Uncertainty propagation in orbital mechanics via tensor decomposition

NASA Astrophysics Data System (ADS)

Sun, Yifei; Kumar, Mrinal

2016-03-01

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker-Planck equation (FPE) is defined on a relatively high dimensional (6-D) state-space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the x-y-z subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors' knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral ("super-fast") convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.

Community ecology in 3D: Tensor decomposition reveals spatio-temporal dynamics of large ecological communities

PubMed Central

Lindegren, Martin; Denker, Tim Spaanheden; Floeter, Jens; Fock, Heino O.; Sguotti, Camilla; Stäbler, Moritz; Otto, Saskia A.; Möllmann, Christian

2017-01-01

Understanding spatio-temporal dynamics of biotic communities containing large numbers of species is crucial to guide ecosystem management and conservation efforts. However, traditional approaches usually focus on studying community dynamics either in space or in time, often failing to fully account for interlinked spatio-temporal changes. In this study, we demonstrate and promote the use of tensor decomposition for disentangling spatio-temporal community dynamics in long-term monitoring data. Tensor decomposition builds on traditional multivariate statistics (e.g. Principal Component Analysis) but extends it to multiple dimensions. This extension allows for the synchronized study of multiple ecological variables measured repeatedly in time and space. We applied this comprehensive approach to explore the spatio-temporal dynamics of 65 demersal fish species in the North Sea, a marine ecosystem strongly altered by human activities and climate change. Our case study demonstrates how tensor decomposition can successfully (i) characterize the main spatio-temporal patterns and trends in species abundances, (ii) identify sub-communities of species that share similar spatial distribution and temporal dynamics, and (iii) reveal external drivers of change. Our results revealed a strong spatial structure in fish assemblages persistent over time and linked to differences in depth, primary production and seasonality. Furthermore, we simultaneously characterized important temporal distribution changes related to the low frequency temperature variability inherent in the Atlantic Multidecadal Oscillation. Finally, we identified six major sub-communities composed of species sharing similar spatial distribution patterns and temporal dynamics. Our case study demonstrates the application and benefits of using tensor decomposition for studying complex community data sets usually derived from large-scale monitoring programs. PMID:29136658

Community ecology in 3D: Tensor decomposition reveals spatio-temporal dynamics of large ecological communities.

PubMed

Frelat, Romain; Lindegren, Martin; Denker, Tim Spaanheden; Floeter, Jens; Fock, Heino O; Sguotti, Camilla; Stäbler, Moritz; Otto, Saskia A; Möllmann, Christian

2017-01-01

Understanding spatio-temporal dynamics of biotic communities containing large numbers of species is crucial to guide ecosystem management and conservation efforts. However, traditional approaches usually focus on studying community dynamics either in space or in time, often failing to fully account for interlinked spatio-temporal changes. In this study, we demonstrate and promote the use of tensor decomposition for disentangling spatio-temporal community dynamics in long-term monitoring data. Tensor decomposition builds on traditional multivariate statistics (e.g. Principal Component Analysis) but extends it to multiple dimensions. This extension allows for the synchronized study of multiple ecological variables measured repeatedly in time and space. We applied this comprehensive approach to explore the spatio-temporal dynamics of 65 demersal fish species in the North Sea, a marine ecosystem strongly altered by human activities and climate change. Our case study demonstrates how tensor decomposition can successfully (i) characterize the main spatio-temporal patterns and trends in species abundances, (ii) identify sub-communities of species that share similar spatial distribution and temporal dynamics, and (iii) reveal external drivers of change. Our results revealed a strong spatial structure in fish assemblages persistent over time and linked to differences in depth, primary production and seasonality. Furthermore, we simultaneously characterized important temporal distribution changes related to the low frequency temperature variability inherent in the Atlantic Multidecadal Oscillation. Finally, we identified six major sub-communities composed of species sharing similar spatial distribution patterns and temporal dynamics. Our case study demonstrates the application and benefits of using tensor decomposition for studying complex community data sets usually derived from large-scale monitoring programs.

The Speech multi features fusion perceptual hash algorithm based on tensor decomposition

NASA Astrophysics Data System (ADS)

Huang, Y. B.; Fan, M. H.; Zhang, Q. Y.

2018-03-01

With constant progress in modern speech communication technologies, the speech data is prone to be attacked by the noise or maliciously tampered. In order to make the speech perception hash algorithm has strong robustness and high efficiency, this paper put forward a speech perception hash algorithm based on the tensor decomposition and multi features is proposed. This algorithm analyses the speech perception feature acquires each speech component wavelet packet decomposition. LPCC, LSP and ISP feature of each speech component are extracted to constitute the speech feature tensor. Speech authentication is done by generating the hash values through feature matrix quantification which use mid-value. Experimental results showing that the proposed algorithm is robust for content to maintain operations compared with similar algorithms. It is able to resist the attack of the common background noise. Also, the algorithm is highly efficiency in terms of arithmetic, and is able to meet the real-time requirements of speech communication and complete the speech authentication quickly.

Analysis of temporal-longitudinal-latitudinal characteristics in the global ionosphere based on tensor rank-1 decomposition

NASA Astrophysics Data System (ADS)

Lu, Shikun; Zhang, Hao; Li, Xihai; Li, Yihong; Niu, Chao; Yang, Xiaoyun; Liu, Daizhi

2018-03-01

Combining analyses of spatial and temporal characteristics of the ionosphere is of great significance for scientific research and engineering applications. Tensor decomposition is performed to explore the temporal-longitudinal-latitudinal characteristics in the ionosphere. Three-dimensional tensors are established based on the time series of ionospheric vertical total electron content maps obtained from the Centre for Orbit Determination in Europe. To obtain large-scale characteristics of the ionosphere, rank-1 decomposition is used to obtain U^{(1)}, U^{(2)}, and U^{(3)}, which are the resulting vectors for the time, longitude, and latitude modes, respectively. Our initial finding is that the correspondence between the frequency spectrum of U^{(1)} and solar variation indicates that rank-1 decomposition primarily describes large-scale temporal variations in the global ionosphere caused by the Sun. Furthermore, the time lags between the maxima of the ionospheric U^{(2)} and solar irradiation range from 1 to 3.7 h without seasonal dependence. The differences in time lags may indicate different interactions between processes in the magnetosphere-ionosphere-thermosphere system. Based on the dataset displayed in the geomagnetic coordinates, the position of the barycenter of U^{(3)} provides evidence for north-south asymmetry (NSA) in the large-scale ionospheric variations. The daily variation in such asymmetry indicates the influences of solar ionization. The diurnal geomagnetic coordinate variations in U^{(3)} show that the large-scale EIA (equatorial ionization anomaly) variations during the day and night have similar characteristics. Considering the influences of geomagnetic disturbance on ionospheric behavior, we select the geomagnetic quiet GIMs to construct the ionospheric tensor. The results indicate that the geomagnetic disturbances have little effect on large-scale ionospheric characteristics.

Identifying key nodes in multilayer networks based on tensor decomposition.

PubMed

Wang, Dingjie; Wang, Haitao; Zou, Xiufen

2017-06-01

The identification of essential agents in multilayer networks characterized by different types of interactions is a crucial and challenging topic, one that is essential for understanding the topological structure and dynamic processes of multilayer networks. In this paper, we use the fourth-order tensor to represent multilayer networks and propose a novel method to identify essential nodes based on CANDECOMP/PARAFAC (CP) tensor decomposition, referred to as the EDCPTD centrality. This method is based on the perspective of multilayer networked structures, which integrate the information of edges among nodes and links between different layers to quantify the importance of nodes in multilayer networks. Three real-world multilayer biological networks are used to evaluate the performance of the EDCPTD centrality. The bar chart and ROC curves of these multilayer networks indicate that the proposed approach is a good alternative index to identify real important nodes. Meanwhile, by comparing the behavior of both the proposed method and the aggregated single-layer methods, we demonstrate that neglecting the multiple relationships between nodes may lead to incorrect identification of the most versatile nodes. Furthermore, the Gene Ontology functional annotation demonstrates that the identified top nodes based on the proposed approach play a significant role in many vital biological processes. Finally, we have implemented many centrality methods of multilayer networks (including our method and the published methods) and created a visual software based on the MATLAB GUI, called ENMNFinder, which can be used by other researchers.

Identifying key nodes in multilayer networks based on tensor decomposition

NASA Astrophysics Data System (ADS)

Wang, Dingjie; Wang, Haitao; Zou, Xiufen

2017-06-01

The identification of essential agents in multilayer networks characterized by different types of interactions is a crucial and challenging topic, one that is essential for understanding the topological structure and dynamic processes of multilayer networks. In this paper, we use the fourth-order tensor to represent multilayer networks and propose a novel method to identify essential nodes based on CANDECOMP/PARAFAC (CP) tensor decomposition, referred to as the EDCPTD centrality. This method is based on the perspective of multilayer networked structures, which integrate the information of edges among nodes and links between different layers to quantify the importance of nodes in multilayer networks. Three real-world multilayer biological networks are used to evaluate the performance of the EDCPTD centrality. The bar chart and ROC curves of these multilayer networks indicate that the proposed approach is a good alternative index to identify real important nodes. Meanwhile, by comparing the behavior of both the proposed method and the aggregated single-layer methods, we demonstrate that neglecting the multiple relationships between nodes may lead to incorrect identification of the most versatile nodes. Furthermore, the Gene Ontology functional annotation demonstrates that the identified top nodes based on the proposed approach play a significant role in many vital biological processes. Finally, we have implemented many centrality methods of multilayer networks (including our method and the published methods) and created a visual software based on the MATLAB GUI, called ENMNFinder, which can be used by other researchers.

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.

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.

ON THE DECOMPOSITION OF STRESS AND STRAIN TENSORS INTO SPHERICAL AND DEVIATORIC PARTS

PubMed Central

Augusti, G.; Martin, J. B.; Prager, W.

1969-01-01

It is well known that Hooke's law for a linearly elastic, isotropic solid may be written in the form of two relations that involve only the spherical or only the deviatoric parts of the tensors of stress and strain. The example of the linearly elastic, transversely isotropic solid is used to show that this decomposition is not, in general, feasible for linearly elastic, anisotropic solids. The discussion is extended to a large class of work-hardening rigid, plastic solids, and it is shown that the considered decomposition can only be achieved for the incompressible solids of this class. PMID:16591754

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.

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.

Databases post-processing in Tensoral

NASA Technical Reports Server (NTRS)

Dresselhaus, Eliot

1994-01-01

The Center for Turbulent Research (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, introduced in this document and currently existing in prototype form, is the foundation of this effort. Tensoral provides a convenient and powerful protocol to connect users who wish to analyze fluids databases with the authors who generate them. In this document we introduce Tensoral and its prototype implementation in the form of a user's guide. This guide focuses on use of Tensoral for post-processing turbulence databases. The corresponding document - the Tensoral 'author's guide' - which focuses on how authors can make databases available to users via the Tensoral system - is currently unwritten. Section 1 of this user's guide defines Tensoral's basic notions: we explain the class of problems at hand and how Tensoral abstracts them. Section 2 defines Tensoral syntax for mathematical expressions. Section 3 shows how these expressions make up Tensoral statements. Section 4 shows how Tensoral statements and expressions are embedded into other computer languages (such as C or Vectoral) to make Tensoral programs. We conclude with a complete example program.

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

Compression of hyper-spectral images using an accelerated nonnegative tensor decomposition

NASA Astrophysics Data System (ADS)

Li, Jin; Liu, Zilong

2017-12-01

Nonnegative tensor Tucker decomposition (NTD) in a transform domain (e.g., 2D-DWT, etc) has been used in the compression of hyper-spectral images because it can remove redundancies between spectrum bands and also exploit spatial correlations of each band. However, the use of a NTD has a very high computational cost. In this paper, we propose a low complexity NTD-based compression method of hyper-spectral images. This method is based on a pair-wise multilevel grouping approach for the NTD to overcome its high computational cost. The proposed method has a low complexity under a slight decrease of the coding performance compared to conventional NTD. We experimentally confirm this method, which indicates that this method has the less processing time and keeps a better coding performance than the case that the NTD is not used. The proposed approach has a potential application in the loss compression of hyper-spectral or multi-spectral images

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

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.

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

NASA Astrophysics Data System (ADS)

Rai, Prashant; Sargsyan, Khachik; Najm, Habib; Hermes, Matthew R.; Hirata, So

2017-09-01

A new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss-Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm-1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

Randomized interpolative decomposition of separated representations

NASA Astrophysics Data System (ADS)

Biagioni, David J.; Beylkin, Daniel; Beylkin, Gregory

2015-01-01

We introduce an algorithm to compute tensor interpolative decomposition (dubbed CTD-ID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy ɛ, a near optimal subset of terms of a CTD to represent the remaining terms via a linear combination of the selected terms. CTD-ID can be used as an alternative to or in combination with the Alternating Least Squares (ALS) algorithm. We present examples of its use within a convergent iteration to compute inverse operators in high dimensions. We also briefly discuss the spectral norm as a computational alternative to the Frobenius norm in estimating approximation errors of tensor ID. We reduce the problem of finding tensor IDs to that of constructing interpolative decompositions of certain matrices. These matrices are generated via randomized projection of the terms of the given tensor. We provide cost estimates and several examples of the new approach to the reduction of separation rank.

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

NASA Technical Reports Server (NTRS)

Leone, Frank A., Jr.

2015-01-01

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

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

Rai, Prashant; Sargsyan, Khachik; Najm, Habib

Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrationalmore » zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm -1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.« less

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

DOE PAGES

Rai, Prashant; Sargsyan, Khachik; Najm, Habib; ...

2017-03-07

Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrationalmore » zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm -1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.« less

The tensor hierarchy algebra

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

Palmkvist, Jakob, E-mail: palmkvist@ihes.fr

We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of ourmore » Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.« less

Towards Interactive Construction of Topical Hierarchy: A Recursive Tensor Decomposition Approach.

PubMed

Wang, Chi; Liu, Xueqing; Song, Yanglei; Han, Jiawei

2015-08-01

Automatic construction of user-desired topical hierarchies over large volumes of text data is a highly desirable but challenging task. This study proposes to give users freedom to construct topical hierarchies via interactive operations such as expanding a branch and merging several branches. Existing hierarchical topic modeling techniques are inadequate for this purpose because (1) they cannot consistently preserve the topics when the hierarchy structure is modified; and (2) the slow inference prevents swift response to user requests. In this study, we propose a novel method, called STROD, that allows efficient and consistent modification of topic hierarchies, based on a recursive generative model and a scalable tensor decomposition inference algorithm with theoretical performance guarantee. Empirical evaluation shows that STROD reduces the runtime of construction by several orders of magnitude, while generating consistent and quality hierarchies.

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.

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.

Atomic-batched tensor decomposed two-electron repulsion integrals

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Atomic-batched tensor decomposed two-electron repulsion integrals.

PubMed

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

2017-04-07

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

Multidimensional Compressed Sensing MRI Using Tensor Decomposition-Based Sparsifying Transform

PubMed Central

Yu, Yeyang; Jin, Jin; Liu, Feng; Crozier, Stuart

2014-01-01

Compressed Sensing (CS) has been applied in dynamic Magnetic Resonance Imaging (MRI) to accelerate the data acquisition without noticeably degrading the spatial-temporal resolution. A suitable sparsity basis is one of the key components to successful CS applications. Conventionally, a multidimensional dataset in dynamic MRI is treated as a series of two-dimensional matrices, and then various matrix/vector transforms are used to explore the image sparsity. Traditional methods typically sparsify the spatial and temporal information independently. In this work, we propose a novel concept of tensor sparsity for the application of CS in dynamic MRI, and present the Higher-order Singular Value Decomposition (HOSVD) as a practical example. Applications presented in the three- and four-dimensional MRI data demonstrate that HOSVD simultaneously exploited the correlations within spatial and temporal dimensions. Validations based on cardiac datasets indicate that the proposed method achieved comparable reconstruction accuracy with the low-rank matrix recovery methods and, outperformed the conventional sparse recovery methods. PMID:24901331

Towards Interactive Construction of Topical Hierarchy: A Recursive Tensor Decomposition Approach

PubMed Central

Wang, Chi; Liu, Xueqing; Song, Yanglei; Han, Jiawei

2015-01-01

Automatic construction of user-desired topical hierarchies over large volumes of text data is a highly desirable but challenging task. This study proposes to give users freedom to construct topical hierarchies via interactive operations such as expanding a branch and merging several branches. Existing hierarchical topic modeling techniques are inadequate for this purpose because (1) they cannot consistently preserve the topics when the hierarchy structure is modified; and (2) the slow inference prevents swift response to user requests. In this study, we propose a novel method, called STROD, that allows efficient and consistent modification of topic hierarchies, based on a recursive generative model and a scalable tensor decomposition inference algorithm with theoretical performance guarantee. Empirical evaluation shows that STROD reduces the runtime of construction by several orders of magnitude, while generating consistent and quality hierarchies. PMID:26705505

Trace Norm Regularized CANDECOMP/PARAFAC Decomposition With Missing Data.

PubMed

Liu, Yuanyuan; Shang, Fanhua; Jiao, Licheng; Cheng, James; Cheng, Hong

2015-11-01

In recent years, low-rank tensor completion (LRTC) problems have received a significant amount of attention in computer vision, data mining, and signal processing. The existing trace norm minimization algorithms for iteratively solving LRTC problems involve multiple singular value decompositions of very large matrices at each iteration. Therefore, they suffer from high computational cost. In this paper, we propose a novel trace norm regularized CANDECOMP/PARAFAC decomposition (TNCP) method for simultaneous tensor decomposition and completion. We first formulate a factor matrix rank minimization model by deducing the relation between the rank of each factor matrix and the mode- n rank of a tensor. Then, we introduce a tractable relaxation of our rank function, and then achieve a convex combination problem of much smaller-scale matrix trace norm minimization. Finally, we develop an efficient algorithm based on alternating direction method of multipliers to solve our problem. The promising experimental results on synthetic and real-world data validate the effectiveness of our TNCP method. Moreover, TNCP is significantly faster than the state-of-the-art methods and scales to larger problems.

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.

The 3 + 1 decomposition of conformal Yano-Killing tensors and ‘momentary’ charges for the spin-2 field

NASA Astrophysics Data System (ADS)

Jezierski, Jacek; Migacz, Szymon

2015-02-01

The ‘fully charged’ spin-2 field solution is presented. This is an analog of the Coulomb solution in electrodynamics and represents the ‘non-waving’ part of the spin-2 field theory. Basic facts and definitions of the spin-2 field and conformal Yano-Killing tensors are introduced. Application of those two objects provides a precise definition of quasi-local gravitational charge. Next, the 3 + 1 decomposition leads to the construction of the momentary gravitational charges on the initial surface, which is applicable for Schwarzschild-like spacetimes.

Implementing the sine transform of fermionic modes as a tensor network

NASA Astrophysics Data System (ADS)

Epple, Hannes; Fries, Pascal; Hinrichsen, Haye

2017-09-01

Based on the algebraic theory of signal processing, we recursively decompose the discrete sine transform of the first kind (DST-I) into small orthogonal block operations. Using a diagrammatic language, we then second-quantize this decomposition to construct a tensor network implementing the DST-I for fermionic modes on a lattice. The complexity of the resulting network is shown to scale as 5/4 n logn (not considering swap gates), where n is the number of lattice sites. Our method provides a systematic approach of generalizing Ferris' spectral tensor network for nontrivial boundary conditions.

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.

Decomposition Mechanism and Decomposition Promoting Factors of Waste Hard Metal for Zinc Decomposition Process (ZDP)

NASA Astrophysics Data System (ADS)

Pee, J. H.; Kim, Y. J.; Kim, J. Y.; Seong, N. E.; Cho, W. S.; Kim, K. J.

2011-10-01

Decomposition promoting factors and decomposition mechanism in the zinc decomposition process of waste hard metals which are composed mostly of tungsten carbide and cobalt were evaluated. Zinc volatility amount was suppressed and zinc steam pressure was produced in the reaction graphite crucible inside an electric furnace for ZDP. Reaction was done for 2 hrs at 650 °C, which 100 % decomposed the waste hard metals that were over 30 mm thick. As for the separation-decomposition of waste hard metals, zinc melted alloy formed a liquid composed of a mixture of γ-β1 phase from the cobalt binder layer (reaction interface). The volume of reacted zone was expanded and the waste hard metal layer was decomposed-separated horizontally from the hard metal. Zinc used in the ZDP process was almost completely removed-collected by decantation and volatilization-collection process at 1000 °C. The small amount of zinc remaining in the tungsten carbide-cobalt powder which was completely decomposed was fully removed by using phosphate solution which had a slow cobalt dissolution speed.

Tensor hypercontraction. II. Least-squares renormalization.

PubMed

Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David

2012-12-14

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)]. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1∕r(12) operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N(5)) effort if exact integrals are decomposed, or O(N(4)) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N(4)) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

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

PubMed

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

2016-08-01

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

A non-statistical regularization approach and a tensor product decomposition method applied to complex flow data

NASA Astrophysics Data System (ADS)

von Larcher, Thomas; Blome, Therese; Klein, Rupert; Schneider, Reinhold; Wolf, Sebastian; Huber, Benjamin

2016-04-01

Handling high-dimensional data sets like they occur e.g. in turbulent flows or in multiscale behaviour of certain types in Geosciences are one of the big challenges in numerical analysis and scientific computing. A suitable solution is to represent those large data sets in an appropriate compact form. In this context, tensor product decomposition methods currently emerge as an important tool. One reason is that these methods often enable one to attack high-dimensional problems successfully, another that they allow for very compact representations of large data sets. We follow the novel Tensor-Train (TT) decomposition method to support the development of improved understanding of the multiscale behavior and the development of compact storage schemes for solutions of such problems. One long-term goal of the project is the construction of a self-consistent closure for Large Eddy Simulations (LES) of turbulent flows that explicitly exploits the tensor product approach's capability of capturing self-similar structures. Secondly, we focus on a mixed deterministic-stochastic subgrid scale modelling strategy currently under development for application in Finite Volume Large Eddy Simulation (LES) codes. Advanced methods of time series analysis for the databased construction of stochastic models with inherently non-stationary statistical properties and concepts of information theory based on a modified Akaike information criterion and on the Bayesian information criterion for the model discrimination are used to construct surrogate models for the non-resolved flux fluctuations. Vector-valued auto-regressive models with external influences form the basis for the modelling approach [1], [2], [4]. Here, we present the reconstruction capabilities of the two modeling approaches tested against 3D turbulent channel flow data computed by direct numerical simulation (DNS) for an incompressible, isothermal fluid at Reynolds number Reτ = 590 (computed by [3]). References [1] I

Tensor hypercontraction. II. Least-squares renormalization

NASA Astrophysics Data System (ADS)

Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

2012-12-01

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

Tensor products of process matrices with indefinite causal structure

NASA Astrophysics Data System (ADS)

Jia, Ding; Sakharwade, Nitica

2018-03-01

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

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.

Biogeochemistry of Decomposition and Detrital Processing

NASA Astrophysics Data System (ADS)

Sanderman, J.; Amundson, R.

2003-12-01

Decomposition is a key ecological process that roughly balances net primary production in terrestrial ecosystems and is an essential process in resupplying nutrients to the plant community. Decomposition consists of three concurrent processes: communition or fragmentation, leaching of water-soluble compounds, and microbial catabolism. Decomposition can also be viewed as a sequential process, what Eijsackers and Zehnder (1990) compare to a Russian matriochka doll. Soil macrofauna fragment and partially solubilize plant residues, facilitating establishment of a community of decomposer microorganisms. This decomposer community will gradually shift as the most easily degraded plant compounds are utilized and the more recalcitrant materials begin to accumulate. Given enough time and the proper environmental conditions, most naturally occurring compounds can completely be mineralized to inorganic forms. Simultaneously with mineralization, the process of humification acts to transform a fraction of the plant residues into stable soil organic matter (SOM) or humus. For reference, Schlesinger (1990) estimated that only ˜0.7% of detritus eventually becomes stabilized into humus.Decomposition plays a key role in the cycling of most plant macro- and micronutrients and in the formation of humus. Figure 1 places the roles of detrital processing and mineralization within the context of the biogeochemical cycling of essential plant nutrients. Chapin (1991) found that while the atmosphere supplied 4% and mineral weathering supplied no nitrogen and <1% of phosphorus, internal nutrient recycling is the source for >95% of all the nitrogen and phosphorus uptake by tundra species in Barrow, Alaska. In a cool temperate forest, nutrient recycling accounted for 93%, 89%, 88%, and 65% of total sources for nitrogen, phosphorus, potassium, and calcium, respectively ( Chapin, 1991). (13K)Figure 1. A decomposition-centric biogeochemical model of nutrient cycling. Although there is significant

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.

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

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.

Aridity and decomposition processes in complex landscapes

NASA Astrophysics Data System (ADS)

Ossola, Alessandro; Nyman, Petter

2015-04-01

Decomposition of organic matter is a key biogeochemical process contributing to nutrient cycles, carbon fluxes and soil development. The activity of decomposers depends on microclimate, with temperature and rainfall being major drivers. In complex terrain the fine-scale variation in microclimate (and hence water availability) as a result of slope orientation is caused by differences in incoming radiation and surface temperature. Aridity, measured as the long-term balance between net radiation and rainfall, is a metric that can be used to represent variations in water availability within the landscape. Since aridity metrics can be obtained at fine spatial scales, they could theoretically be used to investigate how decomposition processes vary across complex landscapes. In this study, four research sites were selected in tall open sclerophyll forest along a aridity gradient (Budyko dryness index ranging from 1.56 -2.22) where microclimate, litter moisture and soil moisture were monitored continuously for one year. Litter bags were packed to estimate decomposition rates (k) using leaves of a tree species not present in the study area (Eucalyptus globulus) in order to avoid home-field advantage effects. Litter mass loss was measured to assess the activity of macro-decomposers (6mm litter bag mesh size), meso-decomposers (1 mm mesh), microbes above-ground (0.2 mm mesh) and microbes below-ground (2 cm depth, 0.2 mm mesh). Four replicates for each set of bags were installed at each site and bags were collected at 1, 2, 4, 7 and 12 months since installation. We first tested whether differences in microclimate due to slope orientation have significant effects on decomposition processes. Then the dryness index was related to decomposition rates to evaluate if small-scale variation in decomposition can be predicted using readily available information on rainfall and radiation. Decomposition rates (k), calculated fitting single pool negative exponential models, generally

Importance of Force Decomposition for Local Stress Calculations in Biomembrane Molecular Simulations.

PubMed

Vanegas, Juan M; Torres-Sánchez, Alejandro; Arroyo, Marino

2014-02-11

Local stress fields are routinely computed from molecular dynamics trajectories to understand the structure and mechanical properties of lipid bilayers. These calculations can be systematically understood with the Irving-Kirkwood-Noll theory. In identifying the stress tensor, a crucial step is the decomposition of the forces on the particles into pairwise contributions. However, such a decomposition is not unique in general, leading to an ambiguity in the definition of the stress tensor, particularly for multibody potentials. Furthermore, a theoretical treatment of constraints in local stress calculations has been lacking. Here, we present a new implementation of local stress calculations that systematically treats constraints and considers a privileged decomposition, the central force decomposition, that leads to a symmetric stress tensor by construction. We focus on biomembranes, although the methodology presented here is widely applicable. Our results show that some unphysical behavior obtained with previous implementations (e.g. nonconstant normal stress profiles along an isotropic bilayer in equilibrium) is a consequence of an improper treatment of constraints. Furthermore, other valid force decompositions produce significantly different stress profiles, particularly in the presence of dihedral potentials. Our methodology reveals the striking effect of unsaturations on the bilayer mechanics, missed by previous stress calculation implementations.

Unsupervised Tensor Mining for Big Data Practitioners.

PubMed

Papalexakis, Evangelos E; Faloutsos, Christos

2016-09-01

Multiaspect data are ubiquitous in modern Big Data applications. For instance, different aspects of a social network are the different types of communication between people, the time stamp of each interaction, and the location associated to each individual. How can we jointly model all those aspects and leverage the additional information that they introduce to our analysis? Tensors, which are multidimensional extensions of matrices, are a principled and mathematically sound way of modeling such multiaspect data. In this article, our goal is to popularize tensors and tensor decompositions to Big Data practitioners by demonstrating their effectiveness, outlining challenges that pertain to their application in Big Data scenarios, and presenting our recent work that tackles those challenges. We view this work as a step toward a fully automated, unsupervised tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry.

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

Tensor Decompositions for Learning Latent Variable Models

DTIC Science & Technology

2012-12-08

and eigenvectors of tensors is generally significantly more complicated than their matrix counterpart (both algebraically [Qi05, CS11, Lim05] and...The reduction First, let W ∈ Rd×k be a linear transformation such that M2(W,W ) = W M2W = I where I is the k × k identity matrix (i.e., W whitens ...approximate the whitening matrix W ∈ Rd×k from second-moment matrix M2 ∈ Rd×d. To do this, one first multiplies M2 by a random matrix R ∈ Rd×k′ for some k′ ≥ k

Data-driven process decomposition and robust online distributed modelling for large-scale processes

NASA Astrophysics Data System (ADS)

Shu, Zhang; Lijuan, Li; Lijuan, Yao; Shipin, Yang; Tao, Zou

2018-02-01

With the increasing attention of networked control, system decomposition and distributed models show significant importance in the implementation of model-based control strategy. In this paper, a data-driven system decomposition and online distributed subsystem modelling algorithm was proposed for large-scale chemical processes. The key controlled variables are first partitioned by affinity propagation clustering algorithm into several clusters. Each cluster can be regarded as a subsystem. Then the inputs of each subsystem are selected by offline canonical correlation analysis between all process variables and its controlled variables. Process decomposition is then realised after the screening of input and output variables. When the system decomposition is finished, the online subsystem modelling can be carried out by recursively block-wise renewing the samples. The proposed algorithm was applied in the Tennessee Eastman process and the validity was verified.

Parallel Tensor Compression for Large-Scale Scientific Data.

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

Kolda, Tamara G.; Ballard, Grey; Austin, Woody Nathan

As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that tracks 64 variables per grid point for 128 time steps yields 8 TB of data. By viewing the data as a dense five way tensor, we can compute a Tucker decomposition to find inherent low-dimensional multilinear structure, achieving compression ratios of up to 10000 on real-world data sets with negligible loss in accuracy. So that we can operate on such massive data, we present the first-ever distributed memorymore » parallel implementation for the Tucker decomposition, whose key computations correspond to parallel linear algebra operations, albeit with nonstandard data layouts. Our approach specifies a data distribution for tensors that avoids any tensor data redistribution, either locally or in parallel. We provide accompanying analysis of the computation and communication costs of the algorithms. To demonstrate the compression and accuracy of the method, we apply our approach to real-world data sets from combustion science simulations. We also provide detailed performance results, including parallel performance in both weak and strong scaling experiments.« less

Parallel processing for pitch splitting decomposition

NASA Astrophysics Data System (ADS)

Barnes, Levi; Li, Yong; Wadkins, David; Biederman, Steve; Miloslavsky, Alex; Cork, Chris

2009-10-01

Decomposition of an input pattern in preparation for a double patterning process is an inherently global problem in which the influence of a local decomposition decision can be felt across an entire pattern. In spite of this, a large portion of the work can be massively distributed. Here, we discuss the advantages of geometric distribution for polygon operations with limited range of influence. Further, we have found that even the naturally global "coloring" step can, in large part, be handled in a geometrically local manner. In some practical cases, up to 70% of the work can be distributed geometrically. We also describe the methods for partitioning the problem into local pieces and present scaling data up to 100 CPUs. These techniques reduce DPT decomposition runtime by orders of magnitude.

Extended vector-tensor theories

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

Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp

Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Procamore » theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.« less

Human action recognition based on point context tensor shape descriptor

NASA Astrophysics Data System (ADS)

Li, Jianjun; Mao, Xia; Chen, Lijiang; Wang, Lan

2017-07-01

Motion trajectory recognition is one of the most important means to determine the identity of a moving object. A compact and discriminative feature representation method can improve the trajectory recognition accuracy. This paper presents an efficient framework for action recognition using a three-dimensional skeleton kinematic joint model. First, we put forward a rotation-scale-translation-invariant shape descriptor based on point context (PC) and the normal vector of hypersurface to jointly characterize local motion and shape information. Meanwhile, an algorithm for extracting the key trajectory based on the confidence coefficient is proposed to reduce the randomness and computational complexity. Second, to decrease the eigenvalue decomposition time complexity, a tensor shape descriptor (TSD) based on PC that can globally capture the spatial layout and temporal order to preserve the spatial information of each frame is proposed. Then, a multilinear projection process is achieved by tensor dynamic time warping to map the TSD to a low-dimensional tensor subspace of the same size. Experimental results show that the proposed shape descriptor is effective and feasible, and the proposed approach obtains considerable performance improvement over the state-of-the-art approaches with respect to accuracy on a public action dataset.

gamAID: Greedy CP tensor decomposition for supervised EHR-based disease trajectory differentiation.

