauge conditions in the proofs of the uniqueness. In the Appendix, the symbolic tensor manipulation software cadabra is briefly described. It is very effective in obtaining various results which would otherwise require lengthy calculations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bordin, Lorenzo; Creminelli, Paolo; Mirbabayi, Mehrdad

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

Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings

NASA Astrophysics Data System (ADS)

Bordin, Lorenzo; Cabass, Giovanni; Creminelli, Paolo; Vernizzi, Filippo

2017-09-01

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlator can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum.

Quantum Max-flow/Min-cut

NASA Astrophysics Data System (ADS)

Cui, Shawn X.; Freedman, Michael H.; Sattath, Or; Stong, Richard; Minton, Greg

2016-06-01

The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a flow network, we can also interpret it as a tensor network and, more specifically, as a linear map from the input space to the output space. The quantum max-flow is defined to be the maximal rank of this linear map over all choices of tensors. The quantum min-cut is defined to be the minimum product of the capacities of edges over all cuts of the tensor network. We show that unlike the classical case, the quantum max-flow=min-cut conjecture is not true in general. Under certain conditions, e.g., when the capacity on each edge is some power of a fixed integer, the quantum max-flow is proved to equal the quantum min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of quantum max-flow/min-cut with entropy of entanglement and the quantum satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity.

Features of plastic strain localization at the yield plateau in Hadfield steel single crystals

NASA Astrophysics Data System (ADS)

Barannikova, S. A.; Zuev, L. B.

2008-07-01

Spatiotemporal distributions of local components of the plastic distortion tensor in Hadfield steel single crystals oriented for single twinning have been studied under active tensile straining conditions using the double-exposure speckle photography technique. Features of the macroscopically inhomogeneous strain localization at the yield plateau are considered. Relations between local components of the plastic distortion tensor in the zone of strain localization are analyzed.

Positivity bound on the imaginary part of the right-chiral tensor coupling gR in polarized top quark decay

NASA Astrophysics Data System (ADS)

Groote, S.; Körner, J. G.

2017-12-01

We derive a positivity bound on the right-chiral tensor coupling Im gR in polarized top quark decay by analyzing the angular decay distribution of the three-body polarized top quark decay t (↑)→b +ℓ++νℓ in next-to-leading order QCD. We obtain the bound -0.0420 ≤Im gR≤0.0420 .

Constraining the break of spatial diffeomorphism invariance with Planck data

NASA Astrophysics Data System (ADS)

Graef, L. L.; Benetti, M.; Alcaniz, J. S.

2017-07-01

The current most accepted paradigm for the early universe cosmology, the inflationary scenario, shows a good agreement with the recent Cosmic Microwave Background (CMB) and polarization data. However, when the inflation consistency relation is relaxed, these observational data exclude a larger range of red tensor tilt values, prevailing the blue ones which are not predicted by the minimal inflationary models. Recently, it has been shown that the assumption of spatial diffeomorphism invariance breaking (SDB) in the context of an effective field theory of inflation leads to interesting observational consequences. Among them, the possibility of generating a blue tensor spectrum, which can recover the specific consistency relation of the String Gas Cosmology, for a certain choice of parameters. We use the most recent CMB data to constrain the SDB model and test its observational viability through a Bayesian analysis assuming as reference an extended ΛCDM+tensor perturbation model, which considers a power-law tensor spectrum parametrized in terms of the tensor-to-scalar ratio, r, and the tensor spectral index, nt. If the inflation consistency relation is imposed, r=-8 nt, we obtain a strong evidence in favor of the reference model whereas if such relation is relaxed, a weak evidence in favor of the model with diffeomorphism breaking is found. We also use the same CMB data set to make an observational comparison between the SDB model, standard inflation and String Gas Cosmology.

Inflation with Whip-Shaped Suppressed Scalar Power Spectra

NASA Astrophysics Data System (ADS)

Hazra, Dhiraj Kumar; Shafieloo, Arman; Smoot, George F.; Starobinsky, Alexei A.

2014-08-01

Motivated by the idea that inflation occurs at the grand unified theory symmetry breaking scale, in this Letter we construct a new class of large field inflaton potentials where the inflaton starts with a power law potential; after an initial period of relatively fast roll that lasts until after a few e folds inside the horizon it transits to the attractor of the slow roll part of the potential with a lower power. Because of the initial fast roll stages of inflation, we find a suppression in scalar primordial power at large scales and at the same time the choice of the potential can provide us a tensor primordial spectrum with a high amplitude. This suppression in scalar power with a large tensor-to-scalar ratio helps us to reconcile the Planck and BICEP2 data in a single framework. We find that a transition from a cubic to quadratic form of inflaton potential generates an appropriate suppression in the power of the scalar primordial spectrum that provides a significant improvement in fit compared to the power law model when compared with Planck and BICEP2 data together. We calculate the extent of non-Gaussianity, specifically, the bispectrum for the best fit potential, and show that it is consistent with Planck bispectrum constraints.

Fast Approximations of the Rotational Diffusion Tensor and their Application to Structural Assembly of Molecular Complexes

PubMed Central

Berlin, Konstantin; O’Leary, Dianne P.; Fushman, David

2011-01-01

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols. PMID:21604302

Fast approximations of the rotational diffusion tensor and their application to structural assembly of molecular complexes.

PubMed

Berlin, Konstantin; O'Leary, Dianne P; Fushman, David

2011-07-01

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols. Copyright © 2011 Wiley-Liss, Inc.

Spherical tensor analysis of polar liquid crystals with biaxial and chiral molecules

NASA Astrophysics Data System (ADS)

Iwamoto, Mitsumasa; Zhong-can, Ou-Yang

2012-11-01

With the help of spherical tensor expression, an irreducible calculus of a Lth-rank macroscopic susceptibility χ for a polar liquid crystal (PLC) of biaxial and chiral molecules written as the average of molecular hyperpolarizability tensor β associated with their spherical orientational order parameters (0⩽l⩽L) is presented. Comprehensive formulas of L=1,2 have been obtained and the latter explains the optical activity and spontaneous splay texture observed in bent-core PLC. The expression of L=3 specifies for the molecules with D2 symmetry which can be applied to analyze the nonlinear optical second harmonic generation (SHG) observed in proteins, peptides, and double-stranded DNA at interfaces.

Clustering fossils in solid inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akhshik, Mohammad, E-mail: m.akhshik@ipm.ir

In solid inflation the single field non-Gaussianity consistency condition is violated. As a result, the long tenor perturbation induces observable clustering fossils in the form of quadrupole anisotropy in large scale structure power spectrum. In this work we revisit the bispectrum analysis for the scalar-scalar-scalar and tensor-scalar-scalar bispectrum for the general parameter space of solid. We consider the parameter space of the model in which the level of non-Gaussianity generated is consistent with the Planck constraints. Specializing to this allowed range of model parameter we calculate the quadrupole anisotropy induced from the long tensor perturbations on the power spectrum ofmore » the scalar perturbations. We argue that the imprints of clustering fossil from primordial gravitational waves on large scale structures can be detected from the future galaxy surveys.« less

Reversible and dissipative macroscopic contributions to the stress tensor: active or passive?

PubMed

Brand, H R; Pleiner, H; Svenšek, D

2014-09-01

The issue of dynamic contributions to the macroscopic stress tensor has been of high interest in the field of bio-inspired active systems over the last few years. Of particular interest is a direct coupling ("active term") of the stress tensor with the order parameter, the latter describing orientational order induced by active processes. Here we analyze more generally possible reversible and irreversible dynamic contributions to the stress tensor for various passive and active macroscopic systems. This includes systems with tetrahedral/octupolar order, polar and non-polar (chiral) nematic and smectic liquid crystals, as well as active fluids with a dynamic preferred (polar or non-polar) direction. We show that it cannot a priori be seen, neither from the symmetry properties of the macroscopic variables involved, nor from the structure of the cross-coupling contributions to the stress tensor, whether the system studied is active or passive. Rather, that depends on whether the variables that give rise to those cross-couplings in the stress tensor are driven or not. We demonstrate that several simplified descriptions of active systems in the literature that neglect the necessary counter term to the active term violate linear irreversible thermodynamics and lead to an unphysical contribution to the entropy production.

Power loss of a single electron charge distribution confined in a quantum plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehramiz, A.; Department of Physics, Faculty of Science, I. K. Int'l University, Qazvin 34149-16818; Mahmoodi, J.

2011-05-15

The dielectric tensor for a quantum plasma is derived by using a linearized quantum hydrodynamic theory. The wave functions for a nanostructure bound system have been investigated. Finally, the power loss for an oscillating charge distribution of a mixed state will be calculated, using the dielectric function formalism.

The scalar-scalar-tensor inflationary three-point function in the axion monodromy model

NASA Astrophysics Data System (ADS)

Chowdhury, Debika; Sreenath, V.; Sriramkumar, L.

2016-11-01

The axion monodromy model involves a canonical scalar field that is governed by a linear potential with superimposed modulations. The modulations in the potential are responsible for a resonant behavior which gives rise to persisting oscillations in the scalar and, to a smaller extent, in the tensor power spectra. Interestingly, such spectra have been shown to lead to an improved fit to the cosmological data than the more conventional, nearly scale invariant, primordial power spectra. The scalar bi-spectrum in the model too exhibits continued modulations and the resonance is known to boost the amplitude of the scalar non-Gaussianity parameter to rather large values. An analytical expression for the scalar bi-spectrum had been arrived at earlier which, in fact, has been used to compare the model with the cosmic microwave background anisotropies at the level of three-point functions involving scalars. In this work, with future applications in mind, we arrive at a similar analytical template for the scalar-scalar-tensor cross-correlation. We also analytically establish the consistency relation (in the squeezed limit) for this three-point function. We conclude with a summary of the main results obtained.

Inevitable inflation in Einstein-Cartan theory with improved energy-momentum tensor with spin

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Bradas, James C.; Smalley, Larry L.

1988-01-01

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic, (Bianchi Type-1) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley improved energy momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density. Shear is not effective in preventing inflation in the ECRS model. The relation between fluid vorticity, torsion, reference axis rotation, and shear ellipsoid precession shows through clearly.

Extended effective field theory of inflation

NASA Astrophysics Data System (ADS)

Ashoorioon, Amjad; Casadio, Roberto; Cicoli, Michele; Geshnizjani, Ghazal; Kim, Hyung J.

2018-02-01

We present a general framework where the effective field theory of single field inflation is extended by the inclusion of operators with mass dimension 3 and 4 in the unitary gauge. These higher dimensional operators introduce quartic and sextic corrections to the dispersion relation. We study the regime of validity of this extended effective field theory of inflation and the effect of these higher dimensional operators on CMB observables associated with scalar perturbations, such as the speed of sound, the amplitude of the power spectrum and the tensor-to-scalar ratio. Tensor perturbations remain instead, unaltered.

Embedded Systems and TensorFlow Frameworks as Assistive Technology Solutions.

PubMed

Mulfari, Davide; Palla, Alessandro; Fanucci, Luca

2017-01-01

In the field of deep learning, this paper presents the design of a wearable computer vision system for visually impaired users. The Assistive Technology solution exploits a powerful single board computer and smart glasses with a camera in order to allow its user to explore the objects within his surrounding environment, while it employs Google TensorFlow machine learning framework in order to real time classify the acquired stills. Therefore the proposed aid can increase the awareness of the explored environment and it interacts with its user by means of audio messages.

Quantum Max-flow/Min-cut

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Shawn X., E-mail: xingshan@math.ucsb.edu; Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052; Freedman, Michael H., E-mail: michaelf@microsoft.com

2016-06-15

The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a flow network, we can also interpret it as a tensor network and, more specifically, as a linear map from the input space to the output space. The quantum max-flow is defined to be the maximal rank of this linear map over all choices of tensors. The quantum min-cut is defined to be the minimum product of the capacities of edges over all cuts ofmore » the tensor network. We show that unlike the classical case, the quantum max-flow=min-cut conjecture is not true in general. Under certain conditions, e.g., when the capacity on each edge is some power of a fixed integer, the quantum max-flow is proved to equal the quantum min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of quantum max-flow/min-cut with entropy of entanglement and the quantum satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity.« less

Constraining the break of spatial diffeomorphism invariance with Planck data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Graef, L.L.; Benetti, M.; Alcaniz, J.S., E-mail: leilagraef@on.br, E-mail: micolbenetti@on.br, E-mail: alcaniz@on.br

The current most accepted paradigm for the early universe cosmology, the inflationary scenario, shows a good agreement with the recent Cosmic Microwave Background (CMB) and polarization data. However, when the inflation consistency relation is relaxed, these observational data exclude a larger range of red tensor tilt values, prevailing the blue ones which are not predicted by the minimal inflationary models. Recently, it has been shown that the assumption of spatial diffeomorphism invariance breaking (SDB) in the context of an effective field theory of inflation leads to interesting observational consequences. Among them, the possibility of generating a blue tensor spectrum, whichmore » can recover the specific consistency relation of the String Gas Cosmology, for a certain choice of parameters. We use the most recent CMB data to constrain the SDB model and test its observational viability through a Bayesian analysis assuming as reference an extended ΛCDM+tensor perturbation model, which considers a power-law tensor spectrum parametrized in terms of the tensor-to-scalar ratio, r , and the tensor spectral index, n {sub t} . If the inflation consistency relation is imposed, r =−8 n {sub t} , we obtain a strong evidence in favor of the reference model whereas if such relation is relaxed, a weak evidence in favor of the model with diffeomorphism breaking is found. We also use the same CMB data set to make an observational comparison between the SDB model, standard inflation and String Gas Cosmology.« less

Werner-Wheeler mass tensor for fusionlike configuration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gherghescu, R.A.; Poenaru, D.N.

2005-08-01

The Werner-Wheeler approach is used to calculate the components of the mass tensor for a binary configuration of two intersected spheroids. Four free coordinates form the deformation space: the small semiaxis of the projectile, the two semiaxis ratios of the spheroids, and the distance between centers. A correction term is also calculated, due to the center of mass motion. Final results are presented for the fusion channel {sup 54}Cr+{sup 240}Pu, and all possible couplings are analyzed.

Measurement of 13C chemical shift tensor principal values with a magic-angle turning experiment.

PubMed

Hu, J Z; Orendt, A M; Alderman, D W; Pugmire, R J; Ye, C; Grant, D M

1994-08-01

The magic-angle turning (MAT) experiment introduced by Gan is developed into a powerful and routine method for measuring the principal values of 13C chemical shift tensors in powdered solids. A large-volume MAT probe with stable rotation frequencies down to 22 Hz is described. A triple-echo MAT pulse sequence is introduced to improve the quality of the two-dimensional baseplane. It is shown that measurements of the principal values of chemical shift tensors in complex compounds can be enhanced by using either short contact times or dipolar dephasing pulse sequences to isolate the powder patterns from protonated or non-protonated carbons, respectively. A model compound, 1,2,3-trimethoxybenzene, is used to demonstrate these techniques, and the 13C principal values in 2,3-dimethylnaphthalene and Pocahontas coal are reported as typical examples.

Chiral primordial blue tensor spectra from the axion-gauge couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Obata, Ippei, E-mail: obata@tap.scphys.kyoto-u.ac.jp

We suggest the new feature of primordial gravitational waves sourced by the axion-gauge couplings, whose forms are motivated by the dimensional reduction of the form field in the string theory. In our inflationary model, as an inflaton we adopt two types of axion, dubbed the model-independent axion and the model-dependent axion, which couple with two gauge groups with different sign combination each other. Due to these forms both polarization modes of gauge fields are amplified and enhance both helicies of tensor modes during inflation. We point out the possibility that a primordial blue-tilted tensor power spectra with small chirality aremore » provided by the combination of these axion-gauge couplings, intriguingly both amplitudes and chirality are potentially testable by future space-based gravitational wave interferometers such as DECIGO and BBO project.« less

δ M formalism and anisotropic chaotic inflation power spectrum

NASA Astrophysics Data System (ADS)

Talebian-Ashkezari, A.; Ahmadi, N.

2018-05-01

A new analytical approach to linear perturbations in anisotropic inflation has been introduced in [A. Talebian-Ashkezari, N. Ahmadi and A.A. Abolhasani, JCAP 03 (2018) 001] under the name of δ M formalism. In this paper we apply the mentioned approach to a model of anisotropic inflation driven by a scalar field, coupled to the kinetic term of a vector field with a U(1) symmetry. The δ M formalism provides an efficient way of computing tensor-tensor, tensor-scalar as well as scalar-scalar 2-point correlations that are needed for the analysis of the observational features of an anisotropic model on the CMB. A comparison between δ M results and the tedious calculations using in-in formalism shows the aptitude of the δ M formalism in calculating accurate two point correlation functions between physical modes of the system.

Transversely Isotropic Hyperelastic Constitutive Model of Short Fiber Reinforced EPDM Based on Tensor Function

NASA Astrophysics Data System (ADS)

Feng, Q. L.; Li, C.; Liao, Y. F.

2017-12-01

Short fiber reinforced EPDM is a new kind of composite material used in solid rocket motor winding and coating. It has relatively large deformation under the small stress condition, and the physical non-linear characteristic is obvious. Due to the addition of fiber in the specific direction of the rubber, the macroscopic mechanical properties are expressed as transversely isotropic properties. In order to describe the mechanical behavior under the impact and vibration, the transversely isotropic hyperelastic constitutive model based on tensor function is proposed. The symmetry of the transversely isotropic incompressible material limits the stress tensor ‘ K ’ to be characterized as a function of 5 tensor invariants and 4 scalar invariants. The third power constitutive equations of the model give 12 independent elastic constants of the transversely isotropic nonlinear elastic material. The experimental results show that the non-zero elastic constants are different in the fiber direction and at the different strain rate. Number and value of adiabatic layer and related products R & D has a reference value.

Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bordin, Lorenzo; Cabass, Giovanni; Creminelli, Paolo

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlatormore » can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Müller-Hermes, Alexander, E-mail: muellerh@ma.tum.de; Wolf, Michael M., E-mail: m.wolf@tum.de; Reeb, David, E-mail: reeb.qit@gmail.com

We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transposemore » bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task.« less

Chameleons with field-dependent couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brax, Philippe; Bruck, Carsten van de; Mota, David F.

2010-10-15

Certain scalar-tensor theories exhibit the so-called chameleon mechanism, whereby observational signatures of scalar fields are hidden by a combination of self-interactions and interactions with ambient matter. Not all scalar-tensor theories exhibit such a chameleon mechanism, which has been originally found in models with inverse power runaway potentials and field-independent couplings to matter. In this paper we investigate field theories with field-dependent couplings and a power-law potential for the scalar field. We show that the theory indeed is a chameleon field theory. We find the thin-shell solution for a spherical body and investigate the consequences for Eoet-Wash experiments, fifth-force searches andmore » Casimir-force experiments. Requiring that the scalar field evades gravitational tests, we find that the coupling is sensitive to a mass scale which is of order of the Hubble scale today.« less

Observable cosmological vector mode in the dark ages

NASA Astrophysics Data System (ADS)

Saga, Shohei

2016-09-01

The second-order vector mode is inevitably induced from the coupling of first-order scalar modes in cosmological perturbation theory and might hinder a possible detection of primordial gravitational waves from inflation through 21 cm lensing observations. Here, we investigate the weak lensing signal in 21 cm photons emitted by neutral hydrogen atoms in the dark ages induced by the second-order vector mode by decomposing the deflection angle of the 21 cm lensing signal into the gradient and curl modes. The curl mode is a good tracer of the cosmological vector and tensor modes since the scalar mode does not induce the curl one. By comparing angular power spectra of the 21 cm lensing curl mode induced by the second-order vector mode and primordial gravitational waves whose amplitude is parametrized by the tensor-to-scalar ratio r , we find that the 21 cm curl mode from the second-order vector mode dominates over that from primordial gravitational waves on almost all scales if r ≲10-5. If we use the multipoles of the power spectrum up to ℓmax=1 05 and 1 06 in reconstructing the curl mode from 21 cm temperature maps, the signal-to-noise ratios of the 21 cm curl mode from the second-order vector mode achieve S /N ≈0.46 and 73, respectively. Observation of 21 cm radiation is, in principle, a powerful tool to explore not only the tensor mode but also the cosmological vector mode.

Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor

NASA Astrophysics Data System (ADS)

Miyaguchi, Tomoshige

2017-10-01

There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here a method is developed to elucidate this fluctuating diffusivity from trajectory data. Time-averaged mean-square displacement (MSD), a common tool in single-particle-tracking (SPT) experiments, is generalized to a second-order tensor with which both magnitude and orientation fluctuations of the diffusivity can be clearly detected. This method is used to analyze the center-of-mass motion of four fundamental polymer models: the Rouse model, the Zimm model, a reptation model, and a rigid rodlike polymer. It is found that these models exhibit distinctly different types of magnitude and orientation fluctuations of diffusivity. This is an advantage of the present method over previous ones, such as the ergodicity-breaking parameter and a non-Gaussian parameter, because with either of these parameters it is difficult to distinguish the dynamics of the four polymer models. Also, the present method of a time-averaged MSD tensor could be used to analyze trajectory data obtained in SPT experiments.

Near-lossless multichannel EEG compression based on matrix and tensor decompositions.

PubMed

Dauwels, Justin; Srinivasan, K; Reddy, M Ramasubba; Cichocki, Andrzej

2013-05-01

A novel near-lossless compression algorithm for multichannel electroencephalogram (MC-EEG) is proposed based on matrix/tensor decomposition models. MC-EEG is represented in suitable multiway (multidimensional) forms to efficiently exploit temporal and spatial correlations simultaneously. Several matrix/tensor decomposition models are analyzed in view of efficient decorrelation of the multiway forms of MC-EEG. A compression algorithm is built based on the principle of “lossy plus residual coding,” consisting of a matrix/tensor decomposition-based coder in the lossy layer followed by arithmetic coding in the residual layer. This approach guarantees a specifiable maximum absolute error between original and reconstructed signals. The compression algorithm is applied to three different scalp EEG datasets and an intracranial EEG dataset, each with different sampling rate and resolution. The proposed algorithm achieves attractive compression ratios compared to compressing individual channels separately. For similar compression ratios, the proposed algorithm achieves nearly fivefold lower average error compared to a similar wavelet-based volumetric MC-EEG compression algorithm.

Tensor Factorization for Precision Medicine in Heart Failure with Preserved Ejection Fraction

PubMed Central

Luo, Yuan; Ahmad, Faraz S.; Shah, Sanjiv J.

2017-01-01

Heart failure with preserved ejection fraction (HFpEF) is a heterogeneous clinical syndrome that may benefit from improved subtyping in order to better characterize its pathophysiology and to develop novel targeted therapies. The United States Precision Medicine Initiative comes amid the rapid growth in quantity and modality of clinical data for HFpEF patients ranging from deep phenotypic to trans-omic data. Tensor factorization, a form of machine learning, allows for the integration of multiple data modalities to derive clinically relevant HFpEF subtypes that may have significant differences in underlying pathophysiology and differential response to therapies. Tensor factorization also allows for better interpretability by supporting dimensionality reduction and identifying latent groups of data for meaningful summarization of both features and disease outcomes. In this narrative review, we analyze the modest literature on the application of tensor factorization to related biomedical fields including genotyping and phenotyping. Based on the cited work including work of our own, we suggest multiple tensor factorization formulations capable of integrating the deep phenotypic and trans-omic modalities of data for HFpEF, or accounting for interactions between genetic variants at different -omic hierarchies. We encourage extensive experimental studies to tackle challenges in applying tensor factorization for precision medicine in HFpEF, including effectively incorporating existing medical knowledge, properly accounting for uncertainty, and efficiently enforcing sparsity for better interpretability. PMID:28116551

In Silico Investigation of Intracranial Blast Mitigation with Relevance to Military Traumatic Brain Injury

DTIC Science & Technology

2010-09-01

how personal protective equipment affects the brain’s response to blasts. In this study we investigated the effect of the Advanced Combat...analyzing stress wave propagation, which is the main dynamic effect loading the brain tissue during a blast event. We consider two key metrics of stress ...Cauchy stress tensor, and sij ¼ σij − 13σkkδij are the compo- nents of the deviatoric stress tensor (24). Fig. 1 shows snapshots of the pressure

Ab initio elastic tensor of cubic Ti0.5Al0.5N alloys: Dependence of elastic constants on size and shape of the supercell model and their convergence

NASA Astrophysics Data System (ADS)

Tasnádi, Ferenc; Odén, M.; Abrikosov, Igor A.

2012-04-01

In this study we discuss the performance of the special quasirandom structure (SQS) method in predicting the elastic properties of B1 (rocksalt) Ti0.5Al0.5N alloy. We use a symmetry-based projection technique, which gives the closest cubic approximate of the elastic tensor and allows us to align the SQSs of different shapes and sizes for a comparison in modeling elastic tensors. We show that the derived closest cubic approximate of the elastic tensor converges faster with respect to SQS size than the elastic tensor itself. That establishes a less demanding computational strategy to achieve convergence for the elastic constants. We determine the cubic elastic constants (Cij) and Zener's type elastic anisotropy (A) of Ti0.5Al0.5N. Optimal supercells, which capture accurately both the configurational disorder and cubic symmetry of elastic tensor, result in C11=447 GPa, C12=158 GPa, and C44=203 GPa with 3% of error and A=1.40 with 6% of error. In addition, we establish the general importance of selecting proper SQS with symmetry arguments to reliably model elasticity of alloys. We suggest the calculation of nine elastic tensor elements: C11, C22, C33, C12, C13, C23, C44, C55, and C66, to analyze the performance of SQSs and predict elastic constants of cubic alloys. The described methodology is general enough to be extended for alloys with other symmetry at arbitrary composition.

Deuteron polarimetry at COSY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiladze, D.; High Energy Physics Institute, Tbilisi State University, 0186 Tbilisi; Grigoriev, K.

2007-06-13

The vector Pz and tensor Pzz polarizations of a deuteron beam have been measured using elastic deuteron-carbon scattering at 75.6 MeV and deuteron-proton scattering at 270 MeV. After acceleration to 1170 MeV inside the COSY storage ring, the polarizations of the deuterons were remeasured by studying the analyzing powers of a variety of nuclear reactions at the ANKE magnetic spetrometer. The overall precisions obtained were about 4% for both Pz and Pzz. One of the motivation for the experimental programme is the direct reconstruction of the spin-dependent amplitudes, including relative phases, of large angle neutron-proton elastic scattering, through the studymore » of the p(d,2p)n charge-exchange reaction up to the highest available deuteron energy at COSY (2.3 GeV)« less

A spaceborne superconducting gravity gradiometer for mapping the earth's gravity field

NASA Technical Reports Server (NTRS)

Paik, H. J.

1981-01-01

The principles of a satellite gravity gradiometer system which measures all five independent components of the gravity gradient tensor with a sensitivity of 0.001 E/Hz to the 1/2 power or better, are analyzed, and the status of development of the system is reviewed. The superconducting gravity gradiometer uses sensitive superconducting accelerometers, each of which are composed of a weakly suspended superconducting proof mass, a superconducting magnetic transducer, and a low-noise superconducting magnetometer. The magnetic field produced by the transducer coils is modulated by the motion of the proof mass and detected by the magnetometer. A combination of two or four of such accelerometers with proper relative orientation of sensitive axes results in an in-line or a cross component gravity gradiometer.

Constraints on brane-world inflation from the CMB power spectrum: revisited

NASA Astrophysics Data System (ADS)

Gangopadhyay, Mayukh R.; Mathews, Grant J.

2018-03-01

We analyze the Randal Sundrum brane-world inflation scenario in the context of the latest CMB constraints from Planck. We summarize constraints on the most popular classes of models and explore some more realistic inflaton effective potentials. The constraint on standard inflationary parameters changes in the brane-world scenario. We confirm that in general the brane-world scenario increases the tensor-to-scalar ratio, thus making this paradigm less consistent with the Planck constraints. Indeed, when BICEP2/Keck constraints are included, all monomial potentials in the brane-world scenario become disfavored compared to the standard scenario. However, for natural inflation the brane-world scenario could fit the constraints better due to larger allowed values of e-foldings N before the end of inflation in the brane-world.

Hybrid Higgs inflation: The use of disformal transformation

NASA Astrophysics Data System (ADS)

Sato, Seiga; Maeda, Kei-ichi

2018-04-01

We propose a hybrid type of the conventional Higgs inflation and new Higgs inflation models. We perform a disformal transformation into the Einstein frame and analyze the background dynamics and the cosmological perturbations in the truncated model, in which we ignore the higher-derivative terms of the Higgs field. From the observed power spectrum of the density perturbations, we obtain the constraint on the nonminimal coupling constant ξ and the mass parameter M in the derivative coupling. Although the primordial tilt ns in the hybrid model barely changes, the tensor-to-scalar ratio r moves from the value in the new Higgs inflationary model to that in the conventional Higgs inflationary model as |ξ | increases. We confirm our results by numerical analysis by ADM formalism of the full theory in the Jordan frame.

Scale-invariant curvature fluctuations from an extended semiclassical gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pinamonti, Nicola, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it; INFN Sezione di Genova, Via Dodecaneso 33, 16146 Genova; Siemssen, Daniel, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it

2015-02-15

We present an extension of the semiclassical Einstein equations which couple n-point correlation functions of a stochastic Einstein tensor to the n-point functions of the quantum stress-energy tensor. We apply this extension to calculate the quantum fluctuations during an inflationary period, where we take as a model a massive conformally coupled scalar field on a perturbed de Sitter space and describe how a renormalization independent, almost-scale-invariant power spectrum of the scalar metric perturbation is produced. Furthermore, we discuss how this model yields a natural basis for the calculation of non-Gaussianities of the considered metric fluctuations.

Polar Codes

DTIC Science & Technology

2014-12-01

independently has a 10% chance of being flipped. Then the decoder should use the majority vote rule: if y is (0, 0, 0), (0, 0, 1), (0, 1, 0), or (1, 0, 0... tensor power, and BN is a square matrix called the bit-reversal operator. Therefore G−1N = (F ⊗n) −1 B−1N . Section VII.B of [1] shows that B −1 N...BN . 18 Also we see by direct computation that FF = I2. Using the tensor product identity (AC) ⊗ (BD) = (A⊗B)(C⊗D), we get that (F ⊗F )(F ⊗F ) = I2

Combining the boundary shift integral and tensor-based morphometry for brain atrophy estimation

NASA Astrophysics Data System (ADS)

Michalkiewicz, Mateusz; Pai, Akshay; Leung, Kelvin K.; Sommer, Stefan; Darkner, Sune; Sørensen, Lauge; Sporring, Jon; Nielsen, Mads

2016-03-01

Brain atrophy from structural magnetic resonance images (MRIs) is widely used as an imaging surrogate marker for Alzheimers disease. Their utility has been limited due to the large degree of variance and subsequently high sample size estimates. The only consistent and reasonably powerful atrophy estimation methods has been the boundary shift integral (BSI). In this paper, we first propose a tensor-based morphometry (TBM) method to measure voxel-wise atrophy that we combine with BSI. The combined model decreases the sample size estimates significantly when compared to BSI and TBM alone.

The observational constraint on constant-roll inflation

NASA Astrophysics Data System (ADS)

Gao, Qing

2018-07-01

We discuss the constant-roll inflation with constant ɛ2 and constant \\bar η . By using the method of Bessel function approximation, the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor to scalar ratio are derived up to the first order of ɛ1. The model with constant ɛ2 is ruled out by the observations at the 3σ confidence level, and the model with constant \\bar η is consistent with the observations at the 1σ confidence level. The potential for the model with constant \\bar η is also obtained from the Hamilton-Jacobi equation. Although the observations constrain the constant-roll inflation to be the slow-roll inflation, the n s- r results from the constant-roll inflation are not the same as those from the slow-roll inflation even when \\bar η 0.01.

Black holes in vector-tensor theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic andmore » quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.« less

Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2011-04-01

We give an overview of the first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach. The special role of Stäckel-Killing and Killing-Yano tensors is pointed out. Some nontrivial examples involving Runge-Lenz type conserved quantities are explicitly worked out. A condition of the electromagnetic field to maintain the hidden symmetry of the system is stated. A concrete realization of this condition is given by the Killing-Maxwell system and exemplified with the Kerr metric. Quantum symmetry operators for the Klein-Gordon and Dirac equations are constructed from Killing tensors. The transfer of the classical conserved quantities to the quantum mechanical level is analyzed in connection with quantum anomalies.

Moment-Tensor Spectra of Source Physics Experiments (SPE) Explosions in Granite

NASA Astrophysics Data System (ADS)

Yang, X.; Cleveland, M.

2016-12-01

We perform frequency-domain moment tensor inversions of Source Physics Experiments (SPE) explosions conducted in granite during Phase I of the experiment. We test the sensitivity of source moment-tensor spectra to factors such as the velocity model, selected dataset and smoothing and damping parameters used in the inversion to constrain the error bound of inverted source spectra. Using source moments and corner frequencies measured from inverted source spectra of these explosions, we develop a new explosion P-wave source model that better describes observed source spectra of these small and over-buried chemical explosions detonated in granite than classical explosion source models derived mainly from nuclear-explosion data. In addition to source moment and corner frequency, we analyze other features in the source spectra to investigate their physical causes.

Active tensor magnetic gradiometer system final report for Project MM–1514

USGS Publications Warehouse

Smith, David V.; Phillips, Jeffrey D.; Hutton, S. Raymond

2014-01-01

An interactive computer simulation program, based on physical models of system sensors, platform geometry, Earth environment, and spheroidal magnetically-permeable targets, was developed to generate synthetic magnetic field data from a conceptual tensor magnetic gradiometer system equipped with an active primary field generator. The system sensors emulate the prototype tensor magnetic gradiometer system (TMGS) developed under a separate contract for unexploded ordnance (UXO) detection and classification. Time-series data from different simulation scenarios were analyzed to recover physical dimensions of the target source. Helbig-Euler simulations were run with rectangular and rod-like source bodies to determine whether such a system could separate the induced component of the magnetization from the remanent component for each target. This report concludes with an engineering assessment of a practical system design.

The total position-spread tensor: Spin partition

DOE Office of Scientific and Technical Information (OSTI.GOV)

El Khatib, Muammar, E-mail: elkhatib@irsamc.ups-tlse.fr; Evangelisti, Stefano, E-mail: stefano@irsamc.ups-tlse.fr; Leininger, Thierry, E-mail: Thierry.Leininger@irsamc.ups-tlse.fr

2015-03-07

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

Foundations of Tensor Analysis for Students of Physics and Engineering With an Introduction to the Theory of Relativity

NASA Technical Reports Server (NTRS)

Kolecki, Joseph C.

2005-01-01

Tensor analysis is one of the more abstruse, even if one of the more useful, higher math subjects enjoined by students of physics and engineering. It is abstruse because of the intellectual gap that exists between where most physics and engineering mathematics leave off and where tensor analysis traditionally begins. It is useful because of its great generality, computational power, and compact, easy to use, notation. This paper bridges the intellectual gap. It is divided into three parts: algebra, calculus, and relativity. Algebra: In tensor analysis, coordinate independent quantities are sought for applications in physics and engineering. Coordinate independence means that the quantities have such coordinate transformations as to leave them invariant relative to a particular observer s coordinate system. Calculus: Non-zero base vector derivatives contribute terms to dynamical equations that correspond to pseudoaccelerations in accelerated coordinate systems and to curvature or gravity in relativity. These derivatives have a specific general form in tensor analysis. Relativity: Spacetime has an intrinsic geometry. Light is the tool for investigating that geometry. Since the observed geometry of spacetime cannot be made to match the classical geometry of Euclid, Einstein applied another more general geometry differential geometry. The merger of differential geometry and cosmology was accomplished in the theory of relativity. In relativity, gravity is equivalent to curvature.

Application of Bayesian model averaging to measurements of the primordial power spectrum

NASA Astrophysics Data System (ADS)

Parkinson, David; Liddle, Andrew R.

2010-11-01

Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for assessing parameter uncertainties in situations where there is also uncertainty in the underlying model. We apply model averaging to the estimation of the parameters associated with the primordial power spectra of curvature and tensor perturbations. We use CosmoNest and MultiNest to compute the model evidences and posteriors, using cosmic microwave data from WMAP, ACBAR, BOOMERanG, and CBI, plus large-scale structure data from the SDSS DR7. We find that the model-averaged 95% credible interval for the spectral index using all of the data is 0.940

Tensor form factor for the D → π(K) transitions with Twisted Mass fermions.

NASA Astrophysics Data System (ADS)

Lubicz, Vittorio; Riggio, Lorenzo; Salerno, Giorgio; Simula, Silvano; Tarantino, Cecilia

2018-03-01

We present a preliminary lattice calculation of the D → π and D → K tensor form factors fT (q2) as a function of the squared 4-momentum transfer q2. ETMC recently computed the vector and scalar form factors f+(q2) and f0(q2) describing D → π(K)lv semileptonic decays analyzing the vector current and the scalar density. The study of the weak tensor current, which is directly related to the tensor form factor, completes the set of hadronic matrix element regulating the transition between these two pseudoscalar mesons within and beyond the Standard Model where a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV and with the valence heavy quark in the mass range from ≃ 0.7 mc to ≃ 1.2mc. The matrix element of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As for the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data. We will present preliminary results on the removal of such hypercubic lattice effects.

Assessing the Uncertainties on Seismic Source Parameters: Towards Realistic Estimates of Moment Tensor Determinations

NASA Astrophysics Data System (ADS)

Magnoni, F.; Scognamiglio, L.; Tinti, E.; Casarotti, E.

2014-12-01

Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Moment tensor catalogues are ordinarily used by geoscientists, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their own analysis. The 2012 May 20 Emilia mainshock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. An uncertainty of ~0.5 units in magnitude leads to a controversial knowledge of the real size of the event. The possible uncertainty associated to this estimate could be critical for the inference of other seismological parameters, suggesting caution for seismic hazard assessment, coulomb stress transfer determination and other analyses where self-consistency is important. In this work, we focus on the variability of the moment tensor solution, highlighting the effect of four different velocity models, different types and ranges of filtering, and two different methodologies. Using a larger dataset, to better quantify the source parameter uncertainty, we also analyze the variability of the moment tensor solutions depending on the number, the epicentral distance and the azimuth of used stations. We endorse that the estimate of seismic moment from moment tensor solutions, as well as the estimate of the other kinematic source parameters, cannot be considered an absolute value and requires to come out with the related uncertainties and in a reproducible framework characterized by disclosed assumptions and explicit processing workflows.

Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

NASA Astrophysics Data System (ADS)

Jiang, Li; Liu, Jie; Zhang, Jianzhong; Feng, Zhibing

2017-12-01

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.

EEG Classification for Hybrid Brain-Computer Interface Using a Tensor Based Multiclass Multimodal Analysis Scheme

PubMed Central

Ji, Hongfei; Li, Jie; Lu, Rongrong; Gu, Rong; Cao, Lei; Gong, Xiaoliang

2016-01-01

Electroencephalogram- (EEG-) based brain-computer interface (BCI) systems usually utilize one type of changes in the dynamics of brain oscillations for control, such as event-related desynchronization/synchronization (ERD/ERS), steady state visual evoked potential (SSVEP), and P300 evoked potentials. There is a recent trend to detect more than one of these signals in one system to create a hybrid BCI. However, in this case, EEG data were always divided into groups and analyzed by the separate processing procedures. As a result, the interactive effects were ignored when different types of BCI tasks were executed simultaneously. In this work, we propose an improved tensor based multiclass multimodal scheme especially for hybrid BCI, in which EEG signals are denoted as multiway tensors, a nonredundant rank-one tensor decomposition model is proposed to obtain nonredundant tensor components, a weighted fisher criterion is designed to select multimodal discriminative patterns without ignoring the interactive effects, and support vector machine (SVM) is extended to multiclass classification. Experiment results suggest that the proposed scheme can not only identify the different changes in the dynamics of brain oscillations induced by different types of tasks but also capture the interactive effects of simultaneous tasks properly. Therefore, it has great potential use for hybrid BCI. PMID:26880873

EEG Classification for Hybrid Brain-Computer Interface Using a Tensor Based Multiclass Multimodal Analysis Scheme.

PubMed

Ji, Hongfei; Li, Jie; Lu, Rongrong; Gu, Rong; Cao, Lei; Gong, Xiaoliang

2016-01-01

Electroencephalogram- (EEG-) based brain-computer interface (BCI) systems usually utilize one type of changes in the dynamics of brain oscillations for control, such as event-related desynchronization/synchronization (ERD/ERS), steady state visual evoked potential (SSVEP), and P300 evoked potentials. There is a recent trend to detect more than one of these signals in one system to create a hybrid BCI. However, in this case, EEG data were always divided into groups and analyzed by the separate processing procedures. As a result, the interactive effects were ignored when different types of BCI tasks were executed simultaneously. In this work, we propose an improved tensor based multiclass multimodal scheme especially for hybrid BCI, in which EEG signals are denoted as multiway tensors, a nonredundant rank-one tensor decomposition model is proposed to obtain nonredundant tensor components, a weighted fisher criterion is designed to select multimodal discriminative patterns without ignoring the interactive effects, and support vector machine (SVM) is extended to multiclass classification. Experiment results suggest that the proposed scheme can not only identify the different changes in the dynamics of brain oscillations induced by different types of tasks but also capture the interactive effects of simultaneous tasks properly. Therefore, it has great potential use for hybrid BCI.

The tensor distribution function.