PubMed

Henderson, Jette; Ho, Joyce; Ghosh, Joydeep

2017-07-01

We propose gamAID, an exploratory, supervised nonnegative tensor factorization method that iteratively extracts phenotypes from tensors constructed from medical count data. Using data from diabetic patients who later on get diagnosed with chronic kidney disorder (CKD) as well as diabetic patients who do not receive a CKD diagnosis, we demonstrate the potential of gamAID to discover phenotypes that characterize patients who are at risk for developing a disease.

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.

Quantifying polymer deformation in viscoelastic turbulence: the geometric decomposition and a Riemannian approach to scalar measures

NASA Astrophysics Data System (ADS)

Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer; Gayme, Dennice

2017-11-01

We develop a new framework to quantify the fluctuating behaviour of the conformation tensor in viscoelastic turbulent flows. This framework addresses two shortcomings of the classical approach based on Reynolds decomposition: the fluctuating part of the conformation tensor is not guaranteed to be positive definite and it does not consistently represent polymer expansions and contractions about the mean. Our approach employs a geometric decomposition that yields a positive-definite fluctuating conformation tensor with a clear physical interpretation as a deformation to the mean conformation. We propose three scalar measures of this fluctuating conformation tensor, which respect the non-Euclidean Riemannian geometry of the manifold of positive-definite tensors: fluctuating polymer volume, geodesic distance from the mean, and an anisotropy measure. We use these scalar quantities to investigate drag-reduced viscoelastic turbulent channel flow. Our approach establishes a systematic method to study viscoelastic turbulence. It also uncovers interesting phenomena that are not apparent using traditional analysis tools, including a logarithmic decrease in anisotropy of the mean conformation tensor away from the wall and polymer fluctuations peaking beyond the buffer layer. This work has been partially funded by the following NSF Grants: CBET-1652244, OCE-1633124, CBET-1511937.

Bimodule structure of the mixed tensor product over Uq sℓ (2 | 1) and quantum walled Brauer algebra

NASA Astrophysics Data System (ADS)

Bulgakova, D. V.; Kiselev, A. M.; Tipunin, I. Yu.

2018-03-01

We study a mixed tensor product 3⊗m ⊗3 ‾ ⊗ n of the three-dimensional fundamental representations of the Hopf algebra Uq sℓ (2 | 1), whenever q is not a root of unity. Formulas for the decomposition of tensor products of any simple and projective Uq sℓ (2 | 1)-module with the generating modules 3 and 3 ‾ are obtained. The centralizer of Uq sℓ (2 | 1) on the mixed tensor product is calculated. It is shown to be the quotient Xm,n of the quantum walled Brauer algebra qw Bm,n. The structure of projective modules over Xm,n is written down explicitly. It is known that the walled Brauer algebras form an infinite tower. We have calculated the corresponding restriction functors on simple and projective modules over Xm,n. This result forms a crucial step in decomposition of the mixed tensor product as a bimodule over Xm,n ⊠Uq sℓ (2 | 1). We give an explicit bimodule structure for all m , n.

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.

Predicting the reference evapotranspiration based on tensor decomposition

NASA Astrophysics Data System (ADS)

Misaghian, Negin; Shamshirband, Shahaboddin; Petković, Dalibor; Gocic, Milan; Mohammadi, Kasra

2017-11-01

Most of the available models for reference evapotranspiration (ET0) estimation are based upon only an empirical equation for ET0. Thus, one of the main issues in ET0 estimation is the appropriate integration of time information and different empirical ET0 equations to determine ET0 and boost the precision. The FAO-56 Penman-Monteith, adjusted Hargreaves, Blaney-Criddle, Priestley-Taylor, and Jensen-Haise equations were utilized in this study for estimating ET0 for two stations of Belgrade and Nis in Serbia using collected data for the period of 1980 to 2010. Three-order tensor is used to capture three-way correlations among months, years, and ET0 information. Afterward, the latent correlations among ET0 parameters were found by the multiway analysis to enhance the quality of the prediction. The suggested method is valuable as it takes into account simultaneous relations between elements, boosts the prediction precision, and determines latent associations. Models are compared with respect to coefficient of determination ( R 2), mean absolute error (MAE), and root-mean-square error (RMSE). The proposed tensor approach has a R 2 value of greater than 0.9 for all selected ET0 methods at both selected stations, which is acceptable for the ET0 prediction. RMSE is ranged between 0.247 and 0.485 mm day-1 at Nis station and between 0.277 and 0.451 mm day-1 at Belgrade station, while MAE is between 0.140 and 0.337 mm day-1 at Nis and between 0.208 and 0.360 mm day-1 at Belgrade station. The best performances are achieved by Priestley-Taylor model at Nis station ( R 2 = 0.985, MAE = 0.140 mm day-1, RMSE = 0.247 mm day-1) and FAO-56 Penman-Monteith model at Belgrade station (MAE = 0.208 mm day-1, RMSE = 0.277 mm day-1, R 2 = 0.975).

Tensor-based classification of an auditory mobile BCI without a subject-specific calibration phase

NASA Astrophysics Data System (ADS)

Zink, Rob; Hunyadi, Borbála; Van Huffel, Sabine; De Vos, Maarten

2016-04-01

Objective. One of the major drawbacks in EEG brain-computer interfaces (BCI) is the need for subject-specific training of the classifier. By removing the need for a supervised calibration phase, new users could potentially explore a BCI faster. In this work we aim to remove this subject-specific calibration phase and allow direct classification. Approach. We explore canonical polyadic decompositions and block term decompositions of the EEG. These methods exploit structure in higher dimensional data arrays called tensors. The BCI tensors are constructed by concatenating ERP templates from other subjects to a target and non-target trial and the inherent structure guides a decomposition that allows accurate classification. We illustrate the new method on data from a three-class auditory oddball paradigm. Main results. The presented approach leads to a fast and intuitive classification with accuracies competitive with a supervised and cross-validated LDA approach. Significance. The described methods are a promising new way of classifying BCI data with a forthright link to the original P300 ERP signal over the conventional and widely used supervised approaches.

Tensor-based classification of an auditory mobile BCI without a subject-specific calibration phase.

PubMed

Zink, Rob; Hunyadi, Borbála; Huffel, Sabine Van; Vos, Maarten De

2016-04-01

One of the major drawbacks in EEG brain-computer interfaces (BCI) is the need for subject-specific training of the classifier. By removing the need for a supervised calibration phase, new users could potentially explore a BCI faster. In this work we aim to remove this subject-specific calibration phase and allow direct classification. We explore canonical polyadic decompositions and block term decompositions of the EEG. These methods exploit structure in higher dimensional data arrays called tensors. The BCI tensors are constructed by concatenating ERP templates from other subjects to a target and non-target trial and the inherent structure guides a decomposition that allows accurate classification. We illustrate the new method on data from a three-class auditory oddball paradigm. The presented approach leads to a fast and intuitive classification with accuracies competitive with a supervised and cross-validated LDA approach. The described methods are a promising new way of classifying BCI data with a forthright link to the original P300 ERP signal over the conventional and widely used supervised approaches.

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.

Using Matrix and Tensor Factorizations for the Single-Trial Analysis of Population Spike Trains

PubMed Central

Onken, Arno; Liu, Jian K.; Karunasekara, P. P. Chamanthi R.; Delis, Ioannis; Gollisch, Tim; Panzeri, Stefano

2016-01-01

Advances in neuronal recording techniques are leading to ever larger numbers of simultaneously monitored neurons. This poses the important analytical challenge of how to capture compactly all sensory information that neural population codes carry in their spatial dimension (differences in stimulus tuning across neurons at different locations), in their temporal dimension (temporal neural response variations), or in their combination (temporally coordinated neural population firing). Here we investigate the utility of tensor factorizations of population spike trains along space and time. These factorizations decompose a dataset of single-trial population spike trains into spatial firing patterns (combinations of neurons firing together), temporal firing patterns (temporal activation of these groups of neurons) and trial-dependent activation coefficients (strength of recruitment of such neural patterns on each trial). We validated various factorization methods on simulated data and on populations of ganglion cells simultaneously recorded in the salamander retina. We found that single-trial tensor space-by-time decompositions provided low-dimensional data-robust representations of spike trains that capture efficiently both their spatial and temporal information about sensory stimuli. Tensor decompositions with orthogonality constraints were the most efficient in extracting sensory information, whereas non-negative tensor decompositions worked well even on non-independent and overlapping spike patterns, and retrieved informative firing patterns expressed by the same population in response to novel stimuli. Our method showed that populations of retinal ganglion cells carried information in their spike timing on the ten-milliseconds-scale about spatial details of natural images. This information could not be recovered from the spike counts of these cells. First-spike latencies carried the majority of information provided by the whole spike train about fine-scale image

Using Matrix and Tensor Factorizations for the Single-Trial Analysis of Population Spike Trains.

PubMed

Onken, Arno; Liu, Jian K; Karunasekara, P P Chamanthi R; Delis, Ioannis; Gollisch, Tim; Panzeri, Stefano

2016-11-01

Advances in neuronal recording techniques are leading to ever larger numbers of simultaneously monitored neurons. This poses the important analytical challenge of how to capture compactly all sensory information that neural population codes carry in their spatial dimension (differences in stimulus tuning across neurons at different locations), in their temporal dimension (temporal neural response variations), or in their combination (temporally coordinated neural population firing). Here we investigate the utility of tensor factorizations of population spike trains along space and time. These factorizations decompose a dataset of single-trial population spike trains into spatial firing patterns (combinations of neurons firing together), temporal firing patterns (temporal activation of these groups of neurons) and trial-dependent activation coefficients (strength of recruitment of such neural patterns on each trial). We validated various factorization methods on simulated data and on populations of ganglion cells simultaneously recorded in the salamander retina. We found that single-trial tensor space-by-time decompositions provided low-dimensional data-robust representations of spike trains that capture efficiently both their spatial and temporal information about sensory stimuli. Tensor decompositions with orthogonality constraints were the most efficient in extracting sensory information, whereas non-negative tensor decompositions worked well even on non-independent and overlapping spike patterns, and retrieved informative firing patterns expressed by the same population in response to novel stimuli. Our method showed that populations of retinal ganglion cells carried information in their spike timing on the ten-milliseconds-scale about spatial details of natural images. This information could not be recovered from the spike counts of these cells. First-spike latencies carried the majority of information provided by the whole spike train about fine-scale image

The processing of aluminum gasarites via thermal decomposition of interstitial hydrides

NASA Astrophysics Data System (ADS)

Licavoli, Joseph J.

Gasarite structures are a unique type of metallic foam containing tubular pores. The original methods for their production limited them to laboratory study despite appealing foam properties. Thermal decomposition processing of gasarites holds the potential to increase the application of gasarite foams in engineering design by removing several barriers to their industrial scale production. The following study characterized thermal decomposition gasarite processing both experimentally and theoretically. It was found that significant variation was inherent to this process therefore several modifications were necessary to produce gasarites using this method. Conventional means to increase porosity and enhance pore morphology were studied. Pore morphology was determined to be more easily replicated if pores were stabilized by alumina additions and powders were dispersed evenly. In order to better characterize processing, high temperature and high ramp rate thermal decomposition data were gathered. It was found that the high ramp rate thermal decomposition behavior of several hydrides was more rapid than hydride kinetics at low ramp rates. This data was then used to estimate the contribution of several pore formation mechanisms to the development of pore structure. It was found that gas-metal eutectic growth can only be a viable pore formation mode if non-equilibrium conditions persist. Bubble capture cannot be a dominant pore growth mode due to high bubble terminal velocities. Direct gas evolution appears to be the most likely pore formation mode due to high gas evolution rate from the decomposing particulate and microstructural pore growth trends. The overall process was evaluated for its economic viability. It was found that thermal decomposition has potential for industrialization, but further refinements are necessary in order for the process to be viable.

Tracking Hierarchical Processing in Morphological Decomposition with Brain Potentials

ERIC Educational Resources Information Center

Lavric, Aureliu; Elchlepp, Heike; Rastle, Kathleen

2012-01-01

One important debate in psycholinguistics concerns the nature of morphological decomposition processes in visual word recognition (e.g., darkness = {dark} + {-ness}). One theory claims that these processes arise during orthographic analysis and prior to accessing meaning (Rastle & Davis, 2008), and another argues that these processes arise through…

Effective metrics and a fully covariant description of constitutive tensors in electrodynamics

NASA Astrophysics Data System (ADS)

Schuster, Sebastian; Visser, Matt

2017-12-01

Using electromagnetism to study analogue space-times is tantamount to considering consistency conditions for when a given (meta-) material would provide an analogue space-time model or—vice versa—characterizing which given metric could be modeled with a (meta-) material. While the consistency conditions themselves are by now well known and studied, the form the metric takes once they are satisfied is not. This question is mostly easily answered by keeping the formalisms of the two research fields here in contact as close to each other as possible. While fully covariant formulations of the electrodynamics of media have been around for a long while, they are usually abandoned for (3 +1 )- or six-dimensional formalisms. Here we use the fully unified and fully covariant approach. This enables us even to generalize the consistency conditions for the existence of an effective metric to arbitrary background metrics beyond flat space-time electrodynamics. We also show how the familiar matrices for permittivity ɛ , permeability μ-1, and magnetoelectric effects ζ can be seen as the three independent pieces of the Bel decomposition for the constitutive tensor Za b c d, i.e., the components of an orthogonal decomposition with respect to a given observer with four-velocity Va. Finally, we use the Moore-Penrose pseudoinverse and the closely related pseudodeterminant to then gain the desired reconstruction of the effective metric in terms of the permittivity tensor ɛa b, the permeability tensor [μ-1]a b, and the magnetoelectric tensor ζa b, as an explicit function geff(ɛ ,μ-1,ζ ).

Low-rank factorization of electron integral tensors and its application in electronic structure theory

DOE PAGES

Peng, Bo; Kowalski, Karol

2017-01-25

In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.

Low-rank factorization of electron integral tensors and its application in electronic structure theory

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

Peng, Bo; Kowalski, Karol

In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.

Low-rank factorization of electron integral tensors and its application in electronic structure theory

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

Peng, Bo; Kowalski, Karol

In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doublesmore » (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.« less

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.

The Exact Solution to Rank-1 L1-Norm TUCKER2 Decomposition

NASA Astrophysics Data System (ADS)

Markopoulos, Panos P.; Chachlakis, Dimitris G.; Papalexakis, Evangelos E.

2018-04-01

We study rank-1 {L1-norm-based TUCKER2} (L1-TUCKER2) decomposition of 3-way tensors, treated as a collection of $N$ $D \\times M$ matrices that are to be jointly decomposed. Our contributions are as follows. i) We prove that the problem is equivalent to combinatorial optimization over $N$ antipodal-binary variables. ii) We derive the first two algorithms in the literature for its exact solution. The first algorithm has cost exponential in $N$; the second one has cost polynomial in $N$ (under a mild assumption). Our algorithms are accompanied by formal complexity analysis. iii) We conduct numerical studies to compare the performance of exact L1-TUCKER2 (proposed) with standard HOSVD, HOOI, GLRAM, PCA, L1-PCA, and TPCA-L1. Our studies show that L1-TUCKER2 outperforms (in tensor approximation) all the above counterparts when the processed data are outlier corrupted.

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

Tensor models, Kronecker coefficients and permutation centralizer algebras

NASA Astrophysics Data System (ADS)

Geloun, Joseph Ben; Ramgoolam, Sanjaye

2017-11-01

We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients (Clebsch-Gordan multiplicities of symmetric groups). The color-exchange symmetry present in the Gaussian model, as well as a large class of interacting models, is used to refine the description of the permutation centralizer algebras. This discussion is extended to a general number of colors d: it is used to prove the integrality of an infinite family of number sequences related to color-symmetrizations of colored graphs, and expressible in terms of symmetric group representation theory data. Generalizing a connection between matrix models and Belyi maps, correlators in Gaussian tensor models are interpreted in terms of covers of singular 2-complexes. There is an intriguing difference, between matrix and higher rank tensor models, in the computational complexity of superficially comparable correlators of observables parametrized by Young diagrams.

Capturing molecular multimode relaxation processes in excitable gases based on decomposition of acoustic relaxation spectra

NASA Astrophysics Data System (ADS)

Zhu, Ming; Liu, Tingting; Wang, Shu; Zhang, Kesheng

2017-08-01

Existing two-frequency reconstructive methods can only capture primary (single) molecular relaxation processes in excitable gases. In this paper, we present a reconstructive method based on the novel decomposition of frequency-dependent acoustic relaxation spectra to capture the entire molecular multimode relaxation process. This decomposition of acoustic relaxation spectra is developed from the frequency-dependent effective specific heat, indicating that a multi-relaxation process is the sum of the interior single-relaxation processes. Based on this decomposition, we can reconstruct the entire multi-relaxation process by capturing the relaxation times and relaxation strengths of N interior single-relaxation processes, using the measurements of acoustic absorption and sound speed at 2N frequencies. Experimental data for the gas mixtures CO2-N2 and CO2-O2 validate our decomposition and reconstruction approach.

Low-Rank Tensor Subspace Learning for RGB-D Action Recognition.

PubMed

Jia, Chengcheng; Fu, Yun

2016-07-09

Since RGB-D action data inherently equip with extra depth information compared with RGB data, recently many works employ RGB-D data in a third-order tensor representation containing spatio-temporal structure to find a subspace for action recognition. However, there are two main challenges of these methods. First, the dimension of subspace is usually fixed manually. Second, preserving local information by finding intraclass and inter-class neighbors from a manifold is highly timeconsuming. In this paper, we learn a tensor subspace, whose dimension is learned automatically by low-rank learning, for RGB-D action recognition. Particularly, the tensor samples are factorized to obtain three Projection Matrices (PMs) by Tucker Decomposition, where all the PMs are performed by nuclear norm in a close-form to obtain the tensor ranks which are used as tensor subspace dimension. Additionally, we extract the discriminant and local information from a manifold using a graph constraint. This graph preserves the local knowledge inherently, which is faster than the previous way by calculating both the intra-class and inter-class neighbors of each sample. We evaluate the proposed method on four widely used RGB-D action datasets including MSRDailyActivity3D, MSRActionPairs, MSRActionPairs skeleton and UTKinect-Action3D datasets, and the experimental results show higher accuracy and efficiency of the proposed method.

Multi-Fault Diagnosis of Rolling Bearings via Adaptive Projection Intrinsically Transformed Multivariate Empirical Mode Decomposition and High Order Singular Value Decomposition.

PubMed

Yuan, Rui; Lv, Yong; Song, Gangbing

2018-04-16

Rolling bearings are important components in rotary machinery systems. In the field of multi-fault diagnosis of rolling bearings, the vibration signal collected from single channels tends to miss some fault characteristic information. Using multiple sensors to collect signals at different locations on the machine to obtain multivariate signal can remedy this problem. The adverse effect of a power imbalance between the various channels is inevitable, and unfavorable for multivariate signal processing. As a useful, multivariate signal processing method, Adaptive-projection has intrinsically transformed multivariate empirical mode decomposition (APIT-MEMD), and exhibits better performance than MEMD by adopting adaptive projection strategy in order to alleviate power imbalances. The filter bank properties of APIT-MEMD are also adopted to enable more accurate and stable intrinsic mode functions (IMFs), and to ease mode mixing problems in multi-fault frequency extractions. By aligning IMF sets into a third order tensor, high order singular value decomposition (HOSVD) can be employed to estimate the fault number. The fault correlation factor (FCF) analysis is used to conduct correlation analysis, in order to determine effective IMFs; the characteristic frequencies of multi-faults can then be extracted. Numerical simulations and the application of multi-fault situation can demonstrate that the proposed method is promising in multi-fault diagnoses of multivariate rolling bearing signal.

Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction

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

Parrish, Robert M.; Sherrill, C. David, E-mail: sherrill@gatech.edu; Hohenstein, Edward G.

2014-05-14

We apply orbital-weighted least-squares tensor hypercontraction decomposition of the electron repulsion integrals to accelerate the coupled cluster singles and doubles (CCSD) method. Using accurate and flexible low-rank factorizations of the electron repulsion integral tensor, we are able to reduce the scaling of the most vexing particle-particle ladder term in CCSD from O(N{sup 6}) to O(N{sup 5}), with remarkably low error. Combined with a T{sub 1}-transformed Hamiltonian, this leads to substantial practical accelerations against an optimized density-fitted CCSD implementation.

Reaction behaviors of decomposition of monocrotophos in aqueous solution by UV and UV/O processes.

PubMed

Ku, Y; Wang, W; Shen, Y S

2000-02-01

The decomposition of monocrotophos (cis-3-dimethoxyphosphinyloxy-N-methyl-crotonamide) in aqueous solution by UV and UV/O(3) processes was studied. The experiments were carried out under various solution pH values to investigate the decomposition efficiencies of the reactant and organic intermediates in order to determine the completeness of decomposition. The photolytic decomposition rate of monocrotophos was increased with increasing solution pH because the solution pH affects the distribution and light absorbance of monocrotophos species. The combination of O(3) with UV light apparently promoted the decomposition and mineralization of monocrotophos in aqueous solution. For the UV/O(3) process, the breakage of the >C=C< bond of monocrotophos by ozone molecules was found to occur first, followed by mineralization by hydroxyl radicals to generate CO(3)(2-), PO4(3-), and NO(3)(-) anions in sequence. The quasi-global kinetics based on a simplified consecutive-parallel reaction scheme was developed to describe the temporal behavior of monocrotophos decomposition in aqueous solution by the UV/O(3) process.

Modal decomposition of turbulent supersonic cavity

NASA Astrophysics Data System (ADS)

Soni, R. K.; Arya, N.; De, A.

2018-06-01

Self-sustained oscillations in a Mach 3 supersonic cavity with a length-to-depth ratio of three are investigated using wall-modeled large eddy simulation methodology for ReD = 3.39× 105 . The unsteady data obtained through computation are utilized to investigate the spatial and temporal evolution of the flow field, especially the second invariant of the velocity tensor, while the phase-averaged data are analyzed over a feedback cycle to study the spatial structures. This analysis is accompanied by the proper orthogonal decomposition (POD) data, which reveals the presence of discrete vortices along the shear layer. The POD analysis is performed in both the spanwise and streamwise planes to extract the coherence in flow structures. Finally, dynamic mode decomposition is performed on the data sequence to obtain the dynamic information and deeper insight into the self-sustained mechanism.

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.

Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains

PubMed Central

Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph

2014-01-01

The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to “lift” this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging -discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the “basis” of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude

Multi-Fault Diagnosis of Rolling Bearings via Adaptive Projection Intrinsically Transformed Multivariate Empirical Mode Decomposition and High Order Singular Value Decomposition

PubMed Central

Lv, Yong; Song, Gangbing

2018-01-01

Rolling bearings are important components in rotary machinery systems. In the field of multi-fault diagnosis of rolling bearings, the vibration signal collected from single channels tends to miss some fault characteristic information. Using multiple sensors to collect signals at different locations on the machine to obtain multivariate signal can remedy this problem. The adverse effect of a power imbalance between the various channels is inevitable, and unfavorable for multivariate signal processing. As a useful, multivariate signal processing method, Adaptive-projection has intrinsically transformed multivariate empirical mode decomposition (APIT-MEMD), and exhibits better performance than MEMD by adopting adaptive projection strategy in order to alleviate power imbalances. The filter bank properties of APIT-MEMD are also adopted to enable more accurate and stable intrinsic mode functions (IMFs), and to ease mode mixing problems in multi-fault frequency extractions. By aligning IMF sets into a third order tensor, high order singular value decomposition (HOSVD) can be employed to estimate the fault number. The fault correlation factor (FCF) analysis is used to conduct correlation analysis, in order to determine effective IMFs; the characteristic frequencies of multi-faults can then be extracted. Numerical simulations and the application of multi-fault situation can demonstrate that the proposed method is promising in multi-fault diagnoses of multivariate rolling bearing signal. PMID:29659510

A statistical approach based on accumulated degree-days to predict decomposition-related processes in forensic studies.

PubMed

Michaud, Jean-Philippe; Moreau, Gaétan

2011-01-01

Using pig carcasses exposed over 3 years in rural fields during spring, summer, and fall, we studied the relationship between decomposition stages and degree-day accumulation (i) to verify the predictability of the decomposition stages used in forensic entomology to document carcass decomposition and (ii) to build a degree-day accumulation model applicable to various decomposition-related processes. Results indicate that the decomposition stages can be predicted with accuracy from temperature records and that a reliable degree-day index can be developed to study decomposition-related processes. The development of degree-day indices opens new doors for researchers and allows for the application of inferential tools unaffected by climatic variability, as well as for the inclusion of statistics in a science that is primarily descriptive and in need of validation methods in courtroom proceedings. © 2010 American Academy of Forensic Sciences.

[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.

Matrix decomposition graphics processing unit solver for Poisson image editing

NASA Astrophysics Data System (ADS)

Lei, Zhao; Wei, Li

2012-10-01

In recent years, gradient-domain methods have been widely discussed in the image processing field, including seamless cloning and image stitching. These algorithms are commonly carried out by solving a large sparse linear system: the Poisson equation. However, solving the Poisson equation is a computational and memory intensive task which makes it not suitable for real-time image editing. A new matrix decomposition graphics processing unit (GPU) solver (MDGS) is proposed to settle the problem. A matrix decomposition method is used to distribute the work among GPU threads, so that MDGS will take full advantage of the computing power of current GPUs. Additionally, MDGS is a hybrid solver (combines both the direct and iterative techniques) and has two-level architecture. These enable MDGS to generate identical solutions with those of the common Poisson methods and achieve high convergence rate in most cases. This approach is advantageous in terms of parallelizability, enabling real-time image processing, low memory-taken and extensive applications.

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.

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.

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

Analysis of benzoquinone decomposition in solution plasma process

NASA Astrophysics Data System (ADS)

Bratescu, M. A.; Saito, N.

2016-01-01

The decomposition of p-benzoquinone (p-BQ) in Solution Plasma Processing (SPP) was analyzed by Coherent Anti-Stokes Raman Spectroscopy (CARS) by monitoring the change of the anti-Stokes signal intensity of the vibrational transitions of the molecule, during and after SPP. Just in the beginning of the SPP treatment, the CARS signal intensities of the ring vibrational molecular transitions increased under the influence of the electric field of plasma. The results show that plasma influences the p-BQ molecules in two ways: (i) plasma produces a polarization and an orientation of the molecules in the local electric field of plasma and (ii) the gas phase plasma supplies, in the liquid phase, hydrogen and hydroxyl radicals, which reduce or oxidize the molecules, respectively, generating different carboxylic acids. The decomposition of p-BQ after SPP was confirmed by UV-visible absorption spectroscopy and liquid chromatography.

CP decomposition approach to blind separation for DS-CDMA system using a new performance index

NASA Astrophysics Data System (ADS)

Rouijel, Awatif; Minaoui, Khalid; Comon, Pierre; Aboutajdine, Driss

2014-12-01

In this paper, we present a canonical polyadic (CP) tensor decomposition isolating the scaling matrix. This has two major implications: (i) the problem conditioning shows up explicitly and could be controlled through a constraint on the so-called coherences and (ii) a performance criterion concerning the factor matrices can be exactly calculated and is more realistic than performance metrics used in the literature. Two new algorithms optimizing the CP decomposition based on gradient descent are proposed. This decomposition is illustrated by an application to direct-sequence code division multiplexing access (DS-CDMA) systems; computer simulations are provided and demonstrate the good behavior of these algorithms, compared to others in the literature.

Reducing tensor magnetic gradiometer data for unexploded ordnance detection

USGS Publications Warehouse

Bracken, Robert E.; Brown, Philip J.

2005-01-01

We performed a survey to demonstrate the effectiveness of a prototype tensor magnetic gradiometer system (TMGS) for detection of buried unexploded ordnance (UXO). In order to achieve a useful result, we designed a data-reduction procedure that resulted in a realistic magnetic gradient tensor and devised a simple way of viewing complicated tensor data, not only to assess the validity of the final resulting tensor, but also to preview the data at interim stages of processing. The final processed map of the surveyed area clearly shows a sharp anomaly that peaks almost directly over the target UXO. This map agrees well with a modeled map derived from dipolar sources near the known target locations. From this agreement, it can be deduced that the reduction process is valid, making the prototype TMGS a foundation for development of future systems and processes.

Finite-width Laplacian sum rules for 2++ tensor glueball in the instanton vacuum model

NASA Astrophysics Data System (ADS)

Chen, Junlong; Liu, Jueping

2017-01-01

The more carefully defined and more appropriate 2++ tensor glueball current is a S Uc(3 ) gauge-invariant, symmetric, traceless, and conserved Lorentz-irreducible tensor. After Lorentz decomposition, the invariant amplitude of the correlation function is abstracted and calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. In addition to taking the perturbative contribution into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width three resonances is adopted. The properties of the 2++ tensor glueball are investigated via a family of the QCD Laplacian sum rules for the invariant amplitude. The values of the mass, decay width, and coupling constants for the 2++ resonance in which the glueball fraction is dominant are obtained.

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.

Decomposition

USGS Publications Warehouse

Middleton, Beth A.

2014-01-01

A cornerstone of ecosystem ecology, decomposition was recognized as a fundamental process driving the exchange of energy in ecosystems by early ecologists such as Lindeman 1942 and Odum 1960). In the history of ecology, studies of decomposition were incorporated into the International Biological Program in the 1960s to compare the nature of organic matter breakdown in various ecosystem types. Such studies still have an important role in ecological studies of today. More recent refinements have brought debates on the relative role microbes, invertebrates and environment in the breakdown and release of carbon into the atmosphere, as well as how nutrient cycling, production and other ecosystem processes regulated by decomposition may shift with climate change. Therefore, this bibliography examines the primary literature related to organic matter breakdown, but it also explores topics in which decomposition plays a key supporting role including vegetation composition, latitudinal gradients, altered ecosystems, anthropogenic impacts, carbon storage, and climate change models. Knowledge of these topics is relevant to both the study of ecosystem ecology as well projections of future conditions for human societies.

Preliminary application of Structure from Motion and GIS to document decomposition and taphonomic processes.

PubMed

Carlton, Connor D; Mitchell, Samantha; Lewis, Patrick

2018-01-01

Over the past decade, Structure from Motion (SfM) has increasingly been used as a means of digital preservation and for documenting archaeological excavations, architecture, and cultural material. However, few studies have tapped the potential of using SfM to document and analyze taphonomic processes affecting burials for forensic sciences purposes. This project utilizes SfM models to elucidate specific post-depositional events that affected a series of three human cadavers deposited at the South East Texas Applied Forensic Science Facility (STAFS). The aim of this research was to test the ability for untrained researchers to employ spatial software and photogrammetry for data collection purposes. For a series of three months a single lens reflex (SLR) camera was used to capture a series of overlapping images at periodic stages in the decomposition process of each cadaver. These images are processed through photogrammetric software that creates a 3D model that can be measured, manipulated, and viewed. This project used photogrammetric and geospatial software to map changes in decomposition and movement of the body from original deposition points. Project results indicate SfM and GIS as a useful tool for documenting decomposition and taphonomic processes. Results indicate photogrammetry is an efficient, relatively simple, and affordable tool for the documentation of decomposition. Copyright © 2017 Elsevier B.V. All rights reserved.

Rank-based decompositions of morphological templates.

PubMed

Sussner, P; Ritter, G X

2000-01-01

Methods for matrix decomposition have found numerous applications in image processing, in particular for the problem of template decomposition. Since existing matrix decomposition techniques are mainly concerned with the linear domain, we consider it timely to investigate matrix decomposition techniques in the nonlinear domain with applications in image processing. The mathematical basis for these investigations is the new theory of rank within minimax algebra. Thus far, only minimax decompositions of rank 1 and rank 2 matrices into outer product expansions are known to the image processing community. We derive a heuristic algorithm for the decomposition of matrices having arbitrary rank.

Factors and processes causing accelerated decomposition in human cadavers - An overview.

PubMed

Zhou, Chong; Byard, Roger W

2011-01-01

Artefactually enhanced putrefactive and autolytic changes may be misinterpreted as indicating a prolonged postmortem interval and throw doubt on the veracity of witness statements. Review of files from Forensic Science SA and the literature revealed a number of external and internal factors that may be responsible for accelerating these processes. Exogenous factors included exposure to elevated environmental temperatures, both outdoors and indoors, exacerbated by increased humidity or fires. Situations indoor involved exposure to central heating, hot water, saunas and electric blankets. Deaths within motor vehicles were also characterized by enhanced decomposition. Failure to quickly or adequately refrigerate bodies may also lead to early decomposition. Endogenous factors included fever, infections, illicit and prescription drugs, obesity and insulin-dependent diabetes mellitus. When these factors or conditions are identified at autopsy less significance should, therefore, be attached to changes of decomposition as markers of time since death. Copyright © 2010 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

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.

Detecting brain dynamics during resting state: a tensor based evolutionary clustering approach

NASA Astrophysics Data System (ADS)

Al-sharoa, Esraa; Al-khassaweneh, Mahmood; Aviyente, Selin

2017-08-01

Human brain is a complex network with connections across different regions. Understanding the functional connectivity (FC) of the brain is important both during resting state and task; as disruptions in connectivity patterns are indicators of different psychopathological and neurological diseases. In this work, we study the resting state functional connectivity networks (FCNs) of the brain from fMRI BOLD signals. Recent studies have shown that FCNs are dynamic even during resting state and understanding the temporal dynamics of FCNs is important for differentiating between different conditions. Therefore, it is important to develop algorithms to track the dynamic formation and dissociation of FCNs of the brain during resting state. In this paper, we propose a two step tensor based community detection algorithm to identify and track the brain network community structure across time. First, we introduce an information-theoretic function to reduce the dynamic FCN and identify the time points that are similar topologically to combine them into a tensor. These time points will be used to identify the different FC states. Second, a tensor based spectral clustering approach is developed to identify the community structure of the constructed tensors. The proposed algorithm applies Tucker decomposition to the constructed tensors and extract the orthogonal factor matrices along the connectivity mode to determine the common subspace within each FC state. The detected community structure is summarized and described as FC states. The results illustrate the dynamic structure of resting state networks (RSNs), including the default mode network, somatomotor network, subcortical network and visual network.

Tensor products of U{sub q}{sup Prime }sl-caret(2)-modules and the big q{sup 2}-Jacobi function transform

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

Gade, R. M.

2013-01-15

Four tensor products of evaluation modules of the quantum affine algebra U{sub q}{sup Prime }sl-caret(2) obtained from the negative and positive series, the complementary and the strange series representations are investigated. Linear operators R(z) satisfying the intertwining property on finite linear combinations of the canonical basis elements of the tensor products are described in terms of two sets of infinite sums {l_brace}{tau}{sup (r,t)}{r_brace}{sub r,t Element-Of Z{sub {>=}{sub 0}}} and {l_brace}{tau}{sup (r,t)}{r_brace}{sub r,t Element-Of Z{sub {>=}{sub 0}}} involving big q{sup 2}-Jacobi functions or related nonterminating basic hypergeometric series. Inhomogeneous recurrence relations can be derived for both sets. Evaluations of the simplestmore » sums provide the corresponding initial conditions. For the first set of sums the relations entail a big q{sup 2}-Jacobi function transform pair. An integral decomposition is obtained for the sum {tau}{sup (r,t)}. A partial description of the relation between the decompositions of the tensor products with respect to U{sub q}sl(2) or with respect to its complement in U{sub q}{sup Prime }sl-caret(2) can be formulated in terms of Askey-Wilson function transforms. For a particular combination of two tensor products, the occurrence of proper U{sub q}{sup Prime }sl-caret(2)-submodules is discussed.« less

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.

Natural chemical shielding analysis of nuclear magnetic resonance shielding tensors from gauge-including atomic orbital calculations

NASA Astrophysics Data System (ADS)

Bohmann, Jonathan A.; Weinhold, Frank; Farrar, Thomas C.

1997-07-01

Nuclear magnetic shielding tensors computed by the gauge including atomic orbital (GIAO) method in the Hartree-Fock self-consistent-field (HF-SCF) framework are partitioned into magnetic contributions from chemical bonds and lone pairs by means of natural chemical shielding (NCS) analysis, an extension of natural bond orbital (NBO) analysis. NCS analysis complements the description provided by alternative localized orbital methods by directly calculating chemical shieldings due to delocalized features in the electronic structure, such as bond conjugation and hyperconjugation. Examples of NCS tensor decomposition are reported for CH4, CO, and H2CO, for which a graphical mnemonic due to Cornwell is used to illustrate the effect of hyperconjugative delocalization on the carbon shielding.

Calculation and Analysis of magnetic gradient tensor components of global magnetic models

NASA Astrophysics Data System (ADS)

Schiffler, Markus; Queitsch, Matthias; Schneider, Michael; Stolz, Ronny; Krech, Wolfram; Meyer, Hans-Georg; Kukowski, Nina

2014-05-01

Magnetic mapping missions like SWARM and its predecessors, e.g. the CHAMP and MAGSAT programs, offer high resolution Earth's magnetic field data. These datasets are usually combined with magnetic observatory and survey data, and subject to harmonic analysis. The derived spherical harmonic coefficients enable magnetic field modelling using a potential series expansion. Recently, new instruments like the JeSSY STAR Full Tensor Magnetic Gradiometry system equipped with very high sensitive sensors can directly measure the magnetic field gradient tensor components. The full understanding of the quality of the measured data requires the extension of magnetic field models to gradient tensor components. In this study, we focus on the extension of the derivation of the magnetic field out of the potential series magnetic field gradient tensor components and apply the new theoretical framework to the International Geomagnetic Reference Field (IGRF) and the High Definition Magnetic Model (HDGM). The gradient tensor component maps for entire Earth's surface produced for the IGRF show low values and smooth variations reflecting the core and mantle contributions whereas those for the HDGM gives a novel tool to unravel crustal structure and deep-situated ore bodies. For example, the Thor Suture and the Sorgenfrei-Thornquist Zone in Europe are delineated by a strong northward gradient. Derived from Eigenvalue decomposition of the magnetic gradient tensor, the scaled magnetic moment, normalized source strength (NSS) and the bearing of the lithospheric sources are presented. The NSS serves as a tool for estimating the lithosphere-asthenosphere boundary as well as the depth of plutons and ore bodies. Furthermore changes in magnetization direction parallel to the mid-ocean ridges can be obtained from the scaled magnetic moment and the normalized source strength discriminates the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European

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.

Inversion of gravity gradient tensor data: does it provide better resolution?

NASA Astrophysics Data System (ADS)

Paoletti, V.; Fedi, M.; Italiano, F.; Florio, G.; Ialongo, S.

2016-04-01

The gravity gradient tensor (GGT) has been increasingly used in practical applications, but the advantages and the disadvantages of the analysis of GGT components versus the analysis of the vertical component of the gravity field are still debated. We analyse the performance of joint inversion of GGT components versus separate inversion of the gravity field alone, or of one tensor component. We perform our analysis by inspection of the Picard Plot, a Singular Value Decomposition tool, and analyse both synthetic data and gradiometer measurements carried out at the Vredefort structure, South Africa. We show that the main factors controlling the reliability of the inversion are algebraic ambiguity (the difference between the number of unknowns and the number of available data points) and signal-to-noise ratio. Provided that algebraic ambiguity is kept low and the noise level is small enough so that a sufficient number of SVD components can be included in the regularized solution, we find that: (i) the choice of tensor components involved in the inversion is not crucial to the overall reliability of the reconstructions; (ii) GGT inversion can yield the same resolution as inversion with a denser distribution of gravity data points, but with the advantage of using fewer measurement stations.

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.

The neural basis of novelty and appropriateness in processing of creative chunk decomposition.

PubMed

Huang, Furong; Fan, Jin; Luo, Jing

2015-06-01

Novelty and appropriateness have been recognized as the fundamental features of creative thinking. However, the brain mechanisms underlying these features remain largely unknown. In this study, we used event-related functional magnetic resonance imaging (fMRI) to dissociate these mechanisms in a revised creative chunk decomposition task in which participants were required to perform different types of chunk decomposition that systematically varied in novelty and appropriateness. We found that novelty processing involved functional areas for procedural memory (caudate), mental rewarding (substantia nigra, SN), and visual-spatial processing, whereas appropriateness processing was mediated by areas for declarative memory (hippocampus), emotional arousal (amygdala), and orthography recognition. These results indicate that non-declarative and declarative memory systems may jointly contribute to the two fundamental features of creative thinking. Copyright © 2015 Elsevier Inc. All rights reserved.

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.

Decomposition of gas-phase trichloroethene by the UV/TiO2 process in the presence of ozone.

PubMed

Shen, Y S; Ku, Y

2002-01-01

The decomposition of gas-phase trichloroethene (TCE) in air streams by direct photolysis, the UV/TiO2 and UV/O3 processes was studied. The experiments were carried out under various UV light intensities and wavelengths, ozone dosages, and initial concentrations of TCE to investigate and compare the removal efficiency of the pollutant. For UV/TiO2 process, the individual contribution to the decomposition of TCE by direct photolysis and hydroxyl radicals destruction was differentiated to discuss the quantum efficiency with 254 and 365 nm UV lamps. The removal of gaseous TCE was found to reduce by UV/TiO2 process in the presence of ozone possibly because of the ozone molecules could scavenge hydroxyl radicals produced from the excitation of TiO2 by UV radiation to inhibit the decomposition of TCE. A photoreactor design equation for the decomposition of gaseous TCE by the UV/TiO2 process in air streams was developed by combining the continuity equation of the pollutant and the surface catalysis reaction rate expression. By the proposed design scheme, the temporal distribution of TCE at various operation conditions by the UV/TiO2 process can be well modeled.

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.

Obtaining orthotropic elasticity tensor using entries zeroing method.

NASA Astrophysics Data System (ADS)

Gierlach, Bartosz; Danek, Tomasz

2017-04-01

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.

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.

Image Corruption Detection in Diffusion Tensor Imaging for Post-Processing and Real-Time Monitoring

PubMed Central

Li, Yue; Shea, Steven M.; Lorenz, Christine H.; Jiang, Hangyi; Chou, Ming-Chung; Mori, Susumu

2013-01-01

Due to the high sensitivity of diffusion tensor imaging (DTI) to physiological motion, clinical DTI scans often suffer a significant amount of artifacts. Tensor-fitting-based, post-processing outlier rejection is often used to reduce the influence of motion artifacts. Although it is an effective approach, when there are multiple corrupted data, this method may no longer correctly identify and reject the corrupted data. In this paper, we introduce a new criterion called “corrected Inter-Slice Intensity Discontinuity” (cISID) to detect motion-induced artifacts. We compared the performance of algorithms using cISID and other existing methods with regard to artifact detection. The experimental results show that the integration of cISID into fitting-based methods significantly improves the retrospective detection performance at post-processing analysis. The performance of the cISID criterion, if used alone, was inferior to the fitting-based methods, but cISID could effectively identify severely corrupted images with a rapid calculation time. In the second part of this paper, an outlier rejection scheme was implemented on a scanner for real-time monitoring of image quality and reacquisition of the corrupted data. The real-time monitoring, based on cISID and followed by post-processing, fitting-based outlier rejection, could provide a robust environment for routine DTI studies. PMID:24204551

PROCESS OF COATING WITH NICKEL BY THE DECOMPOSITION OF NICKEL CARBONYL

DOEpatents

Hoover, T.B.

1959-04-01

An improved process is presented for the deposition of nickel coatings by the thermal decomposition of nickel carbonyl vapor. The improvement consists in incorporating a small amount of hydrogen sulfide gas in the nickel carbonyl plating gas. It is postulated that the hydrogen sulfide functions as a catalyst. i

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

USGS Publications Warehouse

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

2003-01-01

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

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.

Kinetic analysis of overlapping multistep thermal decomposition comprising exothermic and endothermic processes: thermolysis of ammonium dinitramide.

PubMed

Muravyev, Nikita V; Koga, Nobuyoshi; Meerov, Dmitry B; Pivkina, Alla N

2017-01-25

This study focused on kinetic modeling of a specific type of multistep heterogeneous reaction comprising exothermic and endothermic reaction steps, as exemplified by the practical kinetic analysis of the experimental kinetic curves for the thermal decomposition of molten ammonium dinitramide (ADN). It is known that the thermal decomposition of ADN occurs as a consecutive two step mass-loss process comprising the decomposition of ADN and subsequent evaporation/decomposition of in situ generated ammonium nitrate. These reaction steps provide exothermic and endothermic contributions, respectively, to the overall thermal effect. The overall reaction process was deconvoluted into two reaction steps using simultaneously recorded thermogravimetry and differential scanning calorimetry (TG-DSC) curves by considering the different physical meanings of the kinetic data derived from TG and DSC by P value analysis. The kinetic data thus separated into exothermic and endothermic reaction steps were kinetically characterized using kinetic computation methods including isoconversional method, combined kinetic analysis, and master plot method. The overall kinetic behavior was reproduced as the sum of the kinetic equations for each reaction step considering the contributions to the rate data derived from TG and DSC. During reproduction of the kinetic behavior, the kinetic parameters and contributions of each reaction step were optimized using kinetic deconvolution analysis. As a result, the thermal decomposition of ADN was successfully modeled as partially overlapping exothermic and endothermic reaction steps. The logic of the kinetic modeling was critically examined, and the practical usefulness of phenomenological modeling for the thermal decomposition of ADN was illustrated to demonstrate the validity of the methodology and its applicability to similar complex reaction processes.

Bayesian inference and interpretation of centroid moment tensors of the 2016 Kumamoto earthquake sequence, Kyushu, Japan

NASA Astrophysics Data System (ADS)

Hallo, Miroslav; Asano, Kimiyuki; Gallovič, František

2017-09-01

On April 16, 2016, Kumamoto prefecture in Kyushu region, Japan, was devastated by a shallow M JMA7.3 earthquake. The series of foreshocks started by M JMA6.5 foreshock 28 h before the mainshock. They have originated in Hinagu fault zone intersecting the mainshock Futagawa fault zone; hence, the tectonic background for this earthquake sequence is rather complex. Here we infer centroid moment tensors (CMTs) for 11 events with M JMA between 4.8 and 6.5, using strong motion records of the K-NET, KiK-net and F-net networks. We use upgraded Bayesian full-waveform inversion code ISOLA-ObsPy, which takes into account uncertainty of the velocity model. Such an approach allows us to reliably assess uncertainty of the CMT parameters including the centroid position. The solutions show significant systematic spatial and temporal variations throughout the sequence. Foreshocks are right-lateral steeply dipping strike-slip events connected to the NE-SW shear zone. Those located close to the intersection of the Hinagu and Futagawa fault zones are dipping slightly to ESE, while those in the southern area are dipping to WNW. Contrarily, aftershocks are mostly normal dip-slip events, being related to the N-S extensional tectonic regime. Most of the deviatoric moment tensors contain only minor CLVD component, which can be attributed to the velocity model uncertainty. Nevertheless, two of the CMTs involve a significant CLVD component, which may reflect complex rupture process. Decomposition of those moment tensors into two pure shear moment tensors suggests combined right-lateral strike-slip and normal dip-slip mechanisms, consistent with the tectonic settings of the intersection of the Hinagu and Futagawa fault zones.[Figure not available: see fulltext.

Combining Diffusion Tensor Metrics and DSC Perfusion Imaging: Can It Improve the Diagnostic Accuracy in Differentiating Tumefactive Demyelination from High-Grade Glioma?

PubMed

Hiremath, S B; Muraleedharan, A; Kumar, S; Nagesh, C; Kesavadas, C; Abraham, M; Kapilamoorthy, T R; Thomas, B

2017-04-01

Tumefactive demyelinating lesions with atypical features can mimic high-grade gliomas on conventional imaging sequences. The aim of this study was to assess the role of conventional imaging, DTI metrics ( p:q tensor decomposition), and DSC perfusion in differentiating tumefactive demyelinating lesions and high-grade gliomas. Fourteen patients with tumefactive demyelinating lesions and 21 patients with high-grade gliomas underwent brain MR imaging with conventional, DTI, and DSC perfusion imaging. Imaging sequences were assessed for differentiation of the lesions. DTI metrics in the enhancing areas and perilesional hyperintensity were obtained by ROI analysis, and the relative CBV values in enhancing areas were calculated on DSC perfusion imaging. Conventional imaging sequences had a sensitivity of 80.9% and specificity of 57.1% in differentiating high-grade gliomas ( P = .049) from tumefactive demyelinating lesions. DTI metrics ( p : q tensor decomposition) and DSC perfusion demonstrated a statistically significant difference in the mean values of ADC, the isotropic component of the diffusion tensor, the anisotropic component of the diffusion tensor, the total magnitude of the diffusion tensor, and rCBV among enhancing portions in tumefactive demyelinating lesions and high-grade gliomas ( P ≤ .02), with the highest specificity for ADC, the anisotropic component of the diffusion tensor, and relative CBV (92.9%). Mean fractional anisotropy values showed no significant statistical difference between tumefactive demyelinating lesions and high-grade gliomas. The combination of DTI and DSC parameters improved the diagnostic accuracy (area under the curve = 0.901). Addition of a heterogeneous enhancement pattern to DTI and DSC parameters improved it further (area under the curve = 0.966). The sensitivity increased from 71.4% to 85.7% after the addition of the enhancement pattern. DTI and DSC perfusion add profoundly to conventional imaging in differentiating tumefactive

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

DOE PAGES

Song, Chenchen; Martinez, Todd J.

2017-08-29

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementationmore » provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.« less

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

NASA Astrophysics Data System (ADS)

Song, Chenchen; Martínez, Todd J.

2017-10-01

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. The resulting energy conservation in micro-canonical AIMD demonstrates that the implementation provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

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

Song, Chenchen; Martinez, Todd J.

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementationmore » provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.« less

A Tensor-Train accelerated solver for integral equations in complex geometries

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Rahimian, Abtin; Zorin, Denis

2017-04-01

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O (log ⁡ N) and once the inverse is computed, it can be applied in O (Nlog ⁡ N) . We analyze the QTT ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as FMM and HSS. We prove that the QTT ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the QTT decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the QTT-based solver when applied to both translation and non-translation invariant volume integrals in 3D. For boundary integral equations, we demonstrate that using a QTT decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the QTT preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries.

Complete set of invariants of a 4th order tensor: the 12 tasks of HARDI from ternary quartics.

PubMed

Papadopoulo, Théo; Ghosh, Aurobrata; Deriche, Rachid

2014-01-01

Invariants play a crucial role in Diffusion MRI. In DTI (2nd order tensors), invariant scalars (FA, MD) have been successfully used in clinical applications. But DTI has limitations and HARDI models (e.g. 4th order tensors) have been proposed instead. These, however, lack invariant features and computing them systematically is challenging. We present a simple and systematic method to compute a functionally complete set of invariants of a non-negative 3D 4th order tensor with respect to SO3. Intuitively, this transforms the tensor's non-unique ternary quartic (TQ) decomposition (from Hilbert's theorem) to a unique canonical representation independent of orientation - the invariants. The method consists of two steps. In the first, we reduce the 18 degrees-of-freedom (DOF) of a TQ representation by 3-DOFs via an orthogonal transformation. This transformation is designed to enhance a rotation-invariant property of choice of the 3D 4th order tensor. In the second, we further reduce 3-DOFs via a 3D rotation transformation of coordinates to arrive at a canonical set of invariants to SO3 of the tensor. The resulting invariants are, by construction, (i) functionally complete, (ii) functionally irreducible (if desired), (iii) computationally efficient and (iv) reversible (mappable to the TQ coefficients or shape); which is the novelty of our contribution in comparison to prior work. Results from synthetic and real data experiments validate the method and indicate its importance.

SDE decomposition and A-type stochastic interpretation in nonequilibrium processes

NASA Astrophysics Data System (ADS)

Yuan, Ruoshi; Tang, Ying; Ao, Ping

2017-12-01

An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochastic differential equation (SDE) into a dissipative component, a detailed-balance-breaking component, and a dual-role potential landscape has been developed, which has fruitful applications in physics, engineering, chemistry, and biology. It introduces the A-type stochastic interpretation of the SDE beyond the traditional Ito or Stratonovich interpretation or even the α-type interpretation for multidimensional systems. The potential landscape serves as a Hamiltonian-like function in nonequilibrium processes without detailed balance, which extends this important concept from equilibrium statistical physics to the nonequilibrium region. A question on the uniqueness of the SDE decomposition was recently raised. Our review of both the mathematical and physical aspects shows that uniqueness is guaranteed. The demonstration leads to a better understanding of the robustness of the novel framework. In addition, we discuss related issues including the limitations of an approach to obtaining the potential function from a steady-state distribution.

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD

NASA Astrophysics Data System (ADS)

Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Gambhir, Arjun S.; Orginos, Kostas; Savage, Martin J.; Shanahan, Phiala E.; Wagman, Michael L.; Winter, Frank; Nplqcd Collaboration

2018-04-01

Complete flavor decompositions of the matrix elements of the scalar, axial, and tensor currents in the proton, deuteron, diproton, and 3He at SU(3)-symmetric values of the quark masses corresponding to a pion mass mπ˜806 MeV are determined using lattice quantum chromodynamics. At the physical quark masses, the scalar interactions constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor interactions of nuclei constrain their spin content, integrated transversity, and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elements of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. The calculated matrix elements differ from, and are typically smaller than, naive single-nucleon estimates. Given the particularly large, O (10 %), size of nuclear effects in the scalar matrix elements, contributions from correlated multinucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD

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

Chang, Emmanuel; Davoudi, Zohreh; Detmold, William

Complete flavor decompositions of the matrix elements of the scalar, axial, and tensor currents in the proton, deuteron, diproton, and 3He at SU(3)-symmetric values of the quark masses corresponding to a pion mass m π~806 MeV are determined using lattice quantum chromodynamics. At the physical quark masses, the scalar interactions constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor interactions of nuclei constrain their spin content, integrated transversity, and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elementsmore » of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. The calculated matrix elements differ from, and are typically smaller than, naive single-nucleon estimates. Given the particularly large, O(10%), size of nuclear effects in the scalar matrix elements, contributions from correlated multinucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.« less

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD

DOE PAGES

Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; ...

2018-04-13

Complete flavor decompositions of the matrix elements of the scalar, axial, and tensor currents in the proton, deuteron, diproton, and 3He at SU(3)-symmetric values of the quark masses corresponding to a pion mass m π~806 MeV are determined using lattice quantum chromodynamics. At the physical quark masses, the scalar interactions constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor interactions of nuclei constrain their spin content, integrated transversity, and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elementsmore » of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. The calculated matrix elements differ from, and are typically smaller than, naive single-nucleon estimates. Given the particularly large, O(10%), size of nuclear effects in the scalar matrix elements, contributions from correlated multinucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.« less

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD.

PubMed

Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Gambhir, Arjun S; Orginos, Kostas; Savage, Martin J; Shanahan, Phiala E; Wagman, Michael L; Winter, Frank

2018-04-13

Complete flavor decompositions of the matrix elements of the scalar, axial, and tensor currents in the proton, deuteron, diproton, and ^{3}He at SU(3)-symmetric values of the quark masses corresponding to a pion mass m_{π}∼806  MeV are determined using lattice quantum chromodynamics. At the physical quark masses, the scalar interactions constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor interactions of nuclei constrain their spin content, integrated transversity, and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elements of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. The calculated matrix elements differ from, and are typically smaller than, naive single-nucleon estimates. Given the particularly large, O(10%), size of nuclear effects in the scalar matrix elements, contributions from correlated multinucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.

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.

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

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.

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.

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.

Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory

NASA Astrophysics Data System (ADS)

Hohenstein, Edward G.; Parrish, Robert M.; Martínez, Todd J.

2012-07-01

Many approximations have been developed to help deal with the O(N4) growth of the electron repulsion integral (ERI) tensor, where N is the number of one-electron basis functions used to represent the electronic wavefunction. Of these, the density fitting (DF) approximation is currently the most widely used despite the fact that it is often incapable of altering the underlying scaling of computational effort with respect to molecular size. We present a method for exploiting sparsity in three-center overlap integrals through tensor decomposition to obtain a low-rank approximation to density fitting (tensor hypercontraction density fitting or THC-DF). This new approximation reduces the 4th-order ERI tensor to a product of five matrices, simultaneously reducing the storage requirement as well as increasing the flexibility to regroup terms and reduce scaling behavior. As an example, we demonstrate such a scaling reduction for second- and third-order perturbation theory (MP2 and MP3), showing that both can be carried out in O(N4) operations. This should be compared to the usual scaling behavior of O(N5) and O(N6) for MP2 and MP3, respectively. The THC-DF technique can also be applied to other methods in electronic structure theory, such as coupled-cluster and configuration interaction, promising significant gains in computational efficiency and storage reduction.

Application of modern tensor calculus to engineered domain structures. 1. Calculation of tensorial covariants.

PubMed

Kopský, Vojtech

2006-03-01

This article is a roadmap to a systematic calculation and tabulation of tensorial covariants for the point groups of material physics. The following are the essential steps in the described approach to tensor calculus. (i) An exact specification of the considered point groups by their embellished Hermann-Mauguin and Schoenflies symbols. (ii) Introduction of oriented Laue classes of magnetic point groups. (iii) An exact specification of matrix ireps (irreducible representations). (iv) Introduction of so-called typical (standard) bases and variables -- typical invariants, relative invariants or components of the typical covariants. (v) Introduction of Clebsch-Gordan products of the typical variables. (vi) Calculation of tensorial covariants of ascending ranks with consecutive use of tables of Clebsch-Gordan products. (vii) Opechowski's magic relations between tensorial decompositions. These steps are illustrated for groups of the tetragonal oriented Laue class D(4z) -- 4(z)2(x)2(xy) of magnetic point groups and for tensors up to fourth rank.

Residue decomposition of submodel of WEPS

USDA-ARS?s Scientific Manuscript database

The Residue Decomposition submodel of the Wind Erosion Prediction System (WEPS) simulates the decrease in crop residue biomass due to microbial activity. The decomposition process is modeled as a first-order reaction with temperature and moisture as driving variables. Decomposition is a function of ...

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.

Decomposition of 1,4-dioxane by advanced oxidation and biochemical process.

PubMed

Kim, Chang-Gyun; Seo, Hyung-Joon; Lee, Byung-Ryul

2006-01-01

This study was undertaken to determine the optimal decomposition conditions when 1,4-dioxane was degraded using either the AOPs (Advanced Oxidation Processes) or the BAC-TERRA microbial complex. The advanced oxidation was operated with H2O2, in the range 4.7 to 51 mM, under 254 nm (25 W lamp) illumination, while varying the reaction parameters, such as the air flow rate and reaction time. The greatest oxidation rate (96%) of 1,4-dioxane was achieved with H2O2 concentration of 17 mM after a 2-hr reaction. As a result of this reaction, organic acid intermediates were formed, such as acetic, propionic and butyric acids. Furthermore, the study revealed that suspended particles, i.e., bio-flocs, kaolin and pozzolan, in the reaction were able to have an impact on the extent of 1,4-dioxane decomposition. The decomposition of 1,4-dioxane in the presence of bio-flocs was significantly declined due to hindered UV penetration through the solution as a result of the consistent dispersion of bio-particles. In contrast, dosing with pozzolan decomposed up to 98.8% of the 1,4-dioxane after 2 hr of reaction. Two actual wastewaters, from polyester manufacturing, containing 1,4-dioxane in the range 370 to 450 mg/L were able to be oxidized by as high as 100% within 15 min with the introduction of 100:200 (mg/L) Fe(II):H202 under UV illumination. Aerobic biological decomposition, employing BAC-TERRA, was able to remove up to 90% of 1,4-dioxane after 15 days of incubation. In the meantime, the by-products (i.e., acetic, propionic and valeric acid) generated were similar to those formed during the AOPs investigation. According to kinetic studies, both photo-decomposition and biodegradation of 1,4-dioxane followed pseudo first-order reaction kinetics, with k = 5 x 10(-4) s(-1) and 2.38 x 10(-6) s(-1), respectively. It was concluded that 1,4-dioxane could be readily degraded by both AOPs and BAC-TERRA, and that the actual polyester wastewater containing 1,4-dioxane could be successfully

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.

Tensor integrand reduction via Laurent expansion

NASA Astrophysics Data System (ADS)

Hirschi, Valentin; Peraro, Tiziano

2016-06-01

We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C ++ library N inja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface N inja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the N inja library and interfaced it to M adL oop, which is part of the public M adG raph5_ aMC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely C utT ools, S amurai, IREGI, PJF ry++ and G olem95. We find that N inja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem95 which is however more limited and slower than N inja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that N inja's performance scales well with both the rank and multiplicity of the considered process.

Tensor integrand reduction via Laurent expansion

DOE PAGES

Hirschi, Valentin; Peraro, Tiziano

2016-06-09

We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MadLoop, which is part of the public MadGraph5_aMC@NLO framework. We performed a detailed performance study, comparing against other public reductionmore » tools, namely CutTools, Samurai, IREGI, PJFry++ and Golem95. We find that Ninja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem95 which is however more limited and slower than Ninja. Lastly, we considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.« less

Decomposition of 3,5-dinitrobenzamide in aqueous solution during UV/H2O2 and UV/TiO2 oxidation processes.

PubMed

Yan, Yingjie; Liao, Qi-Nan; Ji, Feng; Wang, Wei; Yuan, Shoujun; Hu, Zhen-Hu

2017-02-01

3,5-Dinitrobenzamide has been widely used as a feed additive to control coccidiosis in poultry, and part of the added 3,5-dinitrobenzamide is excreted into wastewater and surface water. The removal of 3,5-dinitrobenzamide from wastewater and surface water has not been reported in previous studies. Highly reactive hydroxyl radicals from UV/hydrogen peroxide (H 2 O 2 ) and UV/titanium dioxide (TiO 2 ) advanced oxidation processes (AOPs) can decompose organic contaminants efficiently. In this study, the decomposition of 3,5-dinitrobenzamide in aqueous solution during UV/H 2 O 2 and UV/TiO 2 oxidation processes was investigated. The decomposition of 3,5-dinitrobenzamide fits well with a fluence-based pseudo-first-order kinetics model. The decomposition in both two oxidation processes was affected by solution pH, and was inhibited under alkaline conditions. Inorganic anions such as NO 3 - , Cl - , SO 4 2- , HCO 3 - , and CO 3 2- inhibited the degradation of 3,5-dinitrobenzamide during the UV/H 2 O 2 and UV/TiO 2 oxidation processes. After complete decomposition in both oxidation processes, approximately 50% of 3,5-dinitrobenzamide was decomposed into organic intermediates, and the rest was mineralized to CO 2 , H 2 O, and other inorganic anions. Ions such as NH 4 + , NO 3 - , and NO 2 - were released into aqueous solution during the degradation. The primary decomposition products of 3,5-dinitrobenzamide were identified using time-of-flight mass spectrometry (LCMS-IT-TOF). Based on these products and ions release, a possible decomposition pathway of 3,5-dinitrobenzamide in both UV/H 2 O 2 and UV/TiO 2 processes was proposed.

Controlled decomposition and oxidation: A treatment method for gaseous process effluents

NASA Technical Reports Server (NTRS)

Mckinley, Roger J. B., Sr.

1990-01-01

The safe disposal of effluent gases produced by the electronics industry deserves special attention. Due to the hazardous nature of many of the materials used, it is essential to control and treat the reactants and reactant by-products as they are exhausted from the process tool and prior to their release into the manufacturing facility's exhaust system and the atmosphere. Controlled decomposition and oxidation (CDO) is one method of treating effluent gases from thin film deposition processes. CDO equipment applications, field experience, and results of the use of CDO equipment and technological advances gained from the field experiences are discussed.

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.

Factors controlling bark decomposition and its role in wood decomposition in five tropical tree species

PubMed Central

Dossa, Gbadamassi G. O.; Paudel, Ekananda; Cao, Kunfang; Schaefer, Douglas; Harrison, Rhett D.

2016-01-01

Organic matter decomposition represents a vital ecosystem process by which nutrients are made available for plant uptake and is a major flux in the global carbon cycle. Previous studies have investigated decomposition of different plant parts, but few considered bark decomposition or its role in decomposition of wood. However, bark can comprise a large fraction of tree biomass. We used a common litter-bed approach to investigate factors affecting bark decomposition and its role in wood decomposition for five tree species in a secondary seasonal tropical rain forest in SW China. For bark, we implemented a litter bag experiment over 12 mo, using different mesh sizes to investigate effects of litter meso- and macro-fauna. For wood, we compared the decomposition of branches with and without bark over 24 mo. Bark in coarse mesh bags decomposed 1.11–1.76 times faster than bark in fine mesh bags. For wood decomposition, responses to bark removal were species dependent. Three species with slow wood decomposition rates showed significant negative effects of bark-removal, but there was no significant effect in the other two species. Future research should also separately examine bark and wood decomposition, and consider bark-removal experiments to better understand roles of bark in wood decomposition. PMID:27698461

Factors controlling bark decomposition and its role in wood decomposition in five tropical tree species.