PubMed

Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M

2009-01-01

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

Supervised non-negative tensor factorization for automatic hyperspectral feature extraction and target discrimination

NASA Astrophysics Data System (ADS)

Anderson, Dylan; Bapst, Aleksander; Coon, Joshua; Pung, Aaron; Kudenov, Michael

2017-05-01

Hyperspectral imaging provides a highly discriminative and powerful signature for target detection and discrimination. Recent literature has shown that considering additional target characteristics, such as spatial or temporal profiles, simultaneously with spectral content can greatly increase classifier performance. Considering these additional characteristics in a traditional discriminative algorithm requires a feature extraction step be performed first. An example of such a pipeline is computing a filter bank response to extract spatial features followed by a support vector machine (SVM) to discriminate between targets. This decoupling between feature extraction and target discrimination yields features that are suboptimal for discrimination, reducing performance. This performance reduction is especially pronounced when the number of features or available data is limited. In this paper, we propose the use of Supervised Nonnegative Tensor Factorization (SNTF) to jointly perform feature extraction and target discrimination over hyperspectral data products. SNTF learns a tensor factorization and a classification boundary from labeled training data simultaneously. This ensures that the features learned via tensor factorization are optimal for both summarizing the input data and separating the targets of interest. Practical considerations for applying SNTF to hyperspectral data are presented, and results from this framework are compared to decoupled feature extraction/target discrimination pipelines.

From non-trivial geometries to power spectra and vice versa

NASA Astrophysics Data System (ADS)

Brooker, D. J.; Tsamis, N. C.; Woodard, R. P.

2018-04-01

We review a recent formalism which derives the functional forms of the primordial—tensor and scalar—power spectra of scalar potential inflationary models. The formalism incorporates the case of geometries with non-constant first slow-roll parameter. Analytic expressions for the power spectra are given that explicitly display the dependence on the geometric properties of the background. Moreover, we present the full algorithm for using our formalism, to reconstruct the model from the observed power spectra. Our techniques are applied to models possessing "features" in their potential with excellent agreement.

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

NASA Astrophysics Data System (ADS)

Crenshaw, Michael E.

2017-08-01

Radiation pressure is an observable consequence of optically induced forces on materials. On cosmic scales, radiation pressure is responsible for the bending of the tails of comets as they pass near the sun. At a much smaller scale, optically induced forces are being investigated as part of a toolkit for micromanipulation and nanofabrication technology [1]. A number of practical applications of the mechanical effects of light-matter interaction are discussed by Qiu, et al. [2]. The promise of the nascent nanophotonic technology for manufacturing small, low-power, high-sensitivity sensors and other devices has likely motivated the substantial current interest in optical manipulation of materials at the nanoscale, see, for example, Ref. [2] and the references therein. While substantial progress toward optical micromanipulation has been achieved, e.g. optical tweezers [1], in this report we limit our consideration to the particular issue of optically induced forces on a transparent dielectric material. As a matter of electromagnetic theory, these forces remain indeterminate and controversial. Due to the potential applications in nanotechnology, the century-old debate regarding these forces, and the associated momentums, has ramped up considerably in the physics community. The energy-momentum tensor is the centerpiece of conservation laws for the unimpeded, inviscid, incompressible flow of non-interacting particles in the continuum limit in an otherwise empty volume. The foundations of the energy-momentum tensor and the associated tensor conservation theory come to electrodynamics from classical continuum dynamics by applying the divergence theorem to a Taylor series expansion of a property density field of a continuous flow in an otherwise empty volume. The dust tensor is a particularly simple example of an energy-momentum tensor that deals with particles of matter in the continuum limit in terms of the mass density ρm, energy density ρmc 2 , and momentum density ρmv. Newtonian fluids can behave very much like dust with the same energy-momentum tensor. The energy and momentum conservation properties of light propagating in the vacuum were long-ago cast in the energy-momentum tensor formalism in terms of the electromagnetic energy density and electromagnetic momentum density. However, extrapolating the tensor theory of energy-momentum conservation for propagation of light in the vacuum to propagation of light in a simple linear dielectric medium has proven to be problematic and controversial. A dielectric medium is not "otherwise empty" and it is typically assumed that optically induced forces accelerate and decelerate nanoscopic material constituents of the dielectric. The corresponding material energy-momentum tensor is added to the electromagnetic energy-momentum tensor to form the total energy-momentum tensor, thereby ensuring that the total energy and the total momentum of the thermodynamically closed system remain constant in time.

Vector- and tensor-meson production and the Pomeron-f identity hypothesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jones, S.T.

Within the context of a model introduced some time ago, the differential and total production cross sections for vector and tensor mesons are shown to be compatible with the hypothesis that the Pomeron and f are a single Regge trajectory. The model incorporates both cylinder and flavoring renormalizations of the Pomeron-f trajectory. The processes K/sup +- /p..-->..K/sup */(892)/sup +- /p, K/sup +- /p ..-->..K/sub 2//sup */(1430)/sup +- /p, and ..pi../sup +- /p..-->..A/sub 2/(1320)/sup +- /p are analyzed in some detail.

Single and double diffractive dissociation and the problem of extraction of the proton-Pomeron cross-section

NASA Astrophysics Data System (ADS)

Petrov, V. A.; Ryutin, R. A.

2016-04-01

Diffractive dissociation processes are analyzed in the framework of covariant reggeization. We have considered the general form of hadronic tensor and its asymptotic behavior for t → 0 in the case of conserved tensor currents before reggeization. Resulting expressions for differential cross-sections of single dissociation (SD) process (pp → pM), double dissociation (DD) (pp → M1M2) and for the proton-Pomeron cross-section are given in detail, and corresponding problems of the approach are discussed.

Computer transformation of partial differential equations into any coordinate system

NASA Technical Reports Server (NTRS)

Sullivan, R. D.

1977-01-01

The use of tensors to provide a compact way of writing partial differential equations in a form valid in all coordinate systems is discussed. In order to find solutions to the equations with their boundary conditions they must be expressed in terms of the coordinate system under consideration. The process of arriving at these expressions from the tensor formulation was automated by a software system, TENSR. An allied system that analyzes the resulting expressions term by term and drops those that are negligible is also described.

Rainbow tensor model with enhanced symmetry and extreme melonic dominance

NASA Astrophysics Data System (ADS)

Itoyama, H.; Mironov, A.; Morozov, A.

2017-08-01

We introduce and briefly analyze the rainbow tensor model where all planar diagrams are melonic. This leads to considerable simplification of the large N limit as compared to that of the matrix model: in particular, what are dressed in this limit are propagators only, which leads to an oversimplified closed set of Schwinger-Dyson equations for multi-point correlators. We briefly touch upon the Ward identities, the substitute of the spectral curve and the AMM/EO topological recursion and their possible connections to Connes-Kreimer theory and forest formulas.

Electron paramagnetic resonance of gamma-irradiated single crystals of 3-nitroacetanilide

NASA Astrophysics Data System (ADS)

Aşik, Biray

2008-06-01

The electron paramagnetic resonance of single crystals of 3-nitroacetanilide has been observed and analyzed for different orientations of the crystal in the magnetic field, after being damaged at 300 K by γ-irradiation. The crystals have been investigated between 123 and 300 K. The spectra were found to be temperature independent. The irradiation of 3-nitroacetanilide by γ-rays produces radicals at the nitrogen atoms in the molecule. The principal values of the hyperfine coupling tensor of the unpaired electron and the principal values of the g-tensor were determined.

Optimizing Tensor Contraction Expressions for Hybrid CPU-GPU Execution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Wenjing; Krishnamoorthy, Sriram; Villa, Oreste

2013-03-01

Tensor contractions are generalized multidimensional matrix multiplication operations that widely occur in quantum chemistry. Efficient execution of tensor contractions on Graphics Processing Units (GPUs) requires several challenges to be addressed, including index permutation and small dimension-sizes reducing thread block utilization. Moreover, to apply the same optimizations to various expressions, we need a code generation tool. In this paper, we present our approach to automatically generate CUDA code to execute tensor contractions on GPUs, including management of data movement between CPU and GPU. To evaluate our tool, GPU-enabled code is generated for the most expensive contractions in CCSD(T), a key coupledmore » cluster method, and incorporated into NWChem, a popular computational chemistry suite. For this method, we demonstrate speedup over a factor of 8.4 using one GPU (instead of one core per node) and over 2.6 when utilizing the entire system using hybrid CPU+GPU solution with 2 GPUs and 5 cores (instead of 7 cores per node). Finally, we analyze the implementation behavior on future GPU systems.« less

Constraining primordial vector mode from B-mode polarization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saga, Shohei; Ichiki, Kiyotomo; Shiraishi, Maresuke, E-mail: saga.shohei@nagoya-u.jp, E-mail: maresuke.shiraishi@pd.infn.it, E-mail: ichiki@a.phys.nagoya-u.ac.jp

The B-mode polarization spectrum of the Cosmic Microwave Background (CMB) may be the smoking gun of not only the primordial tensor mode but also of the primordial vector mode. If there exist nonzero vector-mode metric perturbations in the early Universe, they are known to be supported by anisotropic stress fluctuations of free-streaming particles such as neutrinos, and to create characteristic signatures on both the CMB temperature, E-mode, and B-mode polarization anisotropies. We place constraints on the properties of the primordial vector mode characterized by the vector-to-scalar ratio r{sub v} and the spectral index n{sub v} of the vector-shear power spectrum,more » from the Planck and BICEP2 B-mode data. We find that, for scale-invariant initial spectra, the ΛCDM model including the vector mode fits the data better than the model including the tensor mode. The difference in χ{sup 2} between the vector and tensor models is Δχ{sup 2} = 3.294, because, on large scales the vector mode generates smaller temperature fluctuations than the tensor mode, which is preferred for the data. In contrast, the tensor mode can fit the data set equally well if we allow a significantly blue-tilted spectrum. We find that the best-fitting tensor mode has a large blue tilt and leads to an indistinct reionization bump on larger angular scales. The slightly red-tilted vector mode supported by the current data set can also create O(10{sup -22})-Gauss magnetic fields at cosmological recombination. Our constraints should motivate research that considers models of the early Universe that involve the vector mode.« less

Differentiating G-inflation from string gas cosmology using the effective field theory approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Minxi; Liu, Junyu; Lu, Shiyun

A characteristic signature of String Gas Cosmology is primordial power spectra for scalar and tensor modes which are almost scale-invariant but with a red tilt for scalar modes but a blue tilt for tensor modes. This feature, however, can also be realized in the so-called G-inflation model, in which Horndeski operators are introduced which leads to a blue tensor tilt by softly breaking the Null Energy Condition. In this article we search for potential observational differences between these two cosmologies by performing detailed perturbation analyses based on the Effective Field Theory approach. Our results show that, although both two modelsmore » produce blue tilted tensor perturbations, they behave differently in three aspects. Firstly, String Gas Cosmology predicts a specific consistency relation between the index of the scalar modes n {sub s} and that of tensor ones n {sub t} , which is hard to be reproduced by G-inflation. Secondly, String Gas Cosmology typically predicts non-Gaussianities which are highly suppressed on observable scales, while G-inflation gives rise to observationally large non-Gaussianities because the kinetic terms in the action become important during inflation. However, after finely tuning the model parameters of G-inflation it is possible to obtain a blue tensor spectrum and negligible non-Gaussianities with a degeneracy between the two models. This degeneracy can be broken by a third observable, namely the scale dependence of the nonlinearity parameter, which vanishes for G-inflation but has a blue tilt in the case of String Gas Cosmology. Therefore, we conclude that String Gas Cosmology is in principle observationally distinguishable from the single field inflationary cosmology, even allowing for modifications such as G-inflation.« less

Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states.

PubMed

Kohn, Lucas; Tschirsich, Ferdinand; Keck, Maximilian; Plenio, Martin B; Tamascelli, Dario; Montangero, Simone

2018-01-01

We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground-state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that randomized matrix factorization outperforms truncated singular value decomposition based on state-of-the-art deterministic routines in time-evolving block decimation (TEBD)- and density matrix renormalization group (DMRG)-style simulations, even when the system under study gets close to a phase transition: We report linear speedups in the bond or local dimension of up to 24 times in quasi-two-dimensional cylindrical systems.

Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states

NASA Astrophysics Data System (ADS)

Kohn, Lucas; Tschirsich, Ferdinand; Keck, Maximilian; Plenio, Martin B.; Tamascelli, Dario; Montangero, Simone

2018-01-01

We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground-state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that randomized matrix factorization outperforms truncated singular value decomposition based on state-of-the-art deterministic routines in time-evolving block decimation (TEBD)- and density matrix renormalization group (DMRG)-style simulations, even when the system under study gets close to a phase transition: We report linear speedups in the bond or local dimension of up to 24 times in quasi-two-dimensional cylindrical systems.

An Improved Method for Seismic Event Depth and Moment Tensor Determination: CTBT Related Application

NASA Astrophysics Data System (ADS)

Stachnik, J.; Rozhkov, M.; Baker, B.

2016-12-01

According to the Protocol to CTBT, International Data Center is required to conduct expert technical analysis and special studies to improve event parameters and assist State Parties in identifying the source of specific event. Determination of seismic event source mechanism and its depth is a part of these tasks. It is typically done through a strategic linearized inversion of the waveforms for a complete or subset of source parameters, or similarly defined grid search through precomputed Greens Functions created for particular source models. We show preliminary results using the latter approach from an improved software design and applied on a moderately powered computer. In this development we tried to be compliant with different modes of CTBT monitoring regime and cover wide range of source-receiver distances (regional to teleseismic), resolve shallow source depths, provide full moment tensor solution based on body and surface waves recordings, be fast to satisfy both on-demand studies and automatic processing and properly incorporate observed waveforms and any uncertainties a priori as well as accurately estimate posteriori uncertainties. Implemented HDF5 based Green's Functions pre-packaging allows much greater flexibility in utilizing different software packages and methods for computation. Further additions will have the rapid use of Instaseis/AXISEM full waveform synthetics added to a pre-computed GF archive. Along with traditional post processing analysis of waveform misfits through several objective functions and variance reduction, we follow a probabilistic approach to assess the robustness of moment tensor solution. In a course of this project full moment tensor and depth estimates are determined for DPRK 2009, 2013 and 2016 events and shallow earthquakes using a new implementation of waveform fitting of teleseismic P waves. A full grid search over the entire moment tensor space is used to appropriately sample all possible solutions. A recent method by Tape & Tape (2012) to discretize the complete moment tensor space from a geometric perspective is used. Moment tensors for DPRK events show isotropic percentages greater than 50%. Depth estimates for the DPRK events range from 1.0-1.4 km. Probabilistic uncertainty estimates on the moment tensor parameters provide robustness to solution.

Inversion of calcite twin data for paleostress (1) : improved Etchecopar technique tested on numerically-generated and natural data

NASA Astrophysics Data System (ADS)

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

2015-04-01

Inversion of calcite twin data are known to be a powerful tool to reconstruct the past-state of stress in carbonate rocks of the crust, especially in fold-and-thrust belts and sedimentary basins. This is of key importance to constrain results of geomechanical modelling. Without proposing a new inversion scheme, this contribution reports some recent improvements of the most efficient stress inversion technique to date (Etchecopar, 1984) that allows to reconstruct the 5 parameters of the deviatoric paleostress tensors (principal stress orientations and differential stress magnitudes) from monophase and polyphase twin data sets. The improvements consist in the search of the possible tensors that account for the twin data (twinned and untwinned planes) and the aid to the user to define the best stress tensor solution, among others. We perform a systematic exploration of an hypersphere in 4 dimensions by varying different parameters, Euler's angles and the stress ratio. We first record all tensors with a minimum penalization function accounting for 20% of the twinned planes. We then define clusters of tensors following a dissimilarity criterion based on the stress distance between the 4 parameters of the reduced stress tensors and a degree of disjunction of the related sets of twinned planes. The percentage of twinned data to be explained by each tensor is then progressively increased and tested using the standard Etchecopar procedure until the best solution that explains the maximum number of twinned planes and the whole set of untwinned planes is reached. This new inversion procedure is tested on monophase and polyphase numerically-generated as well as natural calcite twin data in order to more accurately define the ability of the technique to separate more or less similar deviatoric stress tensors applied in sequence on the samples, to test the impact of strain hardening through the change of the critical resolved shear stress for twinning as well as to evaluate the possible bias due to measurement uncertainties or clustering of grain optical axes in the samples.

Three-dimensional smoothed particle hydrodynamics simulation for injection molding flow of short fiber-reinforced polymer composites

NASA Astrophysics Data System (ADS)

He, Liping; Lu, Gang; Chen, Dachuan; Li, Wenjun; Lu, Chunsheng

2017-07-01

This paper investigates the three-dimensional (3D) injection molding flow of short fiber-reinforced polymer composites using a smoothed particle hydrodynamics (SPH) simulation method. The polymer melt was modeled as a power law fluid and the fibers were considered as rigid cylindrical bodies. The filling details and fiber orientation in the injection-molding process were studied. The results indicated that the SPH method could effectively predict the order of filling, fiber accumulation, and heterogeneous distribution of fibers. The SPH simulation also showed that fibers were mainly aligned to the flow direction in the skin layer and inclined to the flow direction in the core layer. Additionally, the fiber-orientation state in the simulation was quantitatively analyzed and found to be consistent with the results calculated by conventional tensor methods.

Renormalization group analysis of the Reynolds stress transport equation

NASA Technical Reports Server (NTRS)

Rubinstein, R.; Barton, J. M.

1992-01-01

The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.

Tensor to scalar ratio and large scale power suppression from pre-slow roll initial conditions

NASA Astrophysics Data System (ADS)

Lello, Louis; Boyanovsky, Daniel

2014-05-01

We study the corrections to the power spectra of curvature and tensor perturbations and the tensor-to-scalar ratio r in single field slow roll inflation with standard kinetic term due to initial conditions imprinted by a ``fast-roll'' stage prior to slow roll. For a wide range of initial inflaton kinetic energy, this stage lasts only a few e-folds and merges smoothly with slow-roll thereby leading to non-Bunch-Davies initial conditions for modes that exit the Hubble radius during slow roll. We describe a program that yields the dynamics in the fast-roll stage while matching to the slow roll stage in a manner that is independent of the inflationary potentials. Corrections to the power spectra are encoded in a ``transfer function'' for initial conditions Script Tα(k), Script Pα(k) = PBDα(k)Script Tα(k), implying a modification of the ``consistency condition'' for the tensor to scalar ratio at a pivot scale k0: r(k0) = -8nT(k0) [Script TT(k0)/Script TScript R(k0)]. We obtain Script Tα(k) to leading order in a Born approximation valid for modes of observational relevance today. A fit yields Script Tα(k) = 1+Aαk-pcos [2πωk/Hsr+varphiα], with 1.5lesssimplesssim2, ω simeq 1 and Hsr the Hubble scale during slow roll inflation, where curvature and tensor perturbations feature the same p,ω for a wide range of initial conditions. These corrections lead to both a suppression of the quadrupole and oscillatory features in both PR(k) and r(k0) with a period of the order of the Hubble scale during slow roll inflation. The results are quite general and independent of the specific inflationary potentials, depending solely on the ratio of kinetic to potential energy κ and the slow roll parameters epsilonV, ηV to leading order in slow roll. For a wide range of κ and the values of epsilonV ηV corresponding to the upper bounds from Planck, we find that the low quadrupole is consistent with the results from Planck, and the oscillations in r(k0) as a function of k0 could be observable if the modes corresponding to the quadrupole and the pivot scale crossed the Hubble radius very few (2-3) e-folds after the onset of slow roll. We comment on possible impact on the recent BICEP2 results.

Fabrication and properties of multilayer structures

NASA Astrophysics Data System (ADS)

Tiller, W. A.

1983-09-01

The synthesis of SiC films and Pd2Si films via single source and dual source sputtering, respectively, has been experimentally investigated while the reactive sputter deposition of SiO sub x films has been theoretically analyzed. The SiO sub x film data requires a mobile precursor adsorption process to be operative for the oxygen and an oxygen sticking coefficient of between 1.56 x 10 to the minus 3rd power and 4.17 x 10 to the minus 3rd power. An analysis of in-situ electrical diagnostics of the films via a non-contact technique shows the method to be of marginal accuracy for the example selected. An important new formulation of the stress and elastic constant tensors in the vicinity of interfaces has been developed and applied to the simple example of adsorbed layer/substrate interactions via a parametric analysis. Atomic modeling of the SiO system yields peroxide bond formation for oxygen-rich (100) alpha-cristobalite surfaces. Radial distribution function and angular distribution function data have been calculated for bulk alpha-quartz and bulk alpha-cristobalite in good agreement with experiment.

Primordial spectra of slow-roll inflation at second-order with the Gauss-Bonnet correction

NASA Astrophysics Data System (ADS)

Wu, Qiang; Zhu, Tao; Wang, Anzhong

2018-05-01

The slow-roll inflation for a single scalar field that couples to the Gauss-Bonnet (GB) term represents an important higher-order curvature correction inspired by string theory. With the arrival of the era of precision cosmology, it is expected that the high-order corrections become more and more important. In this paper we study the observational predictions of the slow-roll inflation with the GB term by using the third-order uniform asymptotic approximation method. We calculate explicitly the primordial power spectra, spectral indices, running of the spectral indices for both scalar and tensor perturbations, and the ratio between tensor and scalar spectra. These expressions are all written in terms of the Hubble and GB coupling flow parameters and expanded up to the next-to-leading order in the slow-roll expansions so they represent the most accurate results obtained so far in the literature. In addition, by studying the theoretical predictions of the scalar spectral index and the tensor-to-scalar ratio with the Planck 2015 constraints in a model with power-law potential and GB coupling, we show that the second-order corrections are important in the future measurements. We expect that the understanding of the GB corrections in the primordial spectra and their constraints by forthcoming observational data will provide clues for the UV complete theory of quantum gravity, such as the string/M-theory.

Dimensions of Attention Associated With the Microstructure of Corona Radiata White Matter.

PubMed

Stave, Elise A; De Bellis, Michael D; Hooper, Steven R; Woolley, Donald P; Chang, Suk Ki; Chen, Steven D

2017-04-01

Mirsky proposed a model of attention that included these dimensions: focus/execute, sustain, stabilize, encode, and shift. The neural correlates of these dimensions were investigated within corona radiata subregions in healthy youth. Diffusion tensor imaging and neuropsychological assessments were conducted in 79 healthy, right-handed youth aged 4-17 years. Diffusion tensor imaging maps were analyzed using standardized parcellation methods. Partial Pearson correlations between neuropsychological standardized scores, representing these attention dimensions, and diffusion tensor imaging measures of corona radiata subregions were calculated after adjusting for gender and IQ. Significant correlations were found between the focus/execute, sustain, stabilize, and shift dimensions and imaging metrics in hypothesized corona radiata subregions. Results suggest that greater microstructural white matter integrity of the corona radiata is partly associated with attention across 4 attention dimensions. Findings suggest that white matter microstructure of the corona radiata is a neural correlate of several, but not all, attention dimensions.

Dimensions of Attention Associated with the Microstructure of Corona Radiata White Matter

PubMed Central

Stave, Elise A.; Hooper, Stephen R.; Woolley, Donald P.; Chang, Suk Ki; Chen, Steven D.

2016-01-01

Mirsky proposed a model of attention that included these dimensions: focus/execute, sustain, stabilize, encode, and shift. The neural correlates of these dimensions were investigated within corona radiate subregions in healthy youth. Diffusion tensor imaging and neuropsychological assessments were conducted in 79 healthy, right-handed youth aged 4–17 years. Diffusion tensor imaging maps were analyzed using standardized parcellation methods. Partial Pearson correlations between neuropsychological standardized scores, representing these attention dimensions, and diffusion tensor imaging measures of corona radiate subregions were calculated after adjusting for gender and IQ. Significant correlations were found between the focus/execute, sustain, stabilize and shift dimensions and imaging metrics in hypothesized corona radiate subregions. Results suggest that greater microstructural white matter integrity of the corona radiata is partly associated with attention across four attention dimensions. Findings suggest that white matter microstructure of the corona radiata is a neural correlate of several, but not all, attention dimensions. PMID:28090797

Observational constraints on monomial warm inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Visinelli, Luca, E-mail: Luca.Visinelli@studio.unibo.it

Warm inflation is, as of today, one of the best motivated mechanisms for explaining an early inflationary period. In this paper, we derive and analyze the current bounds on warm inflation with a monomial potential U ∝ φ {sup p} , using the constraints from the PLANCK mission. In particular, we discuss the parameter space of the tensor-to-scalar ratio r and the potential coupling λ of the monomial warm inflation in terms of the number of e-folds. We obtain that the theoretical tensor-to-scalar ratio r ∼ 10{sup −8} is much smaller than the current observational constrain r ∼< 0.12, despitemore » a relatively large value of the field excursion Δ φ ∼ 0.1 M {sub Pl}. Warm inflation thus eludes the Lyth bound set on the tensor-to-scalar ratio by the field excursion.« less

Quantum-metric contribution to the pair mass in spin-orbit-coupled Fermi superfluids

NASA Astrophysics Data System (ADS)

Iskin, M.

2018-03-01

As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which corresponds to the Berry curvature measuring the emergent gauge field in momentum space. Here, we first derive the Ginzburg-Landau theory near the critical superfluid transition temperature and then identify and analyze the geometric effects on the effective mass tensor of the Cooper pairs. By showing that the quantum-metric contribution accounts for a sizable fraction of the pair mass in a surprisingly large parameter regime throughout the BCS-Bose-Einstein condensate crossover, we not only reveal the physical origin of its governing role in the superfluid density tensor but also hint at its plausible roles in many other observables.

Xray: N-dimensional, labeled arrays for analyzing physical datasets in Python

NASA Astrophysics Data System (ADS)

Hoyer, S.

2015-12-01

Efficient analysis of geophysical datasets requires tools that both preserve and utilize metadata, and that transparently scale to process large datas. Xray is such a tool, in the form of an open source Python library for analyzing the labeled, multi-dimensional array (tensor) datasets that are ubiquitous in the Earth sciences. Xray's approach pairs Python data structures based on the data model of the netCDF file format with the proven design and user interface of pandas, the popular Python data analysis library for labeled tabular data. On top of the NumPy array, xray adds labeled dimensions (e.g., "time") and coordinate values (e.g., "2015-04-10"), which it uses to enable a host of operations powered by these labels: selection, aggregation, alignment, broadcasting, split-apply-combine, interoperability with pandas and serialization to netCDF/HDF5. Many of these operations are enabled by xray's tight integration with pandas. Finally, to allow for easy parallelism and to enable its labeled data operations to scale to datasets that does not fit into memory, xray integrates with the parallel processing library dask.

Viable tensor-to-scalar ratio in a symmetric matter bounce

NASA Astrophysics Data System (ADS)

Nath Raveendran, Rathul; Chowdhury, Debika; Sriramkumar, L.

2018-01-01

Matter bounces refer to scenarios wherein the universe contracts at early times as in a matter dominated epoch until the scale factor reaches a minimum, after which it starts expanding. While such scenarios are known to lead to scale invariant spectra of primordial perturbations after the bounce, the challenge has been to construct completely symmetric bounces that lead to a tensor-to-scalar ratio which is small enough to be consistent with the recent cosmological data. In this work, we construct a model involving two scalar fields (a canonical field and a non-canonical ghost field) to drive the symmetric matter bounce and study the evolution of the scalar perturbations in the model. We find that the model can be completely described in terms of a single parameter, viz. the ratio of the scale associated with the bounce to the value of the scale factor at the bounce. We evolve the scalar perturbations numerically across the bounce and evaluate the scalar power spectra after the bounce. We show that, while the scalar and tensor perturbation spectra are scale invariant over scales of cosmological interest, the tensor-to-scalar ratio proves to be much smaller than the current upper bound from the observations of the cosmic microwave background anisotropies by the Planck mission. We also support our numerical analysis with analytical arguments.

Scalar and tensor perturbations in loop quantum cosmology: high-order corrections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Tao; Wang, Anzhong; Wu, Qiang

2015-10-01

Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using the third-order uniform asymptotic approximations, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratiomore » is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are ∼< 0.15%, these results represent the most accurate results obtained so far in the literature. It is also shown that with the inverse-volume corrections, both scalar and tensor spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on quantum gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.« less

Tensor network states in time-bin quantum optics

NASA Astrophysics Data System (ADS)

Lubasch, Michael; Valido, Antonio A.; Renema, Jelmer J.; Kolthammer, W. Steven; Jaksch, Dieter; Kim, M. S.; Walmsley, Ian; García-Patrón, Raúl

2018-06-01

The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.

Alignments of parity even/odd-only multipoles in CMB

NASA Astrophysics Data System (ADS)

Aluri, Pavan K.; Ralston, John P.; Weltman, Amanda

2017-12-01

We compare the statistics of parity even and odd multipoles of the cosmic microwave background (CMB) sky from Planck full mission temperature measurements. An excess power in odd multipoles compared to even multipoles has previously been found on large angular scales. Motivated by this apparent parity asymmetry, we evaluate directional statistics associated with even compared to odd multipoles, along with their significances. Primary tools are the Power tensor and Alignment tensor statistics. We limit our analysis to the first 60 multipoles i.e. l = [2, 61]. We find no evidence for statistically unusual alignments of even parity multipoles. More than one independent statistic finds evidence for alignments of anisotropy axes of odd multipoles, with a significance equivalent to ∼2σ or more. The robustness of alignment axes is tested by making Galactic cuts and varying the multipole range. Very interestingly, the region spanned by the (a)symmetry axes is found to broadly contain other parity (a)symmetry axes previously observed in the literature.

Brans-Dicke inflation in light of the Planck 2015 data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tahmasebzadeh, B.; Rezazadeh, K.; Karami, K., E-mail: b.tahmasebzadeh@iasbs.ac.ir, E-mail: rezazadeh86@gmail.com, E-mail: kkarami@uok.ac.ir

We study inflation in the Brans-Dicke gravity as a special model of the scalar-tensor gravity. We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of the general form of the potential in the Jordan frame. Then, we compare the results for various inflationary potentials in light of the Planck 2015 data. Our study shows that in the Brans-Dicke gravity, the power-law, inverse power-law and exponential potentials are ruled out by the Planck 2015 data. But, the hilltop, Higgs, Coleman-Weinberg and natural potentialsmore » can be compatible with Planck 2015 TT,TE,EE+lowP data at 95% CL. Moreover, the D-brane, SB SUSY and displaced quadratic potentials can be in well agreement with the observational data since their results can lie inside the 68% CL region of Planck 2015 TT,TE,EE+lowP data.« less

Using EarthScope magnetotelluric data to improve the resilience of the US power grid: rapid predictions of geomagnetically induced currents

NASA Astrophysics Data System (ADS)

Schultz, A.; Bonner, L. R., IV

2016-12-01

Existing methods to predict Geomagnetically Induced Currents (GICs) in power grids, such as the North American Electric Reliability Corporation standard adopted by the power industry, require explicit knowledge of the electrical resistivity structure of the crust and mantle to solve for ground level electric fields along transmission lines. The current standard is to apply regional 1-D resistivity models to this problem, which facilitates rapid solution of the governing equations. The systematic mapping of continental resistivity structure from projects such as EarthScope reveals several orders of magnitude of lateral variations in resistivity on local, regional and continental scales, resulting in electric field intensifications relative to existing 1-D solutions that can impact GICs to first order. The computational burden on the ground resistivity/GIC problem of coupled 3-D solutions inhibits the prediction of GICs in a timeframe useful to protecting power grids. In this work we reduce the problem to applying a set of filters, recognizing that the magnetotelluric impedance tensors implicitly contain all known information about the resistivity structure beneath a given site, and thus provides the required relationship between electric and magnetic fields at each site. We project real-time magnetic field data from distant magnetic observatories through a robustly calculated multivariate transfer function to locations where magnetotelluric impedance tensors had previously been obtained. This provides a real-time prediction of the magnetic field at each of those points. We then project the predicted magnetic fields through the impedance tensors to obtain predictions of electric fields induced at ground level. Thus, electric field predictions can be generated in real-time for an entire array from real-time observatory data, then interpolated onto points representing a power transmission line contained within the array to produce a combined electric field prediction necessary for GIC prediction along that line. This method produces more accurate predictions of ground electric fields in conductively heterogeneous areas that are not limited by distance from the nearest observatory, while still retaining comparable computational speeds as existing methods.

Anisotropy of the Reynolds stress tensor in the wakes of wind turbine arrays in Cartesian arrangements with counter-rotating rotors

NASA Astrophysics Data System (ADS)

Hamilton, Nicholas; Cal, Raúl Bayoán

2015-01-01

A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds stress anisotropy tensor shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean mechanical energy equation indicate correlation between the degree of anisotropy and the regions of the wind turbine wakes where turbulence kinetic energy is produced. The flux of kinetic energy into the momentum-deficit area of the wake from above the canopy is associated with prolate characteristic spheroids. Flux upward into the wake from below the rotor area is associated with oblate characteristic spheroids. Turbulence in the region of the flow directly following the nacelle of the wind turbines demonstrates greater isotropy than regions following the rotor blades. The power and power coefficients for wind turbines indicate that flow structures on the order of magnitude of the spanwise turbine spacing that increase turbine efficiency depending on particular array configuration.

Moment tensor solutions estimated using optimal filter theory for 51 selected earthquakes, 1980-1984

USGS Publications Warehouse

Sipkin, S.A.

1987-01-01

The 51 global events that occurred from January 1980 to March 1984, which were chosen by the convenors of the Symposium on Seismological Theory and Practice, have been analyzed using a moment tensor inversion algorithm (Sipkin). Many of the events were routinely analyzed as part of the National Earthquake Information Center's (NEIC) efforts to publish moment tensor and first-motion fault-plane solutions for all moderate- to large-sized (mb>5.7) earthquakes. In routine use only long-period P-waves are used and the source-time function is constrained to be a step-function at the source (??-function in the far-field). Four of the events were of special interest, and long-period P, SH-wave solutions were obtained. For three of these events, an unconstrained inversion was performed. The resulting time-dependent solutions indicated that, for many cases, departures of the solutions from pure double-couples are caused by source complexity that has not been adequately modeled. These solutions also indicate that source complexity of moderate-sized events can be determined from long-period data. Finally, for one of the events of special interest, an inversion of the broadband P-waveforms was also performed, demonstrating the potential for using broadband waveform data in inversion procedures. ?? 1987.

Effects of viscous pressure on warm inflationary generalized cosmic Chaplygin gas model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharif, M.; Saleem, Rabia, E-mail: msharif.math@pu.edu.pk, E-mail: rabiasaleem1988@yahoo.com

This paper is devoted to study the effects of bulk viscous pressure on an inflationary generalized cosmic Chaplygin gas model using FRW background. The matter contents of the universe are assumed to be inflaton and imperfect fluid. We evaluate inflaton fields, potentials and entropy density for variable as well as constant dissipation and bulk viscous coefficients in weak as well as high dissipative regimes during intermediate era. In order to discuss inflationary perturbations, we evaluate entropy density, scalar (tensor) power spectra, their corresponding spectral indices, tensor-scalar ratio and running of spectral index in terms of inflaton which are constrained usingmore » recent Planck, WMAP7 and Bicep2 probes.« less

Linear Power Spectra in Cold+Hot Dark Matter Models: Analytical Approximations and Applications

NASA Astrophysics Data System (ADS)

Ma, Chung-Pei

1996-11-01

This paper presents simple analytic approximations to the linear power spectra, linear growth rates, and rms mass fluctuations for both components in a family of cold + hot dark matter (CDM + HDM) models that are of current cosmological interest. The formulas are valid for a wide range of wavenumbers, neutrino fractions, redshifts, and Hubble constants: k ≤ 1O h Mpc-1, 0.05 ≤ Ωv le; 0.3 0 ≤ z ≤ 15, and 0.5 ≤ h ≤ 0.8. A new, redshift-dependent shape parameter, Γv = a½Ωvh2, is introduced to simplify the multidimensional parameter space and to characterize the effect of massive neutrinos on the power spectrum. The physical origin of Γv lies in the neutrino free-streaming process, and the analytic approximations can be simplified to depend only on this variable and Ωv. Linear calculations with these power spectra as input are performed to compare the predictions of Ωv ≤ 0.3 models with observational constraints from the reconstructed linear power spectrum and cluster abundance. The usual assumption of an exact scale-invariant primordial power spectrum is relaxed to allow a spectral index of 0.8 ≤ n ≤ 1. It is found that a slight tilt of n = 0.9 (no tensor mode) or n = 0.95 (with tensor mode) in 0.t-0.2 CDM + HDM models gives a power spectrum similar to that of an open CDM model with a shape parameter Γ = 0.25, providing good agreement with the power spectrum reconstructed by Peacock & Dodds and the observed cluster abundance at low redshifts. Late galaxy formation at high redshifts, however, will be a more severe problem in tilted models.

New Methods For Interpretation Of Magnetic Gradient Tensor Data Using Eigenalysis And The Normalized Source Strength

NASA Astrophysics Data System (ADS)

Clark, D.

2012-12-01

In the future, acquisition of magnetic gradient tensor data is likely to become routine. New methods developed for analysis of magnetic gradient tensor data can also be applied to high quality conventional TMI surveys that have been processed using Fourier filtering techniques, or otherwise, to calculate magnetic vector and tensor components. This approach is, in fact, the only practical way at present to analyze vector component data, as measurements of vector components are seriously afflicted by motion noise, which is not as serious a problem for gradient components. In many circumstances, an optimal approach to extracting maximum information from magnetic surveys would be to combine analysis of measured gradient tensor data with vector components calculated from TMI measurements. New methods for inverting gradient tensor surveys to obtain source parameters have been developed for a number of elementary, but useful, models. These include point dipole (sphere), vertical line of dipoles (narrow vertical pipe), line of dipoles (horizontal cylinder), thin dipping sheet, horizontal line current and contact models. A key simplification is the use of eigenvalues and associated eigenvectors of the tensor. The normalized source strength (NSS), calculated from the eigenvalues, is a particularly useful rotational invariant that peaks directly over 3D compact sources, 2D compact sources, thin sheets and contacts, and is independent of magnetization direction for these sources (and only very weakly dependent on magnetization direction in general). In combination the NSS and its vector gradient enable estimation of the Euler structural index, thereby constraining source geometry, and determine source locations uniquely. NSS analysis can be extended to other useful models, such as vertical pipes, by calculating eigenvalues of the vertical derivative of the gradient tensor. Once source locations are determined, information of source magnetizations can be obtained by simple linear inversion of measured or calculated vector and/or tensor data. Inversions based on the vector gradient of the NSS over the Tallawang magnetite deposit in central New South Wales obtained good agreement between the inferred geometry of the tabular magnetite skarn body and drill hole intersections. Inverted magnetizations are consistent with magnetic property measurements on drill core samples from this deposit. Similarly, inversions of calculated tensor data over the Mount Leyshold gold-mineralized porphyry system in Queensland yield good estimates of the centroid location, total magnetic moment and magnetization direction of the magnetite-bearing potassic alteration zone that are consistent with geological and petrophysical information.

Multivariate statistics of the Jacobian matrices in tensor based morphometry and their application to HIV/AIDS.

PubMed

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

2006-01-01

Tensor-based morphometry (TBM) is widely used in computational anatomy as a means to understand shape variation between structural brain images. A 3D nonlinear registration technique is typically used to align all brain images to a common neuroanatomical template, and the deformation fields are analyzed statistically to identify group differences in anatomy. However, the differences are usually computed solely from the determinants of the Jacobian matrices that are associated with the deformation fields computed by the registration procedure. Thus, much of the information contained within those matrices gets thrown out in the process. Only the magnitude of the expansions or contractions is examined, while the anisotropy and directional components of the changes are ignored. Here we remedy this problem by computing multivariate shape change statistics using the strain matrices. As the latter do not form a vector space, means and covariances are computed on the manifold of positive-definite matrices to which they belong. We study the brain morphology of 26 HIV/AIDS patients and 14 matched healthy control subjects using our method. The images are registered using a high-dimensional 3D fluid registration algorithm, which optimizes the Jensen-Rényi divergence, an information-theoretic measure of image correspondence. The anisotropy of the deformation is then computed. We apply a manifold version of Hotelling's T2 test to the strain matrices. Our results complement those found from the determinants of the Jacobians alone and provide greater power in detecting group differences in brain structure.

Accurate determination of chemical shift tensor orientations of single-crystals by solid-state magic angle spinning NMR

NASA Astrophysics Data System (ADS)

Avadhut, Yamini S.; Weber, Johannes; Schmedt auf der Günne, Jörn

2017-09-01

An improved implementation of single-crystal magic-angle-spinning (MAS) NMR is presented which gives access to chemical shift tensors both in orientation (relative to the crystal axis system) and principal axis values. For mounting arbitrary crystals inside ordinary MAS rotors, a mounting tool is described which allows to relate the crystal orientation determined by diffraction techniques to the rotor coordinate system. The crystal is finally mounted into a MAS rotor equipped with a special insert which allows a defined reorientation of the single-crystal by 90°. The approach is based on the idea that the dispersive spectra, which are obtained when applying read-pulses at specific rotor-phases, not only yield the size of the eigenvalues but also encode the orientation of the different chemical shift (rank-2) tensors. For this purpose two 2D-data sets with orthogonal crystal orientation are fitted simultaneously. The presented analysis for chemical shift tensors is supported by an analytical formula which allows fast calculation of phase and amplitude of individual spinning side-bands and by a protocol which solves the problem of finding the correct reference phase of the spectrum. Different rotor-synchronized pulse-sequences are introduced for the same reason. Experiments are performed on L-alanine and O-phosphorylethanolamine and the observed errors are analyzed in detail. The experimental data are opposed to DFT-computed chemical shift tensors which have been obtained by the extended embedded ion method.

Observational constraints on loop quantum cosmology.

PubMed

Bojowald, Martin; Calcagni, Gianluca; Tsujikawa, Shinji

2011-11-18

In the inflationary scenario of loop quantum cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to compare with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background and other cosmological experiments, we place bounds on the quantum corrections.

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.

1984-01-01

The technical progress of researches Alternatives for Jet Engine Control is reported. A numerical study employing feedback tensors for optimal control of nonlinear systems was completed. It is believed that these studies are the first of their kind. State regulation, with a decrease in control power is demonstrated. A detailed treatment follows.