PubMed

Dossa, Gbadamassi G O; Paudel, Ekananda; Cao, Kunfang; Schaefer, Douglas; Harrison, Rhett D

2016-10-04

Organic matter decomposition represents a vital ecosystem process by which nutrients are made available for plant uptake and is a major flux in the global carbon cycle. Previous studies have investigated decomposition of different plant parts, but few considered bark decomposition or its role in decomposition of wood. However, bark can comprise a large fraction of tree biomass. We used a common litter-bed approach to investigate factors affecting bark decomposition and its role in wood decomposition for five tree species in a secondary seasonal tropical rain forest in SW China. For bark, we implemented a litter bag experiment over 12 mo, using different mesh sizes to investigate effects of litter meso- and macro-fauna. For wood, we compared the decomposition of branches with and without bark over 24 mo. Bark in coarse mesh bags decomposed 1.11-1.76 times faster than bark in fine mesh bags. For wood decomposition, responses to bark removal were species dependent. Three species with slow wood decomposition rates showed significant negative effects of bark-removal, but there was no significant effect in the other two species. Future research should also separately examine bark and wood decomposition, and consider bark-removal experiments to better understand roles of bark in wood decomposition.

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.

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.

Characterization of nanosized TiO2 synthesized inside a porous glass ceramic monolith by metallo-organic decomposition process

NASA Astrophysics Data System (ADS)

Mazali, Italo Odone; Alves, Oswaldo Luiz

2005-01-01

This work reports the preparation of TiO2 by decomposition of a metallo-organic precursor (MOD process) in the pores of an α-NbPO5 glass-ceramic monolith (PGC-NbP) and the study of the TiO2 anatase-rutile transition phase. The impregnation of titanium di-(propoxy)-di-(2-ethylhexanoate) in the PGC-NbP was confirmed by diffuse reflectance infrared spectroscopy. In the restrictive porous environment the decomposition of the metallo-organic compound exhibits a lower initial decomposition temperature but a higher final decomposition temperature, in comparison to the free precursor. The pure TiO2 rutile phase is formed only above 700 °C when the titanium precursor is decomposed outside the pores. The TiO2 anatase obtained inside the PGC-NbP was stabilized up to 750 °C and exhibits a smaller average crystallite size in comparison with the MOD process performed without PGC-NbP. Furthemore, the temperature of the TiO2 anatase-rutile transformation depends on crystallite size, which was provided by XRD and Raman spectroscopy. The precursor impregnation-decomposition cycle revealed a linear mass increment inside PGC-NbP. Micro-Raman spectroscopy shows the presence of a gradient concentration of the TiO2 inside the PGC-NbP. The use of the MOD process in the PGC-NbP pores has several advantages: control of the amount and the nature of the phase formed and preservation of the pore structure of PGC-NbP for subsequent treatments and reactions.

Validating the performance of one-time decomposition for fMRI analysis using ICA with automatic target generation process.

PubMed

Yao, Shengnan; Zeng, Weiming; Wang, Nizhuan; Chen, Lei

2013-07-01

Independent component analysis (ICA) has been proven to be effective for functional magnetic resonance imaging (fMRI) data analysis. However, ICA decomposition requires to optimize the unmixing matrix iteratively whose initial values are generated randomly. Thus the randomness of the initialization leads to different ICA decomposition results. Therefore, just one-time decomposition for fMRI data analysis is not usually reliable. Under this circumstance, several methods about repeated decompositions with ICA (RDICA) were proposed to reveal the stability of ICA decomposition. Although utilizing RDICA has achieved satisfying results in validating the performance of ICA decomposition, RDICA cost much computing time. To mitigate the problem, in this paper, we propose a method, named ATGP-ICA, to do the fMRI data analysis. This method generates fixed initial values with automatic target generation process (ATGP) instead of being produced randomly. We performed experimental tests on both hybrid data and fMRI data to indicate the effectiveness of the new method and made a performance comparison of the traditional one-time decomposition with ICA (ODICA), RDICA and ATGP-ICA. The proposed method demonstrated that it not only could eliminate the randomness of ICA decomposition, but also could save much computing time compared to RDICA. Furthermore, the ROC (Receiver Operating Characteristic) power analysis also denoted the better signal reconstruction performance of ATGP-ICA than that of RDICA. Copyright © 2013 Elsevier Inc. All rights reserved.

Photodegradation at day, microbial decomposition at night - decomposition in arid lands

NASA Astrophysics Data System (ADS)

Gliksman, Daniel; Gruenzweig, Jose

2014-05-01

Our current knowledge of decomposition in dry seasons and its role in carbon turnover is fragmentary. So far, decomposition during dry seasons was mostly attributed to abiotic mechanisms, mainly photochemical and thermal degradation, while the contribution of microorganisms to the decay process was excluded. We asked whether microbial decomposition occurs during the dry season and explored its interaction with photochemical degradation under Mediterranean climate. We conducted a litter bag experiment with local plant litter and manipulated litter exposure to radiation using radiation filters. We found notable rates of CO2 fluxes from litter which were related to microbial activity mainly during night-time throughout the dry season. This activity was correlated with litter moisture content and high levels of air humidity and dew. Day-time CO2 fluxes were related to solar radiation, and radiation manipulation suggested photodegradation as the underlying mechanism. In addition, a decline in microbial activity was followed by a reduction in photodegradation-related CO2 fluxes. The levels of microbial decomposition and photodegradation in the dry season were likely the factors influencing carbon mineralization during the subsequent wet season. This study showed that microbial decomposition can be a dominant contributor to CO2 emissions and mass loss in the dry season and it suggests a regulating effect of microbial activity on photodegradation. Microbial decomposition is an important contributor to the dry season decomposition and impacts the annual litter turn-over rates in dry regions. Global warming may lead to reduced moisture availability and dew deposition, which may greatly influence not only microbial decomposition of plant litter, but also photodegradation.

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.

Moment tensor clustering: a tool to monitor mining induced seismicity

NASA Astrophysics Data System (ADS)

Cesca, Simone; Dahm, Torsten; Tolga Sen, Ali

2013-04-01

Automated moment tensor inversion routines have been setup in the last decades for the analysis of global and regional seismicity. Recent developments could be used to analyse smaller events and larger datasets. In particular, applications to microseismicity, e.g. in mining environments, have then led to the generation of large moment tensor catalogues. Moment tensor catalogues provide a valuable information about the earthquake source and details of rupturing processes taking place in the seismogenic region. Earthquake focal mechanisms can be used to discuss the local stress field, possible orientations of the fault system or to evaluate the presence of shear and/or tensile cracks. Focal mechanism and moment tensor solutions are typically analysed for selected events, and quick and robust tools for the automated analysis of larger catalogues are needed. We propose here a method to perform cluster analysis for large moment tensor catalogues and identify families of events which characterize the studied microseismicity. Clusters include events with similar focal mechanisms, first requiring the definition of distance between focal mechanisms. Different metrics are here proposed, both for the case of pure double couple, constrained moment tensor and full moment tensor catalogues. Different clustering approaches are implemented and discussed. The method is here applied to synthetic and real datasets from mining environments to demonstrate its potential: the proposed cluserting techniques prove to be able to automatically recognise major clusters. An important application for mining monitoring concerns the early identification of anomalous rupture processes, which is relevant for the hazard assessment. This study is funded by the project MINE, which is part of the R&D-Programme GEOTECHNOLOGIEN. The project MINE is funded by the German Ministry of Education and Research (BMBF), Grant of project BMBF03G0737.

Three-Component Decomposition of Polarimetric SAR Data Integrating Eigen-Decomposition Results

NASA Astrophysics Data System (ADS)

Lu, Da; He, Zhihua; Zhang, Huan

2018-01-01

This paper presents a novel three-component scattering power decomposition of polarimetric SAR data. There are two problems in three-component decomposition method: volume scattering component overestimation in urban areas and artificially set parameter to be a fixed value. Though volume scattering component overestimation can be partly solved by deorientation process, volume scattering still dominants some oriented urban areas. The speckle-like decomposition results introduced by artificially setting value are not conducive to further image interpretation. This paper integrates the results of eigen-decomposition to solve the aforementioned problems. Two principal eigenvectors are used to substitute the surface scattering model and the double bounce scattering model. The decomposed scattering powers are obtained using a constrained linear least-squares method. The proposed method has been verified using an ESAR PolSAR image, and the results show that the proposed method has better performance in urban area.

Incompressible inelasticity as an essential ingredient for the validity of the kinematic decomposition F =FeFi

NASA Astrophysics Data System (ADS)

Reina, Celia; Conti, Sergio

2017-10-01

The multiplicative decomposition of the total deformation F =FeFi between an elastic (Fe) and an inelastic component (Fi) is standard in the modeling of many irreversible processes such as plasticity, growth, thermoelasticity, viscoelasticty or phase transformations. The heuristic argument for such kinematic assumption is based on the chain rule for the compatible scenario (CurlFi = 0) where the individual deformation tensors are gradients of deformation mappings, i.e. F = D φ = D (φe ∘φi) = (Dφe) ∘φi (Dφi) =FeFi . Yet, the conditions for its validity in the general incompatible case (CurlFi ≠ 0) has so far remained uncertain. We show in this paper that detFi = 1 and CurlFi bounded are necessary and sufficient conditions for the validity of F =FeFi for a wide range of inelastic processes. In particular, in the context of crystal plasticity, we demonstrate via rigorous homogenization from discrete dislocations to the continuum level in two dimensions, that the volume preserving property of the mechanistics of dislocation glide, combined with a finite dislocation density, is sufficient to deliver F =FeFp at the continuum scale. We then generalize this result to general two-dimensional inelastic processes that may be described at a lower dimensional scale via a multiplicative decomposition while exhibiting a finite density of incompatibilities. The necessity of the conditions detFi = 1 and CurlFi bounded for such systems is demonstrated via suitable counterexamples.

Mean template for tensor-based morphometry using deformation tensors.

PubMed

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

2007-01-01

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

Notes on super Killing tensors

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.

Holographic spin networks from tensor network states

NASA Astrophysics Data System (ADS)

Singh, Sukhwinder; McMahon, Nathan A.; Brennen, Gavin K.

2018-01-01

In the holographic correspondence of quantum gravity, a global on-site symmetry at the boundary generally translates to a local gauge symmetry in the bulk. We describe one way how the global boundary on-site symmetries can be gauged within the formalism of the multiscale renormalization ansatz (MERA), in light of the ongoing discussion between tensor networks and holography. We describe how to "lift" the MERA representation of the ground state of a generic one dimensional (1D) local Hamiltonian, which has a global on-site symmetry, to a dual quantum state of a 2D "bulk" lattice on which the symmetry appears gauged. The 2D bulk state decomposes in terms of spin network states, which label a basis in the gauge-invariant sector of the bulk lattice. This decomposition is instrumental to obtain expectation values of gauge-invariant observables in the bulk, and also reveals that the bulk state is generally entangled between the gauge and the remaining ("gravitational") bulk degrees of freedom that are not fixed by the symmetry. We present numerical results for ground states of several 1D critical spin chains to illustrate that the bulk entanglement potentially depends on the central charge of the underlying conformal field theory. We also discuss the possibility of emergent topological order in the bulk using a simple example, and also of emergent symmetries in the nongauge (gravitational) sector in the bulk. More broadly, our holographic model translates the MERA, a tensor network state, to a superposition of spin network states, as they appear in lattice gauge theories in one higher dimension.

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.

On Adapting the Tensor Voting Framework to Robust Color Image Denoising

NASA Astrophysics Data System (ADS)

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

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

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.

Factors influencing leaf litter decomposition: An intersite decomposition experiment across China

USGS Publications Warehouse

Zhou, G.; Guan, L.; Wei, X.; Tang, X.; Liu, S.; Liu, J.; Zhang, Dongxiao; Yan, J.

2008-01-01

The Long-Term Intersite Decomposition Experiment in China (hereafter referred to as LTIDE-China) was established in 2002 to study how substrate quality and macroclimate factors affect leaf litter decomposition. The LTIDE-China includes a wide variety of natural and managed ecosystems, consisting of 12 forest types (eight regional broadleaf forests, three needle-leaf plantations and one broadleaf plantation) at eight locations across China. Samples of mixed leaf litter from the south subtropical evergreen broadleaf forest in Dinghushan (referred to as the DHS sample) were translocated to all 12 forest types. The leaf litter from each of other 11 forest types was placed in its original forest to enable comparison of decomposition rates of DHS and local litters. The experiment lasted for 30 months, involving collection of litterbags from each site every 3 months. Our results show that annual decomposition rate-constants, as represented by regression fitted k-values, ranged from 0.169 to 1.454/year. Climatic factors control the decomposition rate, in which mean annual temperature and annual actual evapotranspiration are dominant and mean annual precipitation is subordinate. Initial C/N and N/P ratios were demonstrated to be important factors of regulating litter decomposition rate. Decomposition process may apparently be divided into two phases controlled by different factors. In our study, 0.75 years is believed to be the dividing line of the two phases. The fact that decomposition rates of DHS litters were slower than those of local litters may have been resulted from the acclimation of local decomposer communities to extraneous substrate. ?? 2008 Springer Science+Business Media B.V.

Tensor-Dictionary Learning with Deep Kruskal-Factor Analysis

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

Stevens, Andrew J.; Pu, Yunchen; Sun, Yannan

We introduce new dictionary learning methods for tensor-variate data of any order. We represent each data item as a sum of Kruskal decomposed dictionary atoms within the framework of beta-process factor analysis (BPFA). Our model is nonparametric and can infer the tensor-rank of each dictionary atom. This Kruskal-Factor Analysis (KFA) is a natural generalization of BPFA. We also extend KFA to a deep convolutional setting and develop online learning methods. We test our approach on image processing and classification tasks achieving state of the art results for 2D & 3D inpainting and Caltech 101. The experiments also show that atom-rankmore » impacts both overcompleteness and sparsity.« less

Retrodictive determinism. [covariant and transformational behavior of tensor fields in hydrodynamics and thermodynamics

NASA Technical Reports Server (NTRS)

Kiehn, R. M.

1976-01-01

With respect to irreversible, non-homeomorphic maps, contravariant and covariant tensor fields have distinctly natural covariance and transformational behavior. For thermodynamic processes which are non-adiabatic, the fact that the process cannot be represented by a homeomorphic map emphasizes the logical arrow of time, an idea which encompasses a principle of retrodictive determinism for covariant tensor fields.

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.

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

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.

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…

Tensor completion for estimating missing values in visual data.

PubMed

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

2013-01-01

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

Irreducible structure, symmetry and average of Eshelby's tensor fields in isotropic elasticity

NASA Astrophysics Data System (ADS)

Zheng, Q.-S.; Zhao, Z.-H.; Du, D.-X.

2006-02-01

The strain field ɛ(x) in an infinitely large, homogenous, and isotropic elastic medium induced by a uniform eigenstrain ɛ0 in a domain ω depends linearly upon ɛ0 : ɛij(x)=Sijklω(x)ɛkl0. It has been a long-standing conjecture that the Eshelby's tensor field Sω(x) is uniform inside ω if and only if ω is ellipsoidally shaped. Because of the minor index symmetry Sijklω=Sjiklω=Sijlkω, Sω might have a maximum of 36 or nine independent components in three or two dimensions, respectively. In this paper, using the irreducible decomposition of Sω, we show that the isotropic part S of Sω vanishes outside ω and is uniform inside ω with the same value as the Eshelby's tensor S0 for 3D spherical or 2D circular domains. We further show that the anisotropic part Aω=Sω-S of Sω is characterized by a second- and a fourth-order deviatoric tensors and therefore have at maximum 14 or four independent components as characteristics of ω's geometry. Remarkably, the above irreducible structure of Sω is independent of ω's geometry (e.g., shape, orientation, connectedness, convexity, boundary smoothness, etc.). Interesting consequences have implication for a number of recently findings that, for example, both the values of Sω at the center of a 2D Cn(n⩾3,n≠4)-symmetric or 3D icosahedral ω and the average value of Sω over such a ω are equal to S0.

Covariant Conformal Decomposition of Einstein Equations

NASA Astrophysics Data System (ADS)

Gourgoulhon, E.; Novak, J.

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-``metric'' (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this ``metric'', of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

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.

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.

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.

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.

Inflationary tensor perturbations after BICEP2.

PubMed

Caligiuri, Jerod; Kosowsky, Arthur

2014-05-16

The measurement of B-mode polarization of the cosmic microwave background at large angular scales by the BICEP experiment suggests a stochastic gravitational wave background from early-Universe inflation with a surprisingly large amplitude. The power spectrum of these tensor perturbations can be probed both with further measurements of the microwave background polarization at smaller scales and also directly via interferometry in space. We show that sufficiently sensitive high-resolution B-mode measurements will ultimately have the ability to test the inflationary consistency relation between the amplitude and spectrum of the tensor perturbations, confirming their inflationary origin. Additionally, a precise B-mode measurement of the tensor spectrum will predict the tensor amplitude on solar system scales to 20% accuracy for an exact power-law tensor spectrum, so a direct detection will then measure the running of the tensor spectral index to high precision.

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

Aging-driven decomposition in zolpidem hemitartrate hemihydrate and the single-crystal structure of its decomposition products.

PubMed

Vega, Daniel R; Baggio, Ricardo; Roca, Mariana; Tombari, Dora

2011-04-01

The "aging-driven" decomposition of zolpidem hemitartrate hemihydrate (form A) has been followed by X-ray powder diffraction (XRPD), and the crystal and molecular structures of the decomposition products studied by single-crystal methods. The process is very similar to the "thermally driven" one, recently described in the literature for form E (Halasz and Dinnebier. 2010. J Pharm Sci 99(2): 871-874), resulting in a two-phase system: the neutral free base (common to both decomposition processes) and, in the present case, a novel zolpidem tartrate monohydrate, unique to the "aging-driven" decomposition. Our room-temperature single-crystal analysis gives for the free base comparable results as the high-temperature XRPD ones already reported by Halasz and Dinnebier: orthorhombic, Pcba, a = 9.6360(10) Å, b = 18.2690(5) Å, c = 18.4980(11) Å, and V = 3256.4(4) Å(3) . The unreported zolpidem tartrate monohydrate instead crystallizes in monoclinic P21 , which, for comparison purposes, we treated in the nonstandard setting P1121 with a = 20.7582(9) Å, b = 15.2331(5) Å, c = 7.2420(2) Å, γ = 90.826(2)°, and V = 2289.73(14) Å(3) . The structure presents two complete moieties in the asymmetric unit (z = 4, z' = 2). The different phases obtained in both decompositions are readily explained, considering the diverse genesis of both processes. Copyright © 2010 Wiley-Liss, Inc.

A study of perturbations in scalar-tensor theory using 1 + 3 covariant approach

NASA Astrophysics Data System (ADS)

Ntahompagaze, Joseph; Abebe, Amare; Mbonye, Manasse

This work discusses scalar-tensor theories of gravity, with a focus on the Brans-Dicke sub-class, and one that also takes note of the latter’s equivalence with f(R) gravitation theories. A 1 + 3 covariant formalism is used in this case to discuss covariant perturbations on a background Friedmann-Laimaître-Robertson-Walker (FLRW) spacetime. Linear perturbation equations are developed based on gauge-invariant gradient variables. Both scalar and harmonic decompositions are applied to obtain second-order equations. These equations can then be used for further analysis of the behavior of the perturbation quantities in such a scalar-tensor theory of gravitation. Energy density perturbations are studied for two systems, namely for a scalar fluid-radiation system and for a scalar fluid-dust system, for Rn models. For the matter-dominated era, it is shown that the dust energy density perturbations grow exponentially, a result which agrees with those already existing in the literatures. In the radiation-dominated era, it is found that the behavior of the radiation energy-density perturbations is oscillatory, with growing amplitudes for n > 1, and with decaying amplitudes for 0 < n < 1. This is a new result.

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.

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.

Variational optical flow estimation based on stick tensor voting.

PubMed

Rashwan, Hatem A; Garcia, Miguel A; Puig, Domenec

2013-07-01

Variational optical flow techniques allow the estimation of flow fields from spatio-temporal derivatives. They are based on minimizing a functional that contains a data term and a regularization term. Recently, numerous approaches have been presented for improving the accuracy of the estimated flow fields. Among them, tensor voting has been shown to be particularly effective in the preservation of flow discontinuities. This paper presents an adaptation of the data term by using anisotropic stick tensor voting in order to gain robustness against noise and outliers with significantly lower computational cost than (full) tensor voting. In addition, an anisotropic complementary smoothness term depending on directional information estimated through stick tensor voting is utilized in order to preserve discontinuity capabilities of the estimated flow fields. Finally, a weighted non-local term that depends on both the estimated directional information and the occlusion state of pixels is integrated during the optimization process in order to denoise the final flow field. The proposed approach yields state-of-the-art results on the Middlebury benchmark.

Cross-scale efficient tensor contractions for coupled cluster computations through multiple programming model backends

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

Ibrahim, Khaled Z.; Epifanovsky, Evgeny; Williams, Samuel

Coupled-cluster methods provide highly accurate models of molecular structure through explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix–matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts tomore » extend the Libtensor framework to work in the distributed memory environment in a scalable and energy-efficient manner. We achieve up to 240× speedup compared with the optimized shared memory implementation of Libtensor. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures (Cray XC30 and XC40, and IBM Blue Gene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance, tasking and bulk synchronous models. Nevertheless, we preserve a unified interface to both programming models to maintain the productivity of computational quantum chemists.« less

Cross-scale efficient tensor contractions for coupled cluster computations through multiple programming model backends

DOE PAGES

Ibrahim, Khaled Z.; Epifanovsky, Evgeny; Williams, Samuel; ...

2017-03-08

Coupled-cluster methods provide highly accurate models of molecular structure through explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix–matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts tomore » extend the Libtensor framework to work in the distributed memory environment in a scalable and energy-efficient manner. We achieve up to 240× speedup compared with the optimized shared memory implementation of Libtensor. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures (Cray XC30 and XC40, and IBM Blue Gene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance, tasking and bulk synchronous models. Nevertheless, we preserve a unified interface to both programming models to maintain the productivity of computational quantum chemists.« less

Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

DOE PAGES

Plantenga, Todd; Kolda, Tamara G.; Hansen, Samantha

2015-04-30

Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g. count data), which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback–Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton andmore » quasi-Newton methods. Finally, we compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.« less

A quantitative acoustic emission study on fracture processes in ceramics based on wavelet packet decomposition

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

Ning, J. G.; Chu, L.; Ren, H. L., E-mail: huilanren@bit.edu.cn

2014-08-28

We base a quantitative acoustic emission (AE) study on fracture processes in alumina ceramics on wavelet packet decomposition and AE source location. According to the frequency characteristics, as well as energy and ringdown counts of AE, the fracture process is divided into four stages: crack closure, nucleation, development, and critical failure. Each of the AE signals is decomposed by a 2-level wavelet package decomposition into four different (from-low-to-high) frequency bands (AA{sub 2}, AD{sub 2}, DA{sub 2}, and DD{sub 2}). The energy eigenvalues P{sub 0}, P{sub 1}, P{sub 2}, and P{sub 3} corresponding to these four frequency bands are calculated. Bymore » analyzing changes in P{sub 0} and P{sub 3} in the four stages, we determine the inverse relationship between AE frequency and the crack source size during ceramic fracture. AE signals with regard to crack nucleation can be expressed when P{sub 0} is less than 5 and P{sub 3} more than 60; whereas AE signals with regard to dangerous crack propagation can be expressed when more than 92% of P{sub 0} is greater than 4, and more than 95% of P{sub 3} is less than 45. Geiger location algorithm is used to locate AE sources and cracks in the sample. The results of this location algorithm are consistent with the positions of fractures in the sample when observed under a scanning electronic microscope; thus the locations of fractures located with Geiger's method can reflect the fracture process. The stage division by location results is in a good agreement with the division based on AE frequency characteristics. We find that both wavelet package decomposition and Geiger's AE source locations are suitable for the identification of the evolutionary process of cracks in alumina ceramics.« less

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

NASA Astrophysics Data System (ADS)

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

2012-08-01

We have previously proven the feasibility of ultrasound-based shear wave imaging (SWI) to non-invasively characterize myocardial fiber orientation in both in vitro porcine and in vivo ovine hearts. The SWI-estimated results were in good correlation with histology. In this study, we proposed a new and robust fiber angle estimation method through a tensor-based approach for SWI, coined together as elastic tensor imaging (ETI), and compared it with magnetic resonance diffusion tensor imaging (DTI), a current gold standard and extensively reported non-invasive imaging technique for mapping fiber architecture. Fresh porcine (n = 5) and ovine (n = 5) myocardial samples (20 × 20 × 30 mm3) were studied. ETI was firstly performed to generate shear waves and to acquire the wave events at ultrafast frame rate (8000 fps). A 2.8 MHz phased array probe (pitch = 0.28 mm), connected to a prototype ultrasound scanner, was mounted on a customized MRI-compatible rotation device, which allowed both the rotation of the probe from -90° to 90° at 5° increments and co-registration between two imaging modalities. Transmural shear wave speed at all propagation directions realized was firstly estimated. The fiber angles were determined from the shear wave speed map using the least-squares method and eigen decomposition. The test myocardial sample together with the rotation device was then placed inside a 7T MRI scanner. Diffusion was encoded in six directions. A total of 270 diffusion-weighted images (b = 1000 s mm-2, FOV = 30 mm, matrix size = 60 × 64, TR = 6 s, TE = 19 ms, 24 averages) and 45 B0 images were acquired in 14 h 30 min. The fiber structure was analyzed by the fiber-tracking module in software, MedINRIA. The fiber orientation in the overlapped myocardial region which both ETI and DTI accessed was therefore compared, thanks to the co-registered imaging system. Results from all ten samples showed good correlation (r2 = 0.81, p < 0.0001) and good agreement (3.05° bias

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.

Accelerated decomposition techniques for large discounted Markov decision processes

NASA Astrophysics Data System (ADS)

Larach, Abdelhadi; Chafik, S.; Daoui, C.

2017-12-01

Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorithm, which is a variant of Tarjan's algorithm that simultaneously finds the SCCs and their belonging levels. Second, a new definition of the restricted MDPs is presented to ameliorate some hierarchical solutions in discounted MDPs using value iteration (VI) algorithm based on a list of state-action successors. Finally, a robotic motion-planning example and the experiment results are presented to illustrate the benefit of the proposed decomposition algorithms.

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

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.

Octupolar tensors for liquid crystals

NASA Astrophysics Data System (ADS)

Chen, Yannan; Qi, Liqun; Virga, Epifanio G.

2018-01-01

A third-rank three-dimensional symmetric traceless tensor, called the octupolar tensor, has been introduced to study tetrahedratic nematic phases in liquid crystals. The octupolar potential, a scalar-valued function generated on the unit sphere by that tensor, should ideally have four maxima (on the vertices of a tetrahedron), but it was recently found to possess an equally generic variant with three maxima instead of four. It was also shown that the irreducible admissible region for the octupolar tensor in a three-dimensional parameter space is bounded by a dome-shaped surface, beneath which is a separatrix surface connecting the two generic octupolar states. The latter surface, which was obtained through numerical continuation, may be physically interpreted as marking a possible intra-octupolar transition. In this paper, by using the resultant theory of algebraic geometry and the E-characteristic polynomial of spectral theory of tensors, we give a closed-form, algebraic expression for both the dome-shaped surface and the separatrix surface. This turns the envisaged intra-octupolar transition into a quantitative, possibly observable prediction.

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.

Quantification of diffusion tensor imaging in normal white matter maturation of early childhood using an automated processing pipeline.

PubMed

Loh, K B; Ramli, N; Tan, L K; Roziah, M; Rahmat, K; Ariffin, H

2012-07-01

The degree and status of white matter myelination can be sensitively monitored using diffusion tensor imaging (DTI). This study looks at the measurement of fractional anistropy (FA) and mean diffusivity (MD) using an automated ROI with an existing DTI atlas. Anatomical MRI and structural DTI were performed cross-sectionally on 26 normal children (newborn to 48 months old), using 1.5-T MRI. The automated processing pipeline was implemented to convert diffusion-weighted images into the NIfTI format. DTI-TK software was used to register the processed images to the ICBM DTI-81 atlas, while AFNI software was used for automated atlas-based volumes of interest (VOIs) and statistical value extraction. DTI exhibited consistent grey-white matter contrast. Triphasic temporal variation of the FA and MD values was noted, with FA increasing and MD decreasing rapidly early in the first 12 months. The second phase lasted 12-24 months during which the rate of FA and MD changes was reduced. After 24 months, the FA and MD values plateaued. DTI is a superior technique to conventional MR imaging in depicting WM maturation. The use of the automated processing pipeline provides a reliable environment for quantitative analysis of high-throughput DTI data. Diffusion tensor imaging outperforms conventional MRI in depicting white matter maturation. • DTI will become an important clinical tool for diagnosing paediatric neurological diseases. • DTI appears especially helpful for developmental abnormalities, tumours and white matter disease. • An automated processing pipeline assists quantitative analysis of high throughput DTI data.

Highly efficient all-dielectric optical tensor impedance metasurfaces for chiral polarization control.

PubMed

Kim, Minseok; Eleftheriades, George V

2016-10-15

We propose a highly efficient (nearly lossless and impedance-matched) all-dielectric optical tensor impedance metasurface that mimics chiral effects at optical wavelengths. By cascading an array of rotated crossed silicon nanoblocks, we realize chiral optical tensor impedance metasurfaces that operate as circular polarization selective surfaces. Their efficiencies are maximized through a nonlinear numerical optimization process in which the tensor impedance metasurfaces are modeled via multi-conductor transmission line theory. From rigorous full-wave simulations that include all material losses, we show field transmission efficiencies of 94% for right- and left-handed circular polarization selective surfaces at 800 nm.

Generic, network schema agnostic sparse tensor factorization for single-pass clustering of heterogeneous information networks

PubMed Central

Meng, Qinggang; Deng, Su; Huang, Hongbin; Wu, Yahui; Badii, Atta

2017-01-01

Heterogeneous information networks (e.g. bibliographic networks and social media networks) that consist of multiple interconnected objects are ubiquitous. Clustering analysis is an effective method to understand the semantic information and interpretable structure of the heterogeneous information networks, and it has attracted the attention of many researchers in recent years. However, most studies assume that heterogeneous information networks usually follow some simple schemas, such as bi-typed networks or star network schema, and they can only cluster one type of object in the network each time. In this paper, a novel clustering framework is proposed based on sparse tensor factorization for heterogeneous information networks, which can cluster multiple types of objects simultaneously in a single pass without any network schema information. The types of objects and the relations between them in the heterogeneous information networks are modeled as a sparse tensor. The clustering issue is modeled as an optimization problem, which is similar to the well-known Tucker decomposition. Then, an Alternating Least Squares (ALS) algorithm and a feasible initialization method are proposed to solve the optimization problem. Based on the tensor factorization, we simultaneously partition different types of objects into different clusters. The experimental results on both synthetic and real-world datasets have demonstrated that our proposed clustering framework, STFClus, can model heterogeneous information networks efficiently and can outperform state-of-the-art clustering algorithms as a generally applicable single-pass clustering method for heterogeneous network which is network schema agnostic. PMID:28245222

Generic, network schema agnostic sparse tensor factorization for single-pass clustering of heterogeneous information networks.

PubMed

Wu, Jibing; Meng, Qinggang; Deng, Su; Huang, Hongbin; Wu, Yahui; Badii, Atta

2017-01-01

Heterogeneous information networks (e.g. bibliographic networks and social media networks) that consist of multiple interconnected objects are ubiquitous. Clustering analysis is an effective method to understand the semantic information and interpretable structure of the heterogeneous information networks, and it has attracted the attention of many researchers in recent years. However, most studies assume that heterogeneous information networks usually follow some simple schemas, such as bi-typed networks or star network schema, and they can only cluster one type of object in the network each time. In this paper, a novel clustering framework is proposed based on sparse tensor factorization for heterogeneous information networks, which can cluster multiple types of objects simultaneously in a single pass without any network schema information. The types of objects and the relations between them in the heterogeneous information networks are modeled as a sparse tensor. The clustering issue is modeled as an optimization problem, which is similar to the well-known Tucker decomposition. Then, an Alternating Least Squares (ALS) algorithm and a feasible initialization method are proposed to solve the optimization problem. Based on the tensor factorization, we simultaneously partition different types of objects into different clusters. The experimental results on both synthetic and real-world datasets have demonstrated that our proposed clustering framework, STFClus, can model heterogeneous information networks efficiently and can outperform state-of-the-art clustering algorithms as a generally applicable single-pass clustering method for heterogeneous network which is network schema agnostic.

Decentralized Dimensionality Reduction for Distributed Tensor Data Across Sensor Networks.