Description and Features of UX-Analyze

DTIC Science & Technology

2009-02-01

POB model and GUI for EM63 Inversion The full Pasion -Oldenburg-Billings (POB) analysis assumes an axially symmetric (axial and transverse) tensor...output from the EM63 inversion. 1 Pasion , L.R., and Oldenburg, D.W., 2001, Locating and

MEASUREMENTS OF SUB-DEGREE B -MODE POLARIZATION IN THE COSMIC MICROWAVE BACKGROUND FROM 100 SQUARE DEGREES OF SPTPOL DATA

DOE PAGES

Keisler, R.; Hoover, S.; Harrington, N.; ...

2015-07-09

We present a measurement of themore » $B$-mode polarization power spectrum (the $BB$ spectrum) from 100 $$\\mathrm{deg}^2$$ of sky observed with SPTpol, a polarization-sensitive receiver currently installed on the South Pole Telescope. The observations used in this work were taken during 2012 and early 2013 and include data in spectral bands centered at 95 and 150 GHz. We report the $BB$ spectrum in five bins in multipole space, spanning the range $$300 \\le \\ell \\le 2300$$, and for three spectral combinations: 95 GHz $$\\times$$ 95 GHz, 95 GHz $$\\times$$ 150 GHz, and 150 GHz $$\\times$$ 150 GHz. We subtract small ($$< 0.5 \\sigma$$ in units of statistical uncertainty) biases from these spectra and account for the uncertainty in those biases. The resulting power spectra are inconsistent with zero power but consistent with predictions for the $BB$ spectrum arising from the gravitational lensing of $E$-mode polarization. If we assume no other source of $BB$ power besides lensed $B$ modes, we determine a preference for lensed $B$ modes of $$4.9 \\sigma$$. After marginalizing over tensor power and foregrounds, namely polarized emission from galactic dust and extragalactic sources, this significance is $$4.3 \\sigma$$. Fitting for a single parameter, $$A_\\mathrm{lens}$$, that multiplies the predicted lensed $B$-mode spectrum, and marginalizing over tensor power and foregrounds, we find $$A_\\mathrm{lens} = 1.08 \\pm 0.26$$, indicating that our measured spectra are consistent with the signal expected from gravitational lensing. The data presented here provide the best measurement to date of the $B$-mode power spectrum on these angular scales.« less

On the initial conditions of scalar and tensor fluctuations in f(R,φ ) gravity

NASA Astrophysics Data System (ADS)

Cheraghchi, S.; Shojai, F.

2018-05-01

We have considered the perturbation equations governing the growth of fluctuations during inflation in generalized scalar tensor theory f(R,φ ). We have found that the scalar metric perturbations at very early times are negligible compared to the scalar field perturbation, just like general relativity. At sufficiently early times, when the physical momentum of perturbation mode, q / a is much larger than the Hubble parameter H, i.e. q/a≫ H, we have obtained the metric and scalar field perturbation in the form of WKB solutions up to an undetermined coefficient. Then we have quantized the scalar fluctuations and expanded the metric and the scalar field perturbations with the help of annihilation and creation operators of the scalar field perturbation. The standard commutation relations of annihilation and creation operators fix the unknown coefficient. Going over to the gauge invariant quantities which are conserved beyond the horizon, we have obtained the initial condition of the generalized Mukhanov-Sasaki equation. Then a similar procedure is performed for the case of tensor metric perturbation. As an example of the generalized Mukhanov-Sasaki equation and its initial condition, we have proposed a power-law functional form as f(R,φ )=f_0 R^m φ ^n and obtained an exact inflationary solution. In this background, then we have discussed how the scalar and tensor fluctuations grow.

An anisotropic universe due to dimension-changing vacuum decay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scargill, James H.C., E-mail: james.scargill@physics.ox.ac.uk

In this paper we consider the question of observational signatures of a false vacuum decay event in the early universe followed by a period of inflation; in particular, motivated by the string landscape, we consider decays in which the parent vacuum has a smaller number of large dimensions than the current vacuum, which leads to an anisotropic universe. We go beyond previous studies, and examine the effects on the CMB temperature and polarisation power spectra, due to both scalar and tensor modes, and consider not only late-time effects but also the full cosmological perturbation theory at early times. We findmore » that whilst the scalar mode behaves as one would expect, and the effects of anisotropy at early times are sub-dominant to the late-time effects already studied, for the tensor modes in fact the the early-time effects grow with multipole and can become much larger than one would expect, even dominating over the late-time effects. Thus these effects should be included if one is looking for such a signal in the tensor modes.« less

Logamediate Inflation in f(T) Teleparallel Gravity

NASA Astrophysics Data System (ADS)

Rezazadeh, Kazem; Abdolmaleki, Asrin; Karami, Kayoomars

2017-02-01

We study logamediate inflation in the context of f(T) teleparallel gravity. f(T)-gravity is a generalization of the teleparallel gravity which is formulated on the Weitzenbock spacetime, characterized by the vanishing curvature tensor (absolute parallelism) and the non-vanishing torsion tensor. We consider an f(T)-gravity model which is sourced by a canonical scalar field. Assuming a power-law f(T) function in the action, we investigate an inflationary universe with a logamediate scale factor. Our results show that, although logamediate inflation is completely ruled out by observational data in the standard inflationary scenario based on Einstein gravity, it can be compatible with the 68% confidence limit joint region of Planck 2015 TT,TE,EE+lowP data in the framework of f(T)-gravity.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rezazadeh, Kazem; Karami, Kayoomars; Abdolmaleki, Asrin, E-mail: rezazadeh86@gmail.com

We study logamediate inflation in the context of f ( T ) teleparallel gravity. f ( T )-gravity is a generalization of the teleparallel gravity which is formulated on the Weitzenbock spacetime, characterized by the vanishing curvature tensor (absolute parallelism) and the non-vanishing torsion tensor. We consider an f ( T )-gravity model which is sourced by a canonical scalar field. Assuming a power-law f ( T ) function in the action, we investigate an inflationary universe with a logamediate scale factor. Our results show that, although logamediate inflation is completely ruled out by observational data in the standard inflationarymore » scenario based on Einstein gravity, it can be compatible with the 68% confidence limit joint region of Planck 2015 TT,TE,EE+lowP data in the framework of f ( T )-gravity.« less

On integrability of the Killing equation

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

Chaplygin gas inspired scalar fields inflation via well-known potentials

NASA Astrophysics Data System (ADS)

Jawad, Abdul; Butt, Sadaf; Rani, Shamaila

2016-08-01

Brane inflationary universe models in the context of modified Chaplygin gas and generalized cosmic Chaplygin gas are being studied. We develop these models in view of standard scalar and tachyon fields. In both models, the implemented inflationary parameters such as scalar and tensor power spectra, scalar spectral index and tensor to scalar ratio are derived under slow roll approximations. We also use chaotic and exponential potential in high energy limits and discuss the characteristics of inflationary parameters for both potentials. These models are compatible with recent astronomical observations provided by WMAP7{+}9 and Planck data, i.e., ηs=1.027±0.051, 1.009±0.049, 0.096±0.025 and r<0.38, 0.36, 0.11.

Limits on tensor coupling from neutron β decay

NASA Astrophysics Data System (ADS)

Pattie, R. W., Jr.; Hickerson, K. P.; Young, A. R.

2013-10-01

Limits on the tensor couplings generating a Fierz interference term b in mixed Gamow-Teller Fermi decays can be derived by combining data from measurements of angular correlation parameters in neutron decay, the neutron lifetime, and GV=GFVud as extracted from measurements of the Ft values from the 0+→0+ superallowed decay data set. These limits are derived by comparing the neutron β-decay rate as predicted in the standard model with the measured decay rate while allowing for the existence of beyond the standard model (BSM) couplings. We analyze limits derived from the electron-neutrino asymmetry a, or the beta asymmetry A, finding that the most stringent limits for CT/CA under the assumption of no right-handed neutrinos is -0.0026

Dense lower crust elevates long-term earthquake rates in the New Madrid seismic zone

USGS Publications Warehouse

Levandowski, William Brower; Boyd, Oliver; Ramirez-Guzman, Leonardo

2016-01-01

Knowledge of the local state of stress is critical in appraising intraplate seismic hazard. Inverting earthquake moment tensors, we demonstrate that principal stress directions in the New Madrid seismic zone (NMSZ) differ significantly from those in the surrounding region. Faults in the NMSZ that are incompatible with slip in the regional stress field are favorably oriented relative to local stress. We jointly analyze seismic velocity, gravity, and topography to develop a 3-D crustal and upper mantle density model, revealing uniquely dense lower crust beneath the NMSZ. Finite element simulations then estimate the stress tensor due to gravitational body forces, which sums with regional stress. The anomalous lower crust both elevates gravity-derived stress at seismogenic depths in the NMSZ and rotates it to interfere more constructively with far-field stress, producing a regionally maximal deviatoric stress coincident with the highest concentration of modern seismicity. Moreover, predicted principal stress directions mirror variations (observed independently in moment tensors) at the NMSZ and across the region.

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

PubMed

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

2016-05-01

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

A Type-2 Block-Component-Decomposition Based 2D AOA Estimation Algorithm for an Electromagnetic Vector Sensor Array

PubMed Central

Gao, Yu-Fei; Gui, Guan; Xie, Wei; Zou, Yan-Bin; Yang, Yue; Wan, Qun

2017-01-01

This paper investigates a two-dimensional angle of arrival (2D AOA) estimation algorithm for the electromagnetic vector sensor (EMVS) array based on Type-2 block component decomposition (BCD) tensor modeling. Such a tensor decomposition method can take full advantage of the multidimensional structural information of electromagnetic signals to accomplish blind estimation for array parameters with higher resolution. However, existing tensor decomposition methods encounter many restrictions in applications of the EMVS array, such as the strict requirement for uniqueness conditions of decomposition, the inability to handle partially-polarized signals, etc. To solve these problems, this paper investigates tensor modeling for partially-polarized signals of an L-shaped EMVS array. The 2D AOA estimation algorithm based on rank-(L1,L2,·) BCD is developed, and the uniqueness condition of decomposition is analyzed. By means of the estimated steering matrix, the proposed algorithm can automatically achieve angle pair-matching. Numerical experiments demonstrate that the present algorithm has the advantages of both accuracy and robustness of parameter estimation. Even under the conditions of lower SNR, small angular separation and limited snapshots, the proposed algorithm still possesses better performance than subspace methods and the canonical polyadic decomposition (CPD) method. PMID:28448431

A Type-2 Block-Component-Decomposition Based 2D AOA Estimation Algorithm for an Electromagnetic Vector Sensor Array.

PubMed

Gao, Yu-Fei; Gui, Guan; Xie, Wei; Zou, Yan-Bin; Yang, Yue; Wan, Qun

2017-04-27

This paper investigates a two-dimensional angle of arrival (2D AOA) estimation algorithm for the electromagnetic vector sensor (EMVS) array based on Type-2 block component decomposition (BCD) tensor modeling. Such a tensor decomposition method can take full advantage of the multidimensional structural information of electromagnetic signals to accomplish blind estimation for array parameters with higher resolution. However, existing tensor decomposition methods encounter many restrictions in applications of the EMVS array, such as the strict requirement for uniqueness conditions of decomposition, the inability to handle partially-polarized signals, etc. To solve these problems, this paper investigates tensor modeling for partially-polarized signals of an L-shaped EMVS array. The 2D AOA estimation algorithm based on rank- ( L 1 , L 2 , · ) BCD is developed, and the uniqueness condition of decomposition is analyzed. By means of the estimated steering matrix, the proposed algorithm can automatically achieve angle pair-matching. Numerical experiments demonstrate that the present algorithm has the advantages of both accuracy and robustness of parameter estimation. Even under the conditions of lower SNR, small angular separation and limited snapshots, the proposed algorithm still possesses better performance than subspace methods and the canonical polyadic decomposition (CPD) method.

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation

PubMed Central

Duarte-Carvajalino, Julio M.; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis. PMID:23596381

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation.

PubMed

Duarte-Carvajalino, Julio M; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis.

Tilted Kantowski-Sachs cosmological model in Brans-Dicke theory of gravitation

NASA Astrophysics Data System (ADS)

Pawar, D. D.; Shahare, S. P.; Dagwal, V. J.

2018-02-01

Tilted Kantowski-Sachs cosmological model in Brans-Dicke theory for perfect fluid has been investigated. The general solution of field equations in Brans-Dicke theory for the combined scalar and tensor field are obtained by using power law relation. Also, some physical and geometrical parameters are obtained and discussed.

Does MRI scan acceleration affect power to track brain change?

PubMed

Ching, Christopher R K; Hua, Xue; Hibar, Derrek P; Ward, Chadwick P; Gunter, Jeffrey L; Bernstein, Matt A; Jack, Clifford R; Weiner, Michael W; Thompson, Paul M

2015-01-01

The Alzheimer's Disease Neuroimaging Initiative recently implemented accelerated T1-weighted structural imaging to reduce scan times. Faster scans may reduce study costs and patient attrition by accommodating people who cannot tolerate long scan sessions. However, little is known about how scan acceleration affects the power to detect longitudinal brain change. Using tensor-based morphometry, no significant difference was detected in numerical summaries of atrophy rates from accelerated and nonaccelerated scans in subgroups of patients with Alzheimer's disease, early or late mild cognitive impairment, or healthy controls over a 6- and 12-month scan interval. Whole-brain voxelwise mapping analyses revealed some apparent regional differences in 6-month atrophy rates when comparing all subjects irrespective of diagnosis (n = 345). No such whole-brain difference was detected for the 12-month scan interval (n = 156). Effect sizes for structural brain changes were not detectably different in accelerated versus nonaccelerated data. Scan acceleration may influence brain measures but has minimal effects on tensor-based morphometry-derived atrophy measures, at least over the 6- and 12-month intervals examined here. Copyright © 2015 Elsevier Inc. All rights reserved.

Equivalence of restricted Boltzmann machines and tensor network states

NASA Astrophysics Data System (ADS)

Chen, Jing; Cheng, Song; Xie, Haidong; Wang, Lei; Xiang, Tao

2018-02-01

The restricted Boltzmann machine (RBM) is one of the fundamental building blocks of deep learning. RBM finds wide applications in dimensional reduction, feature extraction, and recommender systems via modeling the probability distributions of a variety of input data including natural images, speech signals, and customer ratings, etc. We build a bridge between RBM and tensor network states (TNS) widely used in quantum many-body physics research. We devise efficient algorithms to translate an RBM into the commonly used TNS. Conversely, we give sufficient and necessary conditions to determine whether a TNS can be transformed into an RBM of given architectures. Revealing these general and constructive connections can cross fertilize both deep learning and quantum many-body physics. Notably, by exploiting the entanglement entropy bound of TNS, we can rigorously quantify the expressive power of RBM on complex data sets. Insights into TNS and its entanglement capacity can guide the design of more powerful deep learning architectures. On the other hand, RBM can represent quantum many-body states with fewer parameters compared to TNS, which may allow more efficient classical simulations.

On gauge invariant cosmological perturbations in UV-modified Hořava gravity

NASA Astrophysics Data System (ADS)

Shin, Sunyoung; Park, Mu-In

2017-12-01

We consider gauge invariant cosmological perturbations in UV-modified, z = 3 (non-projectable) Hořava gravity with one scalar matter field, which has been proposed as a renormalizable gravity theory without the ghost problem in four dimensions. In order to exhibit its dynamical degrees of freedom, we consider the Hamiltonian reduction method and find that, by solving all the constraint equations, the degrees of freedom are the same as those of Einstein gravity: one scalar and two tensor (graviton) modes when a scalar matter field presents. However, we confirm that there is no extra graviton modes and general relativity is recovered in IR, which achieves the consistency of the model. From the UV-modification terms which break the detailed balance condition in UV, we obtain scale-invariant power spectrums for non-inflationary backgrounds, like the power-law expansions, without knowing the details of early expansion history of Universe. This could provide a new framework for the Big Bang cosmology. Moreover, we find that tensor and scalar fluctuations travel differently in UV, generally. We present also some clarifying remarks about confusing points in the literatures.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chowdhury, Debika; Sriramkumar, L.; Sreenath, V., E-mail: debika@physics.iitm.ac.in, E-mail: sreenath@lsu.edu, E-mail: sriram@physics.iitm.ac.in

The axion monodromy model involves a canonical scalar field that is governed by a linear potential with superimposed modulations. The modulations in the potential are responsible for a resonant behavior which gives rise to persisting oscillations in the scalar and, to a smaller extent, in the tensor power spectra. Interestingly, such spectra have been shown to lead to an improved fit to the cosmological data than the more conventional, nearly scale invariant, primordial power spectra. The scalar bi-spectrum in the model too exhibits continued modulations and the resonance is known to boost the amplitude of the scalar non-Gaussianity parameter tomore » rather large values. An analytical expression for the scalar bi-spectrum had been arrived at earlier which, in fact, has been used to compare the model with the cosmic microwave background anisotropies at the level of three-point functions involving scalars. In this work, with future applications in mind, we arrive at a similar analytical template for the scalar-scalar-tensor cross-correlation. We also analytically establish the consistency relation (in the squeezed limit) for this three-point function. We conclude with a summary of the main results obtained.« less

Homogenized moment tensor and the effect of near-field heterogeneities on nonisotropic radiation in nuclear explosion

NASA Astrophysics Data System (ADS)

Burgos, Gaël.; Capdeville, Yann; Guillot, Laurent

2016-06-01

We investigate the effect of small-scale heterogeneities close to a seismic explosive source, at intermediate periods (20-50 s), with an emphasis on the resulting nonisotropic far-field radiation. First, using a direct numerical approach, we show that small-scale elastic heterogeneities located in the near-field of an explosive source, generate unexpected phases (i.e., long period S waves). We then demonstrate that the nonperiodic homogenization theory applied to 2-D and 3-D elastic models, with various pattern of small-scale heterogeneities near the source, leads to accurate waveforms at a reduced computational cost compared to direct modeling. Further, it gives an interpretation of how nearby small-scale features interact with the source at low frequencies, through an explicit correction to the seismic moment tensor. In 2-D simulations, we find a deviatoric contribution to the moment tensor, as high as 21% for near-source heterogeneities showing a 25% contrast of elastic values (relative to a homogeneous background medium). In 3-D this nonisotropic contribution reaches 27%. Second, we analyze intermediate-periods regional seismic waveforms associated with some underground nuclear explosions conducted at the Nevada National Security Site and invert for the full moment tensor, in order to quantify the relative contribution of the isotropic and deviatoric components of the tensor. The average value of the deviatoric part is about 35%. We conclude that the interactions between an explosive source and small-scale local heterogeneities of moderate amplitude may lead to a deviatoric contribution to the seismic moment, close to what is observed using regional data from nuclear test explosions.

Resurrecting the Power-law, Intermediate, and Logamediate Inflations in the DBI Scenario with Constant Sound Speed

NASA Astrophysics Data System (ADS)

Amani, Roonak; Rezazadeh, Kazem; Abdolmaleki, Asrin; Karami, Kayoomars

2018-02-01

We investigate the power-law, intermediate, and logamediate inflationary models in the framework of DBI non-canonical scalar field with constant sound speed. In the DBI setting, we first represent the power spectrum of both scalar density and tensor gravitational perturbations. Then, we derive different inflationary observables including the scalar spectral index n s , the running of the scalar spectral index {{dn}}s/d{ln}k, and the tensor-to-scalar ratio r. We show that the 95% CL constraint of the Planck 2015 T + E data on the non-Gaussianity parameter {f}{NL}{DBI} leads to the sound speed bound {c}s≥slant 0.087 in the DBI inflation. Moreover, our results imply that, although the predictions of the power-law, intermediate, and logamediate inflations in the standard canonical framework (c s = 1) are not consistent with the Planck 2015 data, in the DBI scenario with constant sound speed {c}s< 1, the result of the r-{n}s diagram for these models can lie inside the 68% CL region favored by Planck 2015 TT,TE,EE+lowP data. We also specify the parameter space of the power-law, intermediate, and logamediate inflations for which our models are compatible with the 68% or 95% CL regions of the Planck 2015 TT,TE,EE+lowP data. Using the allowed ranges of the parameter space of the intermediate and logamediate inflationary models, we estimate the running of the scalar spectral index and find that it is compatible with the 95% CL constraint from the Planck 2015 TT,TE,EE+lowP data.

Global moment tensor computation at GFZ Potsdam

NASA Astrophysics Data System (ADS)

Saul, J.; Becker, J.; Hanka, W.

2011-12-01

As part of its earthquake information service, GFZ Potsdam has started to provide seismic moment tensor solutions for significant earthquakes world-wide. The software used to compute the moment tensors is a GFZ-Potsdam in-house development, which uses the framework of the software SeisComP 3 (Hanka et al., 2010). SeisComP 3 (SC3) is a software package for seismological data acquisition, archival, quality control and analysis. SC3 is developed by GFZ Potsdam with significant contributions from its user community. The moment tensor inversion technique uses a combination of several wave types, time windows and frequency bands depending on magnitude and station distance. Wave types include body, surface and mantle waves as well as the so-called 'W-Phase' (Kanamori and Rivera, 2008). The inversion is currently performed in the time domain only. An iterative centroid search can be performed independently both horizontally and in depth. Moment tensors are currently computed in a semi-automatic fashion. This involves inversions that are performed automatically in near-real time, followed by analyst review prior to publication. The automatic results are quite often good enough to be published without further improvements, sometimes in less than 30 minutes from origin time. In those cases where a manual interaction is still required, the automatic inversion usually does a good job at pre-selecting those traces that are the most relevant for the inversion, keeping the work required for the analyst at a minimum. Our published moment tensors are generally in good agreement with those published by the Global Centroid-Moment-Tensor (GCMT) project for earthquakes above a magnitude of about Mw 5. Additionally we provide solutions for smaller earthquakes above about Mw 4 in Europe, which are normally not analyzed by the GCMT project. We find that for earthquakes above Mw 6, the most robust automatic inversions can usually be obtained using the W-Phase time window. The GFZ earthquake bulletin is located at http://geofon.gfz-potsdam.de/eqinfo For more information on the SeisComP 3 software visit http://www.seiscomp3.org

Analysis of seismicity and stress before and after the Mw 8.1 Pisagua, Chile, 2014 earthquake

NASA Astrophysics Data System (ADS)

Grigoli, F.; Cesca, S.; Dahm, T.; Hainzl, S.

2014-12-01

On April 1st, 2014 at 23:46:50 UTC, a powerful earthquake of magnitude Mw 8.1 occurred offshore the Northern Chile in the region of the North Chilean seismic gap. The epicenter of the earthquake was approximately 50 km offshore the Chilean coast, near the town of Pisagua. Two days after the main event a Mw 7.6 aftershock struck approximately the same area. In order to identify spatio-temporal changes of source parameters and stress before and after the mainshock, we analyzed in detail the local seismicity above magnitude Mw 3.0 within the time period 01/01/2013-30/04/2014 and estimated long term trends in b-values and earthquake productivity. We used data from the IPOC (Integrated Plate boundary Observatory Chile) regional seismic network, consisting of 20 "in land" broadband station deployed and managed by the GFZ-Potsdam. The recorded earthquake catalog shows an intense foreshock activity consisting of more than 1000 M3+ events in the source region. Full waveform techniques are used to derive both locations and focal mechanisms of about 435 seismic events. The location process has been performed by using a waveform stacking method (Grigoli et al 2013, 2014) with a layered velocity model based on CRUST 2.0 (see the attached figure for the location results of one of these events). Moment tensor inversion has been performed by using the KIWI tool software (Cesca et al. 2010), which is based on a two-step inversion approach. The first step consists in the inversion of the amplitude spectra to retrieve the best fitting focal planes, while the second inversion step is carried out in time domain to solve the focal mechanism polarity and to obtain the centroid location and time. Both location and moment tensor inversion resulted in agreement with the geodynamical settings of the region. Mapping the b-value reveals a spatiotemporal anomaly of low b-values characterizing the frequency-magnitude distribution of the foreshocks in the source area of the mainshock. Finally, clustering analysis of the retrieved focal mechanism and a stress tensor inversion has been performed in order to analyze the spatio-temporal evolution of the stress, before and after the mainshock. This work has been funded by the German BMBF "Geothecnologien" project MINE (BMBF03G0737A) and by Hazard and Risk Team (HART) and PBO-Chile of GFZ.

Turbulent statistics in flow field due to interaction of two plane parallel jets

NASA Astrophysics Data System (ADS)

Bisoi, Mukul; Das, Manab Kumar; Roy, Subhransu; Patel, Devendra Kumar

2017-12-01

Turbulent characteristics of flow fields due to the interaction of two plane parallel jets separated by the jet width distance are studied. Numerical simulation is carried out by large eddy simulation with a dynamic Smagorinsky model for the sub-grid scale stresses. The energy spectra are observed to follow the -5/3 power law for the inertial sub-range. A proper orthogonal decomposition study indicates that the energy carrying large coherent structures is present close to the nozzle exit. It is shown that these coherent structures interact with each other and finally disintegrate into smaller vortices further downstream. The turbulent fluctuations in the longitudinal and lateral directions are shown to follow a similarity. The mean flow at the same time also maintains a close similarity. Prandtl's mixing length, the Taylor microscale, and the Kolmogorov length scales are shown along the lateral direction for different downstream locations. The autocorrelation in the longitudinal and transverse directions is seen to follow a similarity profile. By plotting the probability density function, the skewness and the flatness (kurtosis) are analyzed. The Reynolds stress anisotropy tensor is calculated, and the anisotropy invariant map known as Lumley's triangle is presented and analyzed.

Dispersion characteristics of anisotropic unmagnetized ultra-relativistic transverse plasma wave with arbitrary electron degeneracy

NASA Astrophysics Data System (ADS)

Sarfraz, M.; Farooq, H.; Abbas, G.; Noureen, S.; Iqbal, Z.; Rasheed, A.

2018-03-01

Thermal momentum space anisotropy is ubiquitous in many astrophysical and laboratory plasma environments. Using Vlasov-Maxwell's model equations, a generalized polarization tensor for a collisionless ultra-relativistic unmagnetized electron plasma is derived. In particular, the tensor is obtained by considering anisotropy in the momentum space. The integral of moments of Fermi-Dirac distribution function in terms of Polylog functions is used for describing the border line plasma systems (T/e TF e ≈1 ) comprising arbitrary electron degeneracy, where Te and TF e, are thermal and Fermi temperatures, respectively. Furthermore, the effects of variation in thermal momentum space anisotropy on the electron equilibrium number density and the spectrum of electromagnetic waves are analyzed.

Large-scale magnetic fields, non-Gaussianity, and gravitational waves from inflation

NASA Astrophysics Data System (ADS)

Bamba, Kazuharu

2017-12-01

We explore the generation of large-scale magnetic fields in the so-called moduli inflation. The hypercharge electromagnetic fields couple to not only a scalar field but also a pseudoscalar one, so that the conformal invariance of the hypercharge electromagnetic fields can be broken. We explicitly analyze the strength of the magnetic fields on the Hubble horizon scale at the present time, the local non-Gaussianity of the curvature perturbations originating from the massive gauge fields, and the tensor-to-scalar ratio of the density perturbations. As a consequence, we find that the local non-Gaussianity and the tensor-to-scalar ratio are compatible with the recent Planck results.

Simplified moment tensor analysis and unified decomposition of acoustic emission source: Application to in situ hydrofracturing test

NASA Astrophysics Data System (ADS)

Ohtsu, Masayasu

1991-04-01

An application of a moment tensor analysis to acoustic emission (AE) is studied to elucidate crack types and orientations of AE sources. In the analysis, simplified treatment is desirable, because hundreds of AE records are obtained from just one experiment and thus sophisticated treatment is realistically cumbersome. Consequently, a moment tensor inversion based on P wave amplitude is employed to determine six independent tensor components. Selecting only P wave portion from the full-space Green's function of homogeneous and isotropic material, a computer code named SiGMA (simplified Green's functions for the moment tensor analysis) is developed for the AE inversion analysis. To classify crack type and to determine crack orientation from moment tensor components, a unified decomposition of eigenvalues into a double-couple (DC) part, a compensated linear vector dipole (CLVD) part, and an isotropic part is proposed. The aim of the decomposition is to determine the proportion of shear contribution (DC) and tensile contribution (CLVD + isotropic) on AE sources and to classify cracks into a crack type of the dominant motion. Crack orientations determined from eigenvectors are presented as crack-opening vectors for tensile cracks and fault motion vectors for shear cracks, instead of stereonets. The SiGMA inversion and the unified decomposition are applied to synthetic data and AE waveforms detected during an in situ hydrofracturing test. To check the accuracy of the procedure, numerical experiments are performed on the synthetic waveforms, including cases with 10% random noise added. Results show reasonable agreement with assumed crack configurations. Although the maximum error is approximately 10% with respect to the ratios, the differences on crack orientations are less than 7°. AE waveforms detected by eight accelerometers deployed during the hydrofracturing test are analyzed. Crack types and orientations determined are in reasonable agreement with a predicted failure plane from borehole TV observation. The results suggest that tensile cracks are generated first at weak seams and then shear cracks follow on the opened joints.

Ergodic actions of SμU(2) on C∗-algebras from II1 subfactors

NASA Astrophysics Data System (ADS)

Pinzari, Claudia; Roberts, John E.

2010-03-01

To a proper inclusion N⊂M of II factors of finite Jones index [M:N], we associate an ergodic C∗-action of the quantum group SμU(2) (or more generally of certain groups Ao(F)). The higher relative commutant N'∩M can be identified with the spectral space of the rth tensor power u of the defining representation of the quantum group. The index and the deformation parameter are related by -1≤μ<0 and [M:N]=|μ+μ-1|. This ergodic action may be thought of as a virtual subgroup of SμU(2) in the sense of Mackey arising from the tensor category generated by the N-bimodule NMN. μ is negative as NMN is a real bimodule.

Comparing potential-driven DBI-inspired non-minimal kinetic coupling (Dinkic) inflation with observational data

NASA Astrophysics Data System (ADS)

Chen, Jun; Hou, Wenjie; Qiu, Taotao; Hou, Defu

2018-04-01

In our previous work [1], a new kind of inflation model was proposed, which has the interesting property that its perturbation equation of motion gets a correction of k 4, due to the non-linearity of the kinetic term. Nonetheless, the scale-invariance of the power spectrum remains valid, both in large-k and small-k limits. In this paper, we investigate in detail the spectral index, the index running and the tensor/scalar ratio in this model, especially in the potential-driven case, and compare the results with the current PLANCK/BICEP observational data. We also discuss the tensor spectrum in this case, which is expected to be tested by future observations of primordial gravitational waves. Supported by NSFC (11405069, 11653002, 11735007, 111375070)

Finding the chiral gravitational wave background of an axion-S U (2 ) inflationary model using CMB observations and laser interferometers

NASA Astrophysics Data System (ADS)

Thorne, Ben; Fujita, Tomohiro; Hazumi, Masashi; Katayama, Nobuhiko; Komatsu, Eiichiro; Shiraishi, Maresuke

2018-02-01

A detection of B-mode polarization of the cosmic microwave background (CMB) anisotropies would confirm the presence of a primordial gravitational wave background (GWB). In the inflation paradigm, this would be an unprecedented probe of the energy scale of inflation as it is directly proportional to the power spectrum of the GWB. However, similar tensor perturbations can be produced by the matter fields present during inflation, breaking the simple relationship between energy scale and the tensor-to-scalar ratio r . It is therefore important to find ways of distinguishing between the generation mechanisms of the GWB. Without doing a full model selection, we analyze the detectability of a new axion-S U (2 ) gauge field model by calculating the signal-to-noise ratio of future CMB and interferometer observations sensitive to the chirality of the tensor spectrum. We forecast the detectability of the resulting CMB temperature and B-mode (TB) or E-mode and B-mode (EB) cross-correlation by the LiteBIRD satellite, considering the effects of residual foregrounds, gravitational lensing, and assess the ability of such an experiment to jointly detect primordial TB and EB spectra and self-calibrate its polarimeter. We find that LiteBIRD will be able to detect the chiral signal for r*>0.03 , with r* denoting the tensor-to-scalar ratio at the peak scale, and that the maximum signal-to-noise ratio for r*<0.07 is ˜2 . We go on to consider an advanced stage of a LISA-like mission, which is designed to be sensitive to the intensity and polarization of the GWB. We find that such experiments would complement CMB observations as they would be able to detect the chirality of the GWB with high significance on scales inaccessible to the CMB. We conclude that CMB two-point statistics are limited in their ability to distinguish this model from a conventional vacuum fluctuation model of GWB generation, due to the fundamental limits on their sensitivity to parity violation. In order to test the predictions of such a model as compared to vacuum fluctuations, it will be necessary to test deviations from the self-consistency relation or use higher order statistics to leverage the non-Gaussianity of the model. On the other hand, in the case of a spectrum peaked at very small scales inaccessible to the CMB, a highly significant detection could be made using space-based laser interferometers.

Classification of trivial spin-1 tensor network states on a square lattice

NASA Astrophysics Data System (ADS)

Lee, Hyunyong; Han, Jung Hoon

2016-09-01

Classification of possible quantum spin liquid (QSL) states of interacting spin-1/2's in two dimensions has been a fascinating topic of condensed matter for decades, resulting in enormous progress in our understanding of low-dimensional quantum matter. By contrast, relatively little work exists on the identification, let alone classification, of QSL phases for spin-1 systems in dimensions higher than one. Employing the powerful ideas of tensor network theory and its classification, we develop general methods for writing QSL wave functions of spin-1 respecting all the lattice symmetries, spin rotation, and time reversal with trivial gauge structure on the square lattice. We find 25 distinct classes characterized by five binary quantum numbers. Several explicit constructions of such wave functions are given for bond dimensions D ranging from two to four, along with thorough numerical analyses to identify their physical characters. Both gapless and gapped states are found. The topological entanglement entropy of the gapped states is close to zero, indicative of topologically trivial states. In D =4 , several different tensors can be linearly combined to produce a family of states within the same symmetry class. A rich "phase diagram" can be worked out among the phases of these tensors, as well as the phase transitions among them. Among the states we identified in this putative phase diagram is the plaquette-ordered phase, gapped resonating valence bond phase, and a critical phase. A continuous transition separates the plaquette-ordered phase from the resonating valence bond phase.

Cosmology of non-minimal derivative coupling to gravity in Palatini formalism and its chaotic inflation

NASA Astrophysics Data System (ADS)

Kaewkhao, Narakorn; Gumjudpai, Burin

2018-06-01

We consider, in Palatini formalism, a modified gravity of which the scalar field derivative couples to Einstein tensor. In this scenario, Ricci scalar, Ricci tensor and Einstein tensor are functions of connection field. As a result, the connection field gives rise to relation, hμν = fgμν between effective metric, hμν and the usual metric gμν where f = 1 - κϕ,αϕ,α / 2. In FLRW universe, NMDC coupling constant is limited in a range of - 2 /ϕ˙2 < κ ≤ ∞ preserving Lorentz signature of the effective metric. Slowly-rolling regime provides κ < 0 forbidding graviton from traveling at superluminal speed. Effective gravitational coupling and entropy of blackhole's apparent horizon are derived. In case of negative coupling, acceleration could happen even with weff > - 1 / 3. Power-law potentials of chaotic inflation are considered. For V ∝ϕ2 and V ∝ϕ4, it is possible to obtain tensor-to-scalar ratio lower than that of GR so that it satisfies r < 0 . 12 as constrained by Planck 2015 (Ade et al., 2016). The V ∝ϕ2 case yields acceptable range of spectrum index and r values. The quartic potential's spectrum index is disfavored by the Planck results. Viable range of κ for V ∝ϕ2 case lies in positive region, resulting in less blackhole's entropy, superluminal metric, more amount of inflation, avoidance of super-Planckian field initial value and stronger gravitational constant.

Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Orlando, Giorgio

2017-07-01

Considering high-energy modifications of Einstein gravity during inflation is an interesting issue. We can constrain the strength of the new gravitational terms through observations of inflationary imprints in the actual universe. In this paper we analyze the effects on slow-roll models due to a Chern-Simons term coupled to the inflaton field through a generic coupling function f(phi). A well known result is the polarization of primordial gravitational waves (PGW) into left and right eigenstates, as a consequence of parity breaking. In such a scenario the modifications to the power spectrum of PGW are suppressed under the conditions that allow to avoid the production of ghost gravitons at a certain energy scale, the so-called Chern-Simons mass MCS. In general it has been recently pointed out that there is very little hope to efficiently constrain chirality of PGW on the basis solely of two-point statistics from future CMB data, even in the most optimistic cases. Thus we search if significant parity breaking signatures can arise at least in the bispectrum statistics. We find that the tensor-tensor-scalar bispectra langle γ γ ζ rangle for each polarization state are the only ones that are not suppressed. Their amplitude, setting the level of parity breaking during inflation, is proportional to the second derivative of the coupling function f(phi) and they turn out to be maximum in the squeezed limit. We comment on the squeezed-limit consistency relation arising in the case of chiral gravitational waves, and on possible observables to constrain these signatures.

Integrability conditions for Killing-Yano tensors and conformal Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Batista, Carlos

2015-01-01

The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing-Yano tensor of order p to generate a Killing-Yano tensor of order (p -1 ) . Finally, it is proved that in maximally symmetric spaces the covariant derivative of a Killing-Yano tensor is a closed conformal Killing-Yano tensor and that every conformal Killing-Yano tensor is uniquely decomposed as the sum of a Killing-Yano tensor and a closed conformal Killing-Yano tensor.

Diffusion Tensor Imaging of Heterotopia: Changes of Fractional Anisotropy during Radial Migration of Neurons

PubMed Central

Kim, Jinna

2010-01-01

Purpose Diffusion tensor imaging provides better understanding of pathophysiology of congenital anomalies, involving central nervous system. This study was aimed to specify the pathogenetic mechanism of heterotopia, proved by diffusion tensor imaging, and establish new findings of heterotopia on fractional anisotropy maps. Materials and Methods Diffusion-weighted imaging data from 11 patients (M : F = 7 : 4, aged from 1 to 22 years, mean = 12.3 years) who visited the epilepsy clinic and received a routine seizure protocol MRI exam were retrospectively analyzed. Fractional anisotropy (FA) maps were generated from diffusion tensor imaging of 11 patients with heterotopia. Regions of interests (ROI) were placed in cerebral cortex, heterotopic gray matter and deep gray matter, including putamen. ANOVA analysis was performed for comparison of different gray matter tissues. Results Heterotopic gray matter showed signal intensities similar to normal gray matter on T1 and T2 weighted MRI. The measured FA of heterotopic gray matter was higher than that of cortical gray matter (0.236 ± 0.011 vs. 0.169 ± 0.015, p < 0.01, one way ANOVA), and slightly lower than that of deep gray matter (0.236 ± 0.011 vs. 0.259 ± 0.016, p < 0.01). Conclusion Increased FA of heterotopic gray matter suggests arrested neuron during radial migration and provides better understanding of neurodevelopment. PMID:20499428

Structural differences in interictal migraine attack after epilepsy: A diffusion tensor imaging analysis.

PubMed

Huang, Qi; Lv, Xin; He, Yushuang; Wei, Xing; Ma, Meigang; Liao, Yuhan; Qin, Chao; Wu, Yuan

2017-12-01

Patients with epilepsy (PWE) are more likely to suffer from migraine attack, and aberrant white matter (WM) organization may be the mechanism underlying this phenomenon. This study aimed to use diffusion tensor imaging (DTI) technique to quantify WM structural differences in PWE with interictal migraine. Diffusion tensor imaging data were acquired in 13 PWE with migraine and 12 PWE without migraine. Diffusion metrics were analyzed using tract-atlas-based spatial statistics analysis. Atlas-based and tract-based spatial statistical analyses were conducted for robustness analysis. Correlation was explored between altered DTI metrics and clinical parameters. The main results are as follows: (i) Axonal damage plays a key role in PWE with interictal migraine. (ii) Significant diffusing alterations included higher fractional anisotropy (FA) in the fornix, higher mean diffusivity (MD) in the middle cerebellar peduncle (CP), left superior CP, and right uncinate fasciculus, and higher axial diffusivity (AD) in the middle CP and right medial lemniscus. (iii) Diffusion tensor imaging metrics has the tendency of correlation with seizure/migraine type and duration. Results indicate that characteristic structural impairments exist in PWE with interictal migraine. Epilepsy may contribute to migraine by altering WMs in the brain stem. White matter tracts in the fornix and right uncinate fasciculus also mediate migraine after epilepsy. This finding may improve our understanding of the pathological mechanisms underlying migraine attack after epilepsy. Copyright © 2017 Elsevier Inc. All rights reserved.

QTAIM and Stress Tensor Characterization of Intramolecular Interactions Along Dynamics Trajectories of a Light-Driven Rotary Molecular Motor.

PubMed

Wang, Lingling; Huan, Guo; Momen, Roya; Azizi, Alireza; Xu, Tianlv; Kirk, Steven R; Filatov, Michael; Jenkins, Samantha

2017-06-29

A quantum theory of atoms in molecules (QTAIM) and stress tensor analysis was applied to analyze intramolecular interactions influencing the photoisomerization dynamics of a light-driven rotary molecular motor. For selected nonadiabatic molecular dynamics trajectories characterized by markedly different S 1 state lifetimes, the electron densities were obtained using the ensemble density functional theory method. The analysis revealed that torsional motion of the molecular motor blades from the Franck-Condon point to the S 1 energy minimum and the S 1 /S 0 conical intersection is controlled by two factors: greater numbers of intramolecular bonds before the hop-time and unusually strongly coupled bonds between the atoms of the rotor and the stator blades. This results in the effective stalling of the progress along the torsional path for an extended period of time. This finding suggests a possibility of chemical tuning of the speed of photoisomerization of molecular motors and related molecular switches by reshaping their molecular backbones to decrease or increase the degree of coupling and numbers of intramolecular bond critical points as revealed by the QTAIM/stress tensor analysis of the electron density. Additionally, the stress tensor scalar and vector analysis was found to provide new methods to follow the trajectories, and from this, new insight was gained into the behavior of the S 1 state in the vicinity of the conical intersection.

Tensor-driven extraction of developmental features from varying paediatric EEG datasets.

PubMed

Kinney-Lang, Eli; Spyrou, Loukianos; Ebied, Ahmed; Chin, Richard Fm; Escudero, Javier

2018-05-21

Constant changes in developing children's brains can pose a challenge in EEG dependant technologies. Advancing signal processing methods to identify developmental differences in paediatric populations could help improve function and usability of such technologies. Taking advantage of the multi-dimensional structure of EEG data through tensor analysis may offer a framework for extracting relevant developmental features of paediatric datasets. A proof of concept is demonstrated through identifying latent developmental features in resting-state EEG. Approach. Three paediatric datasets (n = 50, 17, 44) were analyzed using a two-step constrained parallel factor (PARAFAC) tensor decomposition. Subject age was used as a proxy measure of development. Classification used support vector machines (SVM) to test if PARAFAC identified features could predict subject age. The results were cross-validated within each dataset. Classification analysis was complemented by visualization of the high-dimensional feature structures using t-distributed Stochastic Neighbour Embedding (t-SNE) maps. Main Results. Development-related features were successfully identified for the developmental conditions of each dataset. SVM classification showed the identified features could accurately predict subject at a significant level above chance for both healthy and impaired populations. t-SNE maps revealed suitable tensor factorization was key in extracting the developmental features. Significance. The described methods are a promising tool for identifying latent developmental features occurring throughout childhood EEG. © 2018 IOP Publishing Ltd.

Low-Dose Dynamic Cerebral Perfusion Computed Tomography Reconstruction via Kronecker-Basis Representation Tensor Sparsity Regularization

PubMed Central

Zeng, Dong; Xie, Qi; Cao, Wenfei; Lin, Jiahui; Zhang, Hao; Zhang, Shanli; Huang, Jing; Bian, Zhaoying; Meng, Deyu; Xu, Zongben; Liang, Zhengrong; Chen, Wufan

2017-01-01

Dynamic cerebral perfusion computed tomography (DCPCT) has the ability to evaluate the hemodynamic information throughout the brain. However, due to multiple 3-D image volume acquisitions protocol, DCPCT scanning imposes high radiation dose on the patients with growing concerns. To address this issue, in this paper, based on the robust principal component analysis (RPCA, or equivalently the low-rank and sparsity decomposition) model and the DCPCT imaging procedure, we propose a new DCPCT image reconstruction algorithm to improve low dose DCPCT and perfusion maps quality via using a powerful measure, called Kronecker-basis-representation tensor sparsity regularization, for measuring low-rankness extent of a tensor. For simplicity, the first proposed model is termed tensor-based RPCA (T-RPCA). Specifically, the T-RPCA model views the DCPCT sequential images as a mixture of low-rank, sparse, and noise components to describe the maximum temporal coherence of spatial structure among phases in a tensor framework intrinsically. Moreover, the low-rank component corresponds to the “background” part with spatial–temporal correlations, e.g., static anatomical contribution, which is stationary over time about structure, and the sparse component represents the time-varying component with spatial–temporal continuity, e.g., dynamic perfusion enhanced information, which is approximately sparse over time. Furthermore, an improved nonlocal patch-based T-RPCA (NL-T-RPCA) model which describes the 3-D block groups of the “background” in a tensor is also proposed. The NL-T-RPCA model utilizes the intrinsic characteristics underlying the DCPCT images, i.e., nonlocal self-similarity and global correlation. Two efficient algorithms using alternating direction method of multipliers are developed to solve the proposed T-RPCA and NL-T-RPCA models, respectively. Extensive experiments with a digital brain perfusion phantom, preclinical monkey data, and clinical patient data clearly demonstrate that the two proposed models can achieve more gains than the existing popular algorithms in terms of both quantitative and visual quality evaluations from low-dose acquisitions, especially as low as 20 mAs. PMID:28880164

Multiple sclerosis: changes in microarchitecture of white matter tracts after training with a video game balance board.

PubMed

Prosperini, Luca; Fanelli, Fulvia; Petsas, Nikolaos; Sbardella, Emilia; Tona, Francesca; Raz, Eytan; Fortuna, Deborah; De Angelis, Floriana; Pozzilli, Carlo; Pantano, Patrizia

2014-11-01

To determine if high-intensity, task-oriented, visual feedback training with a video game balance board (Nintendo Wii) induces significant changes in diffusion-tensor imaging ( DTI diffusion-tensor imaging ) parameters of cerebellar connections and other supratentorial associative bundles and if these changes are related to clinical improvement in patients with multiple sclerosis. The protocol was approved by local ethical committee; each participant provided written informed consent. In this 24-week, randomized, two-period crossover pilot study, 27 patients underwent static posturography and brain magnetic resonance (MR) imaging at study entry, after the first 12-week period, and at study termination. Thirteen patients started a 12-week training program followed by a 12-week period without any intervention, while 14 patients received the intervention in reverse order. Fifteen healthy subjects also underwent MR imaging once and underwent static posturography. Virtual dissection of white matter tracts was performed with streamline tractography; values of DTI diffusion-tensor imaging parameters were then obtained for each dissected tract. Repeated measures analyses of variance were performed to evaluate whether DTI diffusion-tensor imaging parameters significantly changed after intervention, with false discovery rate correction for multiple hypothesis testing. There were relevant differences between patients and healthy control subjects in postural sway and DTI diffusion-tensor imaging parameters (P < .05). Significant main effects of time by group interaction for fractional anisotropy and radial diffusivity of the left and right superior cerebellar peduncles were found (F2,23 range, 5.555-3.450; P = .036-.088 after false discovery rate correction). These changes correlated with objective measures of balance improvement detected at static posturography (r = -0.381 to 0.401, P < .05). However, both clinical and DTI diffusion-tensor imaging changes did not persist beyond 12 weeks after training. Despite the low statistical power (35%) due to the small sample size, the results showed that training with the balance board system modified the microstructure of superior cerebellar peduncles. The clinical improvement observed after training might be mediated by enhanced myelination-related processes, suggesting that high-intensity, task-oriented exercises could induce favorable microstructural changes in the brains of patients with multiple sclerosis.

Probing Fe-V Bonding in a C3-Symmetric Heterobimetallic Complex.

PubMed

Greer, Samuel M; McKay, Johannes; Gramigna, Kathryn M; Thomas, Christine M; Stoian, Sebastian A; Hill, Stephen

2018-04-30

Direct metal-metal bonding of two distinct first-row transition metals remains relatively unexplored compared to their second- and third-row heterobimetallic counterparts. Herein, a recently reported Fe-V triply bonded species, [V( i PrNPPh 2 ) 3 FeI] (1; Kuppuswamy, S.; Powers, T. M.; Krogman, J. P.; Bezpalko, M. W.; Foxman, B. M.; Thomas, C. M. Vanadium-iron complexes featuring metal-metal multiple bonds. Chem. Sci. 2013, 4, 3557-3565), is investigated using high-frequency electron paramagnetic resonance, field- and temperature-dependent 57 Fe nuclear gamma resonance (Mössbauer) spectroscopy, and high-field electron-electron double resonance detected nuclear magnetic resonance. From the use of this suite of physical methods, we have assessed the electronic structure of 1. These studies allow us to establish the effective g̃ tensors as well as the Fe/V electro-nuclear hyperfine interaction tensors of the spin S = 1 / 2 ground state. We have rationalized these tensors in the context of ligand field theory supported by quantum chemical calculations. This theoretical analysis suggests that the S = 1 / 2 ground state originates from a single unpaired electron predominately localized on the Fe site.

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

NASA Astrophysics Data System (ADS)

Dvoeglazov, V. V.

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

Enhancement of Signal-to-noise Ratio in Natural-source Transient Magnetotelluric Data with Wavelet Transform

NASA Astrophysics Data System (ADS)

Zhang, Y.; Paulson, K. V.

For audio-frequency magnetotelluric surveys where the signals are lightning-stroke transients, the conventional Fourier transform method often fails to produce a high quality impedance tensor. An alternative approach is to use the wavelet transform method which is capable of localizing target information simultaneously in both the temporal and frequency domains. Unlike Fourier analysis that yields an average amplitude and phase, the wavelet transform produces an instantaneous estimate of the amplitude and phase of a signal. In this paper a complex well-localized wavelet, the Morlet wavelet, has been used to transform and analyze audio-frequency magnetotelluric data. With the Morlet wavelet, the magnetotelluric impedance tensor can be computed directly in the wavelet transform domain. The lightning-stroke transients are easily identified on the dilation-translation plane. Choosing those wavelet transform values where the signals are located, a higher signal-to-noise ratio estimation of the impedance tensor can be obtained. In a test using real data, the wavelet transform showed a significant improvement in the signal-to-noise ratio over the conventional Fourier transform.

Emergent symmetries in the canonical tensor model

NASA Astrophysics Data System (ADS)

Obster, Dennis; Sasakura, Naoki

2018-04-01

The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent description of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general relativity. The classical CTM produces a general relativistic system in a formal continuum limit, the emergence of which should be explained by the quantum CTM. In this paper we study the symmetry properties of a wave function that exactly solves the quantum constraints of the CTM. We have found that it has strong peaks at configurations invariant under some Lie groups, as predicted by a mechanism described in our previous paper. A surprising result is the preference for configurations invariant not only under Lie groups with positive definite signature, but also with Lorentzian signature. Such symmetries could characterize the global structures of spacetimes, and our results are encouraging towards showing spacetime emergence in the CTM. To verify the asymptotic convergence of the wave function we have also analyzed the asymptotic behavior, which for the most part seems to be well under control.

Bound on largest r ∼< 0.1 from sub-Planckian excursions of inflaton

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chatterjee, Arindam; Mazumdar, Anupam, E-mail: arindam@hri.res.in, E-mail: a.mazumdar@lancaster.ac.uk

2015-01-01

In this paper we will discuss the range of large tensor to scalar ratio, r, obtainable from a sub-Planckian excursion of a single, slow roll driven inflaton field. In order to obtain a large r for such a scenario one has to depart from a monotonic evolution of the slow roll parameters in such a way that one still satisfies all the current constraints of \\texttt(Planck), such as the scalar amplitude, the tilt in the scalar power spectrum, running and running of the tilt close to the pivot scale. Since the slow roll parameters evolve non-monotonically, we will also considermore » the evolution of the power spectrum on the smallest scales, i.e. at P{sub s}(k ∼ 10{sup 16} Mpc{sup −1})∼< 10{sup −2}, to make sure that the amplitude does not become too large. All these constraints tend to keep the tensor to scalar ratio, r ∼< 0.1. We scan three different kinds of potential for supersymmetric flat directions and obtain the benchmark points which satisfy all the constraints. We also show that it is possible to go beyond r ∼> 0.1 provided we relax the upper bound on the power spectrum on the smallest scales.« less

A new Weyl-like tensor of geometric origin

NASA Astrophysics Data System (ADS)

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.

Analysis of multiple pulse NMR in solids. III

NASA Technical Reports Server (NTRS)

Burum, D. P.; Rhim, W. K.

1979-01-01

The paper introduces principles which greatly simplify the process of designing and analyzing compound pulse cycles. These principles are demonstrated by applying them to the design and analysis of several cycles, including a 52-pulse cycle; this pulse cycle combines six different REV-8 cycles and has substantially more resolving power than previously available techniques. Also, a new 24-pulse cycle is introduced which combines three different REV-8 cycles and has a resolving ability equivalent to that of the 52-pulse cycle. The principle of pulse-cycle decoupling provides a method for systematically combining pulse groups into compound cycles in order to achieve enhanced performance. This method is illustrated by a logical development from the two-pulse solid echo sequence to the WAHUHA (Waugh et al., 1968), the REV-8, and the new 24-pulse and 52-pulse cycles, along with the 14-pulse and 12-pulse cycles. Proton chemical shift tensor components for several organic solids, measured by using the 52-pulse cycle, are reported without detailed discussion.

Strength Analysis of Glass-Fiber-Reinforced Plastic during Buckling,

DTIC Science & Technology

An algorithm is developed for calculating and analyzing the stress tensor by the experimental function of deflections during the buckling of glass ... fiber -reinforced plastic shells loaded with a hydrostatic load. Malmeyster’s theory of strength is used to qualitatively establish the possible points of shell failure. (Author-PL)

Strain-induced three-photon effects

NASA Astrophysics Data System (ADS)

Jeong, Jae-Woo; Shin, Sung-Chul; Lyubchanskii, I. L.; Varyukhin, V. N.

2000-11-01

Strain-induced three-photon effects such as optical second-harmonic generation and hyper-Rayleigh light scattering, characterized by electromagnetic radiation at the double frequency of an incident light, are phenomenologically investigated by adopting a nonlinear photoelastic interaction. The relations between the strain and the nonlinear optical susceptibility for crystal surfaces with point symmetries of 4mm and 3m are described by a symmetry analysis of the nonlinear photoelastic tensor. We theoretically demonstrate a possibility of determining the strain components by measuring the rotational anisotropy of radiation at the second-harmonic frequency. Hyper-Rayleigh light scattering by dislocation strain is also described using a nonlinear photoelastic tensor. The angular dependencies of light scattered at the double frequency of an incident light for different scattering geometries are analyzed.

Nonsymmetric gravity theories: Inconsistencies and a cure

NASA Astrophysics Data System (ADS)

Damour, T.; Deser, S.; McCarthy, J.

1993-02-01

Motivated by the apparent dependence of string σ models on the sum of spacetime metric and antisymmetric tensor fields, we reconsider gravity theories constructed from a nonsymmetric metric. We first show, by expanding in powers of the antisymmetric field, that all such ``geometrical'' theories homogeneous in second derivatives violate standard physical requirements: ghost freedom, absence of algebraic inconsistencies, or continuity of degree-of-freedom content. This no-go result applies in particular to the old unified theory of Einstein and its recent avatars. However, we find that the addition of nonderivative, ``cosmological'' terms formally restores consistency by giving a mass to the antisymmetric tensor field, thereby transmuting it into a fifth-force-like massive vector but with novel possible matter couplings. The resulting macroscopic models also exhibit ``van der Waals''-type gravitational effects, and may provide useful phenomenological foils to general relativity.

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

NASA Astrophysics Data System (ADS)

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.

The Weyl curvature tensor, Cotton-York tensor and gravitational waves: A covariant consideration

NASA Astrophysics Data System (ADS)

Osano, Bob

1 + 3 covariant approach to cosmological perturbation theory often employs the electric part (Eab), the magnetic part (Hab) of the Weyl tensor or the shear tensor (σab) in a phenomenological description of gravitational waves. The Cotton-York tensor is rarely mentioned in connection with gravitational waves in this approach. This tensor acts as a source for the magnetic part of the Weyl tensor which should not be neglected in studies of gravitational waves in the 1 + 3 formalism. The tensor is only mentioned in connection with studies of “silent model” but even there the connection with gravitational waves is not exhaustively explored. In this study, we demonstrate that the Cotton-York tensor encodes contributions from both electric and magnetic parts of the Weyl tensor and in directly from the shear tensor. In our opinion, this makes the Cotton-York tensor arguably the natural choice for linear gravitational waves in the 1 + 3 covariant formalism. The tensor is cumbersome to work with but that should negate its usefulness. It is conceivable that the tensor would equally be useful in the metric approach, although we have not demonstrated this in this study. We contend that the use of only one of the Weyl tensor or the shear tensor, although phenomenologically correct, leads to loss of information. Such information is vital particularly when examining the contribution of gravitational waves to the anisotropy of an almost-Friedmann-Lamitre-Robertson-Walker (FLRW) universe. The recourse to this loss is the use Cotton-York tensor.

Interferometric imaging of nonlocal electromechanical power transduction in ferroelectric domains.

PubMed

Zheng, Lu; Dong, Hui; Wu, Xiaoyu; Huang, Yen-Lin; Wang, Wenbo; Wu, Weida; Wang, Zheng; Lai, Keji

2018-05-22

The electrical generation and detection of elastic waves are the foundation for acoustoelectronic and acoustooptic systems. For surface acoustic wave devices, microelectromechanical/nanoelectromechanical systems, and phononic crystals, tailoring the spatial variation of material properties such as piezoelectric and elastic tensors may bring significant improvements to the system performance. Due to the much slower speed of sound than speed of light in solids, it is desirable to study various electroacoustic behaviors at the mesoscopic length scale. In this work, we demonstrate the interferometric imaging of electromechanical power transduction in ferroelectric lithium niobate domain structures by microwave impedance microscopy. In sharp contrast to the traditional standing-wave patterns caused by the superposition of counterpropagating waves, the constructive and destructive fringes in microwave dissipation images exhibit an intriguing one-wavelength periodicity. We show that such unusual interference patterns, which are fundamentally different from the acoustic displacement fields, stem from the nonlocal interaction between electric fields and elastic waves. The results are corroborated by numerical simulations taking into account the sign reversal of piezoelectric tensor in oppositely polarized domains. Our work paves ways to probe nanoscale electroacoustic phenomena in complex structures by near-field electromagnetic imaging.

Early universe with modified scalar-tensor theory of gravity

NASA Astrophysics Data System (ADS)

Mandal, Ranajit; Sarkar, Chandramouli; Sanyal, Abhik Kumar

2018-05-01

Scalar-tensor theory of gravity with non-minimal coupling is a fairly good candidate for dark energy, required to explain late-time cosmic evolution. Here we study the very early stage of evolution of the universe with a modified version of the theory, which includes scalar curvature squared term. One of the key aspects of the present study is that, the quantum dynamics of the action under consideration ends up generically with de-Sitter expansion under semiclassical approximation, rather than power-law. This justifies the analysis of inflationary regime with de-Sitter expansion. The other key aspect is that, while studying gravitational perturbation, the perturbed generalized scalar field equation obtained from the perturbed action, when matched with the perturbed form of the background scalar field equation, relates the coupling parameter and the potential exactly in the same manner as the solution of classical field equations does, assuming de-Sitter expansion. The study also reveals that the quantum theory is well behaved, inflationary parameters fall well within the observational limit and quantum perturbation analysis shows that the power-spectrum does not deviate considerably from the standard one obtained from minimally coupled theory.

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

PubMed

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.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

NASA Astrophysics Data System (ADS)

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.

Quantitative analysis of diffusion tensor imaging (DTI) using statistical parametric mapping (SPM) for brain disorders

NASA Astrophysics Data System (ADS)

Lee, Jae-Seung; Im, In-Chul; Kang, Su-Man; Goo, Eun-Hoe; Kwak, Byung-Joon

2013-07-01

This study aimed to quantitatively analyze data from diffusion tensor imaging (DTI) using statistical parametric mapping (SPM) in patients with brain disorders and to assess its potential utility for analyzing brain function. DTI was obtained by performing 3.0-T magnetic resonance imaging for patients with Alzheimer's disease (AD) and vascular dementia (VD), and the data were analyzed using Matlab-based SPM software. The two-sample t-test was used for error analysis of the location of the activated pixels. We compared regions of white matter where the fractional anisotropy (FA) values were low and the apparent diffusion coefficients (ADCs) were increased. In the AD group, the FA values were low in the right superior temporal gyrus, right inferior temporal gyrus, right sub-lobar insula, and right occipital lingual gyrus whereas the ADCs were significantly increased in the right inferior frontal gyrus and right middle frontal gyrus. In the VD group, the FA values were low in the right superior temporal gyrus, right inferior temporal gyrus, right limbic cingulate gyrus, and right sub-lobar caudate tail whereas the ADCs were significantly increased in the left lateral globus pallidus and left medial globus pallidus. In conclusion by using DTI and SPM analysis, we were able to not only determine the structural state of the regions affected by brain disorders but also quantitatively analyze and assess brain function.

R 2 inflation to probe non-perturbative quantum gravity

NASA Astrophysics Data System (ADS)

Koshelev, Alexey S.; Sravan Kumar, K.; Starobinsky, Alexei A.

2018-03-01

It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, R + R 2, or shortly R 2, inflation is the most successful in accounting for the latest CMB data from the PLANCK satellite and other experiments. Moreover, recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric space-times. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant. We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local R 2 model. We further compute the full second order perturbed action around any background belonging to that class. We proceed by extracting the key inflationary parameters of our model such as a spectral index ( n s ), a tensor-to-scalar ratio ( r) and a tensor tilt ( n t ). It appears that n s remains the same as in the local R 2 inflation in the leading slow-roll approximation, while r and n t get modified due to modification of the tensor power spectrum. This class of models allows for any value of r < 0.07 with a modified consistency relation which can be fixed by future observations of primordial B-modes of the CMB polarization. This makes the UV complete R 2 gravity a natural target for future CMB probes.

Tensor Algebra Library for NVidia Graphics Processing Units

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liakh, Dmitry

This is a general purpose math library implementing basic tensor algebra operations on NVidia GPU accelerators. This software is a tensor algebra library that can perform basic tensor algebra operations, including tensor contractions, tensor products, tensor additions, etc., on NVidia GPU accelerators, asynchronously with respect to the CPU host. It supports a simultaneous use of multiple NVidia GPUs. Each asynchronous API function returns a handle which can later be used for querying the completion of the corresponding tensor algebra operation on a specific GPU. The tensors participating in a particular tensor operation are assumed to be stored in local RAMmore » of a node or GPU RAM. The main research area where this library can be utilized is the quantum many-body theory (e.g., in electronic structure theory).« less

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

PubMed Central

Mohammadi, Siawoosh; Hutton, Chloe; Nagy, Zoltan; Josephs, Oliver; Weiskopf, Nikolaus

2013-01-01

Diffusion tensor imaging is widely used in research and clinical applications, but this modality is highly sensitive to artefacts. We developed an easy-to-implement extension of the original diffusion tensor model to account for physiological noise in diffusion tensor imaging using measures of peripheral physiology (pulse and respiration), the so-called extended tensor model. Within the framework of the extended tensor model two types of regressors, which respectively modeled small (linear) and strong (nonlinear) variations in the diffusion signal, were derived from peripheral measures. We tested the performance of four extended tensor models with different physiological noise regressors on nongated and gated diffusion tensor imaging data, and compared it to an established data-driven robust fitting method. In the brainstem and cerebellum the extended tensor models reduced the noise in the tensor-fit by up to 23% in accordance with previous studies on physiological noise. The extended tensor model addresses both large-amplitude outliers and small-amplitude signal-changes. The framework of the extended tensor model also facilitates further investigation into physiological noise in diffusion tensor imaging. The proposed extended tensor model can be readily combined with other artefact correction methods such as robust fitting and eddy current correction. PMID:22936599

Characterization of Kilopixel TES detector arrays for PIPER

NASA Astrophysics Data System (ADS)

Datta, Rahul; Ade, Peter; Benford, Dominic; Bennett, Charles; Chuss, David; Costen, Nicholas; Coughlin, Kevin; Dotson, Jessie; Eimer, Joseph; Fixsen, Dale; Gandilo, Natalie; Halpern, Mark; Essinger-Hileman, Thomas; Hilton, Gene; Hinshaw, Gary; Irwin, Kent; Jhabvala, Christine; Kimball, Mark; Kogut, Al; Lazear, Justin; Lowe, Luke; Manos, George; McMahon, Jeff; Miller, Timothy; Mirel, Paul; Moseley, Samuel Harvey; Pawlyk, Samuel; Rodriguez, Samelys; Sharp, Elmer; Shirron, Peter; Staguhn, Johannes G.; Sullivan, Dan; Switzer, Eric; Taraschi, Peter; Tucker, Carole; Walts, Alexander; Wollack, Edward

2018-01-01

The Primordial Inflation Polarization ExploreR (PIPER) is a balloon-borne instrument optimized to measure the polarization of the Cosmic Microwave Background (CMB) at large angular scales. It will map 85% of the sky in four frequency bands centered at 200, 270, 350, and 600 GHz to characterize dust foregrounds and constrain the tensor-to-scalar ratio, r. The sky is imaged on to 32x40 pixel arrays of time-domain multiplexed Transition-Edge Sensor (TES) bolometers operating at a bath temperature of 100 mK to achieve background-limited sensitivity. Each kilopixel array is indium-bump-bonded to a 2D superconducting quantum interference device (SQUID) time-domain multiplexer (MUX) chip and read out by warm electronics. Each pixel measures total incident power over a frequency band defined by bandpass filters in front of the array, while polarization sensitivity is provided by the upstream Variable-delay Polarization Modulators (VPMs) and analyzer grids. We present measurements of the detector parameters from the laboratory characterization of the first kilopixel science array for PIPER including transition temperature, saturation power, thermal conductivity, time constant, and noise performance. We also describe the testing of the 2D MUX chips, optimization of the integrated readout parameters, and the overall pixel yield of the array. The first PIPER science flight is planned for June 2018 from Palestine, Texas.

Global diffusion of cosmic rays in random magnetic fields

NASA Astrophysics Data System (ADS)

Snodin, A. P.; Shukurov, A.; Sarson, G. R.; Bushby, P. J.; Rodrigues, L. F. S.

2016-04-01

The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particle's Larmor radius RL and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g. there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of the order of 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least 106 times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to 10-2 ≲ RL/lc ≲ 103, where lc is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for RL/lc ≪ 1, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.

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

PubMed

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.

Closing in on the large-scale CMB power asymmetry

NASA Astrophysics Data System (ADS)

Contreras, D.; Hutchinson, J.; Moss, A.; Scott, D.; Zibin, J. P.

2018-03-01

Measurements of the cosmic microwave background (CMB) temperature anisotropies have revealed a dipolar asymmetry in power at the largest scales, in apparent contradiction with the statistical isotropy of standard cosmological models. The significance of the effect is not very high, and is dependent on a posteriori choices. Nevertheless, a number of models have been proposed that produce a scale-dependent asymmetry. We confront several such models for a physical, position-space modulation with CMB temperature observations. We find that, while some models that maintain the standard isotropic power spectrum are allowed, others, such as those with modulated tensor or uncorrelated isocurvature modes, can be ruled out on the basis of the overproduction of isotropic power. This remains the case even when an extra isocurvature mode fully anticorrelated with the adiabatic perturbations is added to suppress power on large scales.

C%2B%2B tensor toolbox user manual.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Plantenga, Todd D.; Kolda, Tamara Gibson

2012-04-01

The C++ Tensor Toolbox is a software package for computing tensor decompositions. It is based on the Matlab Tensor Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews tensor decomposition mathematics, software capabilities, and installation of the package. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.

Tensor Factorization for Low-Rank Tensor Completion.

PubMed

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.

Similar Tensor Arrays - A Framework for Storage of Tensor Array Data

NASA Astrophysics Data System (ADS)

Brun, Anders; Martin-Fernandez, Marcos; Acar, Burak; Munoz-Moreno, Emma; Cammoun, Leila; Sigfridsson, Andreas; Sosa-Cabrera, Dario; Svensson, Björn; Herberthson, Magnus; Knutsson, Hans

This chapter describes a framework for storage of tensor array data, useful to describe regularly sampled tensor fields. The main component of the framework, called Similar Tensor Array Core (STAC), is the result of a collaboration between research groups within the SIMILAR network of excellence. It aims to capture the essence of regularly sampled tensor fields using a minimal set of attributes and can therefore be used as a “greatest common divisor” and interface between tensor array processing algorithms. This is potentially useful in applied fields like medical image analysis, in particular in Diffusion Tensor MRI, where misinterpretation of tensor array data is a common source of errors. By promoting a strictly geometric perspective on tensor arrays, with a close resemblance to the terminology used in differential geometry, (STAC) removes ambiguities and guides the user to define all necessary information. In contrast to existing tensor array file formats, it is minimalistic and based on an intrinsic and geometric interpretation of the array itself, without references to other coordinate systems.

Electromagnetic stress tensor for an amorphous metamaterial medium

NASA Astrophysics Data System (ADS)

Wang, Neng; Wang, Shubo; Ng, Jack

2018-03-01

We analytically and numerically investigated the internal optical forces exerted by an electromagnetic wave inside an amorphous metamaterial medium. We derived, by using the principle of virtual work, the Helmholtz stress tensor, which takes into account the electrostriction effect. Several examples of amorphous media are considered, and different electromagnetic stress tensors, such as the Einstein-Laub tensor and Minkowski tensor, are also compared. It is concluded that the Helmholtz stress tensor is the appropriate tensor for such systems.

Non-double-couple earthquakes. 1. Theory

USGS Publications Warehouse

Julian, B.R.; Miller, A.D.; Foulger, G.R.

1998-01-01

Historically, most quantitative seismological analyses have been based on the assumption that earthquakes are caused by shear faulting, for which the equivalent force system in an isotropic medium is a pair of force couples with no net torque (a 'double couple,' or DC). Observations of increasing quality and coverage, however, now resolve departures from the DC model for many earthquakes and find some earthquakes, especially in volcanic and geothermal areas, that have strongly non-DC mechanisms. Understanding non-DC earthquakes is important both for studying the process of faulting in detail and for identifying nonshear-faulting processes that apparently occur in some earthquakes. This paper summarizes the theory of 'moment tensor' expansions of equivalent-force systems and analyzes many possible physical non-DC earthquake processes. Contrary to long-standing assumption, sources within the Earth can sometimes have net force and torque components, described by first-rank and asymmetric second-rank moment tensors, which must be included in analyses of landslides and some volcanic phenomena. Non-DC processes that lead to conventional (symmetric second-rank) moment tensors include geometrically complex shear faulting, tensile faulting, shear faulting in an anisotropic medium, shear faulting in a heterogeneous region (e.g., near an interface), and polymorphic phase transformations. Undoubtedly, many non-DC earthquake processes remain to be discovered. Progress will be facilitated by experimental studies that use wave amplitudes, amplitude ratios, and complete waveforms in addition to wave polarities and thus avoid arbitrary assumptions such as the absence of volume changes or the temporal similarity of different moment tensor components.

Skeletal effects in Angle Class II/1 patients treated with the functional regulator type II : Cephalometric and tensor analysis.

PubMed

Schulz, Simone; Koos, Bernd; Duske, Kathrin; Stahl, Franka

2016-11-01

The purpose of this work was to employ both cephalometric and tensor analysis in characterizing the skeletal changes experienced by patients with Angle Class II/1 malocclusion during functional orthodontic treatment with the functional regulator type II. A total of 23 patients with Class II/1 malocclusion based on lateral cephalograms obtained before and after treatment with the functional regulator type II were analyzed. Another 23 patients with Angle Class II/1 malocclusion who had not undergone treatment were included as controls. Our cephalometric data attest to significant therapeutic effects of the functional regulator type II on the skeletal mandibular system, including significant advancement of the mandible, increases in effective mandibular length with enhancement of the chin profile, and reduction of growth-related bite deepening. No treatment-related effects were observed at the cranial-base and midface levels. In addition, tensor analysis revealed significant stimulation of mandibular growth in sagittal directions, without indications of growth effects on the maxilla. Its growth-pattern findings differed from those of cephalometric analysis by indicating that the appliance did promote horizontal development, which supports the functional orthodontic treatment effect in Angle Class II/1 cases. Tensor analysis yielded additional insights into sagittal and vertical growth changes not identifiable by strictly cephalometric means. The functional regulator type II was an effective treatment modality for Angle Class II/1 malocclusion and influenced the skeletal development of these patients in favorable ways.

Tensor Toolbox for MATLAB v. 3.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kola, Tamara; Bader, Brett W.; Acar Ataman, Evrim NMN

Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors using MATLAB's object-oriented features. It also provides algorithms for tensor decomposition and factorization, algorithms for computing tensor eigenvalues, and methods for visualization of results.

Characterizing Atomistic Geometries and Potential Functions Using Strain Functionals

NASA Astrophysics Data System (ADS)

Kober, Edward; Mathew, Nithin; Rudin, Sven

2017-06-01

We demonstrate the use of strain tensor functionals for characterizing arbitrarily ordered atomistic structures. This approach defines a Gaussian-weighted neighborhood around each atom and characterizes that local geometry in terms of n-th order strain tensors, which are equivalent to the n-th order moments/derivatives of the neighborhood. Fourth order expansions can distinguish the cubic structures (and deformations thereof), but sixth order expansions are required to fully characterize hexagonal structures. These functions are continuous and smooth and much less sensitive to thermal fluctuations than other descriptors based on discrete neighborhoods. Reducing these metrics to rotational invariant descriptors allows a large number of defect structures to be readily identified and forms the basis of a classification scheme that allows molecular dynamics simulations to be readily analyzed. Applications to the analysis of shock waves impinging on samples of Cu, Ta and Ti will be presented. The method has been extended to vector fields as well, enabling the local stress to be cast in terms of rotationally invariant functions as well. The stress-strain correlations can then be used as the basis for developing and analyzing potential functions.

Geometrical analysis of woven fabric microstructure based on micron-resolution computed tomography data

NASA Astrophysics Data System (ADS)

Krieger, Helga; Seide, Gunnar; Gries, Thomas; Stapleton, Scott E.

2018-04-01

The global mechanical properties of textiles such as elasticity and strength, as well as transport properties such as permeability depend strongly on the microstructure of the textile. Textiles are heterogeneous structures with highly anisotropic material properties, including local fiber orientation and local fiber volume fraction. In this paper, an algorithm is presented to generate a virtual 3D-model of a woven fabric architecture with information about the local fiber orientation and the local fiber volume fraction. The geometric data of the woven fabric impregnated with resin was obtained by micron-resolution computed tomography (μCT). The volumetric μCT-scan was discretized into cells and the microstructure of each cell was analyzed and homogenized. Furthermore, the discretized data was used to calculate the local permeability tensors of each cell. An example application of the analyzed data is the simulation of the resin flow through a woven fabric based on the determined local permeability tensors and on Darcy's law. The presented algorithm is an automated and robust method of going from μCT-scans to structural or flow models.

Diffusion Tensor Image Registration Using Hybrid Connectivity and Tensor Features

PubMed Central

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

2014-01-01

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. PMID:24293159

Spherical Tensor Calculus for Local Adaptive Filtering

NASA Astrophysics Data System (ADS)

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.

A Guided Tour of Mathematical Methods

NASA Astrophysics Data System (ADS)

Snieder, Roel

2009-04-01

1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical co-ordinates; 5. The gradient; 6. The divergence of a vector field; 7. The curl of a vector field; 8. The theorem of Gauss; 9. The theorem of Stokes; 10. The Laplacian; 11. Conservation laws; 12. Scale analysis; 13. Linear algebra; 14. The Dirac delta function; 15. Fourier analysis; 16. Analytic functions; 17. Complex integration; 18. Green's functions: principles; 19. Green's functions: examples; 20. Normal modes; 21. Potential theory; 22. Cartesian tensors; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Variational calculus; 26. Epilogue, on power and knowledge; References.

Imaging of isotropic and anisotropic conductivities from power densities in three dimensions

NASA Astrophysics Data System (ADS)

Monard, François; Rim, Donsub

2018-07-01

We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality ultrasound modulated electrical impedance tomography for instance. We improve on the algorithms previously derived in Bal et al (2013 Inverse Problems Imaging 7 353–75) Monard and Bal (2013 Commun. PDE 38 1183–207) for both isotropic and anisotropic cases, and we address the well-known issue of vanishing determinants in particular. The algorithm is implemented and we provide numerical results that illustrate the improvements.

Construction of non-Abelian gauge theories on noncommutative spaces

NASA Astrophysics Data System (ADS)

Jurčo, B.; Möller, L.; Schraml, S.; Schupp, P.; Wess, J.

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories.

Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor

NASA Astrophysics Data System (ADS)

Beyer, Florian; Paetz, Tim-Torben

2018-02-01

The Mars-Simon tensor (MST), which, e.g., plays a crucial role to provide gauge invariant characterizations of the Kerr-NUT-(A)(dS) family, satisfies a Bianchi-like equation. In this paper, we analyze this equation in close analogy to the Bianchi equation, in particular it will be shown that the constraints are preserved supposing that a generalized Buchdahl condition holds. This permits the systematic construction of solutions to this equation in terms of a well-posed Cauchy problem. A particular emphasis lies on the asymptotic Cauchy problem, where data are prescribed on a space-like I (i.e., for ∧ > 0). In contrast to the Bianchi equation, the MST equation is of Fuchsian type at I , for which existence and uniqueness results are derived.

Emergent gravity from vanishing energy-momentum tensor

DOE PAGES

Carone, Christopher D.; Erlich, Joshua; Vaman, Diana

2017-03-27

A constraint of vanishing energy-momentum tensor is motivated by a variety of perspectives on quantum gravity. We demonstrate in a concrete example how this constraint leads to a metric-independent theory in which quantum gravity emerges as a nonperturbative artifact of regularization-scale physics. We analyze a scalar theory similar to the Dirac-Born-Infeld (DBI) theory with vanishing gauge fields, with the DBI Lagrangian modulated by a scalar potential. In the limit of a large number of scalars, we explicitly demonstrate the existence of a composite massless spin-2 graviton in the spectrum that couples to matter as in Einstein gravity. As a result,more » we comment on the cosmological constant problem and the generalization to theories with fermions and gauge fields.« less

Global plate tectonics and the secular motion of the pole

NASA Technical Reports Server (NTRS)

Soler, T.

1977-01-01

Astronomical data compiled during the last 70 years by the international organizations providing the coordinates of the instantaneous pole clearly shows a persistent drift of the mean pole. The differential contributions to the earth's second-order tensor of inertia were obtained and applied, resulting in no significant displacement of the earth's principal axis. In view of the above, the effect that theoretical geophysical models for absolute plate velocities may have on an apparent displacement of the mean pole as a consequence of station drifting was analyzed. The investigation also reports new values for the crustal tensor of inertia (assuming an ellipsoidal earth) and the orientation of its axis of figure, reopening the old speculation of a possible sliding of the whole crustover the upper mantle, including the supporting geophysical and astronomic evidence.

Integrative Analysis of Many Weighted Co-Expression Networks Using Tensor Computation

PubMed Central

Li, Wenyuan; Liu, Chun-Chi; Zhang, Tong; Li, Haifeng; Waterman, Michael S.; Zhou, Xianghong Jasmine

2011-01-01

The rapid accumulation of biological networks poses new challenges and calls for powerful integrative analysis tools. Most existing methods capable of simultaneously analyzing a large number of networks were primarily designed for unweighted networks, and cannot easily be extended to weighted networks. However, it is known that transforming weighted into unweighted networks by dichotomizing the edges of weighted networks with a threshold generally leads to information loss. We have developed a novel, tensor-based computational framework for mining recurrent heavy subgraphs in a large set of massive weighted networks. Specifically, we formulate the recurrent heavy subgraph identification problem as a heavy 3D subtensor discovery problem with sparse constraints. We describe an effective approach to solving this problem by designing a multi-stage, convex relaxation protocol, and a non-uniform edge sampling technique. We applied our method to 130 co-expression networks, and identified 11,394 recurrent heavy subgraphs, grouped into 2,810 families. We demonstrated that the identified subgraphs represent meaningful biological modules by validating against a large set of compiled biological knowledge bases. We also showed that the likelihood for a heavy subgraph to be meaningful increases significantly with its recurrence in multiple networks, highlighting the importance of the integrative approach to biological network analysis. Moreover, our approach based on weighted graphs detects many patterns that would be overlooked using unweighted graphs. In addition, we identified a large number of modules that occur predominately under specific phenotypes. This analysis resulted in a genome-wide mapping of gene network modules onto the phenome. Finally, by comparing module activities across many datasets, we discovered high-order dynamic cooperativeness in protein complex networks and transcriptional regulatory networks. PMID:21698123

Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bartolo, Nicola; Orlando, Giorgio, E-mail: nicola.bartolo@pd.infn.it, E-mail: giorgio.orlando@phd.unipd.it

Considering high-energy modifications of Einstein gravity during inflation is an interesting issue. We can constrain the strength of the new gravitational terms through observations of inflationary imprints in the actual universe. In this paper we analyze the effects on slow-roll models due to a Chern-Simons term coupled to the inflaton field through a generic coupling function f (φ). A well known result is the polarization of primordial gravitational waves (PGW) into left and right eigenstates, as a consequence of parity breaking. In such a scenario the modifications to the power spectrum of PGW are suppressed under the conditions that allowmore » to avoid the production of ghost gravitons at a certain energy scale, the so-called Chern-Simons mass M {sub CS}. In general it has been recently pointed out that there is very little hope to efficiently constrain chirality of PGW on the basis solely of two-point statistics from future CMB data, even in the most optimistic cases. Thus we search if significant parity breaking signatures can arise at least in the bispectrum statistics. We find that the tensor-tensor-scalar bispectra ( γ γ ζ ) for each polarization state are the only ones that are not suppressed. Their amplitude, setting the level of parity breaking during inflation, is proportional to the second derivative of the coupling function f (φ) and they turn out to be maximum in the squeezed limit. We comment on the squeezed-limit consistency relation arising in the case of chiral gravitational waves, and on possible observables to constrain these signatures.« less

Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension

NASA Astrophysics Data System (ADS)

Jaschke, Daniel; Wall, Michael L.; Carr, Lincoln D.

2018-04-01

Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States (MPSs), have attracted interest from different fields of quantum physics ranging from solid state systems to quantum simulators and quantum computing. Our open source MPS code provides the community with a toolset to analyze the statics and dynamics of one-dimensional quantum systems. Here, we present our open source library, Open Source Matrix Product States (OSMPS), of MPS methods implemented in Python and Fortran2003. The library includes tools for ground state calculation and excited states via the variational ansatz. We also support ground states for infinite systems with translational invariance. Dynamics are simulated with different algorithms, including three algorithms with support for long-range interactions. Convenient features include built-in support for fermionic systems and number conservation with rotational U(1) and discrete Z2 symmetries for finite systems, as well as data parallelism with MPI. We explain the principles and techniques used in this library along with examples of how to efficiently use the general interfaces to analyze the Ising and Bose-Hubbard models. This description includes the preparation of simulations as well as dispatching and post-processing of them.