PubMed

Liang, Junli; Yu, Guoyang; Chen, Badong; Zhao, Minghua

2016-11-01

This paper develops a novel decentralized dimensionality reduction algorithm for the distributed tensor data across sensor networks. The main contributions of this paper are as follows. First, conventional centralized methods, which utilize entire data to simultaneously determine all the vectors of the projection matrix along each tensor mode, are not suitable for the network environment. Here, we relax the simultaneous processing manner into the one-vector-by-one-vector (OVBOV) manner, i.e., determining the projection vectors (PVs) related to each tensor mode one by one. Second, we prove that in the OVBOV manner each PV can be determined without modifying any tensor data, which simplifies corresponding computations. Third, we cast the decentralized PV determination problem as a set of subproblems with consensus constraints, so that it can be solved in the network environment only by local computations and information communications among neighboring nodes. Fourth, we introduce the null space and transform the PV determination problem with complex orthogonality constraints into an equivalent hidden convex one without any orthogonality constraint, which can be solved by the Lagrange multiplier method. Finally, experimental results are given to show that the proposed algorithm is an effective dimensionality reduction scheme for the distributed tensor data across the sensor networks.

ENVIRONMENTAL ASSESSMENT OF THE BASE CATALYZED DECOMPOSITION (BCD) PROCESS

EPA Science Inventory

This report summarizes laboratory-scale, pilot-scale, and field performance data on BCD (Base Catalyzed Decomposition) and technology, collected to date by various governmental, academic, and private organizations.

Early stage litter decomposition across biomes

Treesearch

Ika Djukic; Sebastian Kepfer-Rojas; Inger Kappel Schmidt; Klaus Steenberg Larsen; Claus Beier; Björn Berg; Kris Verheyen; Adriano Caliman; Alain Paquette; Alba Gutiérrez-Girón; Alberto Humber; Alejandro Valdecantos; Alessandro Petraglia; Heather Alexander; Algirdas Augustaitis; Amélie Saillard; Ana Carolina Ruiz Fernández; Ana I. Sousa; Ana I. Lillebø; Anderson da Rocha Gripp; André-Jean Francez; Andrea Fischer; Andreas Bohner; Andrey Malyshev; Andrijana Andrić; Andy Smith; Angela Stanisci; Anikó Seres; Anja Schmidt; Anna Avila; Anne Probst; Annie Ouin; Anzar A. Khuroo; Arne Verstraeten; Arely N. Palabral-Aguilera; Artur Stefanski; Aurora Gaxiola; Bart Muys; Bernard Bosman; Bernd Ahrends; Bill Parker; Birgit Sattler; Bo Yang; Bohdan Juráni; Brigitta Erschbamer; Carmen Eugenia Rodriguez Ortiz; Casper T. Christiansen; E. Carol Adair; Céline Meredieu; Cendrine Mony; Charles A. Nock; Chi-Ling Chen; Chiao-Ping Wang; Christel Baum; Christian Rixen; Christine Delire; Christophe Piscart; Christopher Andrews; Corinna Rebmann; Cristina Branquinho; Dana Polyanskaya; David Fuentes Delgado; Dirk Wundram; Diyaa Radeideh; Eduardo Ordóñez-Regil; Edward Crawford; Elena Preda; Elena Tropina; Elli Groner; Eric Lucot; Erzsébet Hornung; Esperança Gacia; Esther Lévesque; Evanilde Benedito; Evgeny A. Davydov; Evy Ampoorter; Fabio Padilha Bolzan; Felipe Varela; Ferdinand Kristöfel; Fernando T. Maestre; Florence Maunoury-Danger; Florian Hofhansl; Florian Kitz; Flurin Sutter; Francisco Cuesta; Francisco de Almeida Lobo; Franco Leandro de Souza; Frank Berninger; Franz Zehetner; Georg Wohlfahrt; George Vourlitis; Geovana Carreño-Rocabado; Gina Arena; Gisele Daiane Pinha; Grizelle González; Guylaine Canut; Hanna Lee; Hans Verbeeck; Harald Auge; Harald Pauli; Hassan Bismarck Nacro; Héctor A. Bahamonde; Heike Feldhaar; Heinke Jäger; Helena C. Serrano; Hélène Verheyden; Helge Bruelheide; Henning Meesenburg; Hermann Jungkunst; Hervé Jactel; Hideaki Shibata; Hiroko Kurokawa; Hugo López Rosas; Hugo L. Rojas Villalobos; Ian Yesilonis; Inara Melece; Inge Van Halder; Inmaculada García Quirós; Isaac Makelele; Issaka Senou; István Fekete; Ivan Mihal; Ivika Ostonen; Jana Borovská; Javier Roales; Jawad Shoqeir; Jean-Christophe Lata; Jean-Paul Theurillat; Jean-Luc Probst; Jess Zimmerman; Jeyanny Vijayanathan; Jianwu Tang; Jill Thompson; Jiří Doležal; Joan-Albert Sanchez-Cabeza; Joël Merlet; Joh Henschel; Johan Neirynck; Johannes Knops; John Loehr; Jonathan von Oppen; Jónína Sigríður Þorláksdóttir; Jörg Löffler; José-Gilberto Cardoso-Mohedano; José-Luis Benito-Alonso; Jose Marcelo Torezan; Joseph C. Morina; Juan J. Jiménez; Juan Dario Quinde; Juha Alatalo; Julia Seeber; Jutta Stadler; Kaie Kriiska; Kalifa Coulibaly; Karibu Fukuzawa; Katalin Szlavecz; Katarína Gerhátová; Kate Lajtha; Kathrin Käppeler; Katie A. Jennings; Katja Tielbörger; Kazuhiko Hoshizaki; Ken Green; Lambiénou Yé; Laryssa Helena Ribeiro Pazianoto; Laura Dienstbach; Laura Williams; Laura Yahdjian; Laurel M. Brigham; Liesbeth van den Brink; Lindsey Rustad; al. et

2018-01-01

Through litter decomposition enormous amounts of carbon is emitted to the atmosphere. Numerous large-scale decomposition experiments have been conducted focusing on this fundamental soil process in order to understand the controls on the terrestrial carbon transfer to the atmosphere. However, previous studies were mostly based on site-specific litter and methodologies...

Robust estimation of adaptive tensors of curvature by tensor voting.

PubMed

Tong, Wai-Shun; Tang, Chi-Keung

2005-03-01

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

Seamless Warping of Diffusion Tensor Fields

PubMed Central

Hao, Xuejun; Bansal, Ravi; Plessen, Kerstin J.; Peterson, Bradley S.

2008-01-01

To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create “seams” or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template space where the magnitude of the deformation is large (e.g., |Jacobian| > 1). Backward mapping, in contrast, defines voxels in the template space by mapping them back to locations in the original imaging space. Backward mapping allows every voxel in the template space to be defined without the creation of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT datasets seamlessly from one imaging space to another. Once the bijection has been achieved and tensors have been correctly relocated to the template space, we can appropriately reorient tensors in the template space using a warping method based on Procrustean estimation. PMID:18334425

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.

The Invar tensor package: Differential invariants of Riemann

NASA Astrophysics Data System (ADS)

Martín-García, J. M.; Yllanes, D.; Portugal, R.

2008-10-01

The long standing problem of the relations among the scalar invariants of the Riemann tensor is computationally solved for all 6ṡ10 objects with up to 12 derivatives of the metric. This covers cases ranging from products of up to 6 undifferentiated Riemann tensors to cases with up to 10 covariant derivatives of a single Riemann. We extend our computer algebra system Invar to produce within seconds a canonical form for any of those objects in terms of a basis. The process is as follows: (1) an invariant is converted in real time into a canonical form with respect to the permutation symmetries of the Riemann tensor; (2) Invar reads a database of more than 6ṡ10 relations and applies those coming from the cyclic symmetry of the Riemann tensor; (3) then applies the relations coming from the Bianchi identity, (4) the relations coming from commutations of covariant derivatives, (5) the dimensionally-dependent identities for dimension 4, and finally (6) simplifies invariants that can be expressed as product of dual invariants. Invar runs on top of the tensor computer algebra systems xTensor (for Mathematica) and Canon (for Maple). Program summaryProgram title:Invar Tensor Package v2.0 Catalogue identifier:ADZK_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZK_v2_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:3 243 249 No. of bytes in distributed program, including test data, etc.:939 Distribution format:tar.gz Programming language:Mathematica and Maple Computer:Any computer running Mathematica versions 5.0 to 6.0 or Maple versions 9 and 11 Operating system:Linux, Unix, Windows XP, MacOS RAM:100 Mb Word size:64 or 32 bits Supplementary material:The new database of relations is much larger than that for the previous version and therefore has not been included in

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

DTIC Science & Technology

2011-06-01

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

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

DTIC Science & Technology

2011-06-01

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

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.

The simplicial Ricci tensor

NASA Astrophysics Data System (ADS)

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

2011-08-01

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

Estimation of full moment tensors, including uncertainties, for earthquakes, volcanic events, and nuclear explosions

NASA Astrophysics Data System (ADS)

Alvizuri, Celso R.

We present a catalog of full seismic moment tensors for 63 events from Uturuncu volcano in Bolivia. The events were recorded during 2011-2012 in the PLUTONS seismic array of 24 broadband stations. Most events had magnitudes between 0.5 and 2.0 and did not generate discernible surface waves; the largest event was Mw 2.8. For each event we computed the misfit between observed and synthetic waveforms, and we used first-motion polarity measurements to reduce the number of possible solutions. Each moment tensor solution was obtained using a grid search over the six-dimensional space of moment tensors. For each event we show the misfit function in eigenvalue space, represented by a lune. We identify three subsets of the catalog: (1) 6 isotropic events, (2) 5 tensional crack events, and (3) a swarm of 14 events southeast of the volcanic center that appear to be double couples. The occurrence of positively isotropic events is consistent with other published results from volcanic and geothermal regions. Several of these previous results, as well as our results, cannot be interpreted within the context of either an oblique opening crack or a crack-plus-double-couple model. Proper characterization of uncertainties for full moment tensors is critical for distinguishing among physical models of source processes. A seismic moment tensor is a 3x3 symmetric matrix that provides a compact representation of a seismic source. 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 for each moment tensor and then evaluating a misfit function between the observed and synthetic waveforms. 'The' moment tensor M0 for the event is then the moment tensor with minimum misfit. To describe the uncertainty associated with M0, we first convert the misfit function to a probability function. The uncertainty, or

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.

Symmetric Positive 4th Order Tensors & Their Estimation from Diffusion Weighted MRI⋆

PubMed Central

Barmpoutis, Angelos; Jian, Bing; Vemuri, Baba C.; Shepherd, Timothy M.

2009-01-01

In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. It is now well known that this 2nd-order approximation fails to approximate complex local tissue structures, such as fibers crossings. In this paper we employ a 4th order symmetric positive semi-definite (PSD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the PSD property. There have been several published articles in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positive semi-definite constraint, which is a fundamental constraint since negative values of the diffusivity coefficients are not meaningful. In our methods, we parameterize the 4th order tensors as a sum of squares of quadratic forms by using the so called Gram matrix method from linear algebra and its relation to the Hilbert’s theorem on ternary quartics. This parametric representation is then used in a nonlinear-least squares formulation to estimate the PSD tensors of order 4 from the data. We define a metric for the higher-order tensors and employ it for regularization across the lattice. Finally, performance of this model is depicted on synthetic data as well as real DW-MRI from an isolated rat hippocampus. PMID:17633709

Efficient photoreductive decomposition of N-nitrosodimethylamine by UV/iodide process.

PubMed

Sun, Zhuyu; Zhang, Chaojie; Zhao, Xiaoyun; Chen, Jing; Zhou, Qi

2017-05-05

N-nitrosodimethylamine (NDMA) has aroused extensive concern as a disinfection byproduct due to its high toxicity and elevated concentration levels in water sources. This study investigates the photoreductive decomposition of NDMA by UV/iodide process. The results showed that this process is an effective strategy for the treatment of NDMA with 99.2% NDMA removed within 10min. The depletion of NDMA by UV/iodide process obeyed pseudo-first-order kinetics with a rate constant (k 1 ) of 0.60±0.03min -1 . Hydrated electrons (e aq - ) generated by the UV irradiation of iodide were proven to play a critical role. Dimethylamine (DMA) and nitrite (NO 2 - ) were formed as the main intermediate products, which completely converted to formate (HCOO - ), ammonium (NH 4 + ) and nitrogen (N 2 ). Therefore, not only the high efficiencies in NDMA destruction, but the elimination of toxic intermediates make UV/iodide process advantageous. A photoreduction mechanism was proposed: NDMA initially absorbed photons to a photoexcited state, and underwent a cleavage of NNO bond under the attack of e aq - . The solution pH had little impact on NDMA removal. However, alkaline conditions were more favorable for the elimination of DMA and NO 2 - , thus effectively reducing the secondary pollution. Copyright © 2016 Elsevier B.V. All rights reserved.

A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

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

Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.

We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ''Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbationsmore » that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.« less

Tensor Galileons and gravity

NASA Astrophysics Data System (ADS)

Chatzistavrakidis, Athanasios; Khoo, Fech Scen; Roest, Diederik; Schupp, Peter

2017-03-01

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

Tensor decomposition-based and principal-component-analysis-based unsupervised feature extraction applied to the gene expression and methylation profiles in the brains of social insects with multiple castes.

PubMed

Taguchi, Y-H

2018-05-08

Even though coexistence of multiple phenotypes sharing the same genomic background is interesting, it remains incompletely understood. Epigenomic profiles may represent key factors, with unknown contributions to the development of multiple phenotypes, and social-insect castes are a good model for elucidation of the underlying mechanisms. Nonetheless, previous studies have failed to identify genes associated with aberrant gene expression and methylation profiles because of the lack of suitable methodology that can address this problem properly. A recently proposed principal component analysis (PCA)-based and tensor decomposition (TD)-based unsupervised feature extraction (FE) can solve this problem because these two approaches can deal with gene expression and methylation profiles even when a small number of samples is available. PCA-based and TD-based unsupervised FE methods were applied to the analysis of gene expression and methylation profiles in the brains of two social insects, Polistes canadensis and Dinoponera quadriceps. Genes associated with differential expression and methylation between castes were identified, and analysis of enrichment of Gene Ontology terms confirmed reliability of the obtained sets of genes from the biological standpoint. Biologically relevant genes, shown to be associated with significant differential gene expression and methylation between castes, were identified here for the first time. The identification of these genes may help understand the mechanisms underlying epigenetic control of development of multiple phenotypes under the same genomic conditions.

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.

Decomposition Rate and Pattern in Hanging Pigs.

PubMed

Lynch-Aird, Jeanne; Moffatt, Colin; Simmons, Tal

2015-09-01

Accurate prediction of the postmortem interval requires an understanding of the decomposition process and the factors acting upon it. A controlled experiment, over 60 days at an outdoor site in the northwest of England, used 20 freshly killed pigs (Sus scrofa) as human analogues to study decomposition rate and pattern. Ten pigs were hung off the ground and ten placed on the surface. Observed differences in the decomposition pattern required a new decomposition scoring scale to be produced for the hanging pigs to enable comparisons with the surface pigs. The difference in the rate of decomposition between hanging and surface pigs was statistically significant (p=0.001). Hanging pigs reached advanced decomposition stages sooner, but lagged behind during the early stages. This delay is believed to result from lower variety and quantity of insects, due to restricted beetle access to the aerial carcass, and/or writhing maggots falling from the carcass. © 2015 American Academy of Forensic Sciences.

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

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.

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.

Biological decomposition efficiency in different woodland soils.

PubMed

Herlitzius, H

1983-03-01

The decomposition (meaning disappearance) of different leaf types and artificial leaves made from cellulose hydrate foil was studied in three forests - an alluvial forest (Ulmetum), a beech forest on limestone soil (Melico-Fagetum), and a spruce forest in soil overlying limestone bedrock.Fine, medium, and coarse mesh litter bags of special design were used to investigate the roles of abiotic factors, microorganisms, and meso- and macrofauna in effecting decomposition in the three habitats. Additionally, the experimental design was carefully arranged so as to provide information about the effects on decomposition processes of the duration of exposure and the date or moment of exposure. 1. Exposure of litter samples oor 12 months showed: a) Litter enclosed in fine mesh bags decomposed to some 40-44% of the initial amount placed in each of the three forests. Most of this decomposition can be attributed to abiotic factors and microoganisms. b) Litter placed in medium mesh litter bags reduced by ca. 60% in alluvial forest, ca. 50% in beech forest and ca. 44% in spruce forest. c) Litter enclosed in coarse mesh litter bags was reduced by 71% of the initial weights exposed in alluvial and beech forests; in the spruce forest decomposition was no greater than observed with fine and medium mesh litter bags. Clearly, in spruce forest the macrofauna has little or no part to play in effecting decomposition. 2. Sequential month by month exposure of hazel leaves and cellulose hydrate foil in coarse mesh litter bags in all three forests showed that one month of exposure led to only slight material losses, they did occur smallest between March and May, and largest between June and October/November. 3. Coarse mesh litter bags containing either hazel or artificial leaves of cellulose hydrate foil were exposed to natural decomposition processes in December 1977 and subsampled monthly over a period of one year, this series constituted the From-sequence of experiments. Each of the From

Loop optimization for tensor network renormalization

NASA Astrophysics Data System (ADS)

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

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

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.

Input-decomposition balance of heterotrophic processes in a warm-temperate mixed forest in Japan

NASA Astrophysics Data System (ADS)

Jomura, M.; Kominami, Y.; Ataka, M.; Makita, N.; Dannoura, M.; Miyama, T.; Tamai, K.; Goto, Y.; Sakurai, S.

2010-12-01

Carbon accumulation in forest ecosystem has been evaluated using three approaches. One is net ecosystem exchange (NEE) estimated by tower flux measurement. The second is net ecosystem production (NEP) estimated by biometric measurements. NEP can be expressed as the difference between net primary production and heterotrophic respiration. NEP can also be expressed as the annual increment in the plant biomass (ΔW) plus soil (ΔS) carbon pools defined as follows; NEP = ΔW+ΔS The third approach needs to evaluate annual carbon increment in soil compartment. Soil carbon accumulation rate could not be measured directly in a short term because of the small amount of annual accumulation. Soil carbon accumulation rate can be estimated by a model calculation. Rothamsted carbon model is a soil organic carbon turnover model and a useful tool to estimate the rate of soil carbon accumulation. However, the model has not sufficiently included variations in decomposition processes of organic matters in forest ecosystems. Organic matter in forest ecosystems have a different turnover rate that creates temporal variations in input-decomposition balance and also have a large variation in spatial distribution. Thus, in order to estimate the rate of soil carbon accumulation, temporal and spatial variation in input-decomposition balance of heterotrophic processes should be incorporated in the model. In this study, we estimated input-decomposition balance and the rate of soil carbon accumulation using the modified Roth-C model. We measured respiration rate of many types of organic matters, such as leaf litter, fine root litter, twigs and coarse woody debris using a chamber method. We can illustrate the relation of respiration rate to diameter of organic matters. Leaf and fine root litters have no diameter, so assumed to be zero in diameter. Organic matters in small size, such as leaf and fine root litter, have high decomposition respiration. It could be caused by the difference in

Bayesian ISOLA: new tool for automated centroid moment tensor inversion

NASA Astrophysics Data System (ADS)

Vackář, Jiří; Burjánek, Jan; Gallovič, František; Zahradník, Jiří; Clinton, John

2017-04-01

Focal mechanisms are important for understanding seismotectonics of a region, and they serve as a basic input for seismic hazard assessment. Usually, the point source approximation and the moment tensor (MT) are used. We have developed a new, fully automated tool for the centroid moment tensor (CMT) inversion in a Bayesian framework. It includes automated data retrieval, data selection where station components with various instrumental disturbances and high signal-to-noise are rejected, and full-waveform inversion in a space-time grid around a provided hypocenter. The method is innovative in the following aspects: (i) The CMT inversion is fully automated, no user interaction is required, although the details of the process can be visually inspected latter on many figures which are automatically plotted.(ii) The automated process includes detection of disturbances based on MouseTrap code, so disturbed recordings do not affect inversion.(iii) A data covariance matrix calculated from pre-event noise yields an automated weighting of the station recordings according to their noise levels and also serves as an automated frequency filter suppressing noisy frequencies.(iv) Bayesian approach is used, so not only the best solution is obtained, but also the posterior probability density function.(v) A space-time grid search effectively combined with the least-squares inversion of moment tensor components speeds up the inversion and allows to obtain more accurate results compared to stochastic methods. The method has been tested on synthetic and observed data. It has been tested by comparison with manually processed moment tensors of all events greater than M≥3 in the Swiss catalogue over 16 years using data available at the Swiss data center (http://arclink.ethz.ch). The quality of the results of the presented automated process is comparable with careful manual processing of data. The software package programmed in Python has been designed to be as versatile as possible in

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

Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.

PubMed

Liu, Haofei; Sun, Wei

2017-08-01

Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

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

PubMed

Dibb, Russell; Liu, Chunlei

2017-06-01

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

Geometric decompositions of collective motion

NASA Astrophysics Data System (ADS)

Mischiati, Matteo; Krishnaprasad, P. S.

2017-04-01

Collective motion in nature is a captivating phenomenon. Revealing the underlying mechanisms, which are of biological and theoretical interest, will require empirical data, modelling and analysis techniques. Here, we contribute a geometric viewpoint, yielding a novel method of analysing movement. Snapshots of collective motion are portrayed as tangent vectors on configuration space, with length determined by the total kinetic energy. Using the geometry of fibre bundles and connections, this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space. The resulting decomposition, when interleaved with classical shape space construction, is categorized into a family of kinematic modes-including rigid translations, rigid rotations, inertia tensor transformations, expansions and compressions. Snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy. Such quantitative measures can provide insight into the variation of the driving goals of a collective, as illustrated by applying these methods to a publicly available dataset of pigeon flocking. The geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots.

Geometric decompositions of collective motion

PubMed Central

Krishnaprasad, P. S.

2017-01-01

Collective motion in nature is a captivating phenomenon. Revealing the underlying mechanisms, which are of biological and theoretical interest, will require empirical data, modelling and analysis techniques. Here, we contribute a geometric viewpoint, yielding a novel method of analysing movement. Snapshots of collective motion are portrayed as tangent vectors on configuration space, with length determined by the total kinetic energy. Using the geometry of fibre bundles and connections, this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space. The resulting decomposition, when interleaved with classical shape space construction, is categorized into a family of kinematic modes—including rigid translations, rigid rotations, inertia tensor transformations, expansions and compressions. Snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy. Such quantitative measures can provide insight into the variation of the driving goals of a collective, as illustrated by applying these methods to a publicly available dataset of pigeon flocking. The geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots. PMID:28484319

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.

Ozone decomposition

PubMed Central

Batakliev, Todor; Georgiev, Vladimir; Anachkov, Metody; Rakovsky, Slavcho

2014-01-01

Catalytic ozone decomposition is of great significance because ozone is a toxic substance commonly found or generated in human environments (aircraft cabins, offices with photocopiers, laser printers, sterilizers). Considerable work has been done on ozone decomposition reported in the literature. This review provides a comprehensive summary of the literature, concentrating on analysis of the physico-chemical properties, synthesis and catalytic decomposition of ozone. This is supplemented by a review on kinetics and catalyst characterization which ties together the previously reported results. Noble metals and oxides of transition metals have been found to be the most active substances for ozone decomposition. The high price of precious metals stimulated the use of metal oxide catalysts and particularly the catalysts based on manganese oxide. It has been determined that the kinetics of ozone decomposition is of first order importance. A mechanism of the reaction of catalytic ozone decomposition is discussed, based on detailed spectroscopic investigations of the catalytic surface, showing the existence of peroxide and superoxide surface intermediates. PMID:26109880

Decomposition of sulfamethoxazole and trimethoprim by continuous UVA/LED/TiO2 photocatalysis: Decomposition pathways, residual antibacterial activity and toxicity.

PubMed

Cai, Qinqing; Hu, Jiangyong

2017-02-05

In this study, continuous LED/UVA/TiO 2 photocatalytic decomposition of sulfamethoxazole (SMX) and trimethoprim (TMP) was investigated. More than 90% of SMX and TMP were removed within 20min by the continuous photoreactor (with the initial concentration of 400ppb for each). The removal rates of SMX and TMP decreased with higher initial antibiotics loadings. SMX was much easier decomposed in acidic condition, while pH affected little on TMP's decomposition. 0.003% was found to be the optimum H 2 O 2 dosage to enhance SMX photocatalytic decomposition. Decomposition pathways of SMX and TMP were proposed based on the intermediates identified by using LC-MS-MS and GC-MS. Aniline was identified as a new intermediate generated during SMX photocatalytic decomposition. Antibacterial activity study with a reference Escherichia coli strain was also conducted during the photocatalytic process. Results indicated that with every portion of TMP removed, the residual antibacterial activity decreased by one portion. However, the synergistic effect between SMX and TMP tended to slow down the antibacterial activity removal of SMX and TMP mixture. Chronic toxicity studies conducted with Vibrio fischeri exhibited 13-20% bioluminescence inhibition during the decomposition of 1ppm SMX and 1ppm TMP, no acute toxicity to V. fischeri was observed during the photocatalytic process. Copyright © 2016 Elsevier B.V. All rights reserved.

Thermal decomposition behavior of nano/micro bimodal feedstock with different solids loading

NASA Astrophysics Data System (ADS)

Oh, Joo Won; Lee, Won Sik; Park, Seong Jin

2018-01-01

Debinding is one of the most critical processes for powder injection molding. The parts in debinding process are vulnerable to defect formation, and long processing time of debinding decreases production rate of whole process. In order to determine the optimal condition for debinding process, decomposition behavior of feedstock should be understood. Since nano powder affects the decomposition behavior of feedstock, nano powder effect needs to be investigated for nano/micro bimodal feedstock. In this research, nano powder effect on decomposition behavior of nano/micro bimodal feedstock has been studied. Bimodal powders were fabricated with different ratios of nano powder, and the critical solids loading of each powder was measured by torque rheometer. Three different feedstocks were fabricated for each powder depending on solids loading condition. Thermogravimetric analysis (TGA) experiment was carried out to analyze the thermal decomposition behavior of the feedstocks, and decomposition activation energy was calculated. The result indicated nano powder showed limited effect on feedstocks in lower solids loading condition than optimal range. Whereas, it highly influenced the decomposition behavior in optimal solids loading condition by causing polymer chain scission with high viscosity.

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.

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

Tensor network state correspondence and holography

NASA Astrophysics Data System (ADS)

Singh, Sukhwinder

2018-01-01

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

Time-Optimized High-Resolution Readout-Segmented Diffusion Tensor Imaging

PubMed Central

Reishofer, Gernot; Koschutnig, Karl; Langkammer, Christian; Porter, David; Jehna, Margit; Enzinger, Christian; Keeling, Stephen; Ebner, Franz

2013-01-01

Readout-segmented echo planar imaging with 2D navigator-based reacquisition is an uprising technique enabling the sampling of high-resolution diffusion images with reduced susceptibility artifacts. However, low signal from the small voxels and long scan times hamper the clinical applicability. Therefore, we introduce a regularization algorithm based on total variation that is applied directly on the entire diffusion tensor. The spatially varying regularization parameter is determined automatically dependent on spatial variations in signal-to-noise ratio thus, avoiding over- or under-regularization. Information about the noise distribution in the diffusion tensor is extracted from the diffusion weighted images by means of complex independent component analysis. Moreover, the combination of those features enables processing of the diffusion data absolutely user independent. Tractography from in vivo data and from a software phantom demonstrate the advantage of the spatially varying regularization compared to un-regularized data with respect to parameters relevant for fiber-tracking such as Mean Fiber Length, Track Count, Volume and Voxel Count. Specifically, for in vivo data findings suggest that tractography results from the regularized diffusion tensor based on one measurement (16 min) generates results comparable to the un-regularized data with three averages (48 min). This significant reduction in scan time renders high resolution (1×1×2.5 mm3) diffusion tensor imaging of the entire brain applicable in a clinical context. PMID:24019951

Noise-assisted data processing with empirical mode decomposition in biomedical signals.

PubMed

Karagiannis, Alexandros; Constantinou, Philip

2011-01-01

In this paper, a methodology is described in order to investigate the performance of empirical mode decomposition (EMD) in biomedical signals, and especially in the case of electrocardiogram (ECG). Synthetic ECG signals corrupted with white Gaussian noise are employed and time series of various lengths are processed with EMD in order to extract the intrinsic mode functions (IMFs). A statistical significance test is implemented for the identification of IMFs with high-level noise components and their exclusion from denoising procedures. Simulation campaign results reveal that a decrease of processing time is accomplished with the introduction of preprocessing stage, prior to the application of EMD in biomedical time series. Furthermore, the variation in the number of IMFs according to the type of the preprocessing stage is studied as a function of SNR and time-series length. The application of the methodology in MIT-BIH ECG records is also presented in order to verify the findings in real ECG signals.

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.

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.

Iterative image reconstruction for multienergy computed tomography via structure tensor total variation regularization

NASA Astrophysics Data System (ADS)

Zeng, Dong; Bian, Zhaoying; Gong, Changfei; Huang, Jing; He, Ji; Zhang, Hua; Lu, Lijun; Feng, Qianjin; Liang, Zhengrong; Ma, Jianhua

2016-03-01

Multienergy computed tomography (MECT) has the potential to simultaneously offer multiple sets of energy- selective data belonging to specific energy windows. However, because sufficient photon counts are not available in the specific energy windows compared with that in the whole energy window, the MECT images reconstructed by the analytical approach often suffer from poor signal-to-noise (SNR) and strong streak artifacts. To eliminate this drawback, in this work we present a penalized weighted least-squares (PWLS) scheme by incorporating the new concept of structure tensor total variation (STV) regularization to improve the MECT images quality from low-milliampere-seconds (low-mAs) data acquisitions. Henceforth the present scheme is referred to as `PWLS- STV' for simplicity. Specifically, the STV regularization is derived by penalizing the eigenvalues of the structure tensor of every point in the MECT images. Thus it can provide more robust measures of image variation, which can eliminate the patchy artifacts often observed in total variation regularization. Subsequently, an alternating optimization algorithm was adopted to minimize the objective function. Experiments with a digital XCAT phantom clearly demonstrate that the present PWLS-STV algorithm can achieve more gains than the existing TV-based algorithms and the conventional filtered backpeojection (FBP) algorithm in terms of noise-induced artifacts suppression, resolution preservation, and material decomposition assessment.

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

Ab initio kinetics of gas phase decomposition reactions.

PubMed

Sharia, Onise; Kuklja, Maija M

2010-12-09

The thermal and kinetic aspects of gas phase decomposition reactions can be extremely complex due to a large number of parameters, a variety of possible intermediates, and an overlap in thermal decomposition traces. The experimental determination of the activation energies is particularly difficult when several possible reaction pathways coexist in the thermal decomposition. Ab initio calculations intended to provide an interpretation of the experiment are often of little help if they produce only the activation barriers and ignore the kinetics of the decomposition process. To overcome this ambiguity, a theoretical study of a complete picture of gas phase thermo-decomposition, including reaction energies, activation barriers, and reaction rates, is illustrated with the example of the β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) molecule by means of quantum-chemical calculations. We study three types of major decomposition reactions characteristic of nitramines: the HONO elimination, the NONO rearrangement, and the N-NO(2) homolysis. The reaction rates were determined using the conventional transition state theory for the HONO and NONO decompositions and the variational transition state theory for the N-NO(2) homolysis. Our calculations show that the HMX decomposition process is more complex than it was previously believed to be and is defined by a combination of reactions at any given temperature. At all temperatures, the direct N-NO(2) homolysis prevails with the activation barrier at 38.1 kcal/mol. The nitro-nitrite isomerization and the HONO elimination, with the activation barriers at 46.3 and 39.4 kcal/mol, respectively, are slow reactions at all temperatures. The obtained conclusions provide a consistent interpretation for the reported experimental data.

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…

Adaptive variational mode decomposition method for signal processing based on mode characteristic

NASA Astrophysics Data System (ADS)

Lian, Jijian; Liu, Zhuo; Wang, Haijun; Dong, Xiaofeng

2018-07-01

Variational mode decomposition is a completely non-recursive decomposition model, where all the modes are extracted concurrently. However, the model requires a preset mode number, which limits the adaptability of the method since a large deviation in the number of mode set will cause the discard or mixing of the mode. Hence, a method called Adaptive Variational Mode Decomposition (AVMD) was proposed to automatically determine the mode number based on the characteristic of intrinsic mode function. The method was used to analyze the simulation signals and the measured signals in the hydropower plant. Comparisons have also been conducted to evaluate the performance by using VMD, EMD and EWT. It is indicated that the proposed method has strong adaptability and is robust to noise. It can determine the mode number appropriately without modulation even when the signal frequencies are relatively close.

Nuclear driven water decomposition plant for hydrogen production

NASA Technical Reports Server (NTRS)

Parker, G. H.; Brecher, L. E.; Farbman, G. H.