Refining inflation using non-canonical scalars

NASA Astrophysics Data System (ADS)

Unnikrishnan, Sanil; Sahni, Varun; Toporensky, Aleksey

2012-08-01

This paper revisits the Inflationary scenario within the framework of scalar field models possessing a non-canonical kinetic term. We obtain closed form solutions for all essential quantities associated with chaotic inflation including slow roll parameters, scalar and tensor power spectra, spectral indices, the tensor-to-scalar ratio, etc. We also examine the Hamilton-Jacobi equation and demonstrate the existence of an inflationary attractor. Our results highlight the fact that non-canonical scalars can significantly improve the viability of inflationary models. They accomplish this by decreasing the tensor-to-scalar ratio while simultaneously increasing the value of the scalar spectral index, thereby redeeming models which are incompatible with the cosmic microwave background (CMB) in their canonical version. For instance, the non-canonical version of the chaotic inflationary potential, V(phi) ~ λphi4, is found to agree with observations for values of λ as large as unity! The exponential potential can also provide a reasonable fit to CMB observations. A central result of this paper is that steep potentials (such as Vproptophi-n) usually associated with dark energy, can drive inflation in the non-canonical setting. Interestingly, non-canonical scalars violate the consistency relation r = -8nT, which emerges as a smoking gun test for this class of models.

Short-range correlation in high-momentum antisymmetrized molecular dynamics

NASA Astrophysics Data System (ADS)

Myo, Takayuki

2018-03-01

We propose a new variational method for treating short-range repulsion of bare nuclear force for nuclei in antisymmetrized molecular dynamics (AMD). In AMD, the short-range correlation is described in terms of large imaginary centroids of Gaussian wave packets of nucleon pairs in opposite signs, causing high-momentum components in the nucleon pairs. We superpose these AMD basis states and call this method "high-momentum AMD" (HM-AMD), which is capable of describing the strong tensor correlation [T. Myo et al., Prog. Theor. Exp. Phys., 2017, 111D01 (2017)]. In this letter, we extend HM-AMD by including up to two kinds of nucleon pairs in each AMD basis state utilizing the cluster expansion, which produces many-body correlations involving high-momentum components. We investigate how well HM-AMD describes the short-range correlation by showing the results for ^3H using the Argonne V4^' central potential. It is found that HM-AMD reproduces the results of few-body calculations and also the tensor-optimized AMD. This means that HM-AMD is a powerful approach to describe the short-range correlation in nuclei. In HM-AMD, the momentum directions of nucleon pairs isotropically contribute to the short-range correlation, which is different from the tensor correlation.

Non-equilibrium surface tension of the vapour-liquid interface of active Lennard-Jones particles

NASA Astrophysics Data System (ADS)

Paliwal, Siddharth; Prymidis, Vasileios; Filion, Laura; Dijkstra, Marjolein

2017-08-01

We study a three-dimensional system of self-propelled Brownian particles interacting via the Lennard-Jones potential. Using Brownian dynamics simulations in an elongated simulation box, we investigate the steady states of vapour-liquid phase coexistence of active Lennard-Jones particles with planar interfaces. We measure the normal and tangential components of the pressure tensor along the direction perpendicular to the interface and verify mechanical equilibrium of the two coexisting phases. In addition, we determine the non-equilibrium interfacial tension by integrating the difference of the normal and tangential components of the pressure tensor and show that the surface tension as a function of strength of particle attractions is well fitted by simple power laws. Finally, we measure the interfacial stiffness using capillary wave theory and the equipartition theorem and find a simple linear relation between surface tension and interfacial stiffness with a proportionality constant characterized by an effective temperature.

Emergent gravity from a mass deformation in warped spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gherghetta, Tony; Peloso, Marco; Poppitz, Erich

2005-11-15

We consider a deformation of five-dimensional warped gravity with bulk and boundary mass terms to quadratic order in the action. We show that massless zero modes occur for special choices of the masses. The tensor zero mode is a smooth deformation of the Randall-Sundrum graviton wave function and can be localized anywhere in the bulk. There is also a vector zero mode with similar localization properties, which is decoupled from conserved sources at tree level. Interestingly, there are no scalar modes, and the model is ghost-free at the linearized level. When the tensor zero mode is localized near the IRmore » brane, the dual interpretation is a composite graviton describing an emergent (induced) theory of gravity at the IR scale. In this case Newton's law of gravity changes to a new power law below the millimeter scale, with an exponent that can even be irrational.« less

Entanglement of purification: from spin chains to holography

NASA Astrophysics Data System (ADS)

Nguyen, Phuc; Devakul, Trithep; Halbasch, Matthew G.; Zaletel, Michael P.; Swingle, Brian

2018-01-01

Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.

New Class of Quasinormal Modes of Neutron Stars in Scalar-Tensor Gravity

NASA Astrophysics Data System (ADS)

Mendes, Raissa F. P.; Ortiz, Néstor

2018-05-01

Detection of the characteristic spectrum of pulsating neutron stars can be a powerful tool not only to probe the nuclear equation of state but also to test modifications to general relativity. However, the shift in the oscillation spectrum induced by modified theories of gravity is often small and degenerate with our ignorance of the equation of state. In this Letter, we show that the coupling to additional degrees of freedom present in modified theories of gravity can give rise to new families of modes, with no counterpart in general relativity, which could be sufficiently well resolved in frequency space to allow for clear detection. We present a realization of this idea by performing a thorough study of radial oscillations of neutron stars in massless scalar-tensor theories of gravity. We anticipate astrophysical scenarios where the presence of this class of quasinormal modes could be probed with electromagnetic and gravitational wave measurements.

A tensor network approach to many-body localization

NASA Astrophysics Data System (ADS)

Yu, Xiongjie; Pekker, David; Clark, Bryan

Understanding the many-body localized phase requires access to eigenstates in the middle of the many-body spectrum. While exact-diagonalization is able to access these eigenstates, it is restricted to systems sizes of about 22 spins. To overcome this limitation, we develop tensor network algorithms which increase the accessible system size by an order of magnitude. We describe both our new algorithms as well as the additional physics about MBL we can extract from them. For example, we demonstrate the power of these methods by verifying the breakdown of the Eigenstate Thermalization Hypothesis (ETH) in the many-body localized phase of the random field Heisenberg model, and show the saturation of entanglement in the MBL phase and generate eigenstates that differ by local excitations. Work was supported by AFOSR FA9550-10-1-0524 and FA9550-12-1-0057, the Kaufmann foundation, and SciDAC FG02-12ER46875.

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.

1983-01-01

Tensor model order reduction, recursive tensor model identification, input design for tensor model identification, software development for nonlinear feedback control laws based upon tensors, and development of the CATNAP software package for tensor modeling, identification and simulation were studied. The last of these are discussed.

Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.

PubMed

Kindlmann, Gordon; Estépar, Raúl San José; Niethammer, Marc; Haker, Steven; Westin, Carl-Fredrik

2007-01-01

In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.

Analyses of Disruption of Cerebral White Matter Integrity in Schizophrenia with MR Diffusion Tensor Fiber Tracking Method

NASA Astrophysics Data System (ADS)

Yamamoto, Utako; Kobayashi, Tetsuo; Kito, Shinsuke; Koga, Yoshihiko

We have analyzed cerebral white matter using magnetic resonance diffusion tensor imaging (MR-DTI) to measure the diffusion anisotropy of water molecules. The goal of this study is the quantitative evaluation of schizophrenia. Diffusion tensor images are acquired for patients with schizophrenia and healthy comparison subjects, group-matched for age, sex, and handedness. Fiber tracking is performed on the superior longitudinal fasciculus for the comparison between the patient and comparison groups. We have analysed and compared the cross-sectional area on the starting coronal plane and the mean and standard deviation of the fractional anisotropy and the apparent diffusion coefficient along fibers in the right and left hemispheres. In the right hemisphere, the cross-sectional areas in patient group are significantly smaller than those in the comparison group. Furthermore, in the comparison group, the cross-sectional areas in the right hemisphere are significantly larger than those in the left hemisphere, whereas there is no significant difference in the patient group. These results suggest that we may evaluate the disruption in white matter integrity in schizophrenic patients quantitatively by comparing the cross-sectional area of the superior longitudinal fasciculus in the right and left hemispheres.

White matter fiber tracking computation based on diffusion tensor imaging for clinical applications.

PubMed

Dellani, Paulo R; Glaser, Martin; Wille, Paulo R; Vucurevic, Goran; Stadie, Axel; Bauermann, Thomas; Tropine, Andrei; Perneczky, Axel; von Wangenheim, Aldo; Stoeter, Peter

2007-03-01

Fiber tracking allows the in vivo reconstruction of human brain white matter fiber trajectories based on magnetic resonance diffusion tensor imaging (MR-DTI), but its application in the clinical routine is still in its infancy. In this study, we present a new software for fiber tracking, developed on top of a general-purpose DICOM (digital imaging and communications in medicine) framework, which can be easily integrated into existing picture archiving and communication system (PACS) of radiological institutions. Images combining anatomical information and the localization of different fiber tract trajectories can be encoded and exported in DICOM and Analyze formats, which are valuable resources in the clinical applications of this method. Fiber tracking was implemented based on existing line propagation algorithms, but it includes a heuristic for fiber crossings in the case of disk-shaped diffusion tensors. We successfully performed fiber tracking on MR-DTI data sets from 26 patients with different types of brain lesions affecting the corticospinal tracts. In all cases, the trajectories of the central spinal tract (pyramidal tract) were reconstructed and could be applied at the planning phase of the surgery as well as in intraoperative neuronavigation.

Spin correlations in the {Lambda}{Lambda} and {Lambda}{Lambda}-bar systems generated in relativistic heavy-ion collisions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lyuboshitz, V. L.; Lyuboshitz, V. V., E-mail: Valery.Lyuboshitz@jinr.r

2010-05-15

Spin correlations for the {Lambda}{Lambda} and {Lambda}{Lambda}-bar pairs, generated in relativistic heavy-ion collisions, and related angular correlations at the joint registration of hadronic decays of two hyperons, in which space parity is not conserved, are analyzed. The correlation tensor components can be derived from the double angular distribution of products of two decays by the method of 'moments'. The properties of the 'trace' of the correlation tensor (a sum of three diagonal components), determining the relative fractions of the triplet states and singlet state of respective pairs, are discussed. Spin correlations for two identical particles ({Lambda}{Lambda}) and two nonidentical particlesmore » ({Lambda}{Lambda}-bar) are considered from the viewpoint of the conventional model of one-particle sources. In the framework of this model, correlations vanish at sufficiently large relative momenta. However, under these conditions, in the case of two nonidentical particles ({Lambda}{Lambda}-bar) a noticeable role is played by two-particle annihilation (two-quark, two-gluon) sources, which lead to the difference of the correlation tensor from zero. In particular, such a situation may arise when the system passes through the 'mixed phase.'« less

Visualizing second order tensor fields with hyperstreamlines

NASA Technical Reports Server (NTRS)

Delmarcelle, Thierry; Hesselink, Lambertus

1993-01-01

Hyperstreamlines are a generalization to second order tensor fields of the conventional streamlines used in vector field visualization. As opposed to point icons commonly used in visualizing tensor fields, hyperstreamlines form a continuous representation of the complete tensor information along a three-dimensional path. This technique is useful in visulaizing both symmetric and unsymmetric three-dimensional tensor data. Several examples of tensor field visualization in solid materials and fluid flows are provided.

A Local Fast Marching-Based Diffusion Tensor Image Registration Algorithm by Simultaneously Considering Spatial Deformation and Tensor Orientation

PubMed Central

Xue, Zhong; Li, Hai; Guo, Lei; Wong, Stephen T.C.

2010-01-01

It is a key step to spatially align diffusion tensor images (DTI) to quantitatively compare neural images obtained from different subjects or the same subject at different timepoints. Different from traditional scalar or multi-channel image registration methods, tensor orientation should be considered in DTI registration. Recently, several DTI registration methods have been proposed in the literature, but deformation fields are purely dependent on the tensor features not the whole tensor information. Other methods, such as the piece-wise affine transformation and the diffeomorphic non-linear registration algorithms, use analytical gradients of the registration objective functions by simultaneously considering the reorientation and deformation of tensors during the registration. However, only relatively local tensor information such as voxel-wise tensor-similarity, is utilized. This paper proposes a new DTI image registration algorithm, called local fast marching (FM)-based simultaneous registration. The algorithm not only considers the orientation of tensors during registration but also utilizes the neighborhood tensor information of each voxel to drive the deformation, and such neighborhood tensor information is extracted from a local fast marching algorithm around the voxels of interest. These local fast marching-based tensor features efficiently reflect the diffusion patterns around each voxel within a spherical neighborhood and can capture relatively distinctive features of the anatomical structures. Using simulated and real DTI human brain data the experimental results show that the proposed algorithm is more accurate compared with the FA-based registration and is more efficient than its counterpart, the neighborhood tensor similarity-based registration. PMID:20382233

Antisymmetric tensor generalizations of affine vector fields.

PubMed

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.

On Angular Momentum

DOE R&D Accomplishments Database

Schwinger, J.

1952-01-26

The commutation relations of an arbitrary angular momentum vector can be reduced to those of the harmonic oscillator. This provides a powerful method for constructing and developing the properties of angular momentum eigenvectors. In this paper many known theorems are derived in this way, and some new results obtained. Among the topics treated are the properties of the rotation matrices; the addition of two, three, and four angular momenta; and the theory of tensor operators.

Tensoral for post-processing users and simulation authors

NASA Technical Reports Server (NTRS)

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.

Automatic deformable diffusion tensor registration for fiber population analysis.

PubMed

Irfanoglu, M O; Machiraju, R; Sammet, S; Pierpaoli, C; Knopp, M V

2008-01-01

In this work, we propose a novel method for deformable tensor-to-tensor registration of Diffusion Tensor Images. Our registration method models the distances in between the tensors with Geode-sic-Loxodromes and employs a version of Multi-Dimensional Scaling (MDS) algorithm to unfold the manifold described with this metric. Defining the same shape properties as tensors, the vector images obtained through MDS are fed into a multi-step vector-image registration scheme and the resulting deformation fields are used to reorient the tensor fields. Results on brain DTI indicate that the proposed method is very suitable for deformable fiber-to-fiber correspondence and DTI-atlas construction.

FAST TRACK COMMUNICATION Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

NASA Astrophysics Data System (ADS)

Senovilla, José M. M.

2010-11-01

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.

Analytical structure, dynamics, and coarse graining of a kinetic model of an active fluid

NASA Astrophysics Data System (ADS)

Gao, Tong; Betterton, Meredith D.; Jhang, An-Sheng; Shelley, Michael J.

2017-09-01

We analyze one of the simplest active suspensions with complex dynamics: a suspension of immotile "extensor" particles that exert active extensile dipolar stresses on the fluid in which they are immersed. This is relevant to several experimental systems, such as recently studied tripartite rods that create extensile flows by consuming a chemical fuel. We first describe the system through a Doi-Onsager kinetic theory based on microscopic modeling. This theory captures the active stresses produced by the particles that can drive hydrodynamic instabilities, as well as the steric interactions of rodlike particles that lead to nematic alignment. This active nematic system yields complex flows and disclination defect dynamics very similar to phenomenological Landau-deGennes Q -tensor theories for active nematic fluids, as well as by more complex Doi-Onsager theories for polar microtubule-motor-protein systems. We apply the quasiequilibrium Bingham closure, used to study suspensions of passive microscopic rods, to develop a nonstandard Q -tensor theory. We demonstrate through simulation that this B Q -tensor theory gives an excellent analytical and statistical accounting of the suspension's complex dynamics, at a far reduced computational cost. Finally, we apply the B Q -tensor model to study the dynamics of extensor suspensions in circular and biconcave domains. In circular domains, we reproduce previous results for systems with weak nematic alignment, but for strong alignment we find unusual dynamics with activity-controlled defect production and absorption at the boundaries of the domain. In biconcave domains, a Fredericks-like transition occurs as the width of the neck connecting the two disks is varied.

An infinite swampland of U(1) charge spectra in 6D supergravity theories

NASA Astrophysics Data System (ADS)

Taylor, Washington; Turner, Andrew P.

2018-06-01

We analyze the anomaly constraints on 6D supergravity theories with a single abelian U(1) gauge factor. For theories with charges restricted to q = ±1 , ±2 and no tensor multiplets, anomaly-free models match those models that can be realized from F-theory compactifications almost perfectly. For theories with tensor multiplets or with larger charges, the F-theory constraints are less well understood. We show, however, that there is an infinite class of distinct massless charge spectra in the "swampland" of theories that satisfy all known quantum consistency conditions but do not admit a realization through F-theory or any other known approach to string compactification. We also compare the spectra of charged matter in abelian theories with those that can be realized from breaking nonabelian SU(2) and higher rank gauge symmetries.

Sparse alignment for robust tensor learning.

PubMed

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

2014-10-01

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

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

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.

Multi-site genetic analysis of diffusion images and voxelwise heritability analysis: A pilot project of the ENIGMA–DTI working group

PubMed Central

Jahanshad, Neda; Kochunov, Peter; Sprooten, Emma; Mandl, René C.; Nichols, Thomas E.; Almassy, Laura; Blangero, John; Brouwer, Rachel M.; Curran, Joanne E.; de Zubicaray, Greig I.; Duggirala, Ravi; Fox, Peter T.; Hong, L. Elliot; Landman, Bennett A.; Martin, Nicholas G.; McMahon, Katie L.; Medland, Sarah E.; Mitchell, Braxton D.; Olvera, Rene L.; Peterson, Charles P.; Starr, John M.; Sussmann, Jessika E.; Toga, Arthur W.; Wardlaw, Joanna M.; Wright, Margaret J.; Hulshoff Pol, Hilleke E.; Bastin, Mark E.; McIntosh, Andrew M.; Deary, Ian J.; Thompson, Paul M.; Glahn, David C.

2013-01-01

The ENIGMA (Enhancing NeuroImaging Genetics through Meta-Analysis) Consortium was set up to analyze brain measures and genotypes from multiple sites across the world to improve the power to detect genetic variants that influence the brain. Diffusion tensor imaging (DTI) yields quantitative measures sensitive to brain development and degeneration, and some common genetic variants may be associated with white matter integrity or connectivity. DTI measures, such as the fractional anisotropy (FA) of water diffusion, may be useful for identifying genetic variants that influence brain microstructure. However, genome-wide association studies (GWAS) require large populations to obtain sufficient power to detect and replicate significant effects, motivating a multi-site consortium effort. As part of an ENIGMA–DTI working group, we analyzed high-resolution FA images from multiple imaging sites across North America, Australia, and Europe, to address the challenge of harmonizing imaging data collected at multiple sites. Four hundred images of healthy adults aged 18–85 from four sites were used to create a template and corresponding skeletonized FA image as a common reference space. Using twin and pedigree samples of different ethnicities, we used our common template to evaluate the heritability of tract-derived FA measures. We show that our template is reliable for integrating multiple datasets by combining results through meta-analysis and unifying the data through exploratory mega-analyses. Our results may help prioritize regions of the FA map that are consistently influenced by additive genetic factors for future genetic discovery studies. Protocols and templates are publicly available at (http://enigma.loni.ucla.edu/ongoing/dti-working-group/). PMID:23629049

Tectonic analysis of mine tremor mechanisms from the Upper Silesian Coal Basin

NASA Astrophysics Data System (ADS)

Sagan, Grzegorz; Teper, Lesław; Zuberek, Waclaw M.

1996-07-01

Fault network of the Upper Silesian Coal Basin (USCB) is built of sets of strike-slip, oblique-slip and dip-slip faults. It is a typical product of force couple which acts evenly with the parallel of latitude, causing horizontal and anti-clockwise movement of rock-mass. Earlier research of focal mechanisms of mine tremors, using a standard fault plane solution, has shown that some events are related to tectonic directions in main structural units of the USCB. An attempt was undertaken to analyze the records of mine tremors from the period 1992 1994 in the selected coal fields. The digital records of about 200 mine tremors with energy larger than 1×104 J ( M L >1.23) were analyzed with SMT software for seismic moment tensor inversion. The decomposition of seismic moment tensor of mine tremors was segmented into isotropic (I) part, compensated linear vector dipole (CLVD) part and double-couple (DC) part. The DC part is prevalent (up to 70%) in the majority of quakes from the central region of the USCB. A group of mine tremors with large I element (up to 50%) can also be observed. The spatial orientation of the fault and auxiliary planes were obtained from the computations for the seismic moment DC part. Study of the DC part of the seismic moment tensor made it possible for us to separate the group of events which might be acknowledged to have their origin in unstable energy release on surfaces of faults forming a regional structural pattern. The possible influence of the Cainozoic tectonic history of the USCB on the recent shape of stress field is discussed.

Analysis of Seismic Moment Tensor and Finite-Source Scaling During EGS Resource Development at The Geysers, CA

NASA Astrophysics Data System (ADS)

Boyd, O. S.; Dreger, D. S.; Gritto, R.

2015-12-01

Enhanced Geothermal Systems (EGS) resource development requires knowledge of subsurface physical parameters to quantify the evolution of fracture networks. We investigate seismicity in the vicinity of the EGS development at The Geysers Prati-32 injection well to determine moment magnitude, focal mechanism, and kinematic finite-source models with the goal of developing a rupture area scaling relationship for the Geysers and specifically for the Prati-32 EGS injection experiment. Thus far we have analyzed moment tensors of M ≥ 2 events, and are developing the capability to analyze the large numbers of events occurring as a result of the fluid injection and to push the analysis to smaller magnitude earthquakes. We have also determined finite-source models for five events ranging in magnitude from M 3.7 to 4.5. The scaling relationship between rupture area and moment magnitude of these events resembles that of a published empirical relationship derived for events from M 4.5 to 8.3. We plan to develop a scaling relationship in which moment magnitude and corner frequency are predictor variables for source rupture area constrained by the finite-source modeling. Inclusion of corner frequency in the empirical scaling relationship is proposed to account for possible variations in stress drop. If successful, we will use this relationship to extrapolate to the large numbers of events in the EGS seismicity cloud to estimate the coseismic fracture density. We will present the moment tensor and corner frequency results for the micro earthquakes, and for select events, finite-source models. Stress drop inferred from corner frequencies and from finite-source modeling will be compared.

Surface‐wave Green’s tensors in the near field

USGS Publications Warehouse

Haney, Matt; Nakahara, Hisashi

2014-01-01

We demonstrate the connection between theoretical expressions for the correlation of ambient noise Rayleigh and Love waves and the exact surface‐wave Green’s tensors for a point force. The surface‐wave Green’s tensors are well known in the far‐field limit. On the other hand, the imaginary part of the exact Green’s tensors, including near‐field effects, arises in correlation techniques such as the spatial autocorrelation (SPAC) method. Using the imaginary part of the exact Green’s tensors from the SPAC method, we find the associated real part using the Kramers–Kronig relations. The application of the Kramers–Kronig relations is not straightforward, however, because the causality properties of the different tensor components vary. In addition to the Green’s tensors for a point force, we also derive expressions for a general point moment tensor source.

A Guided Tour of Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Snieder, Roel; van Wijk, Kasper

2015-05-01

1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical coordinates; 5. Gradient; 6. Divergence of a vector field; 7. Curl of a vector field; 8. Theorem of Gauss; 9. Theorem of Stokes; 10. The Laplacian; 11. Scale analysis; 12. Linear algebra; 13. Dirac delta function; 14. Fourier analysis; 15. Analytic functions; 16. Complex integration; 17. Green's functions: principles; 18. Green's functions: examples; 19. Normal modes; 20. Potential-field theory; 21. Probability and statistics; 22. Inverse problems; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Conservation laws; 26. Cartesian tensors; 27. Variational calculus; 28. Epilogue on power and knowledge.

The Absolute Spectrum Polarimeter (ASP)

NASA Technical Reports Server (NTRS)

Kogut, A. J.

2010-01-01

The Absolute Spectrum Polarimeter (ASP) is an Explorer-class mission to map the absolute intensity and linear polarization of the cosmic microwave background and diffuse astrophysical foregrounds over the full sky from 30 GHz to 5 THz. The principal science goal is the detection and characterization of linear polarization from an inflationary epoch in the early universe, with tensor-to-scalar ratio r much greater than 1O(raised to the power of { -3}) and Compton distortion y < 10 (raised to the power of{-6}). We describe the ASP instrument and mission architecture needed to detect the signature of an inflationary epoch in the early universe using only 4 semiconductor bolometers.

Turbulent fluid motion 2: Scalars, vectors, and tensors

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1991-01-01

The author shows that the sum or difference of two vectors is a vector. Similarly the sum of any two tensors of the same order is a tensor of that order. No meaning is attached to the sum of tensors of different orders, say u(sub i) + u(sub ij); that is not a tensor. In general, an equation containing tensors has meaning only if all the terms in the equation are tensors of the same order, and if the same unrepeated subscripts appear in all the terms. These facts will be used in obtaining appropriate equations for fluid turbulence. With the foregoing background, the derivation of appropriate continuum equations for turbulence should be straightforward.

Generalized Higher Order Orthogonal Iteration for Tensor Learning and Decomposition.

PubMed

Liu, Yuanyuan; Shang, Fanhua; Fan, Wei; Cheng, James; Cheng, Hong

2016-12-01

Low-rank tensor completion (LRTC) has successfully been applied to a wide range of real-world problems. Despite the broad, successful applications, existing LRTC methods may become very slow or even not applicable for large-scale problems. To address this issue, a novel core tensor trace-norm minimization (CTNM) method is proposed for simultaneous tensor learning and decomposition, and has a much lower computational complexity. In our solution, first, the equivalence relation of trace norm of a low-rank tensor and its core tensor is induced. Second, the trace norm of the core tensor is used to replace that of the whole tensor, which leads to two much smaller scale matrix TNM problems. Finally, an efficient alternating direction augmented Lagrangian method is developed to solve our problems. Our CTNM formulation needs only O((R N +NRI)log(√{I N })) observations to reliably recover an N th-order I×I×…×I tensor of n -rank (r,r,…,r) , compared with O(rI N-1 ) observations required by those tensor TNM methods ( I > R ≥ r ). Extensive experimental results show that CTNM is usually more accurate than them, and is orders of magnitude faster.

Tensor gauge condition and tensor field decomposition

NASA Astrophysics Data System (ADS)

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.

Multi-field inflation with a random potential

NASA Astrophysics Data System (ADS)

Tye, S.-H. Henry; Xu, Jiajun; Zhang, Yang

2009-04-01

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian-like motion with a drift in the D-dimensional field space, allowing entropic perturbation modes to continuously and randomly feed into the adiabatic mode. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario where the stochastic scatterings are frequent but mild, the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, in which the coarse-grained motion of the inflaton is significantly slowed down by the scatterings, leads to rich phenomenologies. The power spectrum exhibits primordial fluctuations on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and have been smoothed out by binning of data points. With more data coming in the future, we expect these features can be detected or falsified. On the other hand the tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced by the large ratio of the Brownian-like motion speed over the drift speed. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, and is negligible in the weakly random scenario. However, non-Gaussianity can possibly be enhanced by resonant effects in the strongly random scenario or arise from the entropic perturbations during the onset of (p)reheating if the background inflaton trajectory exhibits particular properties. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.

The Topology of Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

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.

Phasic action of the tensor muscle modulates the calling song in cicadas

PubMed

Fonseca; Hennig

1996-01-01

The effect of tensor muscle contraction on sound production by the tymbal was investigated in three species of cicadas (Tettigetta josei, Tettigetta argentata and Tympanistalna gastrica). All species showed a strict time correlation between the activity of the tymbal motoneurone and the discharge of motor units in the tensor nerve during the calling song. Lesion of the tensor nerve abolished the amplitude modulation of the calling song, but this modulation was restored by electrical stimulation of the tensor nerve or by mechanically pushing the tensor sclerite. Electrical stimulation of the tensor nerve at frequencies higher than 30­40 Hz changed the sound amplitude. In Tett. josei and Tett. argentata there was a gradual increase in sound amplitude with increasing frequency of tensor nerve stimulation, while in Tymp. gastrica there was a sudden reduction in sound amplitude at stimulation frequencies higher than 30 Hz. This contrasting effect in Tymp. gastrica was due to a bistable tymbal frame. Changes in sound pulse amplitude were positively correlated with changes in the time lag measured from tymbal motoneurone stimulation to the sound pulse. The tensor muscle acted phasically because electrical stimulation of the tensor nerve during a time window (0­10 ms) before electrical stimulation of the tymbal motoneurone was most effective in eliciting amplitude modulations. In all species, the tensor muscle action visibly changed the shape of the tymbal. Despite the opposite effects of the tensor muscle on sound pulse amplitude observed between Tettigetta and Tympanistalna species, the tensor muscle of both acts by modulating the shape of the tymbal, which changes the force required for the tymbal muscle to buckle the tymbal.

Gauge and Non-Gauge Tensor Multiplets in 5D Conformal Supergravity

NASA Astrophysics Data System (ADS)

Kugo, T.; Ohashi, K.

2002-12-01

An off-shell formulation of two distinct tensor multiplets, a massive tensor multiplet and a tensor gauge multiplet, is presented in superconformal tensor calculus in five-dimensional space-time. Both contain a rank 2 antisymmetric tensor field, but there is no gauge symmetry in the former, while it is a gauge field in the latter. Both multiplets have 4 bosonic and 4 fermionic on-shell modes, but the former consists of 16 (boson)+16 (fermion) component fields, while the latter consists of 8 (boson)+8 (fermion) component fields.

The energy-momentum tensor(s) in classical gauge theories

DOE PAGES

Blaschke, Daniel N.; Gieres, François; Reboud, Méril; ...

2016-07-12

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. In conclusion, the relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed.

Using Perturbation Theory to Reduce Noise in Diffusion Tensor Fields

PubMed Central

Bansal, Ravi; Staib, Lawrence H.; Xu, Dongrong; Laine, Andrew F.; Liu, Jun; Peterson, Bradley S.

2009-01-01

We propose the use of Perturbation theory to reduce noise in Diffusion Tensor (DT) fields. Diffusion Tensor Imaging (DTI) encodes the diffusion of water molecules along different spatial directions in a positive-definite, 3 × 3 symmetric tensor. Eigenvectors and eigenvalues of DTs allow the in vivo visualization and quantitative analysis of white matter fiber bundles across the brain. The validity and reliability of these analyses are limited, however, by the low spatial resolution and low Signal-to-Noise Ratio (SNR) in DTI datasets. Our procedures can be applied to improve the validity and reliability of these quantitative analyses by reducing noise in the tensor fields. We model a tensor field as a three-dimensional Markov Random Field and then compute the likelihood and the prior terms of this model using Perturbation theory. The prior term constrains the tensor field to be smooth, whereas the likelihood term constrains the smoothed tensor field to be similar to the original field. Thus, the proposed method generates a smoothed field that is close in structure to the original tensor field. We evaluate the performance of our method both visually and quantitatively using synthetic and real-world datasets. We quantitatively assess the performance of our method by computing the SNR for eigenvalues and the coherence measures for eigenvectors of DTs across tensor fields. In addition, we quantitatively compare the performance of our procedures with the performance of one method that uses a Riemannian distance to compute the similarity between two tensors, and with another method that reduces noise in tensor fields by anisotropically filtering the diffusion weighted images that are used to estimate diffusion tensors. These experiments demonstrate that our method significantly increases the coherence of the eigenvectors and the SNR of the eigenvalues, while simultaneously preserving the fine structure and boundaries between homogeneous regions, in the smoothed tensor field. PMID:19540791

A T1 and DTI fused 3D corpus callosum analysis in pre- vs. post-season contact sports players

NASA Astrophysics Data System (ADS)

Lao, Yi; Law, Meng; Shi, Jie; Gajawelli, Niharika; Haas, Lauren; Wang, Yalin; Leporé, Natasha

2015-01-01

Sports related traumatic brain injury (TBI) is a worldwide public health issue, and damage to the corpus callosum (CC) has been considered as an important indicator of TBI. However, contact sports players suffer repeated hits to the head during the course of a season even in the absence of diagnosed concussion, and less is known about their effect on callosal anatomy. In addition, T1-weighted and diffusion tensor brain magnetic resonance images (DTI) have been analyzed separately, but a joint analysis of both types of data may increase statistical power and give a more complete understanding of anatomical correlates of subclinical concussions in these athletes. Here, for the first time, we fuse T1 surface-based morphometry and a new DTI analysis on 3D surface representations of the CCs into a single statistical analysis on these subjects. Our new combined method successfully increases detection power in detecting differences between pre- vs. post-season contact sports players. Alterations are found in the ventral genu, isthmus, and splenium of CC. Our findings may inform future health assessments in contact sports players. The new method here is also the first truly multimodal diffusion and T1-weighted analysis of the CC, and may be useful to detect anatomical changes in the corpus callosum in other multimodal datasets.

Light-driven self-assembly of hetero-shaped gold nanorods

NASA Astrophysics Data System (ADS)

Liaw, Jiunn-Woei; Chao, Hsueh-Yu; Huang, Cheng-Wei; Kuo, Mao-Kuen

2018-01-01

Light-driven self-assembly and coalescence of two nearby hetero-shaped gold nanorods (GNRs) with different lengths are studied theoretically. The optical forces and torques, in terms of Maxwell's stress tensor, upon these GNRs provided by a linearly polarized (LP) plane wave are analyzed using the multiple multipole (MMP) method. Numerical results show that the optical torque dominates their alignments and the optical force their attraction. The most likely outcome of the plasmon-mediated light-matter interaction is wavelength dependent. Three different coalescences of the two GNRs could be induced by a LP light in three different wavelength regimes, respectively. For example, the side-by-side coalescence of two GNRs with radius of 15 nm and different lengths (120 and 240 nm) is induced in water as irradiated by a LP light at 633 nm, the T-shaped one at 1064 nm, and the end-to-end one at 1700 nm. The plasmonic attractive force and heating power densities inside GNRs with different gaps are also studied; the smaller the gap, the larger the attractive force and heating power. The results imply that the plasmonic coalescence and heating of two discrete GNRs may cause the local fusion at the junction of the assembly and the subsequent annealing (even recrystallization). Because the heating makes the two discrete GNRs fused to become a new nanostructure, the plasmonic coalescence of optical manipulation is irreversible.

Prediction of neurodevelopmental outcome after hypoxic-ischemic encephalopathy treated with hypothermia by diffusion tensor imaging analyzed using tract-based spatial statistics.

PubMed

Tusor, Nora; Wusthoff, Courtney; Smee, Natalie; Merchant, Nazakat; Arichi, Tomoki; Allsop, Joanna M; Cowan, Frances M; Azzopardi, Denis; Edwards, A David; Counsell, Serena J

2012-07-01

Objective biomarkers are needed to assess neuroprotective therapies after perinatal hypoxic-ischemic encephalopathy (HIE). We tested the hypothesis that, in infants who underwent therapeutic hypothermia after perinatal HIE, neurodevelopmental performance was predicted by fractional anisotropy (FA) values in the white matter (WM) on early diffusion tensor imaging (DTI) as assessed by means of tract-based spatial statistics (TBSS). We studied 43 term infants with HIE. Developmental assessments were carried out at a median (range) age of 24 (12-28) mo. As compared with infants with favorable outcomes, those with unfavorable outcomes had significantly lower FA values (P < 0.05) in the centrum semiovale, corpus callosum (CC), anterior and posterior limbs of the internal capsule, external capsules, fornix, cingulum, cerebral peduncles, optic radiations, and inferior longitudinal fasciculus. In a second analysis in 32 assessable infants, the Griffiths Mental Development Scales (Revised) (GMDS-R) showed a significant linear correlation (P < 0.05) between FA values and developmental quotient (DQ) and all its component subscale scores. DTI analyzed by TBSS provides a qualified biomarker that can be used to assess the efficacy of additional neuroprotective therapies after HIE.

Adaptive Multilinear Tensor Product Wavelets

DOE PAGES

Weiss, Kenneth; Lindstrom, Peter

2015-08-12

Many foundational visualization techniques including isosurfacing, direct volume rendering and texture mapping rely on piecewise multilinear interpolation over the cells of a mesh. However, there has not been much focus within the visualization community on techniques that efficiently generate and encode globally continuous functions defined by the union of multilinear cells. Wavelets provide a rich context for analyzing and processing complicated datasets. In this paper, we exploit adaptive regular refinement as a means of representing and evaluating functions described by a subset of their nonzero wavelet coefficients. We analyze the dependencies involved in the wavelet transform and describe how tomore » generate and represent the coarsest adaptive mesh with nodal function values such that the inverse wavelet transform is exactly reproduced via simple interpolation (subdivision) over the mesh elements. This allows for an adaptive, sparse representation of the function with on-demand evaluation at any point in the domain. In conclusion, we focus on the popular wavelets formed by tensor products of linear B-splines, resulting in an adaptive, nonconforming but crack-free quadtree (2D) or octree (3D) mesh that allows reproducing globally continuous functions via multilinear interpolation over its cells.« less

Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals

NASA Astrophysics Data System (ADS)

Patel, Hiren H.

2017-09-01

This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct propagators, each with arbitrary integer weight, near an arbitrary even number of spacetime dimensions, giving UV divergent, IR divergent, and finite parts at (almost) any real-valued kinematic point. Additionally, it can generate multivariable Taylor series expansions of these integrals around any non-singular kinematic point to arbitrary order. All special functions and abbreviations output by Package-X 2.0 support Mathematica's arbitrary precision evaluation capabilities to deal with issues of numerical stability. Finally, tensor algebraic routines of Package-X have been polished and extended to support open fermion chains both on and off shell. The documentation (equivalent to over 100 printed pages) is accessed through Mathematica's Wolfram Documentation Center and contains information on all Package-X symbols, with over 300 basic usage examples, 3 project-scale tutorials, and instructions on linking to FEYNCALC and LOOPTOOLS. Program files doi:http://dx.doi.org/10.17632/yfkwrd4d5t.1 Licensing provisions: CC by 4.0 Programming language: Mathematica (Wolfram Language) Journal reference of previous version: H. H. Patel, Comput. Phys. Commun 197, 276 (2015) Does the new version supersede the previous version?: Yes Summary of revisions: Extension to four point one-loop integrals with higher powers of denominator factors, separate extraction of UV and IR divergent parts, testing for power IR divergences, construction of Taylor series expansions of one-loop integrals, numerical evaluation with arbitrary precision arithmetic, manipulation of fermion chains, improved tensor algebraic routines, and much expanded documentation. Nature of problem: Analytic calculation of one-loop integrals in relativistic quantum field theory. Solution method: Passarino-Veltman reduction formula, Denner-Dittmaier reduction formulae, and additional algorithms described in the manuscript. Restrictions: One-loop integrals are limited to those involving no more than four denominator factors.

Tensor calculus: unlearning vector calculus

NASA Astrophysics Data System (ADS)

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

2018-02-01

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 serve as a bridge for vector calculus into tensor calculus.

Unifying neural-network quantum states and correlator product states via tensor networks

NASA Astrophysics Data System (ADS)

Clark, Stephen R.

2018-04-01

Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose (unnormalised) amplitudes in a fixed basis can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the lattice, called correlators. Recently Carleo and Troyer (2017 Science 355 602) introduced a new type sampleable ansatz called neural-network quantum states (NQS) that are inspired by the restricted Boltzmann model used in machine learning. By employing the formalism of tensor networks we show that NQS are a special form of CPS with novel properties. Diagramatically a number of simple observations become transparent. Namely, that NQS are CPS built from extensively sized GHZ-form correlators making them uniquely unbiased geometrically. The appearance of GHZ correlators also relates NQS to canonical polyadic decompositions of tensors. Another immediate implication of the NQS equivalence to CPS is that we are able to formulate exact NQS representations for a wide range of paradigmatic states, including superpositions of weighed-graph states, the Laughlin state, toric code states, and the resonating valence bond state. These examples reveal the potential of using higher dimensional hidden units and a second hidden layer in NQS. The major outlook of this study is the elevation of NQS to correlator operators allowing them to enhance conventional well-established variational Monte Carlo approaches for strongly correlated fermions.

Cosmological footprints of loop quantum gravity.

PubMed

Grain, J; Barrau, A

2009-02-27

The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum effects in the early universe. We show that the associated corrections should modify the potential seen by gravitational waves during the inflationary amplification. The resulting power spectrum should exhibit a characteristic tilt. This opens a new window for cosmological tests of quantum gravity.

A Communication-Optimal Framework for Contracting Distributed Tensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei

Tensor contractions are extremely compute intensive generalized matrix multiplication operations encountered in many computational science fields, such as quantum chemistry and nuclear physics. Unlike distributed matrix multiplication, which has been extensively studied, limited work has been done in understanding distributed tensor contractions. In this paper, we characterize distributed tensor contraction algorithms on torus networks. We develop a framework with three fundamental communication operators to generate communication-efficient contraction algorithms for arbitrary tensor contractions. We show that for a given amount of memory per processor, our framework is communication optimal for all tensor contractions. We demonstrate performance and scalability of our frameworkmore » on up to 262,144 cores of BG/Q supercomputer using five tensor contraction examples.« less

On the Tensorial Nature of Fluxes in Continuous Media.