1976-01-01

The conceptual design of a hydrogen production plant using a very-high-temperature nuclear reactor (VHTR) to energize a hybrid electrolytic-thermochemical system for water decomposition has been prepared. A graphite-moderated helium-cooled VHTR is used to produce 1850 F gas for electric power generation and 1600 F process heat for the water-decomposition process which uses sulfur compounds and promises performance superior to normal water electrolysis or other published thermochemical processes. The combined cycle operates at an overall thermal efficiency in excess of 45%, and the overall economics of hydrogen production by this plant have been evaluated predicated on a consistent set of economic ground rules. The conceptual design and evaluation efforts have indicated that development of this type of nuclear-driven water-decomposition plant will permit large-scale economic generation of hydrogen in the 1990s.

Termites promote resistance of decomposition to spatiotemporal variability in rainfall.

PubMed

Veldhuis, Michiel P; Laso, Francisco J; Olff, Han; Berg, Matty P

2017-02-01

The ecological impact of rapid environmental change will depend on the resistance of key ecosystems processes, which may be promoted by species that exert strong control over local environmental conditions. Recent theoretical work suggests that macrodetritivores increase the resistance of African savanna ecosystems to changing climatic conditions, but experimental evidence is lacking. We examined the effect of large fungus-growing termites and other non-fungus-growing macrodetritivores on decomposition rates empirically with strong spatiotemporal variability in rainfall and temperature. Non-fungus-growing larger macrodetritivores (earthworms, woodlice, millipedes) promoted decomposition rates relative to microbes and small soil fauna (+34%) but both groups reduced their activities with decreasing rainfall. However, fungus-growing termites increased decomposition rates strongest (+123%) under the most water-limited conditions, making overall decomposition rates mostly independent from rainfall. We conclude that fungus-growing termites are of special importance in decoupling decomposition rates from spatiotemporal variability in rainfall due to the buffered environment they create within their extended phenotype (mounds), that allows decomposition to continue when abiotic conditions outside are less favorable. This points at a wider class of possibly important ecological processes, where soil-plant-animal interactions decouple ecosystem processes from large-scale climatic gradients. This may strongly alter predictions from current climate change models. © 2016 by the Ecological Society of America.

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.

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.

A review of plutonium oxalate decomposition reactions and effects of decomposition temperature on the surface area of the plutonium dioxide product

NASA Astrophysics Data System (ADS)

Orr, R. M.; Sims, H. E.; Taylor, R. J.

2015-10-01

Plutonium (IV) and (III) ions in nitric acid solution readily form insoluble precipitates with oxalic acid. The plutonium oxalates are then easily thermally decomposed to form plutonium dioxide powder. This simple process forms the basis of current industrial conversion or 'finishing' processes that are used in commercial scale reprocessing plants. It is also widely used in analytical or laboratory scale operations and for waste residues treatment. However, the mechanisms of the thermal decompositions in both air and inert atmospheres have been the subject of various studies over several decades. The nature of intermediate phases is of fundamental interest whilst understanding the evolution of gases at different temperatures is relevant to process control. The thermal decomposition is also used to control a number of powder properties of the PuO2 product that are important to either long term storage or mixed oxide fuel manufacturing. These properties are the surface area, residual carbon impurities and adsorbed volatile species whereas the morphology and particle size distribution are functions of the precipitation process. Available data and experience regarding the thermal and radiation-induced decompositions of plutonium oxalate to oxide are reviewed. The mechanisms of the thermal decompositions are considered with a particular focus on the likely redox chemistry involved. Also, whilst it is well known that the surface area is dependent on calcination temperature, there is a wide variation in the published data and so new correlations have been derived. Better understanding of plutonium (III) and (IV) oxalate decompositions will assist the development of more proliferation resistant actinide co-conversion processes that are needed for advanced reprocessing in future closed nuclear fuel cycles.

Challenges of including nitrogen effects on decomposition in earth system models

NASA Astrophysics Data System (ADS)

Hobbie, S. E.

2011-12-01

Despite the importance of litter decomposition for ecosystem fertility and carbon balance, key uncertainties remain about how this fundamental process is affected by nitrogen (N) availability. Nevertheless, resolving such uncertainties is critical for mechanistic inclusion of such processes in earth system models, towards predicting the ecosystem consequences of increased anthropogenic reactive N. Towards that end, we have conducted a series of experiments examining nitrogen effects on litter decomposition. We found that both substrate N and externally supplied N (regardless of form) accelerated the initial decomposition rate. Faster initial decomposition rates were linked to the higher activity of carbohydrate-degrading enzymes associated with externally supplied N and the greater relative abundances of Gram negative and Gram positive bacteria associated with green leaves and externally supplied organic N (assessed using phospholipid fatty acid analysis, PLFA). By contrast, later in decomposition, externally supplied N slowed decomposition, increasing the fraction of slowly decomposing litter and reducing lignin-degrading enzyme activity and relative abundances of Gram negative and Gram positive bacteria. Our results suggest that elevated atmospheric N deposition may have contrasting effects on the dynamics of different soil carbon pools, decreasing mean residence times of active fractions comprising very fresh litter, while increasing those of more slowly decomposing fractions including more processed litter. Incorporating these contrasting effects of N on decomposition processes into models is complicated by lingering uncertainties about how these effects generalize across ecosystems and substrates.

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

Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.

PubMed

de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos

2011-01-01

In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.

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

Coupling experimental data and a prototype model to probe the physical and chemical processes of 2,4-dinitroimidazole solid-phase thermal decomposition

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

Behrens, R.; Minier, L.; Bulusu, S.

1998-12-31

The time-dependent, solid-phase thermal decomposition behavior of 2,4-dinitroimidazole (2,4-DNI) has been measured utilizing simultaneous thermogravimetric modulated beam mass spectrometry (STMBMS) methods. The decomposition products consist of gaseous and non-volatile polymeric products. The temporal behavior of the gas formation rates of the identified products indicate that the overall thermal decomposition process is complex. In isothermal experiments with 2,4-DNI in the solid phase, four distinguishing features are observed: (1) elevated rates of gas formation are observed during the early stages of the decomposition, which appear to be correlated to the presence of exogenous water in the sample; (2) this is followed bymore » a period of relatively constant rates of gas formation; (3) next, the rates of gas formation accelerate, characteristic of an autocatalytic reaction; (4) finally, the 2,4-DNI is depleted and gaseous decomposition products continue to evolve at a decreasing rate. A physicochemical and mathematical model of the decomposition of 2,4-DNI has been developed and applied to the experimental results. The first generation of this model is described in this paper. Differences between the first generation of the model and the experimental data collected under different conditions suggest refinements for the next generation of the model.« less

Estimation of Uncertainties of Full Moment Tensors

DTIC Science & Technology

2017-10-06

Nevada Test Site (tab. 1 of Ford et al., 2009). Figure 1 shows the three regions and the stations used within the moment tensor inversions . For the...and additional bandpass filtering, were applied during the moment tensor inversions . We use high-frequency P waves for the Uturuncu and NTS events...reliable when we align the P waves on the observed P arrival time. 3.2 Methods Seismic moment tensor inversion requires specifying a misfit function

Thermal decomposition of ammonium hexachloroosmate.

PubMed

Asanova, T I; Kantor, I; Asanov, I P; Korenev, S V; Yusenko, K V

2016-12-07

Structural changes of (NH 4 ) 2 [OsCl 6 ] occurring during thermal decomposition in a reduction atmosphere have been studied in situ using combined energy-dispersive X-ray absorption spectroscopy (ED-XAFS) and powder X-ray diffraction (PXRD). According to PXRD, (NH 4 ) 2 [OsCl 6 ] transforms directly to metallic Os without the formation of any crystalline intermediates but through a plateau where no reactions occur. XANES and EXAFS data by means of Multivariate Curve Resolution (MCR) analysis show that thermal decomposition occurs with the formation of an amorphous intermediate {OsCl 4 } x with a possible polymeric structure. Being revealed for the first time the intermediate was subjected to determine the local atomic structure around osmium. The thermal decomposition of hexachloroosmate is much more complex and occurs within a minimum two-step process, which has never been observed before.

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.

Characterizing dielectric tensors of anisotropic materials from a single measurement

NASA Astrophysics Data System (ADS)

Smith, Paula Kay

Ellipsometry techniques look at changes in polarization states to measure optical properties of thin film materials. A beam reflected from a substrate measures the real and imaginary parts of the index of the material represented as n and k, respectively. Measuring the substrate at several angles gives additional information that can be used to measure multilayer thin film stacks. However, the outstanding problem in standard ellipsometry is that it uses a limited number of incident polarization states (s and p). This limits the technique to isotropic materials. The technique discussed in this paper extends the standard process to measure anisotropic materials by using a larger set of incident polarization states. By using a polarimeter to generate several incident polarization states and measure the polarization properties of the sample, ellipsometry can be performed on biaxial materials. Use of an optimization algorithm in conjunction with biaxial ellipsometry can more accurately determine the dielectric tensor of individual layers in multilayer structures. Biaxial ellipsometry is a technique that measures the dielectric tensors of a biaxial substrate, single-layer thin film, or multi-layer structure. The dielectric tensor of a biaxial material consists of the real and imaginary parts of the three orthogonal principal indices (n x + ikx, ny +iky and nz + i kz) as well as three Euler angles (alpha, beta and gamma) to describe its orientation. The method utilized in this work measures an angle-of-incidence Mueller matrix from a Mueller matrix imaging polarimeter equipped with a pair of microscope objectives that have low polarization properties. To accurately determine the dielectric tensors for multilayer samples, the angle-of-incidence Mueller matrix images are collected for multiple wavelengths. This is done in either a transmission mode or a reflection mode, each incorporates an appropriate dispersion model. Given approximate a priori knowledge of the dielectric

ChIP-PIT: Enhancing the Analysis of ChIP-Seq Data Using Convex-Relaxed Pair-Wise Interaction Tensor Decomposition.

PubMed

Zhu, Lin; Guo, Wei-Li; Deng, Su-Ping; Huang, De-Shuang

2016-01-01

In recent years, thanks to the efforts of individual scientists and research consortiums, a huge amount of chromatin immunoprecipitation followed by high-throughput sequencing (ChIP-seq) experimental data have been accumulated. Instead of investigating them independently, several recent studies have convincingly demonstrated that a wealth of scientific insights can be gained by integrative analysis of these ChIP-seq data. However, when used for the purpose of integrative analysis, a serious drawback of current ChIP-seq technique is that it is still expensive and time-consuming to generate ChIP-seq datasets of high standard. Most researchers are therefore unable to obtain complete ChIP-seq data for several TFs in a wide variety of cell lines, which considerably limits the understanding of transcriptional regulation pattern. In this paper, we propose a novel method called ChIP-PIT to overcome the aforementioned limitation. In ChIP-PIT, ChIP-seq data corresponding to a diverse collection of cell types, TFs and genes are fused together using the three-mode pair-wise interaction tensor (PIT) model, and the prediction of unperformed ChIP-seq experimental results is formulated as a tensor completion problem. Computationally, we propose efficient first-order method based on extensions of coordinate descent method to learn the optimal solution of ChIP-PIT, which makes it particularly suitable for the analysis of massive scale ChIP-seq data. Experimental evaluation the ENCODE data illustrate the usefulness of the proposed model.

Three-dimensional modelling and geothermal process simulation

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

Burns, K.L.

1990-01-01

The subsurface geological model or 3-D GIS is constructed from three kinds of objects, which are a lithotope (in boundary representation), a number of fault systems, and volumetric textures (vector fields). The chief task of the model is to yield an estimate of the conductance tensors (fluid permeability and thermal conductivity) throughout an array of voxels. This is input as material properties to a FEHM numerical physical process model. The main task of the FEHM process model is to distinguish regions of convective from regions of conductive heat flow, and to estimate the fluid phase, pressure and flow paths. Themore » temperature, geochemical, and seismic data provide the physical constraints on the process. The conductance tensors in the Franciscan Complex are to be derived by the addition of two components. The isotropic component is a stochastic spatial variable due to disruption of lithologies in melange. The deviatoric component is deterministic, due to smoothness and continuity in the textural vector fields. This decomposition probably also applies to the engineering hydrogeological properties of shallow terrestrial fluvial systems. However there are differences in quantity. The isotropic component is much more variable in the Franciscan, to the point where volumetric averages are misleading, and it may be necessary to select that component from several, discrete possible states. The deviatoric component is interpolated using a textural vector field. The Franciscan field is much more complicated, and contains internal singularities. 27 refs., 10 figs.« less

Adaptive Fourier decomposition based ECG denoising.

PubMed

Wang, Ze; Wan, Feng; Wong, Chi Man; Zhang, Liming

2016-10-01

A novel ECG denoising method is proposed based on the adaptive Fourier decomposition (AFD). The AFD decomposes a signal according to its energy distribution, thereby making this algorithm suitable for separating pure ECG signal and noise with overlapping frequency ranges but different energy distributions. A stop criterion for the iterative decomposition process in the AFD is calculated on the basis of the estimated signal-to-noise ratio (SNR) of the noisy signal. The proposed AFD-based method is validated by the synthetic ECG signal using an ECG model and also real ECG signals from the MIT-BIH Arrhythmia Database both with additive Gaussian white noise. Simulation results of the proposed method show better performance on the denoising and the QRS detection in comparing with major ECG denoising schemes based on the wavelet transform, the Stockwell transform, the empirical mode decomposition, and the ensemble empirical mode decomposition. Copyright © 2016 Elsevier Ltd. All rights reserved.

Potentials for transverse trace-free tensors

NASA Astrophysics Data System (ADS)

Conboye, Rory; Murchadha, Niall Ó.

2014-04-01

In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space.

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

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.

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.

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).

An analysis of scatter decomposition

NASA Technical Reports Server (NTRS)

Nicol, David M.; Saltz, Joel H.

1990-01-01

A formal analysis of a powerful mapping technique known as scatter decomposition is presented. Scatter decomposition divides an irregular computational domain into a large number of equal sized pieces, and distributes them modularly among processors. A probabilistic model of workload in one dimension is used to formally explain why, and when scatter decomposition works. The first result is that if correlation in workload is a convex function of distance, then scattering a more finely decomposed domain yields a lower average processor workload variance. The second result shows that if the workload process is stationary Gaussian and the correlation function decreases linearly in distance until becoming zero and then remains zero, scattering a more finely decomposed domain yields a lower expected maximum processor workload. Finally it is shown that if the correlation function decreases linearly across the entire domain, then among all mappings that assign an equal number of domain pieces to each processor, scatter decomposition minimizes the average processor workload variance. The dependence of these results on the assumption of decreasing correlation is illustrated with situations where a coarser granularity actually achieves better load balance.

Curvature tensors unified field equations on SEXn

NASA Astrophysics Data System (ADS)

Chung, Kyung Tae; Lee, Il Young

1988-09-01

We study the curvature tensors and field equations in the n-dimensional SE manifold SEXn. We obtain several basic properties of the vectors S λ and U λ and then of the SE curvature tensor and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein tensor. Finally, a system of field equations is discussed in SEXn and one of its particular solutions is constructed and displayed.

Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems

PubMed Central

2015-01-01

We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement. PMID:25844072

A density functional theory study of the decomposition mechanism of nitroglycerin.

PubMed

Pei, Liguan; Dong, Kehai; Tang, Yanhui; Zhang, Bo; Yu, Chang; Li, Wenzuo

2017-08-21

The detailed decomposition mechanism of nitroglycerin (NG) in the gas phase was studied by examining reaction pathways using density functional theory (DFT) and canonical variational transition state theory combined with a small-curvature tunneling correction (CVT/SCT). The mechanism of NG autocatalytic decomposition was investigated at the B3LYP/6-31G(d,p) level of theory. Five possible decomposition pathways involving NG were identified and the rate constants for the pathways at temperatures ranging from 200 to 1000 K were calculated using CVT/SCT. There was found to be a lower energy barrier to the β-H abstraction reaction than to the α-H abstraction reaction during the initial step in the autocatalytic decomposition of NG. The decomposition pathways for CHOCOCHONO 2 (a product obtained following the abstraction of three H atoms from NG by NO 2 ) include O-NO 2 cleavage or isomer production, meaning that the autocatalytic decomposition of NG has two reaction pathways, both of which are exothermic. The rate constants for these two reaction pathways are greater than the rate constants for the three pathways corresponding to unimolecular NG decomposition. The overall process of NG decomposition can be divided into two stages based on the NO 2 concentration, which affects the decomposition products and reactions. In the first stage, the reaction pathway corresponding to O-NO 2 cleavage is the main pathway, but the rates of the two autocatalytic decomposition pathways increase with increasing NO 2 concentration. However, when a threshold NO 2 concentration is reached, the NG decomposition process enters its second stage, with the two pathways for NG autocatalytic decomposition becoming the main and secondary reaction pathways.

Soil fauna and plant litter decomposition in tropical and subalpine forests

Treesearch

G. Gonzalez; T.R. Seastedt

2001-01-01

The decomposition of plant residues is influenced by their chemical composition, the physical-chemical environment, and the decomposer organisms. Most studies interested in latitudinal gradients of decomposition have focused on substrate quality and climate effects on decomposition, and have excluded explicit recognition of the soil organisms involved in the process....

Kinetic Analysis of Isothermal Decomposition Process of Sodium Bicarbonate Using the Weibull Probability Function—Estimation of Density Distribution Functions of the Apparent Activation Energies

NASA Astrophysics Data System (ADS)

Janković, Bojan

2009-10-01

The decomposition process of sodium bicarbonate (NaHCO3) has been studied by thermogravimetry in isothermal conditions at four different operating temperatures (380 K, 400 K, 420 K, and 440 K). It was found that the experimental integral and differential conversion curves at the different operating temperatures can be successfully described by the isothermal Weibull distribution function with a unique value of the shape parameter ( β = 1.07). It was also established that the Weibull distribution parameters ( β and η) show independent behavior on the operating temperature. Using the integral and differential (Friedman) isoconversional methods, in the conversion (α) range of 0.20 ≤ α ≤ 0.80, the apparent activation energy ( E a ) value was approximately constant ( E a, int = 95.2 kJmol-1 and E a, diff = 96.6 kJmol-1, respectively). The values of E a calculated by both isoconversional methods are in good agreement with the value of E a evaluated from the Arrhenius equation (94.3 kJmol-1), which was expressed through the scale distribution parameter ( η). The Málek isothermal procedure was used for estimation of the kinetic model for the investigated decomposition process. It was found that the two-parameter Šesták-Berggren (SB) autocatalytic model best describes the NaHCO3 decomposition process with the conversion function f(α) = α0.18(1-α)1.19. It was also concluded that the calculated density distribution functions of the apparent activation energies ( ddfE a ’s) are not dependent on the operating temperature, which exhibit the highly symmetrical behavior (shape factor = 1.00). The obtained isothermal decomposition results were compared with corresponding results of the nonisothermal decomposition process of NaHCO3.

Surface-Accelerated Decomposition of δ-HMX.

PubMed

Sharia, Onise; Tsyshevsky, Roman; Kuklja, Maija M

2013-03-07

Despite extensive efforts to study the explosive decomposition of HMX, a cyclic nitramine widely used as a solid fuel, explosive, and propellant, an understanding of the physicochemical processes, governing the sensitivity of condensed HMX to detonation initiation is not yet achieved. Experimental and theoretical explorations of the initiation of chemistry are equally challenging because of many complex parallel processes, including the β-δ phase transition and the decomposition from both phases. Among four known polymorphs, HMX is produced in the most stable β-phase, which transforms into the most reactive δ-phase under heat or pressure. In this study, the homolytic NO2 loss and HONO elimination precursor reactions of the gas-phase, ideal crystal, and the (100) surface of δ-HMX are explored by first principles modeling. Our calculations revealed that the high sensitivity of δ-HMX is attributed to interactions of surfaces and molecular dipole moments. While both decomposition reactions coexist, the exothermic HONO-isomer formation catalyzes the N-NO2 homolysis, leading to fast violent explosions.

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.

The Spatial Variability of Organic Matter and Decomposition Processes at the Marsh Scale

NASA Astrophysics Data System (ADS)

Yousefi Lalimi, Fateme; Silvestri, Sonia; D'Alpaos, Andrea; Roner, Marcella; Marani, Marco

2017-04-01

Coastal salt marshes sequester carbon as they respond to the local Rate of Relative Sea Level Rise (RRSLR) and their accretion rate is governed by inorganic soil deposition, organic soil production, and soil organic matter (SOM) decomposition. It is generally recognized that SOM plays a central role in marsh vertical dynamics, but while existing limited observations and modelling results suggest that SOME varies widely at the marsh scale, we lack systematic observations aimed at understanding how SOM production is modulated spatially as a result of biomass productivity and decomposition rate. Marsh topography and distance to the creek can affect biomass and SOM production, while a higher topographic elevation increases drainage, evapotranspiration, aeration, thereby likely inducing higher SOM decomposition rates. Data collected in salt marshes in the northern Venice Lagoon (Italy) show that, even though plant productivity decreases in the lower areas of a marsh located farther away from channel edges, the relative contribution of organic soil production to the overall vertical soil accretion tends to remain constant as the distance from the channel increases. These observations suggest that the competing effects between biomass production and aeration/decomposition determine a contribution of organic soil to total accretion which remains approximately constant with distance from the creek, in spite of the declining plant productivity. Here we test this hypothesis using new observations of SOM and decomposition rates from marshes in North Carolina. The objective is to fill the gap in our understanding of the spatial distribution, at the marsh scale, of the organic and inorganic contributions to marsh accretion in response to RRSLR.

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

Nonequilibrium adiabatic molecular dynamics simulations of methane clathrate hydrate decomposition

NASA Astrophysics Data System (ADS)

Alavi, Saman; Ripmeester, J. A.

2010-04-01

Nonequilibrium, constant energy, constant volume (NVE) molecular dynamics simulations are used to study the decomposition of methane clathrate hydrate in contact with water. Under adiabatic conditions, the rate of methane clathrate decomposition is affected by heat and mass transfer arising from the breakup of the clathrate hydrate framework and release of the methane gas at the solid-liquid interface and diffusion of methane through water. We observe that temperature gradients are established between the clathrate and solution phases as a result of the endothermic clathrate decomposition process and this factor must be considered when modeling the decomposition process. Additionally we observe that clathrate decomposition does not occur gradually with breakup of individual cages, but rather in a concerted fashion with rows of structure I cages parallel to the interface decomposing simultaneously. Due to the concerted breakup of layers of the hydrate, large amounts of methane gas are released near the surface which can form bubbles that will greatly affect the rate of mass transfer near the surface of the clathrate phase. The effects of these phenomena on the rate of methane hydrate decomposition are determined and implications on hydrate dissociation in natural methane hydrate reservoirs are discussed.

Nonequilibrium adiabatic molecular dynamics simulations of methane clathrate hydrate decomposition.

PubMed

Alavi, Saman; Ripmeester, J A

2010-04-14

Nonequilibrium, constant energy, constant volume (NVE) molecular dynamics simulations are used to study the decomposition of methane clathrate hydrate in contact with water. Under adiabatic conditions, the rate of methane clathrate decomposition is affected by heat and mass transfer arising from the breakup of the clathrate hydrate framework and release of the methane gas at the solid-liquid interface and diffusion of methane through water. We observe that temperature gradients are established between the clathrate and solution phases as a result of the endothermic clathrate decomposition process and this factor must be considered when modeling the decomposition process. Additionally we observe that clathrate decomposition does not occur gradually with breakup of individual cages, but rather in a concerted fashion with rows of structure I cages parallel to the interface decomposing simultaneously. Due to the concerted breakup of layers of the hydrate, large amounts of methane gas are released near the surface which can form bubbles that will greatly affect the rate of mass transfer near the surface of the clathrate phase. The effects of these phenomena on the rate of methane hydrate decomposition are determined and implications on hydrate dissociation in natural methane hydrate reservoirs are discussed.

Decomposition of energetic chemicals contaminated with iron or stainless steel.

PubMed

Chervin, Sima; Bodman, Glenn T; Barnhart, Richard W

2006-03-17

Contamination of chemicals or reaction mixtures with iron or stainless steel is likely to take place during chemical processing. If energetic and thermally unstable chemicals are involved in a manufacturing process, contamination with iron or stainless steel can impact the decomposition characteristics of these chemicals and, subsequently, the safety of the processes, and should be investigated. The goal of this project was to undertake a systematic approach to study the impact of iron or stainless steel contamination on the decomposition characteristics of different chemical classes. Differential scanning calorimetry (DSC) was used to study the decomposition reaction by testing each chemical pure, and in mixtures with iron and stainless steel. The following classes of energetic chemicals were investigated: nitrobenzenes, tetrazoles, hydrazines, hydroxylamines and oximes, sulfonic acid derivatives and monomers. The following non-energetic groups were investigated for contributing effects: halogens, hydroxyls, amines, amides, nitriles, sulfonic acid esters, carbonyl halides and salts of hydrochloric acid. Based on the results obtained, conclusions were drawn regarding the sensitivity of the decomposition reaction to contamination with iron and stainless steel for the chemical classes listed above. It was demonstrated that the most sensitive classes are hydrazines and hydroxylamines/oximes. Contamination of these chemicals with iron or stainless steel not only destabilizes them, leading to decomposition at significantly lower temperatures, but also sometimes causes increased severity of the decomposition. The sensitivity of nitrobenzenes to contamination with iron or stainless steel depended upon the presence of other contributing groups: the presence of such groups as acid chlorides or chlorine/fluorine significantly increased the effect of contamination on decomposition characteristics of nitrobenzenes. The decomposition of sulfonic acid derivatives and tetrazoles

Kinetics of non-isothermal decomposition of cinnamic acid

NASA Astrophysics Data System (ADS)

Zhao, Ming-rui; Qi, Zhen-li; Chen, Fei-xiong; Yue, Xia-xin

2014-07-01

The thermal stability and kinetics of decomposition of cinnamic acid were investigated by thermogravimetry and differential scanning calorimetry at four heating rates. The activation energies of this process were calculated from analysis of TG curves by methods of Flynn-Wall-Ozawa, Doyle, Distributed Activation Energy Model, Šatava-Šesták and Kissinger, respectively. There are only one stage of thermal decomposition process in TG and two endothermic peaks in DSC. For this decomposition process of cinnamic acid, E and log A[s-1] were determined to be 81.74 kJ mol-1 and 8.67, respectively. The mechanism was Mampel Power law (the reaction order, n = 1), with integral form G(α) = α (α = 0.1-0.9). Moreover, thermodynamic properties of Δ H ≠, Δ S ≠, Δ G ≠ were 77.96 kJ mol-1, -90.71 J mol-1 K-1, 119.41 kJ mol-1.

Scare Tactics: Evaluating Problem Decompositions Using Failure Scenarios

NASA Technical Reports Server (NTRS)

Helm, B. Robert; Fickas, Stephen

1992-01-01

Our interest is in the design of multi-agent problem-solving systems, which we refer to as composite systems. We have proposed an approach to composite system design by decomposition of problem statements. An automated assistant called Critter provides a library of reusable design transformations which allow a human analyst to search the space of decompositions for a problem. In this paper we describe a method for evaluating and critiquing problem decompositions generated by this search process. The method uses knowledge stored in the form of failure decompositions attached to design transformations. We suggest the benefits of our critiquing method by showing how it could re-derive steps of a published development example. We then identify several open issues for the method.

Decomposition techniques

USGS Publications Warehouse

Chao, T.T.; Sanzolone, R.F.

1992-01-01

Sample decomposition is a fundamental and integral step in the procedure of geochemical analysis. It is often the limiting factor to sample throughput, especially with the recent application of the fast and modern multi-element measurement instrumentation. The complexity of geological materials makes it necessary to choose the sample decomposition technique that is compatible with the specific objective of the analysis. When selecting a decomposition technique, consideration should be given to the chemical and mineralogical characteristics of the sample, elements to be determined, precision and accuracy requirements, sample throughput, technical capability of personnel, and time constraints. This paper addresses these concerns and discusses the attributes and limitations of many techniques of sample decomposition along with examples of their application to geochemical analysis. The chemical properties of reagents as to their function as decomposition agents are also reviewed. The section on acid dissolution techniques addresses the various inorganic acids that are used individually or in combination in both open and closed systems. Fluxes used in sample fusion are discussed. The promising microwave-oven technology and the emerging field of automation are also examined. A section on applications highlights the use of decomposition techniques for the determination of Au, platinum group elements (PGEs), Hg, U, hydride-forming elements, rare earth elements (REEs), and multi-elements in geological materials. Partial dissolution techniques used for geochemical exploration which have been treated in detail elsewhere are not discussed here; nor are fire-assaying for noble metals and decomposition techniques for X-ray fluorescence or nuclear methods be discussed. ?? 1992.

Aspects of the Antisymmetric Tensor Field

NASA Astrophysics Data System (ADS)

Lahiri, Amitabha

1991-02-01

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

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.

Application of decomposition techniques to the preliminary design of a transport aircraft

NASA Technical Reports Server (NTRS)

Rogan, J. E.; Mcelveen, R. P.; Kolb, M. A.

1986-01-01

A multifaceted decomposition of a nonlinear constrained optimization problem describing the preliminary design process for a transport aircraft has been made. Flight dynamics, flexible aircraft loads and deformations, and preliminary structural design subproblems appear prominently in the decomposition. The use of design process decomposition for scheduling design projects, a new system integration approach to configuration control, and the application of object-centered programming to a new generation of design tools are discussed.

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.

Correlators in tensor models from character calculus

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.

2017-11-01

We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz) character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.

Domain Decomposition By the Advancing-Partition Method

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar Z.

2008-01-01

A new method of domain decomposition has been developed for generating unstructured grids in subdomains either sequentially or using multiple computers in parallel. Domain decomposition is a crucial and challenging step for parallel grid generation. Prior methods are generally based on auxiliary, complex, and computationally intensive operations for defining partition interfaces and usually produce grids of lower quality than those generated in single domains. The new technique, referred to as "Advancing Partition," is based on the Advancing-Front method, which partitions a domain as part of the volume mesh generation in a consistent and "natural" way. The benefits of this approach are: 1) the process of domain decomposition is highly automated, 2) partitioning of domain does not compromise the quality of the generated grids, and 3) the computational overhead for domain decomposition is minimal. The new method has been implemented in NASA's unstructured grid generation code VGRID.

On the energy-momentum tensor in Moyal space

DOE PAGES

Balasin, Herbert; Blaschke, Daniel N.; Gieres, François; ...

2015-06-26

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

Application of decomposition techniques to the preliminary design of a transport aircraft

NASA Technical Reports Server (NTRS)

Rogan, J. E.; Kolb, M. A.

1987-01-01

A nonlinear constrained optimization problem describing the preliminary design process for a transport aircraft has been formulated. A multifaceted decomposition of the optimization problem has been made. Flight dynamics, flexible aircraft loads and deformations, and preliminary structural design subproblems appear prominently in the decomposition. The use of design process decomposition for scheduling design projects, a new system integration approach to configuration control, and the application of object-centered programming to a new generation of design tools are discussed.

First-principles study on the initial decomposition process of CH3NH3PbI3

NASA Astrophysics Data System (ADS)

Xue, Yuanbin; Shan, Yueyue; Xu, Hu

2017-09-01

Hybrid perovskites are promising materials for high-performance photovoltaics. Unfortunately, hybrid perovskites readily decompose in particular under humid conditions, and the mechanisms of this phenomenon have not yet been fully understood. In this work, we systematically studied the possible mechanisms and the structural properties during the initial decomposition process of MAPbI3 (MA = CH3NH3+) using first-principles calculations. The theoretical results show that it is energetically favorable for PbI2 to nucleate and crystalize from the MAPbI3 matrix ahead of other decomposition products. Additionally, the structural instability is an intrinsic property of MAPbI3, regardless of whether the system is exposed to humidity. We find that H2O could facilitate the desorption of gaseous components, acting as a catalyst to transfer the H+ ion. These results provide insight into the cause of the instability of MAPbI3 and may improve our understanding of the properties of hybrid perovskites.

Energy-momentum tensor of perturbed tachyon matter

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

Jokela, Niko; Department of Mathematics and Physics, University of Haifa at Oranim, Tivon 36006; Jaervinen, Matti

2009-05-15

We add an initial nonhomogeneous perturbation to an otherwise homogeneous condensing tachyon background and compute its spacetime energy-momentum tensor from world-sheet string theory. We show that in the far future the energy-momentum tensor corresponds to nonhomogeneous pressureless tachyon matter.

Elliptic Relaxation of a Tensor Representation of the Pressure-Strain and Dissipation Rate

NASA Technical Reports Server (NTRS)

Carlson, John R.; Gatski, Thomas B.

2002-01-01

A formulation to include the effects of wall-proximity in a second moment closure model is presented that utilizes a tensor representation for the redistribution term in the Reynolds stress equations. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. DNS data and Reynolds stress solutions using a full differential approach at channel Reynolds number of 590 are compared to the new model.