ERIC Educational Resources Information Center

Stokes, Vijay Kumar; Ramkrishna, Doraiswami

1982-01-01

Argues that mass and energy fluxes in a fluid are vectors. Topics include the stress tensor, theorem for tensor fields, mass flux as a vector, stress as a second order tensor, and energy flux as a tensor. (SK)

A moment-tensor catalog for intermediate magnitude earthquakes in Mexico

NASA Astrophysics Data System (ADS)

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 is difficult. The selection of data windows and filter parameters is tedious without a tool that allows easy viewing of the data prior to the inversion. Therefore, we developed a graphical user interface (GUI), based on Python and the python library ObsPy, that processes in a iterative and interactive way observed and synthetic seismograms prior to the inversion. The processing includes filtering, choosing and discarding traces and manual adjustment of time windows in which synthetics and observed seismograms will be compared. We calculate the Green Functions using the SPECFEM3D_GLOBE algorithm (Komatitsch et al.,2004) which employs a velocity model that is composed of a mantle and a crustal model, S362ANI (Kustowski et al., 2008) and CRUST2.0 (Bassin et al., 2000), respectively. We invert the observed seismograms for the seismic moment tensor using a method developed for earthquakes in California (Liu et al., 2004) and implemented for earthquakes in Mexico (De la Vega, 2014). In this work, we introduce the GUI, the inversion method and the results from the moment-tensor inversions obtained for intermediate-magnitude earthquakes (4.5

Essential core of the Hawking–Ellis types

NASA Astrophysics Data System (ADS)

Martín-Moruno, Prado; Visser, Matt

2018-06-01

The Hawking–Ellis (Segre–Plebański) classification of possible stress–energy tensors is an essential tool in analyzing the implications of the Einstein field equations in a more-or-less model-independent manner. In the current article the basic idea is to simplify the Hawking–Ellis type I, II, III, and IV classification by isolating the ‘essential core’ of the type II, type III, and type IV stress–energy tensors; this being done by subtracting (special cases of) type I to simplify the (Lorentz invariant) eigenvalue structure as much as possible without disturbing the eigenvector structure. We will denote these ‘simplified cores’ type II0, type III0, and type IV0. These ‘simplified cores’ have very nice and simple algebraic properties. Furthermore, types I and II0 have very simple classical interpretations, while type IV0 is known to arise semi-classically (in renormalized expectation values of standard stress–energy tensors). In contrast type III0 stands out in that it has neither a simple classical interpretation, nor even a simple semi-classical interpretation. We will also consider the robustness of this classification considering the stability of the different Hawking–Ellis types under perturbations. We argue that types II and III are definitively unstable, whereas types I and IV are stable.

Diffusion of phonons through (along and across) the ultrathin crystalline films

NASA Astrophysics Data System (ADS)

Šetrajčić, J. P.; Jaćimovski, S. K.; Vučenović, S. M.

2017-11-01

Instead of usual approach, applying displacement-displacement Green's functions, the momentum-momentum Green's functions will be used to calculate the diffusion tensor. With this type of Green's function we have calculated and analyzed dispersion law in film-structures. A small number of phonon energy levels along the direction of boundary surfaces joint of the film are discrete-ones and in this case standing waves could occur. This is consequence of quantum size effects. These Green's functions enter into Kubo's formula defining diffusion properties of the system and possible heat transfer direction through observed structures. Calculation of the diffusion tensor for phonons in film-structure requires solving of the system of difference equations. Boundary conditions are included into mentioned system through the Hamiltonian of the film-structure. It has been shown that the diagonal elements of the diffusion tensor express discrete behavior of the dispersion law of elementary excitations. More important result is-that they are temperature independent and that their values are much higher comparing with bulk structures. This result favors better heat conduction of the film, but in direction which is perpendicular to boundary film surface. In the same time this significantly favors appearance 2D superconducting surfaces inside the ultra-thin crystal structure, which are parallel to the boundary surface.

Trends in biomedical informatics: automated topic analysis of JAMIA articles

PubMed Central

Wang, Shuang; Jiang, Chao; Jiang, Xiaoqian; Kim, Hyeon-Eui; Sun, Jimeng; Ohno-Machado, Lucila

2015-01-01

Biomedical Informatics is a growing interdisciplinary field in which research topics and citation trends have been evolving rapidly in recent years. To analyze these data in a fast, reproducible manner, automation of certain processes is needed. JAMIA is a “generalist” journal for biomedical informatics. Its articles reflect the wide range of topics in informatics. In this study, we retrieved Medical Subject Headings (MeSH) terms and citations of JAMIA articles published between 2009 and 2014. We use tensors (i.e., multidimensional arrays) to represent the interaction among topics, time and citations, and applied tensor decomposition to automate the analysis. The trends represented by tensors were then carefully interpreted and the results were compared with previous findings based on manual topic analysis. A list of most cited JAMIA articles, their topics, and publication trends over recent years is presented. The analyses confirmed previous studies and showed that, from 2012 to 2014, the number of articles related to MeSH terms Methods, Organization & Administration, and Algorithms increased significantly both in number of publications and citations. Citation trends varied widely by topic, with Natural Language Processing having a large number of citations in particular years, and Medical Record Systems, Computerized remaining a very popular topic in all years. PMID:26555018

Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes

NASA Astrophysics Data System (ADS)

Levi, Adam; Ori, Amos

2015-05-01

Computation of the renormalized stress-energy tensor is the most serious obstacle in studying the dynamical, self-consistent, semiclassical evaporation of a black hole in 4D. The difficulty arises from the delicate regularization procedure for the stress-energy tensor, combined with the fact that in practice the modes of the field need to be computed numerically. We have developed a new method for numerical implementation of the point-splitting regularization in 4D, applicable to the renormalized stress-energy tensor as well as to ⟨ϕ2⟩ren , namely the renormalized ⟨ϕ2⟩. So far we have formulated two variants of this method: t -splitting (aimed for stationary backgrounds) and angular splitting (for spherically symmetric backgrounds). In this paper we introduce our basic approach, and then focus on the t -splitting variant, which is the simplest of the two (deferring the angular-splitting variant to a forthcoming paper). We then use this variant, as a first stage, to calculate ⟨ϕ2⟩ren in Schwarzschild spacetime, for a massless scalar field in the Boulware state. We compare our results to previous ones, obtained by a different method, and find full agreement. We discuss how this approach can be applied (using the angular-splitting variant) to analyze the dynamical self-consistent evaporation of black holes.

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

NASA Technical Reports Server (NTRS)

Reifler, Frank; Morris, Randall

1994-01-01

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

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

USGS Publications Warehouse

Haney, Matthew M.; Hisashi Nakahara,

2016-01-01

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

Simultaneous inversion of seismic velocity and moment tensor using elastic-waveform inversion of microseismic data: Application to the Aneth CO2-EOR field

NASA Astrophysics Data System (ADS)

Chen, Y.; Huang, L.

2017-12-01

Moment tensors are key parameters for characterizing CO2-injection-induced microseismic events. Elastic-waveform inversion has the potential to providing accurate results of moment tensors. Microseismic waveforms contains information of source moment tensors and the wave propagation velocity along the wavepaths. We develop an elastic-waveform inversion method to jointly invert the seismic velocity model and moment tensor. We first use our adaptive moment-tensor joint inversion method to estimate moment tensors of microseismic events. Our adaptive moment-tensor inversion method jointly inverts multiple microseismic events with similar waveforms within a cluster to reduce inversion uncertainty for microseismic data recorded using a single borehole geophone array. We use this inversion result as the initial model for our elastic-waveform inversion to minimize the cross-correlated-based data misfit between observed data and synthetic data. We verify our method using synthetic microseismic data and obtain improved results of both moment tensors and seismic velocity model. We apply our new inversion method to microseismic data acquired at a CO2-enhanced oil recovery field in Aneth, Utah, using a single borehole geophone array. The results demonstrate that our new inversion method significantly reduces the data misfit compared to the conventional ray-theory-based moment-tensor inversion.

Effects of a primordial magnetic field with log-normal distribution on the cosmic microwave background

NASA Astrophysics Data System (ADS)

Yamazaki, Dai G.; Ichiki, Kiyotomo; Takahashi, Keitaro

2011-12-01

We study the effect of primordial magnetic fields (PMFs) on the anisotropies of the cosmic microwave background (CMB). We assume the spectrum of PMFs is described by log-normal distribution which has a characteristic scale, rather than power-law spectrum. This scale is expected to reflect the generation mechanisms and our analysis is complementary to previous studies with power-law spectrum. We calculate power spectra of energy density and Lorentz force of the log-normal PMFs, and then calculate CMB temperature and polarization angular power spectra from scalar, vector, and tensor modes of perturbations generated from such PMFs. By comparing these spectra with WMAP7, QUaD, CBI, Boomerang, and ACBAR data sets, we find that the current CMB data set places the strongest constraint at k≃10-2.5Mpc-1 with the upper limit B≲3nG.

A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal and polyhedral meshes (u)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lipnikov, Konstantin; Shashkov, Mikhail

2011-01-11

We construct a new mimetic tensor artificial viscosity on general polygonal and polyhedral meshes. The tensor artificial viscosity is based on a mimetic discretization of coordinate invariant operators, divergence of a tensor and gradient of a vector. The focus of this paper is on the symmetric form, div ({mu},{var_epsilon}(u)), of the tensor artificial viscosity where {var_epsilon}(u) is the symmetrized gradient of u and {mu}, is a tensor. The mimetic discretizations of this operator is derived for the case of a full tensor coefficient {mu}, that may reflect a shock direction. We demonstrate performance of the new viscosity for the Nohmore » implosion, Sedov explosion and Saltzman piston problems in both Cartesian and axisymmetric coordinate systems.« less

Tensor-based spatiotemporal saliency detection

NASA Astrophysics Data System (ADS)

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.

Synchrotron X-ray diffraction investigations on strains in the oxide layer of an irradiated Zircaloy fuel cladding

NASA Astrophysics Data System (ADS)

Chollet, Mélanie; Valance, Stéphane; Abolhassani, Sousan; Stein, Gene; Grolimund, Daniel; Martin, Matthias; Bertsch, Johannes

2017-05-01

For the first time the microstructure of the oxide layer of a Zircaloy-2 cladding after 9 cycles of irradiation in a boiling water reactor has been analyzed with synchrotron micro-X-ray diffraction. Crystallographic strains of the monoclinic and to some extent of the tetragonal ZrO2 are depicted through the thick oxide layer. Thin layers of sub-oxide at the oxide-metal interface as found for autoclave-tested samples and described in the literature, have not been observed in this material maybe resulting from irradiation damage. Shifts of selected diffraction peaks of the monoclinic oxide show that the uniform strain produced during oxidation is orientated in the lattice and displays variations along the oxide layer. Diffraction peaks and their shifts from families of diffracting planes could be translated into a virtual tensor. This virtual tensor exhibits changes through the oxide layer passing by tensile or compressive components.

Polarized deuterium internal target at AmPS (NIKHEF)

NASA Astrophysics Data System (ADS)

Ferro-Luzzi, M.; Zhou, Z.-L.; van den Brand, J. F. J.; Bulten, H. J.; Alarcon, R.; van Bakel, N.; Botto, T.; Bouwhuis, M.; van Buuren, L.; Comfort, J.; Doets, M.; Dolfini, S.; Ent, R.; Geurts, D.; Heimberg, P.; Higinbotham, D. W.; de Jager, C. W.; Lang, J.; de Lange, D. J.; Norum, B.; Passchier, I.; Poolman, H. R.; Six, E.; Steijger, J.; Szczerba, D.; Unal, O.; de Vries, H.

1998-01-01

We describe the polarized deuterium target internal to the NIKHEF medium-energy electron storage ring. Tensor polarized deuterium was produced in an atomic beam source and injected into a storage cell target. A Breit-Rabi polarimeter was used to monitor the injected atomic beam intensity and polarization. An electrostatic ion-extraction system and a Wien filter were utilized to measure on-line the atomic fraction of the target gas in the storage cell. This device was supplemented with a tensor polarization analyzer using the neutron anisotropy of the 3H(d,n)α reaction at 60 keV. This method allows determining the density-averaged nuclear polarization of the target gas, independent of spatial and temporal variations. We address issues important for polarized hydrogen/deuterium internal targets, such as the effects of spin-exchange collisions and resonant transitions induced by the RF fields of the charged particle beam.

Speed of gravitational waves and black hole hair

NASA Astrophysics Data System (ADS)

Tattersall, Oliver J.; Ferreira, Pedro G.; Lagos, Macarena

2018-04-01

The recent detection of GRB 170817A and GW170817 constrains the speed of gravity waves cT to be that of light, which severely restricts the landscape of modified gravity theories that impact the cosmological evolution of the Universe. In this work, we investigate the presence of black hole hair in the remaining viable cosmological theories of modified gravity that respect the constraint cT=1 . We focus mainly on scalar-tensor theories of gravity, analyzing static, asymptotically flat black holes in Horndeski, Beyond Horndeski, Einstein-scalar-Gauss-Bonnet, and Chern-Simons theories. We find that in all of the cases considered here, theories that are cosmologically relevant and respect cT=1 do not allow for hair, or have negligible hair. We further comment on vector-tensor theories including Einstein-Yang-Mills, Einstein-Aether, and generalized Proca theories, as well as bimetric theories.

ON THE SPIN CORRELATIONS OF MUONS AND TAU LEPTONS GENERATED IN THE ANNIHILATION PROCESSES e+e- → μ+μ-, e+e- → τ+τ-

NASA Astrophysics Data System (ADS)

Lyuboshitz, Valery V.; Lyuboshitz, Vladimir L.

2014-12-01

Using the technique of helicity amplitudes, the electromagnetic process e+e- → μ+μ-(τ+τ-) is theoretically studied in the one-photon approximation. The structure of the triplet states of the final (μ+μ-) system is analyzed. It is shown that in the case of unpolarized electron and positron the final muons are also unpolarized, but their spins are strongly correlated. Explicit expressions for the components of the correlation tensor of the (μ+μ-) system are derived. The formula for the angular correlation at the decays of final muons μ+ and μ- is obtained. It is demonstrated that spin correlations of muons in the considered process have the purely quantum character, since one of the Bell-type incoherence inequalities for the correlation tensor components is always violated.

Pseudoscalar Meson Electroproduction and Transversity

NASA Astrophysics Data System (ADS)

Goldstein, Gary R.; Liuti, Simonetta

2011-02-01

Exclusive meson leptoproduction from nucleons in the deeply virtual exchanged boson limit can be described by generalized parton distributions (GPDs). Including spin dependence in the description requires 8 independent quark-parton and gluon-parton functions. The chiral even subset of 4 quark-nucleon GPDs are related to nucleon form factors and to parton distribution functions. The chiral odd set of 4 quark-nucleon GPDs are related to transversity, the tensor charge, and other quantities related to transversity. Different meson or photon production processes access different combinations of GPDs. This is analyzed in terms of t-channel exchange quantum numbers, JPC and it is shown that pseudoscalar production can isolate chiral odd GPDs. There is a sensitive dependence in various cross sections and asymmetries on the tensor charge of the nucleon and other transversity parameters. In a second section, analyticity and completeness are shown to limit the partonic interpret ation of the GPDs in the ERBL region.

Polarizability tensor invariants of H2, HD, and D2

NASA Astrophysics Data System (ADS)

Raj, Ankit; Hamaguchi, Hiro-o.; Witek, Henryk A.

2018-03-01

We report an exhaustive compilation of wavelength-dependent matrix elements over the mean polarizability (α ¯ ) and polarizability anisotropy (γ) operators for the rovibrational states of the H2, HD, and D2 molecules together with an accompanying computer program for their evaluation. The matrix elements can be readily evaluated using the provided codes for rovibrational states with J = 0-15 and v = 0-4 and for any laser wavelengths in the interval 182.25-1320.6 nm corresponding to popular, commercially available lasers. The presented results substantially extend the scope of the data available in the literature, both in respect of the rovibrational transitions analyzed and the range of covered laser frequencies. The presented detailed tabulation of accurate polarizability tensor invariants is essential for successful realization of our main long-term goal: developing a universal standard for determining absolute Raman cross sections and absolute Raman intensities in experimental Rayleigh and Raman scattering studies of molecules.

Contribution to the development of low frequency terahertz coherent Raman micro-spectroscopy and microscopy

NASA Astrophysics Data System (ADS)

Ujj, Laszlo

2018-06-01

We report the construction and characterization of a coherent Raman tabletop system utilizing a novel astigmatic optical focusing geometry, a broadband nanosecond optical parametric oscillator and volumetric Bragg filters assisting 3CBCRS measuring system for the first time. In order to illustrate the versatility of the measurements and reveal the molecular information obtainable, two well-characterized chemicals were selected. Polarization sensitive epi-detected 3CBCRS spectra of liquid CCl4 and calcite crystal were recorded and analyzed. An unexpected polarization dependence of the signals of the lowest frequency modes of CCl4 was observed. The 1122 third order susceptibility component was phase flipped. The non-resonant susceptibility normalized 1122 component was found to be larger than the 1111 component for the lowest vibrational modes. This anomalous comportment was attributable to the anisotropy Raman tensor invariant in the third order nonlinear susceptibility tensor.

Lattice dynamical and dielectric properties of L-amino acids

NASA Astrophysics Data System (ADS)

Tulip, P. R.; Clark, S. J.

2006-08-01

We present the results of ab initio calculations of the lattice dynamical and dielectric properties of the L-amino acids L-alanine, L-leucine, and L-isoleucine. Normal-mode frequencies and dielectric permittivity tensors are obtained using density-functional perturbation theory implemented within the plane-wave pseudopotential approximation. IR spectra are calculated and are used to analyze the effects of intermolecular interactions and zwitterionization upon the lattice dynamics. It is found that vibronic modes associated with the carboxy and amino functional groups undergo modification from their free-molecule values due to the presence of hydrogen bonds. The role of macroscopic electric fields set up by zone-center normal modes in the lattice dynamics is investigated by analysis of the Born effective charge. Calculated permittivity tensors are found to be greater than would be obtained by a naive use of the isolated molecular values, indicating the role of intermolecular interactions in increasing molecular polarizability.

Polarized deuterium internal target at AmPS (NIKHEF)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Norum, Blaine; De Jager, Cornelis; Geurts, D.

1997-08-01

We describe the polarized deuterium target internal to the NIKHEF medium-energy electron storage ring. Tensor polarized deuterium was produced in an atomic beam source and injected into a storage cell target. A Breit-Rabi polarimeter was used to monitor the injected atomic beam intensity and polarization. An electrostatic ion-extraction system and a Wien filter were utilized to measure on-line the atomic fraction of the target gas in the storage cell. This device was supplemented with a tensor polarization analyzer using the neutron anisotropy of the 3H(d,n)sigma reaction at 60 keV. This method allows determining the density-averaged nuclear polarization of the targetmore » gas, independent of spatial and temporal variations. We address issues important for polarized hydrogen/deuterium internal targets, such as the effects of spin-exchange collisions and resonant transitions induced by the RF fields of the charged particle beam.« less

Polarized deuterium internal target at AmPS (NIKHEF)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferro-Luzzi, M.; NIKHEF, P.O. Box 41882, 1009 DB Amsterdam; Zhou, Z.-L.

1998-01-20

We describe the polarized deuterium target internal to the NIKHEF medium-energy electron storage ring. Tensor polarized deuterium was produced in an atomic beam source and injected into a storage cell target. A Breit-Rabi polarimeter was used to monitor the injected atomic beam intensity and polarization. An electrostatic ion-extraction system and a Wien filter were utilized to measure on-line the atomic fraction of the target gas in the storage cell. This device was supplemented with a tensor polarization analyzer using the neutron anisotropy of the {sup 3}H(d,n){alpha} reaction at 60 keV. This method allows determining the density-averaged nuclear polarization of themore » target gas, independent of spatial and temporal variations. We address issues important for polarized hydrogen/deuterium internal targets, such as the effects of spin-exchange collisions and resonant transitions induced by the RF fields of the charged particle beam.« less

Change-point analysis data of neonatal diffusion tensor MRI in preterm and term-born infants.

PubMed

Wu, Dan; Chang, Linda; Akazawa, Kentaro; Oishi, Kumiko; Skranes, Jon; Ernst, Thomas; Oishi, Kenichi

2017-06-01

The data presented in this article are related to the research article entitled "Mapping the Critical Gestational Age at Birth that Alters Brain Development in Preterm-born Infants using Multi-Modal MRI" (Wu et al., 2017) [1]. Brain immaturity at birth poses critical neurological risks in the preterm-born infants. We used a novel change-point model to analyze the critical gestational age at birth (GAB) that could affect postnatal development, based on diffusion tensor MRI (DTI) acquired from 43 preterm and 43 term-born infants in 126 brain regions. In the corresponding research article, we presented change-point analysis of fractional anisotropy (FA) and mean diffusivities (MD) measurements in these infants. In this article, we offered the relative changes of axonal and radial diffusivities (AD and RD) in relation to the change of FA and FA-based change-points, and we also provided the AD- and RD-based change-point results.

Sum-Frequency Generation from a Thin Cylindrical Layer

NASA Astrophysics Data System (ADS)

Shamyna, A. A.; Kapshai, V. N.

2018-01-01

In the Rayleigh-Gans-Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.

Tensor network method for reversible classical computation

NASA Astrophysics Data System (ADS)

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.

Sparse Tensor Decomposition for Haplotype Assembly of Diploids and Polyploids.

PubMed

Hashemi, Abolfazl; Zhu, Banghua; Vikalo, Haris

2018-03-21

Haplotype assembly is the task of reconstructing haplotypes of an individual from a mixture of sequenced chromosome fragments. Haplotype information enables studies of the effects of genetic variations on an organism's phenotype. Most of the mathematical formulations of haplotype assembly are known to be NP-hard and haplotype assembly becomes even more challenging as the sequencing technology advances and the length of the paired-end reads and inserts increases. Assembly of haplotypes polyploid organisms is considerably more difficult than in the case of diploids. Hence, scalable and accurate schemes with provable performance are desired for haplotype assembly of both diploid and polyploid organisms. We propose a framework that formulates haplotype assembly from sequencing data as a sparse tensor decomposition. We cast the problem as that of decomposing a tensor having special structural constraints and missing a large fraction of its entries into a product of two factors, U and [Formula: see text]; tensor [Formula: see text] reveals haplotype information while U is a sparse matrix encoding the origin of erroneous sequencing reads. An algorithm, AltHap, which reconstructs haplotypes of either diploid or polyploid organisms by iteratively solving this decomposition problem is proposed. The performance and convergence properties of AltHap are theoretically analyzed and, in doing so, guarantees on the achievable minimum error correction scores and correct phasing rate are established. The developed framework is applicable to diploid, biallelic and polyallelic polyploid species. The code for AltHap is freely available from https://github.com/realabolfazl/AltHap . AltHap was tested in a number of different scenarios and was shown to compare favorably to state-of-the-art methods in applications to haplotype assembly of diploids, and significantly outperforms existing techniques when applied to haplotype assembly of polyploids.

Axial diffusivity of the corona radiata correlated with ventricular size in adult hydrocephalus.

PubMed

Cauley, Keith A; Cataltepe, Oguz

2014-07-01

Hydrocephalus causes changes in the diffusion-tensor properties of periventricular white matter. Understanding the nature of these changes may aid in the diagnosis and treatment planning of this relatively common neurologic condition. Because ventricular size is a common measure of the severity of hydrocephalus, we hypothesized that a quantitative correlation could be made between the ventricular size and diffusion-tensor changes in the periventricular corona radiata. In this article, we investigated this relationship in adult patients with hydrocephalus and in healthy adult subjects. Diffusion-tensor imaging metrics of the corona radiata were correlated with ventricular size in 14 adult patients with acute hydrocephalus, 16 patients with long-standing hydrocephalus, and 48 consecutive healthy adult subjects. Regression analysis was performed to investigate the relationship between ventricular size and the diffusion-tensor metrics of the corona radiata. Subject age was analyzed as a covariable. There is a linear correlation between fractional anisotropy of the corona radiata and ventricular size in acute hydrocephalus (r = 0.784, p < 0.001), with positive correlation with axial diffusivity (r = 0.636, p = 0.014) and negative correlation with radial diffusivity (r = 0.668, p = 0.009). In healthy subjects, axial diffusion in the periventricular corona radiata is more strongly correlated with ventricular size than with patient age (r = 0.466, p < 0.001, compared with r = 0.058, p = 0.269). Axial diffusivity of the corona radiata is linearly correlated with ventricular size in healthy adults and in patients with hydrocephalus. Radial diffusivity of the corona radiata decreases linearly with ventricular size in acute hydrocephalus but is not significantly correlated with ventricular size in healthy subjects or in patients with long-standing hydrocephalus.

Fermionic vacuum polarization by an Abelian magnetic tube in the cosmic string spacetime

NASA Astrophysics Data System (ADS)

Maior de Sousa, M. S.; Ribeiro, R. F.; Bezerra de Mello, E. R.

2017-02-01

In this paper, we consider a charged massive fermionic quantum field in the idealized cosmic string spacetime and in the presence of a magnetic field confined in a cylindrical tube of finite radius. Three distinct configurations for the magnetic fields are taken into account: (i) a cylindrical shell of radius a , (ii) a magnetic field proportional to 1 /r , and (iii) a constant magnetic field. In these three cases, the axis of the infinitely long tube of radius a coincides with the cosmic string. Our main objectives in this paper are to analyze the fermionic condensate (FC) and the vacuum expectation value (VEV) of the fermionic energy-momentum tensor. In order to do that, we explicitly construct the complete set of normalized wave functions for each configuration of the magnetic field. We show that in the region outside the tube, the FC and the VEV of the energy-momentum tensor are decomposed into two parts: The first ones correspond to the zero-thickness magnetic flux contributions, and the second ones are induced by the nontrivial structure of the magnetic field, named core-induced contributions. The latter present specific forms depending on the magnetic field configuration considered. We also show that the VEV of the energy-momentum tensor is diagonal and obeys the conservation condition, and its trace is expressed in terms of the fermionic condensate. The zero-thickness contributions to the FC and VEV of the energy-momentum tensor depend only on the fractional part of the ration of the magnetic flux inside the tube by the quantum one. As to the core-induced contributions, they depend on the total magnetic flux inside the tube and, consequently, in general, are not a periodic function of the magnetic flux.

Brain structural changes in spasmodic dysphonia: A multimodal magnetic resonance imaging study.

PubMed

Kostic, Vladimir S; Agosta, Federica; Sarro, Lidia; Tomić, Aleksandra; Kresojević, Nikola; Galantucci, Sebastiano; Svetel, Marina; Valsasina, Paola; Filippi, Massimo

2016-04-01

The pathophysiology of spasmodic dysphonia is poorly understood. This study evaluated patterns of cortical morphology, basal ganglia, and white matter microstructural alterations in patients with spasmodic dysphonia relative to healthy controls. T1-weighted and diffusion tensor magnetic resonance imaging (MRI) scans were obtained from 13 spasmodic dysphonia patients and 30 controls. Tract-based spatial statistics was applied to compare diffusion tensor MRI indices (i.e., mean, radial and axial diffusivities, and fractional anisotropy) between groups on a voxel-by-voxel basis. Cortical measures were analyzed using surface-based morphometry. Basal ganglia were segmented on T1-weighted images, and volumes and diffusion tensor MRI metrics of nuclei were measured. Relative to controls, patients with spasmodic dysphonia showed increased cortical surface area of the primary somatosensory cortex bilaterally in a region consistent with the buccal sensory representation, as well as right primary motor cortex, left superior temporal, supramarginal and superior frontal gyri. A decreased cortical area was found in the rolandic operculum bilaterally, left superior/inferior parietal and lingual gyri, as well as in the right angular gyrus. Compared to controls, spasmodic dysphonia patients showed increased diffusivities and decreased fractional anisotropy of the corpus callosum and major white matter tracts, in the right hemisphere. Altered diffusion tensor MRI measures were found in the right caudate and putamen nuclei with no volumetric changes. Multi-level alterations in voice-controlling networks, that included regions devoted not only to sensorimotor integration, motor preparation and motor execution, but also processing of auditory and visual information during speech, might have a role in the pathophysiology of spasmodic dysphonia. Copyright © 2016 Elsevier Ltd. All rights reserved.

Casimir Effect in de Sitter Spacetime

NASA Astrophysics Data System (ADS)

Saharian, A. A.

2011-06-01

The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background spacetime decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.

One-loop gravitational wave spectrum in de Sitter spacetime

NASA Astrophysics Data System (ADS)

Fröb, Markus B.; Roura, Albert; Verdaguer, Enric

2012-08-01

The two-point function for tensor metric perturbations around de Sitter spacetime including one-loop corrections from massless conformally coupled scalar fields is calculated exactly. We work in the Poincaré patch (with spatially flat sections) and employ dimensional regularization for the renormalization process. Unlike previous studies we obtain the result for arbitrary time separations rather than just equal times. Moreover, in contrast to existing results for tensor perturbations, ours is manifestly invariant with respect to the subgroup of de Sitter isometries corresponding to a simultaneous time translation and rescaling of the spatial coordinates. Having selected the right initial state for the interacting theory via an appropriate iepsilon prescription is crucial for that. Finally, we show that although the two-point function is a well-defined spacetime distribution, the equal-time limit of its spatial Fourier transform is divergent. Therefore, contrary to the well-defined distribution for arbitrary time separations, the power spectrum is strictly speaking ill-defined when loop corrections are included.

Simple inflationary models in Gauss-Bonnet brane-world cosmology

NASA Astrophysics Data System (ADS)

Okada, Nobuchika; Okada, Satomi

2016-06-01

In light of the recent Planck 2015 results for the measurement of the cosmic microwave background (CMB) anisotropy, we study simple inflationary models in the context of the Gauss-Bonnet (GB) brane-world cosmology. The brane-world cosmological effect modifies the power spectra of scalar and tensor perturbations generated by inflation and causes a dramatic change for the inflationary predictions of the spectral index (n s) and the tensor-to-scalar ratio (r) from those obtained in the standard cosmology. In particular, the predicted r values in the inflationary models favored by the Planck 2015 results are suppressed due to the GB brane-world cosmological effect, which is in sharp contrast with inflationary scenario in the Randall-Sundrum brane-world cosmology, where the r values are enhanced. Hence, these two brane-world cosmological scenarios are distinguishable. With the dramatic change of the inflationary predictions, the inflationary scenario in the GB brane-world cosmology can be tested by more precise measurements of n s and future observations of the CMB B-mode polarization.

Structure formation in f(T) gravity and a solution for H0 tension

NASA Astrophysics Data System (ADS)

Nunes, Rafael C.

2018-05-01

We investigate the evolution of scalar perturbations in f(T) teleparallel gravity and its effects on the cosmic microwave background (CMB) anisotropy. The f(T) gravity generalizes the teleparallel gravity which is formulated on the Weitzenböck spacetime, characterized by the vanishing curvature tensor (absolute parallelism) and the non-vanishing torsion tensor. For the first time, we derive the observational constraints on the modified teleparallel gravity using the CMB temperature power spectrum from Planck's estimation, in addition to data from baryonic acoustic oscillations (BAO) and local Hubble constant measurements. We find that a small deviation of the f(T) gravity model from the ΛCDM cosmology is slightly favored. Besides that, the f(T) gravity model does not show tension on the Hubble constant that prevails in the ΛCDM cosmology. It is clear that f(T) gravity is also consistent with the CMB observations, and undoubtedly it can serve as a viable candidate amongst other modified gravity theories.

ECCD-induced tearing mode stabilization in coupled IPS/NIMROD/GENRAY HPC simulations

NASA Astrophysics Data System (ADS)

Jenkins, Thomas; Kruger, S. E.; Held, E. D.; Harvey, R. W.; Elwasif, W. R.

2012-03-01

We summarize ongoing developments toward an integrated, predictive model for determining optimal ECCD-based NTM stabilization strategies in ITER. We demonstrate the capability of the SWIM Project's Integrated Plasma Simulator (IPS) framework to choreograph multiple executions of, and data exchanges between, physics codes modeling various spatiotemporal scales of this coupled RF/MHD problem on several thousand HPC processors. As NIMROD evolves fluid equations to model bulk plasma behavior, self-consistent propagation/deposition of RF power in the ensuing plasma profiles is calculated by GENRAY. Data from both codes is then processed by computational geometry packages to construct the RF-induced quasilinear diffusion tensor; moments of this tensor (entering as additional terms in NIMROD's fluid equations due to the disparity in RF/MHD spatiotemporal scales) influence the dynamics of current, momentum, and energy evolution as well as the MHD closures. Initial results are shown to correctly capture the physics of magnetic island stabilization; we also discuss the development of a numerical plasma control system for active feedback stabilization of tearing modes.

The Kummer tensor density in electrodynamics and in gravity

NASA Astrophysics Data System (ADS)

Baekler, Peter; Favaro, Alberto; Itin, Yakov; Hehl, Friedrich W.

2014-10-01

Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T, which is antisymmetric in its first two and its last two indices: T=-T=-T. Thus, K∼T3, see Eq. (46). (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R of a Riemann-Cartan spacetime, then K∼R3 and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3).

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE

PubMed Central

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

2017-01-01

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 lp-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. PMID:28286347

Relativistic interpretation of the nature of the nuclear tensor force

NASA Astrophysics Data System (ADS)

Zong, Yao-Yao; Sun, Bao-Yuan

2018-02-01

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

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

PubMed

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.

Gravitoelectromagnetic analogy based on tidal tensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costa, L. Filipe O.; Herdeiro, Carlos A. R.

2008-07-15

We propose a new approach to a physical analogy between general relativity and electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations, which makes transparent both the similarities and key differences between the two interactions. The following realizations of the analogy are given. The first one matches linearized gravitational tidal tensors to exact electromagnetic tidal tensors in Minkowski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultrastationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third wemore » show that our approach leads to a two-step exact derivation of Papapetrou's equation describing the force exerted on a spinning test particle. Analogous scalar invariants built from tidal tensors of both theories are also discussed.« less

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

PubMed

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 < 0.01). Two-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.

Robust Likelihoods for Inflationary Gravitational Waves from Maps of Cosmic Microwave Background Polarization

NASA Technical Reports Server (NTRS)

Switzer, Eric Ryan; Watts, Duncan J.

2016-01-01

The B-mode polarization of the cosmic microwave background provides a unique window into tensor perturbations from inflationary gravitational waves. Survey effects complicate the estimation and description of the power spectrum on the largest angular scales. The pixel-space likelihood yields parameter distributions without the power spectrum as an intermediate step, but it does not have the large suite of tests available to power spectral methods. Searches for primordial B-modes must rigorously reject and rule out contamination. Many forms of contamination vary or are uncorrelated across epochs, frequencies, surveys, or other data treatment subsets. The cross power and the power spectrum of the difference of subset maps provide approaches to reject and isolate excess variance. We develop an analogous joint pixel-space likelihood. Contamination not modeled in the likelihood produces parameter-dependent bias and complicates the interpretation of the difference map. We describe a null test that consistently weights the difference map. Excess variance should either be explicitly modeled in the covariance or be removed through reprocessing the data.

Covariant density functional theory: predictive power and first attempts of a microscopic derivation

NASA Astrophysics Data System (ADS)

Ring, Peter

2018-05-01

We discuss systematic global investigations with modern covariant density functionals. The number of their phenomenological parameters can be reduced considerable by using microscopic input from ab-initio calculations in nuclear matter. The size of the tensor force is still an open problem. Therefore we use the first full relativistic Brueckner-Hartree-Fock calculations in finite nuclear systems in order to study properties of such functionals, which cannot be obtained from nuclear matter calculations.

Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays - Part 1

DTIC Science & Technology

2013-05-14

include tensor contractions, the direct N-body algorithm, and database join. 1This indicates that this is the first of 5 times that matrix multiplication...and database join. Section 8 summarizes our results, and outlines the contents of Part 2 of this paper. Part 2 will discuss how to compute lower...contractions, the direct N–body algo- rithm, database join, and computing matrix powers Ak. 2 Geometric Model We begin by reviewing the geometric

Practical Implementation of Multiple Model Adaptive Estimation Using Neyman-Pearson Based Hypothesis Testing and Spectral Estimation Tools

DTIC Science & Technology

1996-09-01

Generalized Likelihood Ratio (GLR) and voting techniques. The third class consisted of multiple hypothesis filter detectors, specifically the MMAE. The...vector version, versus a tensor if we use the matrix version of the power spectral density estimate. Using this notation, we will derive an...as MATLAB , have an intrinsic sample covariance computation available, which makes this method quite easy to implement. In practice, the mean for the

Extracting Effective Higgs Couplings in the Golden Channel

DOE PAGES

Chen, Yi; Vega-Morales, Roberto

2014-04-08

Kinematic distributions in Higgs decays to four charged leptons, the so called ‘golden channel, are a powerful probe of the tensor structure of its couplings to neutral electroweak gauge bosons. In this study we construct the first part of a comprehensive analysis framework designed to maximize the information contained in this channel in order to perform direct extraction of the various possible Higgs couplings. We first complete an earlier analytic calculation of the leading order fully differential cross sections for the golden channel signal and background to include the 4e and 4μ final states with interference between identical final states.more » We also examine the relative fractions of the different possible combinations of scalar-tensor couplings by integrating the fully differential cross section over all kinematic variables as well as show various doubly differential spectra for both the signal and background. From these analytic expressions we then construct a ‘generator level’ analysis framework based on the maximum likelihood method. Then, we demonstrate the ability of our framework to perform multi-parameter extractions of all the possible effective couplings of a spin-0 scalar to pairs of neutral electroweak gauge bosons including any correlations. Furthermore, this framework provides a powerful method for study of these couplings and can be readily adapted to include the relevant detector and systematic effects which we demonstrate in an accompanying study to follow.« less

Evaluating the predictive power of multivariate tensor-based morphometry in Alzheimer's disease progression via convex fused sparse group Lasso

NASA Astrophysics Data System (ADS)

Tsao, Sinchai; Gajawelli, Niharika; Zhou, Jiayu; Shi, Jie; Ye, Jieping; Wang, Yalin; Lepore, Natasha

2014-03-01

Prediction of Alzheimers disease (AD) progression based on baseline measures allows us to understand disease progression and has implications in decisions concerning treatment strategy. To this end we combine a predictive multi-task machine learning method1 with novel MR-based multivariate morphometric surface map of the hippocampus2 to predict future cognitive scores of patients. Previous work by Zhou et al.1 has shown that a multi-task learning framework that performs prediction of all future time points (or tasks) simultaneously can be used to encode both sparsity as well as temporal smoothness. They showed that this can be used in predicting cognitive outcomes of Alzheimers Disease Neuroimaging Initiative (ADNI) subjects based on FreeSurfer-based baseline MRI features, MMSE score demographic information and ApoE status. Whilst volumetric information may hold generalized information on brain status, we hypothesized that hippocampus specific information may be more useful in predictive modeling of AD. To this end, we applied Shi et al.2s recently developed multivariate tensor-based (mTBM) parametric surface analysis method to extract features from the hippocampal surface. We show that by combining the power of the multi-task framework with the sensitivity of mTBM features of the hippocampus surface, we are able to improve significantly improve predictive performance of ADAS cognitive scores 6, 12, 24, 36 and 48 months from baseline.

Small field models with gravitational wave signature supported by CMB data

PubMed Central

Brustein, Ramy

2018-01-01

We study scale dependence of the cosmic microwave background (CMB) power spectrum in a class of small, single-field models of inflation which lead to a high value of the tensor to scalar ratio. The inflaton potentials that we consider are degree 5 polynomials, for which we precisely calculate the power spectrum, and extract the cosmological parameters: the scalar index ns, the running of the scalar index nrun and the tensor to scalar ratio r. We find that for non-vanishing nrun and for r as small as r = 0.001, the precisely calculated values of ns and nrun deviate significantly from what the standard analytic treatment predicts. We study in detail, and discuss the probable reasons for such deviations. As such, all previously considered models (of this kind) are based upon inaccurate assumptions. We scan the possible values of potential parameters for which the cosmological parameters are within the allowed range by observations. The 5 parameter class is able to reproduce all of the allowed values of ns and nrun for values of r that are as high as 0.001. Subsequently this study at once refutes previous such models built using the analytical Stewart-Lyth term, and revives the small field brand, by building models that do yield an appreciable r while conforming to known CMB observables. PMID:29795608

Notes on super Killing tensors

NASA Astrophysics Data System (ADS)

Howe, P. S.; Lindström, U.

2016-03-01

The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.

Tensor Train Neighborhood Preserving Embedding

NASA Astrophysics Data System (ADS)

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.

Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence

DOE PAGES

Rubinstein, Robert; Kurien, Susan; Cambon, Claude

2015-06-22

The representation theory of the rotation group is applied to construct a series expansion of the correlation tensor in homogeneous anisotropic turbulence. The resolution of angular dependence is the main analytical difficulty posed by anisotropic turbulence; representation theory parametrises this dependence by a tensor analogue of the standard spherical harmonics expansion of a scalar. As a result, the series expansion is formulated in terms of explicitly constructed tensor bases with scalar coefficients determined by angular moments of the correlation tensor.

Spin and Pseudospin Symmetries of Hellmann Potential with Three Tensor Interactions Using Nikiforov-Uvarov Method

NASA Astrophysics Data System (ADS)

Akpan, N. Ikot; Hassan, Hassanabadi; Tamunoimi, M. Abbey

2015-12-01

The Dirac equation with Hellmann potential is presented in the presence of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT), and Hulthen-type tensor (HLT) interactions by using Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions are obtained approximately within the framework of spin and pseudospin symmetries limit. We have also reported some numerical results and figures to show the effects of the tensor interactions. Special cases of the potential are also discussed.

Geometry of Lax pairs: Particle motion and Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Cariglia, Marco; Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2013-01-01

A geometric formulation of the Lax pair equation on a curved manifold is studied using the phase-space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is discussed. It is shown that when the Hamilton equations of motion are used, the conservation of the Lax tensor translates directly to the well-known Lax pair equation, with one matrix identified with components of the Lax tensor and the other matrix constructed from the (metric) connection. A generalization to Clifford objects is also discussed. Nontrivial examples of Lax tensors for geodesic and charged particle motion are found in spacetimes admitting a hidden symmetry of Killing-Yano tensors.

On Lovelock analogs of the Riemann tensor

NASA Astrophysics Data System (ADS)

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.

MRI diffusion tensor reconstruction with PROPELLER data acquisition.

PubMed

Cheryauka, Arvidas B; Lee, James N; Samsonov, Alexei A; Defrise, Michel; Gullberg, Grant T

2004-02-01

MRI diffusion imaging is effective in measuring the diffusion tensor in brain, cardiac, liver, and spinal tissue. Diffusion tensor tomography MRI (DTT MRI) method is based on reconstructing the diffusion tensor field from measurements of projections of the tensor field. Projections are obtained by appropriate application of rotated diffusion gradients. In the present paper, the potential of a novel data acquisition scheme, PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction), is examined in combination with DTT MRI for its capability and sufficiency for diffusion imaging. An iterative reconstruction algorithm is used to reconstruct the diffusion tensor field from rotated diffusion weighted blades by appropriate rotated diffusion gradients. DTT MRI with PROPELLER data acquisition shows significant potential to reduce the number of weighted measurements, avoid ambiguity in reconstructing diffusion tensor parameters, increase signal-to-noise ratio, and decrease the influence of signal distortion.

Current density tensors

NASA Astrophysics Data System (ADS)

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.

Entanglement branching operator

NASA Astrophysics Data System (ADS)

Harada, Kenji

2018-01-01

We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.

Spacetime encodings. IV. The relationship between Weyl curvature and Killing tensors in stationary axisymmetric vacuum spacetimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brink, Jeandrew

The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst potential is considered. The coupling between the nonlocal curvature content of the spacetime as encoded in the Weyl tensor, and the existence of a Killing tensor is explored and a constructive, algebraic test for a fourth-order Killing tensor suggested. The approach used exploits the variables defined for the Baecklund transformations to clarify the relationship between Weyl curvature, constants of geodesic motion, expressed as Killing tensors, and the solution-generation techniques. A new symmetricmore » noncovariant formulation of the Killing equations is given. This formulation transforms the problem of looking for fourth-order Killing tensors in 4D into one of looking for four interlocking two-manifolds admitting fourth-order Killing tensors in 2D.« less

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

ERIC Educational Resources Information Center

Barmpoutis, Angelos

2009-01-01

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

Monograph On Tensor Notations

NASA Technical Reports Server (NTRS)

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.

Einstein Revisited - Gravity in Curved Spacetime Without Event Horizons

NASA Astrophysics Data System (ADS)

Leiter, Darryl

2000-04-01

In terms of covariant derivatives with respect to flat background spacetimes upon which the physical curved spacetime is imposed (1), covariant conservation of energy momentum requires, via the Bianchi Identity, that the Einstein tensor be equated to the matter energy momentum tensor. However the Einstein tensor covariantly splits (2) into two tensor parts: (a) a term proportional to the gravitational stress energy momentum tensor, and (b) an anti-symmetric tensor which obeys a covariant 4-divergence identity called the Freud Identity. Hence covariant conservation of energy momentum requires, via the Freud Identity, that the Freud tensor be equal to a constant times the matter energy momentum tensor. The resultant field equations (3) agree with the Einstein equations to first order, but differ in higher orders (4) such that black holes are replaced by "red holes" i.e., dense objects collapsed inside of their photon orbits with no event horizons. (1) Rosen, N., (1963), Ann. Phys. v22, 1; (2) Rund, H., (1991), Alg. Grps. & Geom. v8, 267; (3) Yilmaz, Hl, (1992), Nuo. Cim. v107B, 946; (4) Roberstson, S., (1999),Ap.J. v515, 365.

A Tensor-Based Subspace Approach for Bistatic MIMO Radar in Spatial Colored Noise

PubMed Central

Wang, Xianpeng; Wang, Wei; Li, Xin; Wang, Junxiang

2014-01-01

In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD) and the direction of arrival (DOA) for bistatic multiple-input multiple-output (MIMO) radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD) of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen's method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method. PMID:24573313

A tensor-based subspace approach for bistatic MIMO radar in spatial colored noise.

PubMed

Wang, Xianpeng; Wang, Wei; Li, Xin; Wang, Junxiang

2014-02-25

In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD) and the direction of arrival (DOA) for bistatic multiple-input multiple-output (MIMO) radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD) of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen's method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method.

Tensor-based Dictionary Learning for Spectral CT Reconstruction

PubMed Central

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

An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU

NASA Astrophysics Data System (ADS)

Lyakh, Dmitry I.

2015-04-01

An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typically appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the naïve scattering algorithm (no memory access optimization). The tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).

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

PubMed

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.

Local recovery of lithospheric stress tensor from GOCE gravitational tensor

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi

2017-04-01

The sublithospheric stress due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics (SHs) or Legendre polynomials is involved in the expressions. Here, new relations between the SH coefficients of the stress and gravitational tensor elements are presented. Thereafter, integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer mission (GOCE), in 2009 November, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.

Comparative study of methods for recognition of an unknown person's action from a video sequence

NASA Astrophysics Data System (ADS)

Hori, Takayuki; Ohya, Jun; Kurumisawa, Jun

2009-02-01

This paper proposes a Tensor Decomposition Based method that can recognize an unknown person's action from a video sequence, where the unknown person is not included in the database (tensor) used for the recognition. The tensor consists of persons, actions and time-series image features. For the observed unknown person's action, one of the actions stored in the tensor is assumed. Using the motion signature obtained from the assumption, the unknown person's actions are synthesized. The actions of one of the persons in the tensor are replaced by the synthesized actions. Then, the core tensor for the replaced tensor is computed. This process is repeated for the actions and persons. For each iteration, the difference between the replaced and original core tensors is computed. The assumption that gives the minimal difference is the action recognition result. For the time-series image features to be stored in the tensor and to be extracted from the observed video sequence, the human body silhouette's contour shape based feature is used. To show the validity of our proposed method, our proposed method is experimentally compared with Nearest Neighbor rule and Principal Component analysis based method. Experiments using 33 persons' seven kinds of action show that our proposed method achieves better recognition accuracies for the seven actions than the other methods.

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue.

PubMed

Pajevic, Sinisa; Aldroubi, Akram; Basser, Peter J

2002-01-01

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.

Tensor Calculus: Unlearning Vector Calculus

ERIC Educational Resources Information Center

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…

Killing-Yano tensors in spaces admitting a hypersurface orthogonal Killing vector

NASA Astrophysics Data System (ADS)

Garfinkle, David; Glass, E. N.

2013-03-01

Methods are presented for finding Killing-Yano tensors, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector. These methods are similar to a method developed by the authors for finding Killing tensors. In all cases one decomposes both the tensor and the equation it satisfies into pieces along the Killing vector and pieces orthogonal to the Killing vector. Solving the separate equations that result from this decomposition requires less computing than integrating the original equation. In each case, examples are given to illustrate the method.

Killing-Yano tensors of order n - 1

NASA Astrophysics Data System (ADS)

Batista, Carlos

2014-08-01

The properties of a Killing-Yano tensor of order n-1 in an n-dimensional manifold are investigated. The integrability conditions are worked out and all metrics admitting a Killing-Yano tensor of order n-1 are found. A connection between such tensors and a generalization of the concept of angular momentum is pointed out. A theorem on how to generate closed conformal Killing vectors using the symmetries of a manifold is proved and used to find all Killing-Yano tensors of order n-1 of a maximally symmetric space.

Dictionary-Based Tensor Canonical Polyadic Decomposition

NASA Astrophysics Data System (ADS)

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.

Decomposition of a symmetric second-order tensor

NASA Astrophysics Data System (ADS)

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.

On physical property tensors invariant under line groups.

PubMed

Litvin, Daniel B

2014-03-01

The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a polymer can be determined from the point group of its symmetry group, one of an infinite number of line groups. Such forms are calculated using a method based on the use of trigonometric summations. With this method, it is shown that materials invariant under infinite subsets of line groups have physical property tensors of the same form. For line group types of a family of line groups characterized by an index n and a physical property tensor of rank m, the form of the tensor for all line group types indexed with n > m is the same, leaving only a finite number of tensor forms to be determined.

Local White Matter Geometry from Diffusion Tensor Gradients

PubMed Central

Savadjiev, Peter; Kindlmann, Gordon L.; Bouix, Sylvain; Shenton, Martha E.; Westin, Carl-Fredrik

2009-01-01

We introduce a mathematical framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it possible to define scalar indices (or measures) that describe the local white matter geometry directly from the diffusion tensor field and its gradient, without requiring prior tractography. We derive new scalar indices of (1) fibre dispersion and (2) fibre curving, and we demonstrate them on synthetic and in vivo data. Finally, we illustrate their applicability to a group study on schizophrenia. PMID:19896542

Local White Matter Geometry from Diffusion Tensor Gradients

PubMed Central

Savadjiev, Peter; Kindlmann, Gordon L.; Bouix, Sylvain; Shenton, Martha E.; Westin, Carl-Fredrik

2010-01-01

We introduce a mathematical framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it possible to define scalar indices (or measures) that describe the local white matter geometry directly from the diffusion tensor field and its gradient, without requiring prior tractography. We derive new scalar indices of (1) fibre dispersion and (2) fibre curving, and we demonstrate them on synthetic and in vivo data. Finally, we illustrate their applicability to a group study on schizophrenia. PMID:20426006

Rortex—A new vortex vector definition and vorticity tensor and vector decompositions

NASA Astrophysics Data System (ADS)

Liu, Chaoqun; Gao, Yisheng; Tian, Shuling; Dong, Xiangrui

2018-03-01

A vortex is intuitively recognized as the rotational/swirling motion of the fluids. However, an unambiguous and universally accepted definition for vortex is yet to be achieved in the field of fluid mechanics, which is probably one of the major obstacles causing considerable confusions and misunderstandings in turbulence research. In our previous work, a new vector quantity that is called vortex vector was proposed to accurately describe the local fluid rotation and clearly display vortical structures. In this paper, the definition of the vortex vector, named Rortex here, is revisited from the mathematical perspective. The existence of the possible rotational axis is proved through real Schur decomposition. Based on real Schur decomposition, a fast algorithm for calculating Rortex is also presented. In addition, new vorticity tensor and vector decompositions are introduced: the vorticity tensor is decomposed to a rigidly rotational part and a non-rotationally anti-symmetric part, and the vorticity vector is decomposed to a rigidly rotational vector which is called the Rortex vector and a non-rotational vector which is called the shear vector. Several cases, including the 2D Couette flow, 2D rigid rotational flow, and 3D boundary layer transition on a flat plate, are studied to demonstrate the justification of the definition of Rortex. It can be observed that Rortex identifies both the precise swirling strength and the rotational axis, and thus it can reasonably represent the local fluid rotation and provide a new powerful tool for vortex dynamics and turbulence research.

Mid-Crustal Stress Magnitude and Rotation Transients Related to the Seismic Cycle

NASA Astrophysics Data System (ADS)

Nüchter, J. A.; Ellis, S.

2008-12-01

Seismic slip causes a stress drop in the upper crust, and a major stress increase at the lower termination of the fault in the middle crust. Previous numerical models show how these stresses relax during an episode of postseismic creep. Natural evidence for postseismic stress and strain transients at depth is provided by 1) the geological record of exhumed metamorphic rocks, and 2) from postseismic surface deformation transients. In the present study, we use numerical models to investigate the changes in the geometry of the mid-crustal stress field caused by seismic slip along normal faults within an extensional tectonic setting. We model a 100x30km crustal section, with a fault reaching down to 20km and dipping at 60°. A non-linear thermal gradient and constant elastic parameters are applied. Thermally activated creep is described by values derived from laboratory creep experiments on wet quartzite. The crust is loaded by horizontal extension at a constant rate, and earthquakes are triggered by a short term decrease in the frictional coefficient of the fault. During the interseismic period, this coefficient is set to high values to lock the fault. A sequence of 30 earthquakes with a constant recurrence interval of 500y is simulated, and the results for the last seismic cycle are analyzed. In such a tectonic setting, the Anderson theory predicts that the maximum principal stress is vertical. A stress field consistent to this theory is reached after an initial stage of 15ka extension without earthquake activity. The results for the 30th seismic cycle imply that seismic slip causes a major stress increase of at least 50MPa at a depth level below the brittle ductile transition, which is in accordance to reports on seismic stress increase derived from the record of metamorphic rocks. In the hanging wall, the stress increase results mainly from an increase in the maximum principal stress and the stress tensor rotates counter-clockwise by 10-30°. In the footwall the stress increase results mainly from a drop in the minimum principal stress, and the stress tensor rotates clockwise by 45-60°. A change in the magnitude of differential stress can be addressed by the addition of an incremental stress tensor resulting from elastic strain to the preexisting stress tensor. In an isotropic medium, the orientation of the maximum and the minimum principal stress changes are controlled by the directions of maximum compression and maximum extension, respectively. The magnitude and the orientation of the resulting stress tensor depend: 1) on the absolute magnitudes and on the ratio of the magnitudes of pre-existing stress and incremental change in the stress tensor; and 2) on the mis-orientation between existing stress and stress change principal directions. The zone of coseismic loading correlates to the interval in which seismic slip tapers off with depth. For a normal fault, the crust here is subjected to fault-parallel compression in the hanging wall, and to extension in the footwall. The resulting orientation of the seismic principal compressive stress change parallel to the fault in the hanging wall and normal to the fault in the footwall causes the particular deflection of the resulting stress tensor . During the interseismic period, the stress peak relaxes by thermally activated creep, while the deflection of the stress tensor is persistent. We show that significant mis- orientations of the stress tensor can be preserved over timescales typical for a seismic cycle, in dependence on the far field extension rate. We conclude that seismic activity causes 1) a non-steady state mid-crustal stress field, and 2) a persistent deflection of the stress tensor orientation from the predictions of the Anderson theory.

Using the full power of the cosmic microwave background to probe axion dark matter

NASA Astrophysics Data System (ADS)

Hložek, Renée; Marsh, David J. E.; Grin, Daniel

2018-05-01

The cosmic microwave background (CMB) places stringent constraints on models of dark matter (DM), and on the initial conditions of the Universe. The full Planck data set is used to test the possibility that some fraction of the DM is composed of ultralight axions (ULAs). This represents the first use of CMB lensing to test the ULA model. We find no evidence for a ULA component in the mass range 10-33 ≤ ma ≤ 10-24 eV. We put percent-level constraints on the ULA contribution to the DM, improving by up to a factor of two compared using temperature anisotropies alone. Axion DM also provides a low-energy window on to the physics of inflation through isocurvature perturbations. We perform the first systematic investigation into the parameter space of ULA isocurvature, using an accurate isocurvature transfer function at all ma values. We precisely identify a `window of co-existence' for 10-25 eV ≤ ma ≤ 10-24 eV where the data allow, simultaneously, a {˜ }10 {per cent} contribution of ULAs to the DM, and {˜ } 1 {per cent} contributions of isocurvature and tensor modes to the CMB power. ULAs in this window (and all lighter ULAs) are shown to be consistent with a large inflationary Hubble parameter, HI ˜ 1014 GeV. The window of co-existence will be fully probed by proposed CMB Stage-IV observations with increased accuracy in the high-ℓ lensing power and low-ℓ E- and B-mode polarizations. If ULAs in the window exist, this could allow for two independent measurements of HI in the CMB using isocurvature, and the tensor contribution to B modes.

The Primordial Inflation Polarization Explorer (PIPER)

NASA Technical Reports Server (NTRS)

Lazear, Justin Scott; Ade, Peter A.; Benford, Dominic J.; Bennett, Charles L.; Chuss, David T.; Dotson, Jessie L.; Eimer, Joseph R.; Fixsen, Dale J.; Halpern, Mark; Hinderks, James;

Electromagnetic van Kampen waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ignatov, A. M., E-mail: aign@fpl.gpi.ru

2017-01-15

The theory of van Kampen waves in plasma with an arbitrary anisotropic distribution function is developed. The obtained solutions are explicitly expressed in terms of the permittivity tensor. There are three types of perturbations, one of which is characterized by the frequency dependence on the wave vector, while for the other two, the dispersion relation is lacking. Solutions to the conjugate equations allowing one to solve the initial value problem are analyzed.

Strain mapping in TEM using precession electron diffraction

DOEpatents

Taheri, Mitra Lenore; Leff, Asher Calvin

2017-02-14

A sample material is scanned with a transmission electron microscope (TEM) over multiple steps having a predetermined size at a predetermined angle. Each scan at a predetermined step and angle is compared to a template, wherein the template is generated from parameters of the material and the scanning. The data is then analyzed using local mis-orientation mapping and/or Nye's tensor analysis to provide information about local strain states.

Resonant-state expansion for open optical systems: generalization to magnetic, chiral, and bi-anisotropic materials

NASA Astrophysics Data System (ADS)

Muljarov, E. A.; Weiss, T.

2018-05-01

The resonant-state expansion, a recently developed powerful method in electrodynamics, is generalized here for open optical systems containing magnetic, chiral, or bi-anisotropic materials. It is shown that the key matrix eigenvalue equation of the method remains the same, but the matrix elements of the perturbation now contain variations of the permittivity, permeability, and bi-anisotropy tensors. A general normalization of resonant states in terms of the electric and magnetic fields is presented.

Analysing seismic-source mechanisms by linear-programming methods.

USGS Publications Warehouse

Julian, B.R.

1986-01-01

Linear-programming methods are powerful and efficient tools for objectively analysing seismic focal mechanisms and are applicable to a wide range of problems, including tsunami warning and nuclear explosion identification. The source mechanism is represented as a point in the 6-D space of moment-tensor components. The present method can easily be extended to fit observed seismic-wave amplitudes (either signed or absolute) subject to polarity constraints, and to assess the range of mechanisms consistent with a set of measured amplitudes. -from Author

Volume in moment tensor space in terms of distance

NASA Astrophysics Data System (ADS)

Tape, Walter; Tape, Carl

2017-07-01

Suppose that we want to assess the extent to which some large collection of moment tensors is concentrated near a fixed moment tensor m. We are naturally led to consider the distribution of the distances of the moment tensors from m. This distribution, however, can only be judged in conjunction with the distribution of distances from m for randomly chosen moment tensors. In cumulative form, the latter distribution is the same as the fractional volume \\hat{V}(ω ) of the set of all moment tensors that are within distance ω of m. This definition of \\hat{V}(ω ) assumes that a reasonable universe {M} of moment tensors has been specified at the outset and that it includes the original collection as a subset. Our main goal in this article is to derive a formula for \\hat{V}(ω ) when {M} is the set [Λ]_{U} of all moment tensors having a specified eigenvalue triple Λ. We find that \\hat{V}(ω ) depends strongly on Λ, and we illustrate the dependence by plotting the derivative curves \\hat{V}^' }(ω ) for various seismologically relevant Λs. The exotic and unguessable shapes of these curves underscores the futility of interpreting the distribution of distances for the original moment tensors without knowing \\hat{V}(ω ) or \\hat{V}^' }(ω ). The derivation of the formula for \\hat{V}(ω ) relies on a certain ϕ σz coordinate system for [Λ]_{U}, which we treat in detail. Our underlying motivation for the paper is the estimation of uncertainties in moment tensor inversion.

Trends in biomedical informatics: automated topic analysis of JAMIA articles.

PubMed

Han, Dong; Wang, Shuang; Jiang, Chao; Jiang, Xiaoqian; Kim, Hyeon-Eui; Sun, Jimeng; Ohno-Machado, Lucila

2015-11-01

Biomedical Informatics is a growing interdisciplinary field in which research topics and citation trends have been evolving rapidly in recent years. To analyze these data in a fast, reproducible manner, automation of certain processes is needed. JAMIA is a "generalist" journal for biomedical informatics. Its articles reflect the wide range of topics in informatics. In this study, we retrieved Medical Subject Headings (MeSH) terms and citations of JAMIA articles published between 2009 and 2014. We use tensors (i.e., multidimensional arrays) to represent the interaction among topics, time and citations, and applied tensor decomposition to automate the analysis. The trends represented by tensors were then carefully interpreted and the results were compared with previous findings based on manual topic analysis. A list of most cited JAMIA articles, their topics, and publication trends over recent years is presented. The analyses confirmed previous studies and showed that, from 2012 to 2014, the number of articles related to MeSH terms Methods, Organization & Administration, and Algorithms increased significantly both in number of publications and citations. Citation trends varied widely by topic, with Natural Language Processing having a large number of citations in particular years, and Medical Record Systems, Computerized remaining a very popular topic in all years. © The Author 2015. Published by Oxford University Press on behalf of the American Medical Informatics Association. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Effects of Orientation and Anisometry of Magnetic Resonance Imaging Acquisitions on Diffusion Tensor Imaging and Structural Connectomes.

PubMed

Tudela, Raúl; Muñoz-Moreno, Emma; López-Gil, Xavier; Soria, Guadalupe

2017-01-01

Diffusion-weighted imaging (DWI) quantifies water molecule diffusion within tissues and is becoming an increasingly used technique. However, it is very challenging as correct quantification depends on many different factors, ranging from acquisition parameters to a long pipeline of image processing. In this work, we investigated the influence of voxel geometry on diffusion analysis, comparing different acquisition orientations as well as isometric and anisometric voxels. Diffusion-weighted images of one rat brain were acquired with four different voxel geometries (one isometric and three anisometric in different directions) and three different encoding orientations (coronal, axial and sagittal). Diffusion tensor scalar measurements, tractography and the brain structural connectome were analyzed for each of the 12 acquisitions. The acquisition direction with respect to the main magnetic field orientation affected the diffusion results. When the acquisition slice-encoding direction was not aligned with the main magnetic field, there were more artifacts and a lower signal-to-noise ratio that led to less anisotropic tensors (lower fractional anisotropic values), producing poorer quality results. The use of anisometric voxels generated statistically significant differences in the values of diffusion metrics in specific regions. It also elicited differences in tract reconstruction and in different graph metric values describing the brain networks. Our results highlight the importance of taking into account the geometric aspects of acquisitions, especially when comparing diffusion data acquired using different geometries.

Nucleon scalar and tensor charges using lattice QCD simulations at the physical value of the pion mass

NASA Astrophysics Data System (ADS)

Alexandrou, C.; Constantinou, M.; Dimopoulos, P.; Frezzotti, R.; Hadjiyiannakou, K.; Jansen, K.; Kallidonis, C.; Kostrzewa, B.; Koutsou, G.; Mangin-Brinet, M.; Vaquero Avilès-Casco, A.; Wenger, U.

2017-06-01

We present results on the light, strange and charm nucleon scalar and tensor charges from lattice QCD, using simulations with Nf=2 flavors of twisted mass clover-improved fermions with a physical value of the pion mass. Both connected and disconnected contributions are included, enabling us to extract the isoscalar, strange and charm charges for the first time directly at the physical point. Furthermore, the renormalization is computed nonperturbatively for both isovector and isoscalar quantities. We investigate excited state effects by analyzing several sink-source time separations and by employing a set of methods to probe ground state dominance. Our final results for the scalar charges are gSu=5.20 (42 )(15 )(12 ), gSd=4.27 (26 )(15 )(12 ), gSs=0.33 (7 )(1 )(4 ), and gSc=0.062 (13 )(3 )(5 ) and for the tensor charges gTu=0.794 (16 )(2 )(13 ), gTd=-0.210 (10 )(2 )(13 ), gTs=0.00032 (24 )(0 ), and gTc=0.00062 (85 )(0 ) in the MS ¯ scheme at 2 GeV. The first error is statistical, the second is the systematic error due to the renormalization and the third the systematic arising from estimating the contamination due to the excited states, when our data are precise enough to probe the first excited state.

Characterizing and Discovering Spatiotemporal Social Contact Patterns for Healthcare.

PubMed

Yang, Bo; Pei, Hongbin; Chen, Hechang; Liu, Jiming; Xia, Shang

2017-08-01

During an epidemic, the spatial, temporal and demographic patterns of disease transmission are determined by multiple factors. In addition to the physiological properties of the pathogens and hosts, the social contact of the host population, which characterizes the reciprocal exposures of individuals to infection according to their demographic structure and various social activities, are also pivotal to understanding and predicting the prevalence of infectious diseases. How social contact is measured will affect the extent to which we can forecast the dynamics of infections in the real world. Most current work focuses on modeling the spatial patterns of static social contact. In this work, we use a novel perspective to address the problem of how to characterize and measure dynamic social contact during an epidemic. We propose an epidemic-model-based tensor deconvolution framework in which the spatiotemporal patterns of social contact are represented by the factors of the tensors. These factors can be discovered using a tensor deconvolution procedure with the integration of epidemic models based on rich types of data, mainly heterogeneous outbreak surveillance data, socio-demographic census data and physiological data from medical reports. Using reproduction models that include SIR/SIS/SEIR/SEIS models as case studies, the efficacy and applications of the proposed framework are theoretically analyzed, empirically validated and demonstrated through a set of rigorous experiments using both synthetic and real-world data.

Nonlocal homogenization theory in metamaterials: Effective electromagnetic spatial dispersion and artificial chirality

NASA Astrophysics Data System (ADS)

Ciattoni, Alessandro; Rizza, Carlo

2015-05-01

We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with nonmagnetic inclusions in the long-wavelength limit, including spatial dispersion up to the second order. Specifically, by resorting to a suitable multiscale technique, we show that the effective medium permittivity tensor and the first- and second-order tensors describing spatial dispersion can be evaluated by averaging suitable spatially rapidly varying fields, each satisfying electrostatic-like equations within the metamaterial unit cell. For metamaterials with negligible second-order spatial dispersion, we exploit the equivalence of first-order spatial dispersion and reciprocal bianisotropic electromagnetic response to deduce a simple expression for the metamaterial chirality tensor. Such an expression allows us to systematically analyze the effect of the composite spatial symmetry properties on electromagnetic chirality. We find that even if a metamaterial is geometrically achiral, i.e., it is indistinguishable from its mirror image, it shows pseudo-chiral-omega electromagnetic chirality if the rotation needed to restore the dielectric profile after the reflection is either a 0∘ or 90∘ rotation around an axis orthogonal to the reflection plane. These two symmetric situations encompass two-dimensional and one-dimensional metamaterials with chiral response. As an example admitting full analytical description, we discuss one-dimensional metamaterials whose single chirality parameter is shown to be directly related to the metamaterial dielectric profile by quadratures.

A novel registration-based methodology for prediction of trabecular bone fabric from clinical QCT: A comprehensive analysis

PubMed Central

Reyes, Mauricio; Zysset, Philippe

2017-01-01

Osteoporosis leads to hip fractures in aging populations and is diagnosed by modern medical imaging techniques such as quantitative computed tomography (QCT). Hip fracture sites involve trabecular bone, whose strength is determined by volume fraction and orientation, known as fabric. However, bone fabric cannot be reliably assessed in clinical QCT images of proximal femur. Accordingly, we propose a novel registration-based estimation of bone fabric designed to preserve tensor properties of bone fabric and to map bone fabric by a global and local decomposition of the gradient of a non-rigid image registration transformation. Furthermore, no comprehensive analysis on the critical components of this methodology has been previously conducted. Hence, the aim of this work was to identify the best registration-based strategy to assign bone fabric to the QCT image of a patient’s proximal femur. The normalized correlation coefficient and curvature-based regularization were used for image-based registration and the Frobenius norm of the stretch tensor of the local gradient was selected to quantify the distance among the proximal femora in the population. Based on this distance, closest, farthest and mean femora with a distinction of sex were chosen as alternative atlases to evaluate their influence on bone fabric prediction. Second, we analyzed different tensor mapping schemes for bone fabric prediction: identity, rotation-only, rotation and stretch tensor. Third, we investigated the use of a population average fabric atlas. A leave one out (LOO) evaluation study was performed with a dual QCT and HR-pQCT database of 36 pairs of human femora. The quality of the fabric prediction was assessed with three metrics, the tensor norm (TN) error, the degree of anisotropy (DA) error and the angular deviation of the principal tensor direction (PTD). The closest femur atlas (CTP) with a full rotation (CR) for fabric mapping delivered the best results with a TN error of 7.3 ± 0.9%, a DA error of 6.6 ± 1.3% and a PTD error of 25 ± 2°. The closest to the population mean femur atlas (MTP) using the same mapping scheme yielded only slightly higher errors than CTP for substantially less computing efforts. The population average fabric atlas yielded substantially higher errors than the MTP with the CR mapping scheme. Accounting for sex did not bring any significant improvements. The identified fabric mapping methodology will be exploited in patient-specific QCT-based finite element analysis of the proximal femur to improve the prediction of hip fracture risk. PMID:29176881

Estimation of full moment tensors, including uncertainties, for earthquakes, volcanic events, and nuclear explosions

NASA Astrophysics Data System (ADS)

Alvizuri, Celso; Silwal, Vipul; Krischer, Lion; Tape, Carl

2017-04-01

A seismic moment tensor is a 3 × 3 symmetric matrix that provides a compact representation of seismic events within Earth's crust. We develop an algorithm to estimate moment tensors and their uncertainties from observed seismic data. For a given event, the algorithm performs a grid search over the six-dimensional space of moment tensors by generating synthetic waveforms at each grid point and then evaluating a misfit function between the observed and synthetic waveforms. 'The' moment tensor M for the event is then the moment tensor with minimum misfit. To describe the uncertainty associated with M, we first convert the misfit function to a probability function. The uncertainty, or rather the confidence, is then given by the 'confidence curve' P(V ), where P(V ) is the probability that the true moment tensor for the event lies within the neighborhood of M that has fractional volume V . The area under the confidence curve provides a single, abbreviated 'confidence parameter' for M. We apply the method to data from events in different regions and tectonic settings: small (Mw < 2.5) events at Uturuncu volcano in Bolivia, moderate (Mw > 4) earthquakes in the southern Alaska subduction zone, and natural and man-made events at the Nevada Test Site. Moment tensor uncertainties allow us to better discriminate among moment tensor source types and to assign physical processes to the events.

APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER*

PubMed Central

BARMPOUTIS, ANGELOS; JEFFREY, HO; VEMURI, BABA C.

2012-01-01

Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of even order. Although the space P02m of 2mth-order symmetric positive semi-definite tensors is known to be a convex cone, enforcing positivity constraint directly on P02m is usually not straightforward computationally because there is no known analytic description of P02m for m > 1. In this paper, we propose a novel approach for enforcing the positivity constraint on even-order tensors by approximating the cone P02m for the cases 0 < m < 3, and presenting an explicit characterization of the approximation Σ2m ⊂ Ω2m for m ≥ 1, using the subset Ω2m⊂P02m of semi-definite tensors that can be written as a sum of squares of tensors of order m. Furthermore, we show that this approximation leads to a non-negative linear least-squares (NNLS) optimization problem with the complexity that equals the number of generators in Σ2m. Finally, we experimentally validate the proposed approach and we present an application for computing 2mth-order diffusion tensors from Diffusion Weighted Magnetic Resonance Images. PMID:23285313

Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

PubMed

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.

Random SU(2) invariant tensors

NASA Astrophysics Data System (ADS)

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.

An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU

DOE PAGES

Lyakh, Dmitry I.

2015-01-05

An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typicallymore » appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the na ve scattering algorithm (no memory access optimization). Furthermore, the tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).« less

On improving the efficiency of tensor voting.

PubMed

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.

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

NASA Astrophysics Data System (ADS)

Luo, Yao; Wu, Mei-Ping; Wang, Ping; Duan, Shu-Ling; Liu, Hao-Jun; Wang, Jin-Long; An, Zhan-Feng

2015-09-01

The full magnetic gradient tensor (MGT) refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.

Consistent scalar and tensor perturbation power spectra in single fluid matter bounce with dark energy era

NASA Astrophysics Data System (ADS)

Bacalhau, Anna Paula; Pinto-Neto, Nelson; Vitenti, Sandro Dias Pinto

2018-04-01

We investigate cosmological scenarios containing one canonical scalar field with an exponential potential in the context of bouncing models, in which the bounce happens due to quantum cosmological effects. The only possible bouncing solutions in this scenario (discarding an infinitely fine-tuned exception) must have one and only one dark energy phase, occurring either in the contracting era or in the expanding era. Hence, these bounce solutions are necessarily asymmetric. Naturally, the more convenient solution is the one in which the dark energy phase happens in the expanding era, in order to be a possible explanation for the current accelerated expansion indicated by cosmological observations. In this case, one has the picture of a Universe undergoing a classical dust contraction from very large scales, the initial repeller of the model, moving to a classical stiff-matter contraction near the singularity, which is avoided due to the quantum bounce. The Universe is then launched to a dark energy era, after passing through radiation- and dust-dominated phases, finally returning to the dust expanding phase, the final attractor of the model. We calculate the spectral indices and amplitudes of scalar and tensor perturbations numerically, considering the whole history of the model, including the bounce phase itself, without making any approximation nor using any matching condition on the perturbations. As the background model is necessarily dust dominated in the far past, the usual adiabatic vacuum initial conditions can be easily imposed in this era. Hence, this is a cosmological model in which the presence of dark energy behavior in the Universe does not turn the usual vacuum initial conditions prescription for cosmological perturbation in bouncing models problematic. Scalar and tensor perturbations end up being almost scale invariant, as expected. The background parameters can be adjusted, without fine-tunings, to yield the observed amplitude for scalar perturbations and also for the ratio between tensor and scalar amplitudes, r =T /S ≲0.1 . The amplification of scalar perturbations over tensor perturbations takes place only around the bounce, due to quantum effects, and it would not occur if General Relativity has remained valid throughout this phase. Hence, this is a bouncing model in which a single field induces not only an expanding background dark energy phase but also produces all observed features of cosmological perturbations of quantum mechanical origin at linear order.

Uni10: an open-source library for tensor network algorithms

NASA Astrophysics Data System (ADS)

Kao, Ying-Jer; Hsieh, Yun-Da; Chen, Pochung

2015-09-01

We present an object-oriented open-source library for developing tensor network algorithms written in C++ called Uni10. With Uni10, users can build a symmetric tensor from a collection of bonds, while the bonds are constructed from a list of quantum numbers associated with different quantum states. It is easy to label and permute the indices of the tensors and access a block associated with a particular quantum number. Furthermore a network class is used to describe arbitrary tensor network structure and to perform network contractions efficiently. We give an overview of the basic structure of the library and the hierarchy of the classes. We present examples of the construction of a spin-1 Heisenberg Hamiltonian and the implementation of the tensor renormalization group algorithm to illustrate the basic usage of the library. The library described here is particularly well suited to explore and fast prototype novel tensor network algorithms and to implement highly efficient codes for existing algorithms.

Inference of segmented color and texture description by tensor voting.

PubMed

Jia, Jiaya; Tang, Chi-Keung

2004-06-01

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

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

NASA Astrophysics Data System (ADS)

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.

Classification of materials for conducting spheroids based on the first order polarization tensor

NASA Astrophysics Data System (ADS)

Khairuddin, TK Ahmad; Mohamad Yunos, N.; Aziz, ZA; Ahmad, T.; Lionheart, WRB

2017-09-01

Polarization tensor is an old terminology in mathematics and physics with many recent industrial applications including medical imaging, nondestructive testing and metal detection. In these applications, it is theoretically formulated based on the mathematical modelling either in electrics, electromagnetics or both. Generally, polarization tensor represents the perturbation in the electric or electromagnetic fields due to the presence of conducting objects and hence, it also desribes the objects. Understanding the properties of the polarization tensor is necessary and important in order to apply it. Therefore, in this study, when the conducting object is a spheroid, we show that the polarization tensor is positive-definite if and only if the conductivity of the object is greater than one. In contrast, we also prove that the polarization tensor is negative-definite if and only if the conductivity of the object is between zero and one. These features categorize the conductivity of the spheroid based on in its polarization tensor and can then help to classify the material of the spheroid.

Multivariate statistical analysis of diffusion imaging parameters using partial least squares: Application to white matter variations in Alzheimer's disease.

PubMed

Konukoglu, Ender; Coutu, Jean-Philippe; Salat, David H; Fischl, Bruce

2016-07-01

Diffusion magnetic resonance imaging (dMRI) is a unique technology that allows the noninvasive quantification of microstructural tissue properties of the human brain in healthy subjects as well as the probing of disease-induced variations. Population studies of dMRI data have been essential in identifying pathological structural changes in various conditions, such as Alzheimer's and Huntington's diseases (Salat et al., 2010; Rosas et al., 2006). The most common form of dMRI involves fitting a tensor to the underlying imaging data (known as diffusion tensor imaging, or DTI), then deriving parametric maps, each quantifying a different aspect of the underlying microstructure, e.g. fractional anisotropy and mean diffusivity. To date, the statistical methods utilized in most DTI population studies either analyzed only one such map or analyzed several of them, each in isolation. However, it is most likely that variations in the microstructure due to pathology or normal variability would affect several parameters simultaneously, with differing variations modulating the various parameters to differing degrees. Therefore, joint analysis of the available diffusion maps can be more powerful in characterizing histopathology and distinguishing between conditions than the widely used univariate analysis. In this article, we propose a multivariate approach for statistical analysis of diffusion parameters that uses partial least squares correlation (PLSC) analysis and permutation testing as building blocks in a voxel-wise fashion. Stemming from the common formulation, we present three different multivariate procedures for group analysis, regressing-out nuisance parameters and comparing effects of different conditions. We used the proposed procedures to study the effects of non-demented aging, Alzheimer's disease and mild cognitive impairment on the white matter. Here, we present results demonstrating that the proposed PLSC-based approach can differentiate between effects of different conditions in the same region as well as uncover spatial variations of effects across the white matter. The proposed procedures were able to answer questions on structural variations such as: "are there regions in the white matter where Alzheimer's disease has a different effect than aging or similar effect as aging?" and "are there regions in the white matter that are affected by both mild cognitive impairment and Alzheimer's disease but with differing multivariate effects?" Copyright © 2016 Elsevier Inc. All rights reserved.

Multivariate Statistical Analysis of Diffusion Imaging Parameters using Partial Least Squares: Application to White Matter Variations in Alzheimer’s Disease

PubMed Central

Konukoglu, Ender; Coutu, Jean-Philippe; Salat, David H.; Fischl, Bruce

2016-01-01

Diffusion magnetic resonance imaging (dMRI) is a unique technology that allows the noninvasive quantification of microstructural tissue properties of the human brain in healthy subjects as well as the probing of disease-induced variations. Population studies of dMRI data have been essential in identifying pathological structural changes in various conditions, such as Alzheimer’s and Huntington’s diseases1,2. The most common form of dMRI involves fitting a tensor to the underlying imaging data (known as Diffusion Tensor Imaging, or DTI), then deriving parametric maps, each quantifying a different aspect of the underlying microstructure, e.g. fractional anisotropy and mean diffusivity. To date, the statistical methods utilized in most DTI population studies either analyzed only one such map or analyzed several of them, each in isolation. However, it is most likely that variations in the microstructure due to pathology or normal variability would affect several parameters simultaneously, with differing variations modulating the various parameters to differing degrees. Therefore, joint analysis of the available diffusion maps can be more powerful in characterizing histopathology and distinguishing between conditions than the widely used univariate analysis. In this article, we propose a multivariate approach for statistical analysis of diffusion parameters that uses partial least squares correlation (PLSC) analysis and permutation testing as building blocks in a voxel-wise fashion. Stemming from the common formulation, we present three different multivariate procedures for group analysis, regressing-out nuisance parameters and comparing effects of different conditions. We used the proposed procedures to study the effects of non-demented aging, Alzheimer’s disease and mild cognitive impairment on the white matter. Here, we present results demonstrating that the proposed PLSC-based approach can differentiate between effects of different conditions in the same region as well as uncover spatial variations of effects across the white matter. The proposed procedures were able to answer questions on structural variations such as: “are there regions in the white matter where Alzheimer’s disease has a different effect than aging or similar effect as aging?” and “are there regions in the white matter that are affected by both mild cognitive impairment and Alzheimer’s disease but with differing multivariate effects?” PMID:27103138

An efficient matrix-matrix multiplication based antisymmetric tensor contraction engine for general order coupled cluster.

PubMed

Hanrath, Michael; Engels-Putzka, Anna

2010-08-14

In this paper, we present an efficient implementation of general tensor contractions, which is part of a new coupled-cluster program. The tensor contractions, used to evaluate the residuals in each coupled-cluster iteration are particularly important for the performance of the program. We developed a generic procedure, which carries out contractions of two tensors irrespective of their explicit structure. It can handle coupled-cluster-type expressions of arbitrary excitation level. To make the contraction efficient without loosing flexibility, we use a three-step procedure. First, the data contained in the tensors are rearranged into matrices, then a matrix-matrix multiplication is performed, and finally the result is backtransformed to a tensor. The current implementation is significantly more efficient than previous ones capable of treating arbitrary high excitations.

Measurement tensors in diffusion MRI: generalizing the concept of diffusion encoding.

PubMed

Westin, Carl-Fredrik; Szczepankiewicz, Filip; Pasternak, Ofer; Ozarslan, Evren; Topgaard, Daniel; Knutsson, Hans; Nilsson, Markus

2014-01-01

In traditional diffusion MRI, short pulsed field gradients (PFG) are used for the diffusion encoding. The standard Stejskal-Tanner sequence uses one single pair of such gradients, known as single-PFG (sPFG). In this work we describe how trajectories in q-space can be used for diffusion encoding. We discuss how such encoding enables the extension of the well-known scalar b-value to a tensor-valued entity we call the diffusion measurement tensor. The new measurements contain information about higher order diffusion propagator covariances not present in sPFG. As an example analysis, we use this new information to estimate a Gaussian distribution over diffusion tensors in each voxel, described by its mean (a diffusion tensor) and its covariance (a 4th order tensor).

Prescribed curvature tensor in locally conformally flat manifolds

NASA Astrophysics Data System (ADS)

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.