Entangled scalar and tensor fluctuations during inflation

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

Collins, Hael; Vardanyan, Tereza

2016-11-29

We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with amore » simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.« less

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

Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

NASA Astrophysics Data System (ADS)

Šprlák, Michal; Novák, Pavel

2017-02-01

New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.

CO2 decomposition using electrochemical process in molten salts

NASA Astrophysics Data System (ADS)

Otake, Koya; Kinoshita, Hiroshi; Kikuchi, Tatsuya; Suzuki, Ryosuke O.

2012-08-01

The electrochemical decomposition of CO2 gas to carbon and oxygen gas in LiCl-Li2O and CaCl2-CaO molten salts was studied. This process consists of electrochemical reduction of Li2O and CaO, as well as the thermal reduction of CO2 gas by the respective metallic Li and Ca. Two kinds of ZrO2 solid electrolytes were tested as an oxygen ion conductor, and the electrolytes removed oxygen ions from the molten salts to the outside of the reactor. After electrolysis in both salts, the aggregations of nanometer-scale amorphous carbon and rod-like graphite crystals were observed by transmission electron microscopy. When 9.7 %CO2-Ar mixed gas was blown into LiCl-Li2O and CaCl2-CaO molten salts, the current efficiency was evaluated to be 89.7 % and 78.5 %, respectively, by the exhaust gas analysis and the supplied charge. When a solid electrolyte with higher ionic conductivity was used, the current and carbon production became larger. It was found that the rate determining step is the diffusion of oxygen ions into the ZrO2 solid electrolyte.

Basic dye decomposition kinetics in a photocatalytic slurry reactor.

PubMed

Wu, Chun-Hsing; Chang, Hung-Wei; Chern, Jia-Ming

2006-09-01

Wastewater effluent from textile plants using various dyes is one of the major water pollutants to the environment. Traditional chemical, physical and biological processes for treating textile dye wastewaters have disadvantages such as high cost, energy waste and generating secondary pollution during the treatment process. The photocatalytic process using TiO2 semiconductor particles under UV light illumination has been shown to be potentially advantageous and applicable in the treatment of wastewater pollutants. In this study, the dye decomposition kinetics by nano-size TiO2 suspension at natural solution pH was experimentally studied by varying the agitation speed (50-200 rpm), TiO2 suspension concentration (0.25-1.71 g/L), initial dye concentration (10-50 ppm), temperature (10-50 degrees C), and UV power intensity (0-96 W). The experimental results show the agitation speed, varying from 50 to 200 rpm, has a slight influence on the dye decomposition rate and the pH history; the dye decomposition rate increases with the TiO2 suspension concentration up to 0.98 g/L, then decrease with increasing TiO2 suspension concentration; the initial dye decomposition rate increases with the initial dye concentration up to a certain value depending upon the temperature, then decreases with increasing initial dye concentration; the dye decomposition rate increases with the UV power intensity up to 64 W to reach a plateau. Kinetic models have been developed to fit the experimental kinetic data well.

Linear friction weld process monitoring of fixture cassette deformations using empirical mode decomposition

NASA Astrophysics Data System (ADS)

Bakker, O. J.; Gibson, C.; Wilson, P.; Lohse, N.; Popov, A. A.

2015-10-01

Due to its inherent advantages, linear friction welding is a solid-state joining process of increasing importance to the aerospace, automotive, medical and power generation equipment industries. Tangential oscillations and forge stroke during the burn-off phase of the joining process introduce essential dynamic forces, which can also be detrimental to the welding process. Since burn-off is a critical phase in the manufacturing stage, process monitoring is fundamental for quality and stability control purposes. This study aims to improve workholding stability through the analysis of fixture cassette deformations. Methods and procedures for process monitoring are developed and implemented in a fail-or-pass assessment system for fixture cassette deformations during the burn-off phase. Additionally, the de-noised signals are compared to results from previous production runs. The observed deformations as a consequence of the forces acting on the fixture cassette are measured directly during the welding process. Data on the linear friction-welding machine are acquired and de-noised using empirical mode decomposition, before the burn-off phase is extracted. This approach enables a direct, objective comparison of the signal features with trends from previous successful welds. The capacity of the whole process monitoring system is validated and demonstrated through the analysis of a large number of signals obtained from welding experiments.

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

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

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

Error reduction in EMG signal decomposition

PubMed Central

Kline, Joshua C.

2014-01-01

Decomposition of the electromyographic (EMG) signal into constituent action potentials and the identification of individual firing instances of each motor unit in the presence of ambient noise are inherently probabilistic processes, whether performed manually or with automated algorithms. Consequently, they are subject to errors. We set out to classify and reduce these errors by analyzing 1,061 motor-unit action-potential trains (MUAPTs), obtained by decomposing surface EMG (sEMG) signals recorded during human voluntary contractions. Decomposition errors were classified into two general categories: location errors representing variability in the temporal localization of each motor-unit firing instance and identification errors consisting of falsely detected or missed firing instances. To mitigate these errors, we developed an error-reduction algorithm that combines multiple decomposition estimates to determine a more probable estimate of motor-unit firing instances with fewer errors. The performance of the algorithm is governed by a trade-off between the yield of MUAPTs obtained above a given accuracy level and the time required to perform the decomposition. When applied to a set of sEMG signals synthesized from real MUAPTs, the identification error was reduced by an average of 1.78%, improving the accuracy to 97.0%, and the location error was reduced by an average of 1.66 ms. The error-reduction algorithm in this study is not limited to any specific decomposition strategy. Rather, we propose it be used for other decomposition methods, especially when analyzing precise motor-unit firing instances, as occurs when measuring synchronization. PMID:25210159

Kinetics of Thermal Decomposition of Ammonium Perchlorate by TG/DSC-MS-FTIR

NASA Astrophysics Data System (ADS)

Zhu, Yan-Li; Huang, Hao; Ren, Hui; Jiao, Qing-Jie

2014-01-01

The method of thermogravimetry/differential scanning calorimetry-mass spectrometry-Fourier transform infrared (TG/DSC-MS-FTIR) simultaneous analysis has been used to study thermal decomposition of ammonium perchlorate (AP). The processing of nonisothermal data at various heating rates was performed using NETZSCH Thermokinetics. The MS-FTIR spectra showed that N2O and NO2 were the main gaseous products of the thermal decomposition of AP, and there was a competition between the formation reaction of N2O and that of NO2 during the process with an iso-concentration point of N2O and NO2. The dependence of the activation energy calculated by Friedman's iso-conversional method on the degree of conversion indicated that the AP decomposition process can be divided into three stages, which are autocatalytic, low-temperature diffusion and high-temperature, stable-phase reaction. The corresponding kinetic parameters were determined by multivariate nonlinear regression and the mechanism of the AP decomposition process was proposed.

A Continuum Damage Mechanics Model to Predict Kink-Band Propagation Using Deformation Gradient Tensor Decomposition

NASA Technical Reports Server (NTRS)

Bergan, Andrew C.; Leone, Frank A., Jr.

2016-01-01

A new model is proposed that represents the kinematics of kink-band formation and propagation within the framework of a mesoscale continuum damage mechanics (CDM) model. The model uses the recently proposed deformation gradient decomposition approach to represent a kink band as a displacement jump via a cohesive interface that is embedded in an elastic bulk material. The model is capable of representing the combination of matrix failure in the frame of a misaligned fiber and instability due to shear nonlinearity. In contrast to conventional linear or bilinear strain softening laws used in most mesoscale CDM models for longitudinal compression, the constitutive response of the proposed model includes features predicted by detailed micromechanical models. These features include: 1) the rotational kinematics of the kink band, 2) an instability when the peak load is reached, and 3) a nonzero plateau stress under large strains.

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)

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

Wood decomposition following clearcutting at Coweeta Hydrologic Laboratory

Treesearch

Kim G. Mattson; Wayne T. Swank

2014-01-01

Most of the forest on Watershed (WS) 7 was cut and ledt on site to decompose. This Chapter describes the rate and manner of wood decomposition and also quantifies the fluxes from decaying wood to the forest floor on WS 7. In doing so, we make the case that wood and its process of decomposition contributes to ecosystem stability. We also review some of the history of...

Microbial Community Functional Change during Vertebrate Carrion Decomposition

PubMed Central

Pechal, Jennifer L.; Crippen, Tawni L.; Tarone, Aaron M.; Lewis, Andrew J.; Tomberlin, Jeffery K.; Benbow, M. Eric

2013-01-01

Microorganisms play a critical role in the decomposition of organic matter, which contributes to energy and nutrient transformation in every ecosystem. Yet, little is known about the functional activity of epinecrotic microbial communities associated with carrion. The objective of this study was to provide a description of the carrion associated microbial community functional activity using differential carbon source use throughout decomposition over seasons, between years and when microbial communities were isolated from eukaryotic colonizers (e.g., necrophagous insects). Additionally, microbial communities were identified at the phyletic level using high throughput sequencing during a single study. We hypothesized that carrion microbial community functional profiles would change over the duration of decomposition, and that this change would depend on season, year and presence of necrophagous insect colonization. Biolog EcoPlates™ were used to measure the variation in epinecrotic microbial community function by the differential use of 29 carbon sources throughout vertebrate carrion decomposition. Pyrosequencing was used to describe the bacterial community composition in one experiment to identify key phyla associated with community functional changes. Overall, microbial functional activity increased throughout decomposition in spring, summer and winter while it decreased in autumn. Additionally, microbial functional activity was higher in 2011 when necrophagous arthropod colonizer effects were tested. There were inconsistent trends in the microbial function of communities isolated from remains colonized by necrophagous insects between 2010 and 2011, suggesting a greater need for a mechanistic understanding of the process. These data indicate that functional analyses can be implemented in carrion studies and will be important in understanding the influence of microbial communities on an essential ecosystem process, carrion decomposition. PMID:24265741

Decomposition and biodegradability enhancement of textile wastewater using a combination of electron beam irradiation and activated sludge process.

PubMed

Mohd Nasir, Norlirubayah; Teo Ming, Ting; Ahmadun, Fakhru'l-Razi; Sobri, Shafreeza

2010-01-01

The research conducted a study on decomposition and biodegradability enhancement of textile wastewater using a combination of electron beam irradiation and activated sludge process. The purposes of this research are to remove pollutant through decomposition and to enhance the biodegradability of textile wastewater. The wastewater is treated using electron beam irradiation as a pre-treatment before undergo an activated sludge process. As a result, for non-irradiated wastewater, the COD removal was achieved to be between 70% and 79% after activated sludge process. The improvement of COD removal efficiency increased to 94% after irradiation of treated effluent at the dose of 50 kGy. Meanwhile, the BOD(5) removal efficiencies of non-irradiated and irradiated textile wastewater were reported to be between 80 and 87%, and 82 and 99.2%, respectively. The maximum BOD(5) removal efficiency was achieved at day 1 (HRT 5 days) of the process of an irradiated textile wastewater which is 99.2%. The biodegradability ratio of non-irradiated wastewater was reported to be between 0.34 and 0.61, while the value of biodegradability ratio of an irradiated wastewater increased to be between 0.87 and 0.96. The biodegradability enhancement of textile wastewater is increased with increasing the doses. Therefore, an electron beam radiation holds a greatest application of removing pollutants and also on enhancing the biodegradability of textile wastewater.

Computer Tensor Codes to Design the War Drive

NASA Astrophysics Data System (ADS)

Maccone, C.

To address problems in Breakthrough Propulsion Physics (BPP) and design the Warp Drive one needs sheer computing capabilities. This is because General Relativity (GR) and Quantum Field Theory (QFT) are so mathematically sophisticated that the amount of analytical calculations is prohibitive and one can hardly do all of them by hand. In this paper we make a comparative review of the main tensor calculus capabilities of the three most advanced and commercially available “symbolic manipulator” codes. We also point out that currently one faces such a variety of different conventions in tensor calculus that it is difficult or impossible to compare results obtained by different scholars in GR and QFT. Mathematical physicists, experimental physicists and engineers have each their own way of customizing tensors, especially by using different metric signatures, different metric determinant signs, different definitions of the basic Riemann and Ricci tensors, and by adopting different systems of physical units. This chaos greatly hampers progress toward the design of the Warp Drive. It is thus suggested that NASA would be a suitable organization to establish standards in symbolic tensor calculus and anyone working in BPP should adopt these standards. Alternatively other institutions, like CERN in Europe, might consider the challenge of starting the preliminary implementation of a Universal Tensor Code to design the Warp Drive.

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

Scalar-tensor linear inflation

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

Artymowski, Michał; Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee

2017-04-01

We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead tomore » linear inflation in the strong coupling limit.« less

Using Empirical Mode Decomposition to process Marine Magnetotelluric Data

NASA Astrophysics Data System (ADS)

Chen, J.; Jegen, M. D.; Heincke, B. H.; Moorkamp, M.

2014-12-01

The magnetotelluric (MT) data always exhibits nonstationarities due to variations of source mechanisms causing MT variations on different time and spatial scales. An additional non-stationary component is introduced through noise, which is particularly pronounced in marine MT data through motion induced noise caused by time-varying wave motion and currents. We present a new heuristic method for dealing with the non-stationarity of MT time series based on Empirical Mode Decomposition (EMD). The EMD method is used in combination with the derived instantaneous spectra to determine impedance estimates. The procedure is tested on synthetic and field MT data. In synthetic tests the reliability of impedance estimates from EMD-based method is compared to the synthetic responses of a 1D layered model. To examine how estimates are affected by noise, stochastic stationary and non-stationary noise are added on the time series. Comparisons reveal that estimates by the EMD-based method are generally more stable than those by simple Fourier analysis. Furthermore, the results are compared to those derived by a commonly used Fourier-based MT data processing software (BIRRP), which incorporates additional sophisticated robust estimations to deal with noise issues. It is revealed that the results from both methods are already comparable, even though no robust estimate procedures are implemented in the EMD approach at present stage. The processing scheme is then applied to marine MT field data. Testing is performed on short, relatively quiet segments of several data sets, as well as on long segments of data with many non-stationary noise packages. Compared to BIRRP, the new method gives comparable or better impedance estimates, furthermore, the estimates are extended to lower frequencies and less noise biased estimates with smaller error bars are obtained at high frequencies. The new processing methodology represents an important step towards deriving a better resolved Earth model to

Relationship between the Decomposition Process of Coarse Woody Debris and Fungal Community Structure as Detected by High-Throughput Sequencing in a Deciduous Broad-Leaved Forest in Japan

PubMed Central

Yamashita, Satoshi; Masuya, Hayato; Abe, Shin; Masaki, Takashi; Okabe, Kimiko

2015-01-01

We examined the relationship between the community structure of wood-decaying fungi, detected by high-throughput sequencing, and the decomposition rate using 13 years of data from a forest dynamics plot. For molecular analysis and wood density measurements, drill dust samples were collected from logs and stumps of Fagus and Quercus in the plot. Regression using a negative exponential model between wood density and time since death revealed that the decomposition rate of Fagus was greater than that of Quercus. The residual between the expected value obtained from the regression curve and the observed wood density was used as a decomposition rate index. Principal component analysis showed that the fungal community compositions of both Fagus and Quercus changed with time since death. Principal component analysis axis scores were used as an index of fungal community composition. A structural equation model for each wood genus was used to assess the effect of fungal community structure traits on the decomposition rate and how the fungal community structure was determined by the traits of coarse woody debris. Results of the structural equation model suggested that the decomposition rate of Fagus was affected by two fungal community composition components: one that was affected by time since death and another that was not affected by the traits of coarse woody debris. In contrast, the decomposition rate of Quercus was not affected by coarse woody debris traits or fungal community structure. These findings suggest that, in the case of Fagus coarse woody debris, the fungal community structure is related to the decomposition process of its host substrate. Because fungal community structure is affected partly by the decay stage and wood density of its substrate, these factors influence each other. Further research on interactive effects is needed to improve our understanding of the relationship between fungal community structure and the woody debris decomposition process

Full moment tensors for small events (Mw < 3) at Uturuncu volcano, Bolivia

NASA Astrophysics Data System (ADS)

Alvizuri, Celso; Tape, Carl

2016-09-01

We present a catalogue of full seismic moment tensors for 63 events from Uturuncu volcano in Bolivia. The events were recorded during 2011-2012 in the PLUTONS seismic array of 24 broad-band stations. Most events had magnitudes between 0.5 and 2.0 and did not generate discernible surface waves; the largest event was Mw 2.8. For each event we computed the misfit between observed and synthetic waveforms, and we used first-motion polarity measurements to reduce the number of possible solutions. Each moment tensor solution was obtained using a grid search over the 6-D space of moment tensors. For each event, we show the misfit function in eigenvalue space, represented by a lune. We identify three subsets of the catalogue: (1) six isotropic events, (2) five tensional crack events, and (3) a swarm of 14 events southeast of the volcanic centre that appear to be double couples. The occurrence of positively isotropic events is consistent with other published results from volcanic and geothermal regions. Several of these previous results, as well as our results, cannot be interpreted within the context of either an oblique opening crack or a crack-plus-double-couple model. Proper characterization of uncertainties for full moment tensors is critical for distinguishing among physical models of source processes.

ADVANCED OXIDATION: OXALATE DECOMPOSITION TESTING WITH OZONE

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

Ketusky, E.; Subramanian, K.

At the Savannah River Site (SRS), oxalic acid is currently considered the preferred agent for chemically cleaning the large underground Liquid Radioactive Waste Tanks. It is applied only in the final stages of emptying a tank when generally less than 5,000 kg of waste solids remain, and slurrying based removal methods are no-longer effective. The use of oxalic acid is preferred because of its combined dissolution and chelating properties, as well as the fact that corrosion to the carbon steel tank walls can be controlled. Although oxalic acid is the preferred agent, there are significant potential downstream impacts. Impacts include:more » (1) Degraded evaporator operation; (2) Resultant oxalate precipitates taking away critically needed operating volume; and (3) Eventual creation of significant volumes of additional feed to salt processing. As an alternative to dealing with the downstream impacts, oxalate decomposition using variations of ozone based Advanced Oxidation Process (AOP) were investigated. In general AOPs use ozone or peroxide and a catalyst to create hydroxyl radicals. Hydroxyl radicals have among the highest oxidation potentials, and are commonly used to decompose organics. Although oxalate is considered among the most difficult organic to decompose, the ability of hydroxyl radicals to decompose oxalate is considered to be well demonstrated. In addition, as AOPs are considered to be 'green' their use enables any net chemical additions to the waste to be minimized. In order to test the ability to decompose the oxalate and determine the decomposition rates, a test rig was designed, where 10 vol% ozone would be educted into a spent oxalic acid decomposition loop, with the loop maintained at 70 C and recirculated at 40L/min. Each of the spent oxalic acid streams would be created from three oxalic acid strikes of an F-area simulant (i.e., Purex = high Fe/Al concentration) and H-area simulant (i.e., H area modified Purex = high Al/Fe concentration) after

Hidden discriminative features extraction for supervised high-order time series modeling.

PubMed

Nguyen, Ngoc Anh Thi; Yang, Hyung-Jeong; Kim, Sunhee

2016-11-01

In this paper, an orthogonal Tucker-decomposition-based extraction of high-order discriminative subspaces from a tensor-based time series data structure is presented, named as Tensor Discriminative Feature Extraction (TDFE). TDFE relies on the employment of category information for the maximization of the between-class scatter and the minimization of the within-class scatter to extract optimal hidden discriminative feature subspaces that are simultaneously spanned by every modality for supervised tensor modeling. In this context, the proposed tensor-decomposition method provides the following benefits: i) reduces dimensionality while robustly mining the underlying discriminative features, ii) results in effective interpretable features that lead to an improved classification and visualization, and iii) reduces the processing time during the training stage and the filtering of the projection by solving the generalized eigenvalue issue at each alternation step. Two real third-order tensor-structures of time series datasets (an epilepsy electroencephalogram (EEG) that is modeled as channel×frequency bin×time frame and a microarray data that is modeled as gene×sample×time) were used for the evaluation of the TDFE. The experiment results corroborate the advantages of the proposed method with averages of 98.26% and 89.63% for the classification accuracies of the epilepsy dataset and the microarray dataset, respectively. These performance averages represent an improvement on those of the matrix-based algorithms and recent tensor-based, discriminant-decomposition approaches; this is especially the case considering the small number of samples that are used in practice. Copyright © 2016 Elsevier Ltd. All rights reserved.

Plant Identity Influences Decomposition through More Than One Mechanism

PubMed Central

McLaren, Jennie R.; Turkington, Roy

2011-01-01

Plant litter decomposition is a critical ecosystem process representing a major pathway for carbon flux, but little is known about how it is affected by changes in plant composition and diversity. Single plant functional groups (graminoids, legumes, non-leguminous forbs) were removed from a grassland in northern Canada to examine the impacts of functional group identity on decomposition. Removals were conducted within two different environmental contexts (fertilization and fungicide application) to examine the context-dependency of these identity effects. We examined two different mechanisms by which the loss of plant functional groups may impact decomposition: effects of the living plant community on the decomposition microenvironment, and changes in the species composition of the decomposing litter, as well as the interaction between these mechanisms. We show that the identity of the plant functional group removed affects decomposition through both mechanisms. Removal of both graminoids and forbs slowed decomposition through changes in the decomposition microenvironment. We found non-additive effects of litter mixing, with both the direction and identity of the functional group responsible depending on year; in 2004 graminoids positively influenced decomposition whereas in 2006 forbs negatively influenced decomposition rate. Although these two mechanisms act independently, their effects may be additive if both mechanisms are considered simultaneously. It is essential to understand the variety of mechanisms through which even a single ecosystem property is affected if we are to predict the future consequences of biodiversity loss. PMID:21858210

Iterative image-domain decomposition for dual-energy CT

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

Niu, Tianye; Dong, Xue; Petrongolo, Michael

2014-04-15

Purpose: Dual energy CT (DECT) imaging plays an important role in advanced imaging applications due to its capability of material decomposition. Direct decomposition via matrix inversion suffers from significant degradation of image signal-to-noise ratios, which reduces clinical values of DECT. Existing denoising algorithms achieve suboptimal performance since they suppress image noise either before or after the decomposition and do not fully explore the noise statistical properties of the decomposition process. In this work, the authors propose an iterative image-domain decomposition method for noise suppression in DECT, using the full variance-covariance matrix of the decomposed images. Methods: The proposed algorithm ismore » formulated in the form of least-square estimation with smoothness regularization. Based on the design principles of a best linear unbiased estimator, the authors include the inverse of the estimated variance-covariance matrix of the decomposed images as the penalty weight in the least-square term. The regularization term enforces the image smoothness by calculating the square sum of neighboring pixel value differences. To retain the boundary sharpness of the decomposed images, the authors detect the edges in the CT images before decomposition. These edge pixels have small weights in the calculation of the regularization term. Distinct from the existing denoising algorithms applied on the images before or after decomposition, the method has an iterative process for noise suppression, with decomposition performed in each iteration. The authors implement the proposed algorithm using a standard conjugate gradient algorithm. The method performance is evaluated using an evaluation phantom (Catphan©600) and an anthropomorphic head phantom. The results are compared with those generated using direct matrix inversion with no noise suppression, a denoising method applied on the decomposed images, and an existing algorithm with similar formulation

Interacting effects of insects and flooding on wood decomposition.

Treesearch

Michael Ulyshen

2014-01-01

Saproxylic arthropods are thought to play an important role in wood decomposition but very few efforts have been made to quantify their contributions to the process and the factors controlling their activities are not well understood. In the current study, mesh exclusion bags were used to quantify how arthropods affect loblolly pine (Pinus taeda L.) decomposition rates...

Characteristic of root decomposition in a tropical rainforest in Sarawak, Malaysi

NASA Astrophysics Data System (ADS)

Ohashi, Mizue; Makita, Naoki; Katayam, Ayumi; Kume, Tomonori; Matsumoto, Kazuho; Khoon Kho, L.

2016-04-01

Woody roots play a significant role in forest carbon cycling, as up to 60 percent of tree photosynthetic production can be allocated to belowground. Root decay is one of the main processes of soil C dynamics and potentially relates to soil C sequestration. However, much less attention has been paid for root litter decomposition compared to the studies of leaf litter because roots are hidden from view. Previous studies have revealed that physico-chemical quality of roots, climate, and soil organisms affect root decomposition significantly. However, patterns and mechanisms of root decomposition are still poorly understood because of the high variability of root properties, field environment and potential decomposers. For example, root size would be a factor controlling decomposition rates, but general understanding of the difference between coarse and fine root decompositions is still lacking. Also, it is known that root decomposition is performed by soil animals, fungi and bacteria, but their relative importance is poorly understood. In this study, therefore, we aimed to characterize the root decomposition in a tropical rainforest in Sarawak, Malaysia, and clarify the impact of soil living organisms and root sizes on root litter decomposition. We buried soil cores with fine and coarse root litter bags in soil in Lambir Hills National Park. Three different types of soil cores that are covered by 1.5 cm plastic mesh, root-impermeable sheet (50um) and fungi-impermeable sheet (1um) were prepared. The soil cores were buried in February 2013 and collected 4 times, 134 days, 226 days, 786 days and 1151 days after the installation. We found that nearly 80 percent of the coarse root litter was decomposed after two years, whereas only 60 percent of the fine root litter was decomposed. Our results also showed significantly different ratio of decomposition between different cores, suggesting the different contribution of soil living organisms to decomposition process.

Polymer stress tensor in turbulent shear flows.

PubMed

L'vov, Victor S; Pomyalov, Anna; Procaccia, Itamar; Tiberkevich, Vasil

2005-01-01

The interaction of polymers with turbulent shear flows is examined. We focus on the structure of the elastic stress tensor, which is proportional to the polymer conformation tensor. We examine this object in turbulent flows of increasing complexity. First is isotropic turbulence, then anisotropic (but homogenous) shear turbulence, and finally wall bounded turbulence. The main result of this paper is that for all these flows the polymer stress tensor attains a universal structure in the limit of large Deborah number De > 1. We present analytic results for the suppression of the coil-stretch transition at large Deborah numbers. Above the transition the turbulent velocity fluctuations are strongly correlated with the polymer's elongation: there appear high-quality "hydroelastic" waves in which turbulent kinetic energy turns into polymer potential energy and vice versa. These waves determine the trace of the elastic stress tensor but practically do not modify its universal structure. We demonstrate that the influence of the polymers on the balance of energy and momentum can be accurately described by an effective polymer viscosity that is proportional to the cross-stream component of the elastic stress tensor. This component is smaller than the streamwise component by a factor proportional to De2. Finally we tie our results to wall bounded turbulence and clarify some puzzling facts observed in the problem of drag reduction by polymers.

Susceptibility Tensor Imaging (STI) of the Brain

PubMed Central

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

2016-01-01

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

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.

Cadaver decomposition in terrestrial ecosystems

NASA Astrophysics Data System (ADS)

Carter, David O.; Yellowlees, David; Tibbett, Mark

2007-01-01

A dead mammal (i.e. cadaver) is a high quality resource (narrow carbon:nitrogen ratio, high water content) that releases an intense, localised pulse of carbon and nutrients into the soil upon decomposition. Despite the fact that as much as 5,000 kg of cadaver can be introduced to a square kilometre of terrestrial ecosystem each year, cadaver decomposition remains a neglected microsere. Here we review the processes associated with the introduction of cadaver-derived carbon and nutrients into soil from forensic and ecological settings to show that cadaver decomposition can have a greater, albeit localised, effect on belowground ecology than plant and faecal resources. Cadaveric materials are rapidly introduced to belowground floral and faunal communities, which results in the formation of a highly concentrated island of fertility, or cadaver decomposition island (CDI). CDIs are associated with increased soil microbial biomass, microbial activity (C mineralisation) and nematode abundance. Each CDI is an ephemeral natural disturbance that, in addition to releasing energy and nutrients to the wider ecosystem, acts as a hub by receiving these materials in the form of dead insects, exuvia and puparia, faecal matter (from scavengers, grazers and predators) and feathers (from avian scavengers and predators). As such, CDIs contribute to landscape heterogeneity. Furthermore, CDIs are a specialised habitat for a number of flies, beetles and pioneer vegetation, which enhances biodiversity in terrestrial ecosystems.

Thermal Decomposition Mechanism of Butyraldehyde

NASA Astrophysics Data System (ADS)

Hatten, Courtney D.; Warner, Brian; Wright, Emily; Kaskey, Kevin; McCunn, Laura R.

2013-06-01

The thermal decomposition of butyraldehyde, CH_3CH_2CH_2C(O)H, has been studied in a resistively heated SiC tubular reactor. Products of pyrolysis were identified via matrix-isolation FTIR spectroscopy and photoionization mass spectrometry in separate experiments. Carbon monoxide, ethene, acetylene, water and ethylketene were among the products detected. To unravel the mechanism of decomposition, pyrolysis of a partially deuterated sample of butyraldehyde was studied. Also, the concentration of butyraldehyde in the carrier gas was varied in experiments to determine the presence of bimolecular reactions. The results of these experiments can be compared to the dissociation pathways observed in similar aldehydes and are relevant to the processing of biomass, foods, and tobacco.

Matrix- and tensor-based recommender systems for the discovery of currently unknown inorganic compounds

NASA Astrophysics Data System (ADS)

Seko, Atsuto; Hayashi, Hiroyuki; Kashima, Hisashi; Tanaka, Isao

2018-01-01

Chemically relevant compositions (CRCs) and atomic arrangements of inorganic compounds have been collected as inorganic crystal structure databases. Machine learning is a unique approach to search for currently unknown CRCs from vast candidates. Herein we propose matrix- and tensor-based recommender system approaches to predict currently unknown CRCs from database entries of CRCs. Firstly, the performance of the recommender system approaches to discover currently unknown CRCs is examined. A Tucker decomposition recommender system shows the best discovery rate of CRCs as the majority of the top 100 recommended ternary and quaternary compositions correspond to CRCs. Secondly, systematic density functional theory (DFT) calculations are performed to investigate the phase stability of the recommended compositions. The phase stability of the 27 compositions reveals that 23 currently unknown compounds are newly found to be stable. These results indicate that the recommender system has great potential to accelerate the discovery of new compounds.

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.

Conception of discrete systems decomposition algorithm using p-invariants and hypergraphs

NASA Astrophysics Data System (ADS)

Stefanowicz, Ł.

2016-09-01

In the article author presents an idea of decomposition algorithm of discrete systems described by Petri Nets using pinvariants. Decomposition process is significant from the point of view of discrete systems design, because it allows separation of the smaller sequential parts. Proposed algorithm uses modified Martinez-Silva method as well as author's selection algorithm. The developed method is a good complement of classical decomposition algorithms using graphs and hypergraphs.

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.

Ward identities and combinatorics of rainbow tensor models

NASA Astrophysics Data System (ADS)

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

2017-06-01

We discuss the notion of renormalization group (RG) completion of non-Gaussian Lagrangians and its treatment within the framework of Bogoliubov-Zimmermann theory in application to the matrix and tensor models. With the example of the simplest non-trivial RGB tensor theory (Aristotelian rainbow), we introduce a few methods, which allow one to connect calculations in the tensor models to those in the matrix models. As a byproduct, we obtain some new factorization formulas and sum rules for the Gaussian correlators in the Hermitian and complex matrix theories, square and rectangular. These sum rules describe correlators as solutions to finite linear systems, which are much simpler than the bilinear Hirota equations and the infinite Virasoro recursion. Search for such relations can be a way to solving the tensor models, where an explicit integrability is still obscure.

Fermionic topological quantum states as tensor networks

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Energetic contaminants inhibit plant litter decomposition in soil.

PubMed

Kuperman, Roman G; Checkai, Ronald T; Simini, Michael; Sunahara, Geoffrey I; Hawari, Jalal

2018-05-30

Individual effects of nitrogen-based energetic materials (EMs) 2,4-dinitrotoluene (2,4-DNT), 2-amino-4,6-dinitrotoluene (2-ADNT), 4-amino-2,6-dinitrotoluene (4-ADNT), nitroglycerin (NG), and 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane (CL-20) on litter decomposition, an essential biologically-mediated soil process, were assessed using Orchard grass (Dactylis glomerata) straw in Sassafras sandy loam (SSL) soil, which has physicochemical characteristics that support "very high" qualitative relative bioavailability for organic chemicals. Batches of SSL soil were separately amended with individual EMs or acetone carrier control. To quantify the decomposition rates, one straw cluster was harvested from a set of randomly selected replicate containers from within each treatment, after 1, 2, 3, 4, 6, and 8 months of exposure. Results showed that soil amended with 2,4-DNT or NG inhibited litter decomposition rates based on the median effective concentration (EC50) values of 1122 mg/kg and 860 mg/kg, respectively. Exposure to 2-ADNT, 4-ADNT or CL-20 amended soil did not significantly affect litter decomposition in SSL soil at ≥ 10,000 mg/kg. These ecotoxicological data will be helpful in identifying concentrations of EMs in soil that present an acceptable ecological risk for biologically-mediated soil processes. Published by Elsevier Inc.