Conformal Yano-Killing Tensors in General Relativity

NASA Astrophysics Data System (ADS)

Jezierski, Jacek

2011-09-01

How CYK tensors appear in General Relativity? Geometric definition of the asymptotic flat spacetime: strong asymptotic flatness, which guarantees well defined total angular momentum [2, 3, 4] Conserved quantities - asymptotic charges (ℐ, 𝓲0) [2, 3, 4, 5, 6, 9] Quasi-local mass and "rotational energy" for Kerr black hole [5] Constants of motion along geodesics and symmetric Killing tensors [5, 6] Spacetimes possessing CYK tensor [10]: Minkowski (quadratic polynomials) [5] (Anti-)deSitter (natural construction) [7, 8, 9] Kerr (type D spacetime) [5] Taub-NUT (new symmetric conformal Killing tensors) [6] Other applications: Symmetries of Dirac operator Symmetries of Maxwell equations

Approximate arbitrary κ-state solutions of Dirac equation with Schiöberg and Manning-Rosen potentials within the coulomb-like Yukawa-like and generalized tensor interactions

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Hassanabadi, Hassan; Obong, Hillary Patrick; Mehraban, H.; Yazarloo, Bentol Hoda

2015-07-01

The effects of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT) and generalized tensor (GLT) interactions are investigated in the Dirac theory with Schiöberg and Manning-Rosen potentials within the framework of spin and pseudospin symmetries using the Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions have been approximately obtained in the case of spin and pseudospin symmetries. We have also reported some numerical results and figures to show the effects these tensor interactions.

LiDAR point classification based on sparse representation

NASA Astrophysics Data System (ADS)

Li, Nan; Pfeifer, Norbert; Liu, Chun

2017-04-01

In order to combine the initial spatial structure and features of LiDAR data for accurate classification. The LiDAR data is represented as a 4-order tensor. Sparse representation for classification(SRC) method is used for LiDAR tensor classification. It turns out SRC need only a few of training samples from each class, meanwhile can achieve good classification result. Multiple features are extracted from raw LiDAR points to generate a high-dimensional vector at each point. Then the LiDAR tensor is built by the spatial distribution and feature vectors of the point neighborhood. The entries of LiDAR tensor are accessed via four indexes. Each index is called mode: three spatial modes in direction X ,Y ,Z and one feature mode. Sparse representation for classification(SRC) method is proposed in this paper. The sparsity algorithm is to find the best represent the test sample by sparse linear combination of training samples from a dictionary. To explore the sparsity of LiDAR tensor, the tucker decomposition is used. It decomposes a tensor into a core tensor multiplied by a matrix along each mode. Those matrices could be considered as the principal components in each mode. The entries of core tensor show the level of interaction between the different components. Therefore, the LiDAR tensor can be approximately represented by a sparse tensor multiplied by a matrix selected from a dictionary along each mode. The matrices decomposed from training samples are arranged as initial elements in the dictionary. By dictionary learning, a reconstructive and discriminative structure dictionary along each mode is built. The overall structure dictionary composes of class-specified sub-dictionaries. Then the sparse core tensor is calculated by tensor OMP(Orthogonal Matching Pursuit) method based on dictionaries along each mode. It is expected that original tensor should be well recovered by sub-dictionary associated with relevant class, while entries in the sparse tensor associated with other classed should be nearly zero. Therefore, SRC use the reconstruction error associated with each class to do data classification. A section of airborne LiDAR points of Vienna city is used and classified into 6classes: ground, roofs, vegetation, covered ground, walls and other points. Only 6 training samples from each class are taken. For the final classification result, ground and covered ground are merged into one same class(ground). The classification accuracy for ground is 94.60%, roof is 95.47%, vegetation is 85.55%, wall is 76.17%, other object is 20.39%.

On the Lighthill relationship and sound generation from isotropic turbulence

NASA Technical Reports Server (NTRS)

Zhou, YE; Praskovsky, Alexander; Oncley, Steven

1994-01-01

In 1952, Lighthill developed a theory for determining the sound generated by a turbulent motion of a fluid. With some statistical assumptions, Proudman applied this theory to estimate the acoustic power of isotropic turbulence. Recently, Lighthill established a simple relationship that relates the fourth-order retarded time and space covariance of his stress tensor to the corresponding second-order covariance and the turbulent flatness factor, without making statistical assumptions for a homogeneous turbulence. Lilley revisited Proudman's work and applied the Lighthill relationship to evaluate directly the radiated acoustic power from isotropic turbulence. After choosing the time separation dependence in the two-point velocity time and space covariance based on the insights gained from direct numerical simulations, Lilley concluded that the Proudman constant is determined by the turbulent flatness factor and the second-order spatial velocity covariance. In order to estimate the Proudman constant at high Reynolds numbers, we analyzed a unique data set of measurements in a large wind tunnel and atmospheric surface layer that covers a range of the Taylor microscale based on Reynolds numbers 2.0 x 10(exp 3) less than or equal to R(sub lambda) less than or equal to 12.7 x 10(exp 3). Our measurements demonstrate that the Lighthill relationship is a good approximation, providing additional support to Lilley's approach. The flatness factor is found between 2.7 - 3.3 and the second order spatial velocity covariance is obtained. Based on these experimental data, the Proudman constant is estimated to be 0.68 - 3.68.

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

ERIC Educational Resources Information Center

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…

Influence of N-H...O and C-H...O hydrogen bonds on the 17O NMR tensors in crystalline uracil: computational study.

PubMed

Ida, Ramsey; De Clerk, Maurice; Wu, Gang

2006-01-26

We report a computational study for the 17O NMR tensors (electric field gradient and chemical shielding tensors) in crystalline uracil. We found that N-H...O and C-H...O hydrogen bonds around the uracil molecule in the crystal lattice have quite different influences on the 17O NMR tensors for the two C=O groups. The computed 17O NMR tensors on O4, which is involved in two strong N-H...O hydrogen bonds, show remarkable sensitivity toward the choice of cluster model, whereas the 17O NMR tensors on O2, which is involved in two weak C-H...O hydrogen bonds, show much smaller improvement when the cluster model includes the C-H...O hydrogen bonds. Our results demonstrate that it is important to have accurate hydrogen atom positions in the molecular models used for 17O NMR tensor calculations. In the absence of low-temperature neutron diffraction data, an effective way to generate reliable hydrogen atom positions in the molecular cluster model is to employ partial geometry optimization for hydrogen atom positions using a cluster model that includes all neighboring hydrogen-bonded molecules. Using an optimized seven-molecule model (a total of 84 atoms), we were able to reproduce the experimental 17O NMR tensors to a reasonably good degree of accuracy. However, we also found that the accuracy for the calculated 17O NMR tensors at O2 is not as good as that found for the corresponding tensors at O4. In particular, at the B3LYP/6-311++G(d,p) level of theory, the individual 17O chemical shielding tensor components differ by less than 10 and 30 ppm from the experimental values for O4 and O2, respectively. For the 17O quadrupole coupling constant, the calculated values differ by 0.30 and 0.87 MHz from the experimental values for O4 and O2, respectively.

Full moment tensors with uncertainties for the 2017 North Korea declared nuclear test and for a collocated, subsequent event

NASA Astrophysics Data System (ADS)

Alvizuri, C. R.; Tape, C.

2017-12-01

A seismic moment tensor is a 3×3 symmetric matrix that characterizes the far-field seismic radiation from a source, whether it be an earthquake, volcanic event, explosion. We estimate full moment tensors and their uncertainties for the North Korea declared nuclear test and for a collocated event that occurred eight minutes later. The nuclear test and the subsequent event occurred on September 3, 2017 at around 03:30 and 03:38 UTC time. We perform a grid search over the six-dimensional space of moment tensors, generating synthetic waveforms at each moment tensor grid point and then evaluating a misfit function between the observed and synthetic waveforms. The synthetic waveforms are computed using a 1-D structure model for the region; this approximation requires careful assessment of time shifts between data and synthetics, as well as careful choice of the bandpass for filtering. For each moment tensor we characterize its uncertainty in terms of waveform misfit, a probability function, and a confidence curve for the probability that the true moment tensor lies within the neighborhood of the optimal moment tensor. For each event we estimate its moment tensor using observed waveforms from all available seismic stations within a 2000-km radius. We use as much of the waveform as possible, including surface waves for all stations, and body waves above 1 Hz for some of the closest stations. Our preliminary magnitude estimates are Mw 5.1-5.3 for the first event and Mw 4.7 for the second event. Our results show a dominantly positive isotropic moment tensor for the first event, and a dominantly negative isotropic moment tensor for the subsequent event. As expected, the details of the probability density, waveform fit, and confidence curves are influenced by the structural model, the choice of filter frequencies, and the selection of stations.

Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

PubMed

Khoromskaia, Venera; Khoromskij, Boris N

2015-12-21

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

Tensor-based dynamic reconstruction method for electrical capacitance tomography

NASA Astrophysics Data System (ADS)

Lei, J.; Mu, H. P.; Liu, Q. B.; Li, Z. H.; Liu, S.; Wang, X. Y.

2017-03-01

Electrical capacitance tomography (ECT) is an attractive visualization measurement method, in which the acquisition of high-quality images is beneficial for the understanding of the underlying physical or chemical mechanisms of the dynamic behaviors of the measurement objects. In real-world measurement environments, imaging objects are often in a dynamic process, and the exploitation of the spatial-temporal correlations related to the dynamic nature will contribute to improving the imaging quality. Different from existing imaging methods that are often used in ECT measurements, in this paper a dynamic image sequence is stacked into a third-order tensor that consists of a low rank tensor and a sparse tensor within the framework of the multiple measurement vectors model and the multi-way data analysis method. The low rank tensor models the similar spatial distribution information among frames, which is slowly changing over time, and the sparse tensor captures the perturbations or differences introduced in each frame, which is rapidly changing over time. With the assistance of the Tikhonov regularization theory and the tensor-based multi-way data analysis method, a new cost function, with the considerations of the multi-frames measurement data, the dynamic evolution information of a time-varying imaging object and the characteristics of the low rank tensor and the sparse tensor, is proposed to convert the imaging task in the ECT measurement into a reconstruction problem of a third-order image tensor. An effective algorithm is developed to search for the optimal solution of the proposed cost function, and the images are reconstructed via a batching pattern. The feasibility and effectiveness of the developed reconstruction method are numerically validated.

Power law f(𝒢,T) gravity models supporting wormhole solutions

NASA Astrophysics Data System (ADS)

Shamir, M. Farasat; Ahmad, Mushtaq

This work provides some feasible regions for the existence of traversable wormhole geometries in modified f(𝒢,T) gravity. For this purpose, three different matter contents have been studied with special emphasis on anisotropic fluid by considering a specific f(𝒢,T) gravity power law model. It has been shown that the null energy conditions for the effective energy-momentum tensor are widely violated for the ordinary matter content. However, some small feasible regions to support the wormhole solutions have been noted. Furthermore, the stability of the anisotropic feasible regions for the wormhole solutions has been discussed. It is concluded that the wormhole geometries threaded by the ordinary matter actually exist and are well stable in f(𝒢,T) gravity.

On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity

NASA Astrophysics Data System (ADS)

Vallée, Claude; Fortuné, Danielle; Lerintiu, Camelia

2008-11-01

Elastic materials are governed by a constitutive law relating the second Piola-Kirchhoff stress tensor Σ and the right Cauchy-Green strain tensor C=FF. Isotropic elastic materials are the special cases for which the Cauchy stress tensor σ depends solely on the left Cauchy-Green strain tensor B=FF. In this Note we revisit the following property of isotropic hyperelastic materials: if the constitutive law relating Σ and C is derivable from a potential ϕ, then σ and lnB are related by a constitutive law derived from the compound potential ϕ○exp. We give a new and concise proof which is based on an explicit integral formula expressing the derivative of the exponential of a tensor. To cite this article: C. Vallée et al., C. R. Mecanique 336 (2008).

Tensor sufficient dimension reduction

PubMed Central

Zhong, Wenxuan; Xing, Xin; Suslick, Kenneth

2015-01-01

Tensor is a multiway array. With the rapid development of science and technology in the past decades, large amount of tensor observations are routinely collected, processed, and stored in many scientific researches and commercial activities nowadays. The colorimetric sensor array (CSA) data is such an example. Driven by the need to address data analysis challenges that arise in CSA data, we propose a tensor dimension reduction model, a model assuming the nonlinear dependence between a response and a projection of all the tensor predictors. The tensor dimension reduction models are estimated in a sequential iterative fashion. The proposed method is applied to a CSA data collected for 150 pathogenic bacteria coming from 10 bacterial species and 14 bacteria from one control species. Empirical performance demonstrates that our proposed method can greatly improve the sensitivity and specificity of the CSA technique. PMID:26594304

Determining anisotropic conductivity using diffusion tensor imaging data in magneto-acoustic tomography with magnetic induction

NASA Astrophysics Data System (ADS)

Ammari, Habib; Qiu, Lingyun; Santosa, Fadil; Zhang, Wenlong

2017-12-01

In this paper we present a mathematical and numerical framework for a procedure of imaging anisotropic electrical conductivity tensor by integrating magneto-acoutic tomography with data acquired from diffusion tensor imaging. Magneto-acoustic tomography with magnetic induction (MAT-MI) is a hybrid, non-invasive medical imaging technique to produce conductivity images with improved spatial resolution and accuracy. Diffusion tensor imaging (DTI) is also a non-invasive technique for characterizing the diffusion properties of water molecules in tissues. We propose a model for anisotropic conductivity in which the conductivity is proportional to the diffusion tensor. Under this assumption, we propose an optimal control approach for reconstructing the anisotropic electrical conductivity tensor. We prove convergence and Lipschitz type stability of the algorithm and present numerical examples to illustrate its accuracy and feasibility.

PREFACE: 1st Tensor Polarized Solid Target Workshop

NASA Astrophysics Data System (ADS)

2014-10-01

These are the proceedings of the first Tensor Spin Observables Workshop that was held in March 2014 at the Thomas Jefferson National Accelerator Facility in Newport News, Virginia. The conference was convened to study the physics that can be done with the recently approved E12-13-011 polarized target. A tensor polarized target holds the potential of initiating a new generation of tensor spin physics at Jefferson Lab. Experiments which utilize tensor polarized targets can help clarify how nuclear properties arise from partonic degrees of freedom, provide unique insight into short-range correlations and quark angular momentum, and also help pin down the polarization of the quark sea with a future Electron Ion Collider. This three day workshop was focused on tensor spin observables and the associated tensor target development. The workshop goals were to stimulate progress in the theoretical treatment of polarized spin-1 systems, foster the development of new proposals, and to reach a consensus on the optimal polarized target configuration for the tensor spin program. The workshop was sponsored by the University of New Hampshire, the Jefferson Science Associates, Florida International University, and Jefferson Lab. It was organized by Karl Slifer (chair), Patricia Solvignon, and Elena Long of the University of New Hampshire, Douglas Higinbotham and Christopher Keith of Jefferson Lab, and Misak Sargsian of the Florida International University. These proceedings represent the effort put forth by the community to begin exploring the possibilities that a high-luminosity, high-tensor polarized solid target can offer.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lizarraga, Joanes; Urrestilla, Jon; Daverio, David

We present cosmic microwave background (CMB) power spectra from recent numerical simulations of cosmic strings in the Abelian Higgs model and compare them to CMB power spectra measured by Planck . We obtain revised constraints on the cosmic string tension parameter G μ. For example, in the ΛCDM model with the addition of strings and no primordial tensor perturbations, we find G μ < 2.0 × 10{sup −7} at 95% confidence, about 20% lower than the value obtained from previous simulations, which had 1/64 of the spatial volume. The increased computational volume also makes it possible to simulate fully themore » physical equations of motion, in which the string cores shrink in comoving coordinates. We find however that this, and the larger dynamic range, changes the amplitude of the power spectra by only about 10%. The main cause of the stronger constraints on G μ is instead an improved treatment of the string evolution across the radiation-matter transition.« less

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

PubMed

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

2017-08-01

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

Moment Tensor Analysis of Shallow Sources

NASA Astrophysics Data System (ADS)

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

2015-12-01

A potential issue for moment tensor inversion of shallow seismic sources is that some moment tensor components have vanishing amplitudes at the free surface, which can result in bias in the moment tensor solution. The effects of the free-surface on the stability of the moment tensor method becomes important as we continue to investigate and improve the capabilities of regional full moment tensor inversion for source-type identification and discrimination. It is important to understand these free surface effects on discriminating shallow explosive sources for nuclear monitoring purposes. It may also be important in natural systems that have shallow seismicity such as volcanoes and geothermal systems. In this study, we apply the moment tensor based discrimination method to the HUMMING ALBATROSS quarry blasts. These shallow chemical explosions at approximately 10 m depth and recorded up to several kilometers distance represent rather severe source-station geometry in terms of vanishing traction issues. We show that the method is capable of recovering a predominantly explosive source mechanism, and the combined waveform and first motion method enables the unique discrimination of these events. Recovering the correct yield using seismic moment estimates from moment tensor inversion remains challenging but we can begin to put error bounds on our moment estimates using the NSS technique.

Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm

NASA Astrophysics Data System (ADS)

Nakatani, Naoki; Chan, Garnet Kin-Lic

2013-04-01

We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.

Conservation laws and stress-energy-momentum tensors for systems with background fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gratus, Jonathan, E-mail: j.gratus@lancaster.ac.uk; The Cockcroft Institute, Daresbury Laboratory, Warrington WA4 4AD; Obukhov, Yuri N., E-mail: yo@thp.uni-koeln.de

2012-10-15

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics inmore » media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields. - Highlights: Black-Right-Pointing-Pointer The role of background fields in diffeomorphism invariant actions is demonstrated. Black-Right-Pointing-Pointer Interrelations between different stress-energy-momentum tensors are emphasised. Black-Right-Pointing-Pointer The Abraham and Minkowski electromagnetic tensors are discussed in this context. Black-Right-Pointing-Pointer Conservation laws in the presence of nondynamic background fields are formulated. Black-Right-Pointing-Pointer The discussion is facilitated by the development of a new variational calculus.« less

Groupwise Registration and Atlas Construction of 4th-Order Tensor Fields Using the ℝ+ Riemannian Metric*

PubMed Central

Barmpoutis, Angelos

2010-01-01

Registration of Diffusion-Weighted MR Images (DW-MRI) can be achieved by registering the corresponding 2nd-order Diffusion Tensor Images (DTI). However, it has been shown that higher-order diffusion tensors (e.g. order-4) outperform the traditional DTI in approximating complex fiber structures such as fiber crossings. In this paper we present a novel method for unbiased group-wise non-rigid registration and atlas construction of 4th-order diffusion tensor fields. To the best of our knowledge there is no other existing method to achieve this task. First we define a metric on the space of positive-valued functions based on the Riemannian metric of real positive numbers (denoted by ℝ+). Then, we use this metric in a novel functional minimization method for non-rigid 4th-order tensor field registration. We define a cost function that accounts for the 4th-order tensor re-orientation during the registration process and has analytic derivatives with respect to the transformation parameters. Finally, the tensor field atlas is computed as the minimizer of the variance defined using the Riemannian metric. We quantitatively compare the proposed method with other techniques that register scalar-valued or diffusion tensor (rank-2) representations of the DWMRI. PMID:20436782

Mapping the magnonic landscape in patterned magnetic structures

NASA Astrophysics Data System (ADS)

Davies, C. S.; Poimanov, V. D.; Kruglyak, V. V.

2017-09-01

We report the development of a hybrid numerical/analytical model capable of mapping the spatially varying distributions of the local ferromagnetic resonance (FMR) frequency and dynamic magnetic susceptibility in a wide class of patterned and compositionally modulated magnetic structures. Starting from the numerically simulated static micromagnetic state, the magnetization is deliberately deflected orthogonally to its equilibrium orientation, and the magnetic fields generated in response to this deflection are evaluated using micromagnetic software. This allows us to calculate the elements of the effective demagnetizing tensor, which are then used within a linear analytical formalism to map the local FMR frequency and dynamic magnetic susceptibility. To illustrate the typical results that one can obtain using this model, we analyze three micromagnetic systems boasting nonuniformity in either one or two dimensions, and successfully explain the spin-wave emission observed in each case, demonstrating the ubiquitous nature of the Schlömann excitation mechanism underpinning the observations. Finally, the developed model of local FMR frequency can be used to explain how spin waves could be confined and steered using magnetic nonuniformities of various origins, rendering it a powerful tool for the mapping of the graded magnonic index in magnonics.

UNC-Utah NA-MIC framework for DTI fiber tract analysis.

PubMed

Verde, Audrey R; Budin, Francois; Berger, Jean-Baptiste; Gupta, Aditya; Farzinfar, Mahshid; Kaiser, Adrien; Ahn, Mihye; Johnson, Hans; Matsui, Joy; Hazlett, Heather C; Sharma, Anuja; Goodlett, Casey; Shi, Yundi; Gouttard, Sylvain; Vachet, Clement; Piven, Joseph; Zhu, Hongtu; Gerig, Guido; Styner, Martin

2014-01-01

Diffusion tensor imaging has become an important modality in the field of neuroimaging to capture changes in micro-organization and to assess white matter integrity or development. While there exists a number of tractography toolsets, these usually lack tools for preprocessing or to analyze diffusion properties along the fiber tracts. Currently, the field is in critical need of a coherent end-to-end toolset for performing an along-fiber tract analysis, accessible to non-technical neuroimaging researchers. The UNC-Utah NA-MIC DTI framework represents a coherent, open source, end-to-end toolset for atlas fiber tract based DTI analysis encompassing DICOM data conversion, quality control, atlas building, fiber tractography, fiber parameterization, and statistical analysis of diffusion properties. Most steps utilize graphical user interfaces (GUI) to simplify interaction and provide an extensive DTI analysis framework for non-technical researchers/investigators. We illustrate the use of our framework on a small sample, cross sectional neuroimaging study of eight healthy 1-year-old children from the Infant Brain Imaging Study (IBIS) Network. In this limited test study, we illustrate the power of our method by quantifying the diffusion properties at 1 year of age on the genu and splenium fiber tracts.

UNC-Utah NA-MIC framework for DTI fiber tract analysis

PubMed Central

Verde, Audrey R.; Budin, Francois; Berger, Jean-Baptiste; Gupta, Aditya; Farzinfar, Mahshid; Kaiser, Adrien; Ahn, Mihye; Johnson, Hans; Matsui, Joy; Hazlett, Heather C.; Sharma, Anuja; Goodlett, Casey; Shi, Yundi; Gouttard, Sylvain; Vachet, Clement; Piven, Joseph; Zhu, Hongtu; Gerig, Guido; Styner, Martin

2014-01-01

Diffusion tensor imaging has become an important modality in the field of neuroimaging to capture changes in micro-organization and to assess white matter integrity or development. While there exists a number of tractography toolsets, these usually lack tools for preprocessing or to analyze diffusion properties along the fiber tracts. Currently, the field is in critical need of a coherent end-to-end toolset for performing an along-fiber tract analysis, accessible to non-technical neuroimaging researchers. The UNC-Utah NA-MIC DTI framework represents a coherent, open source, end-to-end toolset for atlas fiber tract based DTI analysis encompassing DICOM data conversion, quality control, atlas building, fiber tractography, fiber parameterization, and statistical analysis of diffusion properties. Most steps utilize graphical user interfaces (GUI) to simplify interaction and provide an extensive DTI analysis framework for non-technical researchers/investigators. We illustrate the use of our framework on a small sample, cross sectional neuroimaging study of eight healthy 1-year-old children from the Infant Brain Imaging Study (IBIS) Network. In this limited test study, we illustrate the power of our method by quantifying the diffusion properties at 1 year of age on the genu and splenium fiber tracts. PMID:24409141

Studies of Second Order Optical Nonlinearities of 4-Aminobenzophenone (ABP) Single Crystal Films

NASA Astrophysics Data System (ADS)

Bhowmik, Achintya; Thakur, Mrinal

1998-03-01

Specific organic materials exhibit very high second order optical susceptibilities. Growth of single crystal films of these materials and characterization of nonlinear optical properties are necessary for implementation of device applications. We have grown large-area films ( 1 cm^2 area, 4 μm thick) of ABP by a modification of the shear method. Single crystal nature of the films was confirmed by polarized optical microscopy. X-ray diffraction analysis showed a [100] surface orientation. The absorption spectra revealed transparency from 390 nm to 1940 nm. Significant elements of the second order optical susceptibility tensor were measured by detailed SHG experiments using a Nd:YAG laser (1064 nm, 100 ps, 82 MHz). Second-harmonic power was measured using lock-in detection with carefully selected polarization conditions while the film was rotated about the propagation direction. Using LiNbØas the reference, d-coefficients of ABP were found to be d_23=7.2 pm/V and d_22=0.7 pm/V. Type-I and type-II phase-matching directions were identified on the film by analyzing the optical indicatrix surfaces at fundamental and second-harmonic frequencies.

On the magnetic polarizability tensor of US coinage

NASA Astrophysics Data System (ADS)

Davidson, John L.; Abdel-Rehim, Omar A.; Hu, Peipei; Marsh, Liam A.; O'Toole, Michael D.; Peyton, Anthony J.

2018-03-01

The magnetic dipole polarizability tensor of a metallic object gives unique information about the size, shape and electromagnetic properties of the object. In this paper, we present a novel method of coin characterization based on the spectroscopic response of the absolute tensor. The experimental measurements are validated using a combination of tests with a small set of bespoke coin surrogates and simulated data. The method is applied to an uncirculated set of US coins. Measured and simulated spectroscopic tensor responses of the coins show significant differences between different coin denominations. The presented results are encouraging as they strongly demonstrate the ability to characterize coins using an absolute tensor approach.

The Topology of Three-Dimensional Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

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

Ryu-Takayanagi formula for symmetric random tensor networks

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

2018-06-01

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

A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization

NASA Astrophysics Data System (ADS)

Sulyok, G.

2017-07-01

Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the ultraviolet (UV-)divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast to existing recursion schemes, we are able to present a general analytic result in closed form that enables direct determination of the UV-divergent part of any one-loop tensor N-point coefficient independent from UV-divergent parts of other one-loop tensor N-point coefficients. Simplified formulas and explicit expressions are presented for A-, B-, C-, D-, E-, and F-functions.

Evidence for inflation in an axion landscape

NASA Astrophysics Data System (ADS)

Nath, Pran; Piskunov, Maksim

2018-03-01

We discuss inflation models within supersymmetry and supergravity frameworks with a landscape of chiral superfields and one U(1) shift symmetry which is broken by non-perturbative symmetry breaking terms in the superpotential. We label the pseudo scalar component of the chiral fields axions and their real parts saxions. Thus in the models only one combination of axions will be a pseudo-Nambu-Goldstone-boson which will act as the inflaton. The proposed models constitute consistent inflation for the following reasons: the inflation potential arises dynamically with stabilized saxions, the axion decay constant can lie in the sub-Planckian region, and consistency with the Planck data is achieved. The axion landscape consisting of m axion pairs is assumed with the axions in each pair having opposite charges. A fast roll-slow roll splitting mechanism for the axion potential is proposed which is realized with a special choice of the axion basis. In this basis the 2 m coupled equations split into 2 m - 1 equations which enter in the fast roll and there is one unique linear combination of the 2 m fields which controls the slow roll and thus the power spectrum of curvature and tensor perturbations. It is shown that a significant part of the parameter space exists where inflation is successful, i.e., N pivot = [50, 60], the spectral index n s of curvature perturbations, and the ratio r of the power spectrum of tensor perturbations and curvature perturbations, lie in the experimentally allowed regions given by the Planck experiment. Further, it is shown that the model allows for a significant region of the parameter space where the effective axion decay constant can lie in the sub-Planckian domain. An analysis of the tensor spectral index n t is also given and the future experimental data which constraints n t will further narrow down the parameter space of the proposed inflationary models. Topics of further interest include implications of the model for gravitational waves and non-Gaussianities in the curvature perturbations. Also of interest is embedding of the model in strings which are expected to possess a large axionic landscape.

Quantitative Tractography and Volumetric MRI in Blast and Blunt Force TBI: Predictors of Neurocognitive and Behavioral Outcome

DTIC Science & Technology

2016-10-01

are related to mechanism of injury as well as white matter integrity using diffusion tensor imaging (DTI). We are also collecting and analyzing...APOE ε4] and brain-derived neurotrophic factor [BDNF]) to brain integrity , neuropsychological functioning, and neurobehavioral outcome. 15. SUBJECT...contribution of genetic factors (Apolipoprotein-E ε-4 [APOE ε4] and brain-derived neurotrophic factor [BDNF]) to brain integrity , neuropsychological

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lyakh, Dmitry I.

An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typicallymore » appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the na ve scattering algorithm (no memory access optimization). Furthermore, the tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).« less

Visualization of 3-D tensor fields

NASA Technical Reports Server (NTRS)

Hesselink, L.

1996-01-01

Second-order tensor fields have applications in many different areas of physics, such as general relativity and fluid mechanics. The wealth of multivariate information in tensor fields makes them more complex and abstract than scalar and vector fields. Visualization is a good technique for scientists to gain new insights from them. Visualizing a 3-D continuous tensor field is equivalent to simultaneously visualizing its three eigenvector fields. In the past, research has been conducted in the area of two-dimensional tensor fields. It was shown that degenerate points, defined as points where eigenvalues are equal to each other, are the basic singularities underlying the topology of tensor fields. Moreover, it was shown that eigenvectors never cross each other except at degenerate points. Since we live in a three-dimensional world, it is important for us to understand the underlying physics of this world. In this report, we describe a new method for locating degenerate points along with the conditions for classifying them in three-dimensional space. Finally, we discuss some topological features of three-dimensional tensor fields, and interpret topological patterns in terms of physical properties.

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

PubMed

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.

Simplified derivation of the gravitational wave stress tensor from the linearized Einstein field equations.

PubMed

Balbus, Steven A

2016-10-18

A conserved stress energy tensor for weak field gravitational waves propagating in vacuum is derived directly from the linearized general relativistic wave equation alone, for an arbitrary gauge. In any harmonic gauge, the form of the tensor leads directly to the classical expression for the outgoing wave energy. The method described here, however, is a much simpler, shorter, and more physically motivated approach than is the customary procedure, which involves a lengthy and cumbersome second-order (in wave-amplitude) calculation starting with the Einstein tensor. Our method has the added advantage of exhibiting the direct coupling between the outgoing wave energy flux and the work done by the gravitational field on the sources. For nonharmonic gauges, the directly derived wave stress tensor has an apparent index asymmetry. This coordinate artifact may be straightforwardly removed, and the symmetrized (still gauge-invariant) tensor then takes on its widely used form. Angular momentum conservation follows immediately. For any harmonic gauge, however, the stress tensor found is manifestly symmetric from the start, and its derivation depends, in its entirety, on the structure of the linearized wave equation.

Theory of electron g-tensor in bulk and quantum-well semiconductors

NASA Astrophysics Data System (ADS)

Lau, Wayne H.; Flatte', Michael E.

2004-03-01

We present quantitative calculations for the electron g-tensors in bulk and quantum-well semiconductors based on a generalized P.p envelope function theory solved in a fourteen-band restricted basis set. The dependences of g-tensor on structure, magnetic field, carrier density, temperature, and spin polarization have been explored and will be described. It is found that at temperatures of a few Kelvin and fields of a few Tesla, the g-tensors for bulk semiconductors develop quasi-steplike dependences on carrier density or magnetic field due to magnetic quantization, and this effect is even more pronounced in quantum-well semiconductors due to the additional electric quantization along the growth direction. The influence of quantum confinement on the electron g-tensors in QWs is studied by examining the dependence of electron g-tensors on well width. Excellent agreement between these calculated electron g-tensors and measurements [1-2] is found for GaAs/AlGaAs QWs. This work was supported by DARPA/ARO. [1] A. Malinowski and R. T. Harley, Phys. Rev. B 62, 2051 (2000);[2] Le Jeune et al., Semicond. Sci. Technol. 12, 380 (1997).

Polarized-cathodoluminescence study of uniaxial and biaxial stress in GaAs/Si

NASA Technical Reports Server (NTRS)

Rich, D. H.; Ksendzov, A.; Terhune, R. W.; Grunthaner, F. J.; Wilson, B. A.; Shen, H.; Dutta, M.; Vernon, S. M.; Dixon, T. M.

1991-01-01

The strain-induced splitting of the heavy-hole (hh) and light-hole (lh) valence bands for 4-microns thick GaAs/Si is examined on a microscopic scale using linear polarized-cathodoluminescence imaging and spectroscopy. The energies and intensities of the hh- and lh-exciton luminescence are quantitatively analyzed to determine spatial variations in the stress tensor. The results indicate that regions near and far from the microcracks are primarily subject to uniaxial and biaxial tensile stresses, respectively. The transition region where biaxial stress gradually converts to uniaxial stress is analyzed, and reveals a mixing of lh and hh characters in the strain-split bands.

Reconstructing a f ( R ) theory from the α-Attractors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miranda, T.; Fabris, J. C.; Piattella, O. F., E-mail: tays.andrade@aluno.ufes.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: fabris@pq.cnpq.br

We show an analogy at high curvature between a f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2} theory and the α-Attractors. We calculate the expressions of the parameters a , b and n as functions of α and the predictions of the model f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2} on the scalar spectral index n {sub s} and the tensor-to-scalar ratio r . We find that the power law correction R {sup n} {sup −} {sup 1} allowsmore » for a production of gravitational waves enhanced with respect to the one in the Starobinsky model, while maintaining a viable prediction on n {sub s}. We numerically reconstruct the full α-Attractors class of models testing the goodness of our high-energy approximation f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2}. Moreover, we also investigate the case of a single power law f ( R ) = γ R {sup 2} {sup −} {sup δ} theory, with γ and δ free parameters. We calculate analytically the predictions of this model on the scalar spectral index n {sub s} and the tensor-to-scalar ratio r and the values of δ which are allowed from the current observational results. We find that −0.015 < δ < 0.016, confirming once again the excellent agreement between the Starobinsky model and observation.« less

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

DOE PAGES

Mohamed, Mamdouh S.; Larson, Bennett C.; Tischler, Jonathan Z.; ...

2015-05-18

The statistical properties of the elastic distortion fields of dislocations in deforming crystals are investigated using the method of discrete dislocation dynamics to simulate dislocation structures and dislocation density evolution under tensile loading. Probability distribution functions (PDF) and pair correlation functions (PCF) of the simulated internal elastic strains and lattice rotations are generated for tensile strain levels up to 0.85%. The PDFs of simulated lattice rotation are compared with sub-micrometer resolution three-dimensional X-ray microscopy measurements of rotation magnitudes and deformation length scales in 1.0% and 2.3% compression strained Cu single crystals to explore the linkage between experiment and the theoreticalmore » analysis. The statistical properties of the deformation simulations are analyzed through determinations of the Nye and Kr ner dislocation density tensors. The significance of the magnitudes and the length scales of the elastic strain and the rotation parts of dislocation density tensors are demonstrated, and their relevance to understanding the fundamental aspects of deformation is discussed.« less

Neotectonic activity and parameters of seismotectonic deformations of seismic belts in Northeast Asia

NASA Astrophysics Data System (ADS)

Imaeva, Lyudmila; Gusev, Georgy; Imaev, Valerii; Mel'nikova, Valentina

2017-10-01

The Arctic-Asian and Okhotsk-Chukotka seismic belts bordering the Kolyma-Chukotka crustal plate are the subject of our study aimed at reconstructing the stress-strain state of the crust and defining the types of seismotectonic deformation (STD) in the region. Based on the degrees of activity of geodynamic processes, the regional principles for ranking neotectonic structures were constrained, and the corresponding classes of the discussed neotectonic structures were substantiated. We analyzed the structural tectonic positions of the modern structures, their deep structure parameters, and the systems of active faults in the Laptev, Kharaulakh, Koryak, and Chukotka segments and Chersky seismotectonic zone, as well as the tectonic stress fields revealed by tectonophysical analysis of the Late Cenozoic faults and folds. From the earthquake focal mechanisms, the average seismotectonic strain tensors were estimated. Using the geological, geostructural, geophysical and GPS data, and corresponding average tensors, the directions of the principal stress axes were determined. A regularity in the changes of tectonic settings in the Northeast Arctic was revealed.

Symmetry operators and decoupled equations for linear fields on black hole spacetimes

NASA Astrophysics Data System (ADS)

Araneda, Bernardo

2017-02-01

In the class of vacuum Petrov type D spacetimes with cosmological constant, which includes the Kerr-(A)dS black hole as a particular case, we find a set of four-dimensional operators that, when composed off shell with the Dirac, Maxwell and linearized gravity equations, give a system of equations for spin weighted scalars associated with the linear fields, that decouple on shell. Using these operator relations we give compact reconstruction formulae for solutions of the original spinor and tensor field equations in terms of solutions of the decoupled scalar equations. We also analyze the role of Killing spinors and Killing-Yano tensors in the spin weight zero equations and, in the case of spherical symmetry, we compare our four-dimensional formulation with the standard 2  +  2 decomposition and particularize to the Schwarzschild-(A)dS black hole. Our results uncover a pattern that generalizes a number of previous results on Teukolsky-like equations and Debye potentials for higher spin fields.

White matter microstructure and cognitive decline in metabolic syndrome: a review of diffusion tensor imaging.

PubMed

Alfaro, Freddy J; Gavrieli, Anna; Saade-Lemus, Patricia; Lioutas, Vasileios-Arsenios; Upadhyay, Jagriti; Novak, Vera

2018-01-01

Metabolic syndrome is a cluster of cardiovascular risk factors defined by the presence of abdominal obesity, glucose intolerance, hypertension and/or dyslipidemia. It is a major public health epidemic worldwide, and a known risk factor for the development of cognitive dysfunction and dementia. Several studies have demonstrated a positive association between the presence of metabolic syndrome and worse cognitive outcomes, however, evidence of brain structure pathology is limited. Diffusion tensor imaging has offered new opportunities to detect microstructural white matter changes in metabolic syndrome, and a possibility to detect associations between functional and structural abnormalities. This review analyzes the impact of metabolic syndrome on white matter microstructural integrity, brain structure abnormalities and their relationship to cognitive function. Each of the metabolic syndrome components exerts a specific signature of white matter microstructural abnormalities. Metabolic syndrome and its components exert both additive/synergistic, as well as, independent effects on brain microstructure thus accelerating brain aging and cognitive decline. Copyright © 2017 Elsevier Inc. All rights reserved.

Strain Rate Tensor Estimation in Cine Cardiac MRI Based on Elastic Image Registration

NASA Astrophysics Data System (ADS)

Sánchez-Ferrero, Gonzalo Vegas; Vega, Antonio Tristán; Grande, Lucilio Cordero; de La Higuera, Pablo Casaseca; Fernández, Santiago Aja; Fernández, Marcos Martín; López, Carlos Alberola

In this work we propose an alternative method to estimate and visualize the Strain Rate Tensor (SRT) in Magnetic Resonance Images (MRI) when Phase Contrast MRI (PCMRI) and Tagged MRI (TMRI) are not available. This alternative is based on image processing techniques. Concretely, image registration algorithms are used to estimate the movement of the myocardium at each point. Additionally, a consistency checking method is presented to validate the accuracy of the estimates when no golden standard is available. Results prove that the consistency checking method provides an upper bound of the mean squared error of the estimate. Our experiments with real data show that the registration algorithm provides a useful deformation field to estimate the SRT fields. A classification between regional normal and dysfunctional contraction patterns, as compared with experts diagnosis, points out that the parameters extracted from the estimated SRT can represent these patterns. Additionally, a scheme for visualizing and analyzing the local behavior of the SRT field is presented.

The 2017 North Korea M6 seismic sequence: moment tensor, source time function, and aftershocks

NASA Astrophysics Data System (ADS)

Ni, S.; Zhan, Z.; Chu, R.; He, X.

2017-12-01

On September 3rd, 2017, an M6 seismic event occurred in North Korea, with location near previous nuclear test sites. The event features strong P waves and short period Rayleigh waves are observed in contrast to weak S waves, suggesting mostly explosion mechanism. We performed joint inversion for moment tensor and depth with both local and teleseismic waveforms, and find that the event is shallow with mostly isotropic yet substantial non-isotropic components. Deconvolution of seismic waveforms of this event with respect to previous nuclear test events shows clues of complexity in source time function. The event is followed by smaller earthquakes, as early as 8.5 minutes and lasted at least to October. The later events occurred in a compact region, and show clear S waves, suggesting double couple focal mechanism. Via analyzing Rayleigh wave spectrum, these smaller events are found to be shallow. Relative locations, difference in waveforms of the events are used to infer their possible links and generation mechanism.

Charting the complete elastic properties of inorganic crystalline compounds

PubMed Central

de Jong, Maarten; Chen, Wei; Angsten, Thomas; Jain, Anubhav; Notestine, Randy; Gamst, Anthony; Sluiter, Marcel; Krishna Ande, Chaitanya; van der Zwaag, Sybrand; Plata, Jose J; Toher, Cormac; Curtarolo, Stefano; Ceder, Gerbrand; Persson, Kristin A.; Asta, Mark

2015-01-01

The elastic constant tensor of an inorganic compound provides a complete description of the response of the material to external stresses in the elastic limit. It thus provides fundamental insight into the nature of the bonding in the material, and it is known to correlate with many mechanical properties. Despite the importance of the elastic constant tensor, it has been measured for a very small fraction of all known inorganic compounds, a situation that limits the ability of materials scientists to develop new materials with targeted mechanical responses. To address this deficiency, we present here the largest database of calculated elastic properties for inorganic compounds to date. The database currently contains full elastic information for 1,181 inorganic compounds, and this number is growing steadily. The methods used to develop the database are described, as are results of tests that establish the accuracy of the data. In addition, we document the database format and describe the different ways it can be accessed and analyzed in efforts related to materials discovery and design. PMID:25984348