Character Decomposition and Transposition Processes of Chinese Compound Words in Rapid Serial Visual Presentation.

PubMed

Cao, Hong-Wen; Yang, Ke-Yu; Yan, Hong-Mei

2017-01-01

Character order information is encoded at the initial stage of Chinese word processing, however, its time course remains underspecified. In this study, we assess the exact time course of the character decomposition and transposition processes of two-character Chinese compound words (canonical, transposed, or reversible words) compared with pseudowords using dual-target rapid serial visual presentation (RSVP) of stimuli appearing at 30 ms per character with no inter-stimulus interval. The results indicate that Chinese readers can identify words with character transpositions in rapid succession; however, a transposition cost is involved in identifying transposed words compared to canonical words. In RSVP reading, character order of words is more likely to be reversed during the period from 30 to 180 ms for canonical and reversible words, but the period from 30 to 240 ms for transposed words. Taken together, the findings demonstrate that the holistic representation of the base word is activated, however, the order of the two constituent characters is not strictly processed during the very early stage of visual word processing.

An integrated condition-monitoring method for a milling process using reduced decomposition features

NASA Astrophysics Data System (ADS)

Liu, Jie; Wu, Bo; Wang, Yan; Hu, Youmin

2017-08-01

Complex and non-stationary cutting chatter affects productivity and quality in the milling process. Developing an effective condition-monitoring approach is critical to accurately identify cutting chatter. In this paper, an integrated condition-monitoring method is proposed, where reduced features are used to efficiently recognize and classify machine states in the milling process. In the proposed method, vibration signals are decomposed into multiple modes with variational mode decomposition, and Shannon power spectral entropy is calculated to extract features from the decomposed signals. Principal component analysis is adopted to reduce feature size and computational cost. With the extracted feature information, the probabilistic neural network model is used to recognize and classify the machine states, including stable, transition, and chatter states. Experimental studies are conducted, and results show that the proposed method can effectively detect cutting chatter during different milling operation conditions. This monitoring method is also efficient enough to satisfy fast machine state recognition and classification.

Superconducting tensor gravity gradiometer

NASA Technical Reports Server (NTRS)

Paik, H. J.

1981-01-01

The employment of superconductivity and other material properties at cryogenic temperatures to fabricate sensitive, low-drift, gravity gradiometer is described. The device yields a reduction of noise of four orders of magnitude over room temperature gradiometers, and direct summation and subtraction of signals from accelerometers in varying orientations are possible with superconducting circuitry. Additional circuits permit determination of the linear and angular acceleration vectors independent of the measurement of the gravity gradient tensor. A dewar flask capable of maintaining helium in a liquid state for a year's duration is under development by NASA, and a superconducting tensor gravity gradiometer for the NASA Geodynamics Program is intended for a LEO polar trajectory to measure the harmonic expansion coefficients of the earth's gravity field up to order 300.

Microbial community assembly and metabolic function during mammalian corpse decomposition

USGS Publications Warehouse

Metcalf, Jessica L; Xu, Zhenjiang Zech; Weiss, Sophie; Lax, Simon; Van Treuren, Will; Hyde, Embriette R.; Song, Se Jin; Amir, Amnon; Larsen, Peter; Sangwan, Naseer; Haarmann, Daniel; Humphrey, Greg C; Ackermann, Gail; Thompson, Luke R; Lauber, Christian; Bibat, Alexander; Nicholas, Catherine; Gebert, Matthew J; Petrosino, Joseph F; Reed, Sasha C.; Gilbert, Jack A; Lynne, Aaron M; Bucheli, Sibyl R; Carter, David O; Knight, Rob

2016-01-01

Vertebrate corpse decomposition provides an important stage in nutrient cycling in most terrestrial habitats, yet microbially mediated processes are poorly understood. Here we combine deep microbial community characterization, community-level metabolic reconstruction, and soil biogeochemical assessment to understand the principles governing microbial community assembly during decomposition of mouse and human corpses on different soil substrates. We find a suite of bacterial and fungal groups that contribute to nitrogen cycling and a reproducible network of decomposers that emerge on predictable time scales. Our results show that this decomposer community is derived primarily from bulk soil, but key decomposers are ubiquitous in low abundance. Soil type was not a dominant factor driving community development, and the process of decomposition is sufficiently reproducible to offer new opportunities for forensic investigations.

Effect of the carbon coating in Fe-C-TiO(2) photocatalyst on phenol decomposition under UV irradiation via photo-Fenton process.

PubMed

Tryba, Beata; Morawski, Antoni W; Inagaki, Michio; Toyoda, Masahiro

2006-08-01

Fe-C-TiO(2) photocatalysts which contained the residue carbon (0.2-3.3 mass%) were prepared from a mixture of TiO(2) and FeC(2)O(4) through the heating at 673-1173 K in Ar. These photocatalysts did not show a high adsorption of phenol, but they were active in photo-Fenton reactions during decomposition of phenol under UV irradiation with addition of H(2)O(2). It was proved that Fe(2+) governed the photoactivity of Fe-C-TiO(2) photocatalysts, it decreased with heat-treatment temperature above 773 K. For comparison, Fe-TiO(2) photocatalyst was prepared by heating TiO(2) and FeC(2)O(4) at 823 K in air for 3h. Phenol decomposition was going much slower on Fe-TiO(2) photocatalyst in comparison with Fe-C-TiO(2), of which mechanism was different, on the former phenol was decomposed by the radical reaction, on the latter through a complex reaction with iron and intermediates of phenol decomposition. Therefore carbon-coating TiO(2) was found to be advantageous for mounting iron and its application for the phenol decomposition via photo-Fenton process.

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).

Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of nonsparse low-rank matrices

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Siopsis, George; Weedbrook, Christian

2018-02-01

With the significant advancement in quantum computation during the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used technique in supervised classical machine learning. Here we introduce an algorithm for Gaussian process regression using continuous-variable quantum systems that can be realized with technology based on photonic quantum computers under certain assumptions regarding distribution of data and availability of efficient quantum access. Our algorithm shows that by using a continuous-variable quantum computer a dramatic speedup in computing Gaussian process regression can be achieved, i.e., the possibility of exponentially reducing the time to compute. Furthermore, our results also include a continuous-variable quantum-assisted singular value decomposition method of nonsparse low rank matrices and forms an important subroutine in our Gaussian process regression algorithm.

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.

Study on the mechanism of copper-ammonia complex decomposition in struvite formation process and enhanced ammonia and copper removal.

PubMed

Peng, Cong; Chai, Liyuan; Tang, Chongjian; Min, Xiaobo; Song, Yuxia; Duan, Chengshan; Yu, Cheng

2017-01-01

Heavy metals and ammonia are difficult to remove from wastewater, as they easily combine into refractory complexes. The struvite formation method (SFM) was applied for the complex decomposition and simultaneous removal of heavy metal and ammonia. The results indicated that ammonia deprivation by SFM was the key factor leading to the decomposition of the copper-ammonia complex ion. Ammonia was separated from solution as crystalline struvite, and the copper mainly co-precipitated as copper hydroxide together with struvite. Hydrogen bonding and electrostatic attraction were considered to be the main surface interactions between struvite and copper hydroxide. Hydrogen bonding was concluded to be the key factor leading to the co-precipitation. In addition, incorporation of copper ions into the struvite crystal also occurred during the treatment process. Copyright © 2016. Published by Elsevier B.V.

Optimal cost design of water distribution networks using a decomposition approach

NASA Astrophysics Data System (ADS)

Lee, Ho Min; Yoo, Do Guen; Sadollah, Ali; Kim, Joong Hoon

2016-12-01

Water distribution network decomposition, which is an engineering approach, is adopted to increase the efficiency of obtaining the optimal cost design of a water distribution network using an optimization algorithm. This study applied the source tracing tool in EPANET, which is a hydraulic and water quality analysis model, to the decomposition of a network to improve the efficiency of the optimal design process. The proposed approach was tested by carrying out the optimal cost design of two water distribution networks, and the results were compared with other optimal cost designs derived from previously proposed optimization algorithms. The proposed decomposition approach using the source tracing technique enables the efficient decomposition of an actual large-scale network, and the results can be combined with the optimal cost design process using an optimization algorithm. This proves that the final design in this study is better than those obtained with other previously proposed optimization algorithms.

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.

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.

Reactivity continuum modeling of leaf, root, and wood decomposition across biomes

NASA Astrophysics Data System (ADS)

Koehler, Birgit; Tranvik, Lars J.

2015-07-01

Large carbon dioxide amounts are released to the atmosphere during organic matter decomposition. Yet the large-scale and long-term regulation of this critical process in global carbon cycling by litter chemistry and climate remains poorly understood. We used reactivity continuum (RC) modeling to analyze the decadal data set of the "Long-term Intersite Decomposition Experiment," in which fine litter and wood decomposition was studied in eight biome types (224 time series). In 32 and 46% of all sites the litter content of the acid-unhydrolyzable residue (AUR, formerly referred to as lignin) and the AUR/nitrogen ratio, respectively, retarded initial decomposition rates. This initial rate-retarding effect generally disappeared within the first year of decomposition, and rate-stimulating effects of nutrients and a rate-retarding effect of the carbon/nitrogen ratio became more prevalent. For needles and leaves/grasses, the influence of climate on decomposition decreased over time. For fine roots, the climatic influence was initially smaller but increased toward later-stage decomposition. The climate decomposition index was the strongest climatic predictor of decomposition. The similar variability in initial decomposition rates across litter categories as across biome types suggested that future changes in decomposition may be dominated by warming-induced changes in plant community composition. In general, the RC model parameters successfully predicted independent decomposition data for the different litter-biome combinations (196 time series). We argue that parameterization of large-scale decomposition models with RC model parameters, as opposed to the currently common discrete multiexponential models, could significantly improve their mechanistic foundation and predictive accuracy across climate zones and litter categories.

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.

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.

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

PubMed

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

2017-07-01

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

Associational Patterns of Scavenger Beetles to Decomposition Stages.

PubMed

Zanetti, Noelia I; Visciarelli, Elena C; Centeno, Nestor D

2015-07-01

Beetles associated with carrion play an important role in recycling organic matter in an ecosystem. Four experiments on decomposition, one per season, were conducted in a semirural area in Bahía Blanca, Argentina. Melyridae are reported for the first time of forensic interest. Apart from adults and larvae of Scarabaeidae, thirteen species and two genera of other coleopteran families are new forensic records in Argentina. Diversity, abundance, and species composition of beetles showed differences between stages and seasons. Our results differed from other studies conducted in temperate regions. Four guilds and succession patterns were established in relation to decomposition stages and seasons. Dermestidae (necrophages) predominated in winter during the decomposition process; Staphylinidae (necrophiles) in Fresh and Bloat stages during spring, summer, and autumn; and Histeridae (necrophiles) and Cleridae (omnivores) in the following stages during those seasons. Finally, coleopteran activity, diversity and abundance, and decomposition rate change with biogeoclimatic characteristics, which is of significance in forensics. © 2015 American Academy of Forensic Sciences.

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

Kolda, Tamara Gibson

We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The first operator, which we call the Tucker operator, is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor and can be employed to concisely express the Tucker decomposition. The second operator, which we call the Kruskal operator, is shorthand for the sum of the outer-products of the columns of N matrices and allows a divorce from a matricized representation and a very concise expression of the PARAFAC decomposition. We explore the properties ofmore » the Tucker and Kruskal operators independently of the related decompositions. Additionally, we provide a review of the matrix and tensor operations that are frequently used in the context of tensor decompositions.« less

A unified tensor level set for image segmentation.

PubMed

Wang, Bin; Gao, Xinbo; Tao, Dacheng; Li, Xuelong

2010-06-01

This paper presents a new region-based unified tensor level set model for image segmentation. This model introduces a three-order tensor to comprehensively depict features of pixels, e.g., gray value and the local geometrical features, such as orientation and gradient, and then, by defining a weighted distance, we generalized the representative region-based level set method from scalar to tensor. The proposed model has four main advantages compared with the traditional representative method as follows. First, involving the Gaussian filter bank, the model is robust against noise, particularly the salt- and pepper-type noise. Second, considering the local geometrical features, e.g., orientation and gradient, the model pays more attention to boundaries and makes the evolving curve stop more easily at the boundary location. Third, due to the unified tensor pixel representation representing the pixels, the model segments images more accurately and naturally. Fourth, based on a weighted distance definition, the model possesses the capacity to cope with data varying from scalar to vector, then to high-order tensor. We apply the proposed method to synthetic, medical, and natural images, and the result suggests that the proposed method is superior to the available representative region-based level set method.

Binocular stereo matching method based on structure tensor

NASA Astrophysics Data System (ADS)

Song, Xiaowei; Yang, Manyi; Fan, Yubo; Yang, Lei

2016-10-01

In a binocular visual system, to recover the three-dimensional information of the object, the most important step is to acquire matching points. Structure tensor is the vector representation of each point in its local neighborhood. Therefore, structure tensor performs well in region detection of local structure, and it is very suitable for detecting specific graphics such as pedestrians, cars and road signs in the image. In this paper, the structure tensor is combined with the luminance information to form the extended structure tensor. The directional derivatives of luminance in x and y directions are calculated, so that the local structure of the image is more prominent. Meanwhile, the Euclidean distance between the eigenvectors of key points is used as the similarity determination metric of key points in the two images. By matching, the coordinates of the matching points in the detected target are precisely acquired. In this paper, experiments were performed on the captured left and right images. After the binocular calibration, image matching was done to acquire the matching points, and then the target depth was calculated according to these matching points. By comparison, it is proved that the structure tensor can accurately acquire the matching points in binocular stereo matching.

Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order

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

Gu Zhengcheng; Wen Xiaogang

2009-10-15

We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization approach that removes local entanglement and produces a coarse-grained lattice, we show that the resulting renormalization flow of the tensors in the tensor network has a nice fixed-point structure. The isolated fixed-point tensors T{sub inv} plus the symmetry group G{sub sym} of the tensors (i.e., the symmetry group of the Lagrangian) characterize various phases of the system. Such a characterization can describe both the symmetry breaking phases and topological phases, asmore » illustrated by two-dimensional (2D) statistical Ising model, 2D statistical loop-gas model, and 1+1D quantum spin-1/2 and spin-1 models. In particular, using such a (G{sub sym},T{sub inv}) characterization, we show that the Haldane phase for a spin-1 chain is a phase protected by the time-reversal, parity, and translation symmetries. Thus the Haldane phase is a symmetry-protected topological phase. The (G{sub sym},T{sub inv}) characterization is more general than the characterizations based on the boundary spins and string order parameters. The tensor renormalization approach also allows us to study continuous phase transitions between symmetry breaking phases and/or topological phases. The scaling dimensions and the central charges for the critical points that describe those continuous phase transitions can be calculated from the fixed-point tensors at those critical points.« less

Exploring Patterns of Soil Organic Matter Decomposition with Students through the Global Decomposition Project (GDP) and the Interactive Model of Leaf Decomposition (IMOLD)

NASA Astrophysics Data System (ADS)

Steiner, S. M.; Wood, J. H.

2015-12-01

As decomposition rates are affected by climate change, understanding crucial soil interactions that affect plant growth and decomposition becomes a vital part of contributing to the students' knowledge base. The Global Decomposition Project (GDP) is designed to introduce and educate students about soil organic matter and decomposition through a standardized protocol for collecting, reporting, and sharing data. The Interactive Model of Leaf Decomposition (IMOLD) utilizes animations and modeling to learn about the carbon cycle, leaf anatomy, and the role of microbes in decomposition. Paired together, IMOLD teaches the background information and allows simulation of numerous scenarios, and the GDP is a data collection protocol that allows students to gather usable measurements of decomposition in the field. Our presentation will detail how the GDP protocol works, how to obtain or make the materials needed, and how results will be shared. We will also highlight learning objectives from the three animations of IMOLD, and demonstrate how students can experiment with different climates and litter types using the interactive model to explore a variety of decomposition scenarios. The GDP demonstrates how scientific methods can be extended to educate broader audiences, and data collected by students can provide new insight into global patterns of soil decomposition. Using IMOLD, students will gain a better understanding of carbon cycling in the context of litter decomposition, as well as learn to pose questions they can answer with an authentic computer model. Using the GDP protocols and IMOLD provide a pathway for scientists and educators to interact and reach meaningful education and research goals.

Microbial community assembly and metabolic function during mammalian corpse decomposition

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

Metcalf, J. L.; Xu, Z. Z.; Weiss, S.

2015-12-10

Vertebrate corpse decomposition provides an important stage in nutrient cycling in most terrestrial habitats, yet microbially mediated processes are poorly understood. Here we combine deep microbial community characterization, community-level metabolic reconstruction, and soil biogeochemical assessment to understand the principles governing microbial community assembly during decomposition of mouse and human corpses on different soil substrates. We find a suite of bacterial and fungal groups that contribute to nitrogen cycling and a reproducible network of decomposers that emerge on predictable time scales. Our results show that this decomposer community is derived primarily from bulk soil, but key decomposers are ubiquitous in lowmore » abundance. Soil type was not a dominant factor driving community development, and the process of decomposition is sufficiently reproducible to offer new opportunities for forensic investigations.« less

Kinetics of the cellular decomposition of supersaturated solid solutions

NASA Astrophysics Data System (ADS)

Ivanov, M. A.; Naumuk, A. Yu.

2014-09-01

A consistent description of the kinetics of the cellular decomposition of supersaturated solid solutions with the development of a spatially periodic structure of lamellar (platelike) type, which consists of alternating phases of precipitates on the basis of the impurity component and depleted initial solid solution, is given. One of the equations, which determines the relationship between the parameters that describe the process of decomposition, has been obtained from a comparison of two approaches in order to determine the rate of change in the free energy of the system. The other kinetic parameters can be described with the use of a variational method, namely, by the maximum velocity of motion of the decomposition boundary at a given temperature. It is shown that the mutual directions of growth of the lamellae of different phases are determined by the minimum value of the interphase surface energy. To determine the parameters of the decomposition, a simple thermodynamic model of states with a parabolic dependence of the free energy on the concentrations has been used. As a result, expressions that describe the decomposition rate, interlamellar distance, and the concentration of impurities in the phase that remain after the decomposition have been derived. This concentration proves to be equal to the half-sum of the initial concentration and the equilibrium concentration corresponding to the decomposition temperature.

Tensor perturbations during inflation in a spatially closed Universe

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

Bonga, Béatrice; Gupt, Brajesh; Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu

2017-05-01

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

Federated Tensor Factorization for Computational Phenotyping

PubMed Central

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

2017-01-01

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

Quantum electromagnetic stress tensor in an inhomogeneous medium

NASA Astrophysics Data System (ADS)

Parashar, Prachi; Milton, Kimball A.; Li, Yang; Day, Hannah; Guo, Xin; Fulling, Stephen A.; Cavero-Peláez, Inés

2018-06-01

Continuing a program of examining the behavior of the vacuum expectation value of the stress tensor in a background which varies only in a single direction, we here study the electromagnetic stress tensor in a medium with permittivity depending on a single spatial coordinate, specifically, a planar dielectric half-space facing a vacuum region. There are divergences occurring that are regulated by temporal and spatial point splitting, which have a universal character for both transverse electric and transverse magnetic modes. The nature of the divergences depends on the model of dispersion adopted. And there are singularities occurring at the edge between the dielectric and vacuum regions, which also have a universal character, depending on the structure of the discontinuities in the material properties there. Remarks are offered concerning renormalization of such models, and the significance of the stress tensor. The ambiguity in separating "bulk" and "scattering" parts of the stress tensor is discussed.

Ionization-Enhanced Decomposition of 2,4,6-Trinitrotoluene (TNT) Molecules

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

Wang, Bin; Wright, David; Cliffel, David

2011-01-01

The unimolecular decomposition reaction of TNT can in principle be used to design ways to either detect or remove TNT from the environment. Here, we report the results of a density functional theory study of possible ways to lower the reaction barrier for this decomposition process by ionization, so that decomposition and/or detection can occur at room temperature. We find that ionizing TNT lowers the reaction barrier for the initial step of this decomposition. We further show that a similar effect can occur if a positive moiety is bound to the TNT molecule. The positive charge produces a pronounced electronmore » redistribution and dipole formation in TNT with minimal charge transfer from TNT to the positive moiety.« less

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

Tensor modes in pure natural inflation

NASA Astrophysics Data System (ADS)

Nomura, Yasunori; Yamazaki, Masahito

2018-05-01

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

Traffic speed data imputation method based on tensor completion.

PubMed

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

2015-01-01

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

An eigenvalue localization set for tensors and its applications.

PubMed

Zhao, Jianxing; Sang, Caili

2017-01-01

A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li et al . (Linear Algebra Appl. 481:36-53, 2015) and Huang et al . (J. Inequal. Appl. 2016:254, 2016). As an application of this set, new bounds for the minimum eigenvalue of [Formula: see text]-tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huang et al ., the advantage of our results is that, without considering the selection of nonempty proper subsets S of [Formula: see text], we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of [Formula: see text]-tensors. Finally, numerical examples are given to verify the theoretical results.

What Role Does Photodegradation Play in Influencing Plant Litter Decomposition and Biogeochemistry in Coastal Marsh Ecosystems?

NASA Astrophysics Data System (ADS)

Tobler, M.; White, D. A.; Abbene, M. L.; Burst, S. L.; McCulley, R. L.; Barnes, P. W.

2016-02-01

Decomposition is a crucial component of global biogeochemical cycles that influences the fate and residence time of carbon and nutrients in organic matter pools, yet the processes controlling litter decomposition in coastal marshes are not fully understood. We conducted a series of field studies to examine what role photodegradation, a process driven in part by solar UV radiation (280-400 nm), plays in the decomposition of the standing dead litter of Sagittaria lancifolia and Spartina patens, two common species in marshes of intermediate salinity in southern Louisiana, USA. Results indicate that the exclusion of solar UV significantly altered litter mass loss, but the magnitude and direction of these effects varied depending on species, height of the litter above the water surface and the stage of decomposition. Over one growing season, S. lancifolia litter exposed to ambient solar UV had significantly less mass loss compared to litter exposed to attenuated UV over the initial phase of decomposition (0-5 months; ANOVA P=0.004) then treatment effects switched in the latter phase of the study (5-7 months; ANOVA P<0.001). Similar results were found in S. patens over an 11-month period. UV exposure reduced total C, N and lignin by 24-33% in remaining tissue with treatment differences most pronounced in S. patens. Phospholipid fatty-acid analysis (PFLA) indicated that UV also significantly altered microbial (bacterial) biomass and bacteria:fungi ratios of decomposing litter. These findings, and others, indicate that solar UV can have positive and negative net effects on litter decomposition in marsh plants with inhibition of biotic (microbial) processes occurring early in the decomposition process then shifting to enhancement of decomposition via abiotic (photodegradation) processes later in decomposition. Photodegradation of standing litter represents a potentially significant pathway of C and N loss from these coastal wetland ecosystems.

A simple method for decomposition of peracetic acid in a microalgal cultivation system.

PubMed

Sung, Min-Gyu; Lee, Hansol; Nam, Kibok; Rexroth, Sascha; Rögner, Matthias; Kwon, Jong-Hee; Yang, Ji-Won

2015-03-01

A cost-efficient process devoid of several washing steps was developed, which is related to direct cultivation following the decomposition of the sterilizer. Peracetic acid (PAA) is known to be an efficient antimicrobial agent due to its high oxidizing potential. Sterilization by 2 mM PAA demands at least 1 h incubation time for an effective disinfection. Direct degradation of PAA was demonstrated by utilizing components in conventional algal medium. Consequently, ferric ion and pH buffer (HEPES) showed a synergetic effect for the decomposition of PAA within 6 h. On the contrary, NaNO3, one of the main components in algal media, inhibits the decomposition of PAA. The improved growth of Chlorella vulgaris and Synechocystis PCC6803 was observed in the prepared BG11 by decomposition of PAA. This process involving sterilization and decomposition of PAA should help cost-efficient management of photobioreactors in a large scale for the production of value-added products and biofuels from microalgal biomass.

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.

Multiple seismogenic processes for high-frequency earthquakes at Katmai National Park, Alaska: Evidence from stress tensor inversions of fault-plane solutions

USGS Publications Warehouse

Moran, S.C.

2003-01-01

The volcanological significance of seismicity within Katmai National Park has been debated since the first seismograph was installed in 1963, in part because Katmai seismicity consists almost entirely of high-frequency earthquakes that can be caused by a wide range of processes. I investigate this issue by determining 140 well-constrained first-motion fault-plane solutions for shallow (depth < 9 km) earthquakes occuring between 1995 and 2001 and inverting these solutions for the stress tensor in different regions within the park. Earthquakes removed by several kilometers from the volcanic axis occur in a stress field characterized by horizontally oriented ??1 and ??3 axes, with ??1 rotated slightly (12??) relative to the NUVELIA subduction vector, indicating that these earthquakes are occurring in response to regional tectonic forces. On the other hand, stress tensors for earthquake clusters beneath several Katmai cluster volcanoes have vertically oriented ??1 axes, indicating that these events are occuring in response to local, not regional, processes. At Martin-Mageik, vertically oriented ??1 is most consistent with failure under edifice loading conditions in conjunction with localized pore pressure increases associated with hydrothermal circulation cells. At Trident-Novarupta, it is consistent with a number of possible models, including occurence along fractures formed during the 1912 eruption that now serve as horizontal conduits for migrating fluids and/or volatiles from nearby degassing and cooling magma bodies. At Mount Katmai, it is most consistent with continued seismicity along ring-fracture systems created in the 1912 eruption, perhaps enhanced by circulating hydrothermal fluids and/or seepage from the caldera-filling lake.

The Multi-Orientable Random Tensor Model, a Review

NASA Astrophysics Data System (ADS)

Tanasa, Adrian

2016-06-01

After its introduction (initially within a group field theory framework) in [Tanasa A., J. Phys. A: Math. Theor. 45 (2012), 165401, 19 pages, arXiv:1109.0694], the multi-orientable (MO) tensor model grew over the last years into a solid alternative of the celebrated colored (and colored-like) random tensor model. In this paper we review the most important results of the study of this MO model: the implementation of the 1/N expansion and of the large N limit (N being the size of the tensor), the combinatorial analysis of the various terms of this expansion and finally, the recent implementation of a double scaling limit.

Using Perturbation Theory to Compute the Morphological Similarity of Diffusion Tensors

PubMed Central

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

2008-01-01

Computing the morphological similarity of Diffusion Tensors (DTs) at neighboring voxels within a DT image, or at corresponding locations across different DT images, is a fundamental and ubiquitous operation in the post-processing of DT images. The morphological similarity of DTs typically has been computed using either the Principal Directions (PDs) of DTs (i.e., the direction along which water molecules diffuse preferentially) or their tensor elements. Although comparing PDs allows the similarity of one morphological feature of DTs to be visualized directly in eigenspace, this method takes into account only a single eigenvector, and it is therefore sensitive to the presence of noise in the images that can introduce error into the estimation of that vector. Although comparing tensor elements, rather than PDs, is comparatively more robust to the effects of noise, the individual elements of a given tensor do not directly reflect the diffusion properties of water molecules. We propose a measure for computing the morphological similarity of DTs that uses both their eigenvalues and eigenvectors, and that also accounts for the noise levels present in DT images. Our measure presupposes that DTs in a homogeneous region within or across DT images are random perturbations of one another in the presence of noise. The similarity values that are computed using our method are smooth (in the sense that small changes in eigenvalues and eigenvectors cause only small changes in similarity), and they are symmetric when differences in eigenvalues and eigenvectors are also symmetric. In addition, our method does not presuppose that the corresponding eigenvectors across two DTs have been identified accurately, an assumption that is problematic in the presence of noise. Because we compute the similarity between DTs using their eigenspace components, our similarity measure relates directly to both the magnitude and the direction of the diffusion of water molecules. The favorable

Efficient material decomposition method for dual-energy X-ray cargo inspection system

NASA Astrophysics Data System (ADS)

Lee, Donghyeon; Lee, Jiseoc; Min, Jonghwan; Lee, Byungcheol; Lee, Byeongno; Oh, Kyungmin; Kim, Jaehyun; Cho, Seungryong

2018-03-01

Dual-energy X-ray inspection systems are widely used today for it provides X-ray attenuation contrast of the imaged object and also its material information. Material decomposition capability allows a higher detection sensitivity of potential targets including purposely loaded impurities in agricultural product inspections and threats in security scans for example. Dual-energy X-ray transmission data can be transformed into two basis material thickness data, and its transformation accuracy heavily relies on a calibration of material decomposition process. The calibration process in general can be laborious and time consuming. Moreover, a conventional calibration method is often challenged by the nonuniform spectral characteristics of the X-ray beam in the entire field-of-view (FOV). In this work, we developed an efficient material decomposition calibration process for a linear accelerator (LINAC) based high-energy X-ray cargo inspection system. We also proposed a multi-spot calibration method to improve the decomposition performance throughout the entire FOV. Experimental validation of the proposed method has been demonstrated by use of a cargo inspection system that supports 6 MV and 9 MV dual-energy imaging.

Aligning observed and modelled behaviour based on workflow decomposition

NASA Astrophysics Data System (ADS)

Wang, Lu; Du, YuYue; Liu, Wei

2017-09-01

When business processes are mostly supported by information systems, the availability of event logs generated from these systems, as well as the requirement of appropriate process models are increasing. Business processes can be discovered, monitored and enhanced by extracting process-related information. However, some events cannot be correctly identified because of the explosion of the amount of event logs. Therefore, a new process mining technique is proposed based on a workflow decomposition method in this paper. Petri nets (PNs) are used to describe business processes, and then conformance checking of event logs and process models is investigated. A decomposition approach is proposed to divide large process models and event logs into several separate parts that can be analysed independently; while an alignment approach based on a state equation method in PN theory enhances the performance of conformance checking. Both approaches are implemented in programmable read-only memory (ProM). The correctness and effectiveness of the proposed methods are illustrated through experiments.

Robust photometric invariant features from the color tensor.

PubMed

van de Weijer, Joost; Gevers, Theo; Smeulders, Arnold W M

2006-01-01

Luminance-based features are widely used as low-level input for computer vision applications, even when color data is available. The extension of feature detection to the color domain prevents information loss due to isoluminance and allows us to exploit the photometric information. To fully exploit the extra information in the color data, the vector nature of color data has to be taken into account and a sound framework is needed to combine feature and photometric invariance theory. In this paper, we focus on the structure tensor, or color tensor, which adequately handles the vector nature of color images. Further, we combine the features based on the color tensor with photometric invariant derivatives to arrive at photometric invariant features. We circumvent the drawback of unstable photometric invariants by deriving an uncertainty measure to accompany the photometric invariant derivatives. The uncertainty is incorporated in the color tensor, hereby allowing the computation of robust photometric invariant features. The combination of the photometric invariance theory and tensor-based features allows for detection of a variety of features such as photometric invariant edges, corners, optical flow, and curvature. The proposed features are tested for noise characteristics and robustness to photometric changes. Experiments show that the proposed features are robust to scene incidental events and that the proposed uncertainty measure improves the applicability of full invariants.

Placement-aware decomposition of a digital standard cells library for double patterning lithography

NASA Astrophysics Data System (ADS)

Wassal, Amr G.; Sharaf, Heba; Hammouda, Sherif

2012-11-01

To continue scaling the circuit features down, Double Patterning (DP) technology is needed in 22nm technologies and lower. DP requires decomposing the layout features into two masks for pitch relaxation, such that the spacing between any two features on each mask is greater than the minimum allowed mask spacing. The relaxed pitches of each mask are then processed on two separate exposure steps. In many cases, post-layout decomposition fails to decompose the layout into two masks due to the presence of conflicts. Post-layout decomposition of a standard cells block can result in native conflicts inside the cells (internal conflict), or native conflicts on the boundary between two cells (boundary conflict). Resolving native conflicts requires a redesign and/or multiple iterations for the placement and routing phases to get a clean decomposition. Therefore, DP compliance must be considered in earlier phases, before getting the final placed cell block. The main focus of this paper is generating a library of decomposed standard cells to be used in a DP-aware placer. This library should contain all possible decompositions for each standard cell, i.e., these decompositions consider all possible combinations of boundary conditions. However, the large number of combinations of boundary conditions for each standard cell will significantly increase the processing time and effort required to obtain all possible decompositions. Therefore, an efficient methodology is required to reduce this large number of combinations. In this paper, three different reduction methodologies are proposed to reduce the number of different combinations processed to get the decomposed library. Experimental results show a significant reduction in the number of combinations and decompositions needed for the library processing. To generate and verify the proposed flow and methodologies, a prototype for a placement-aware DP-ready cell-library is developed with an optimized number of cell views.

Character Decomposition and Transposition Processes in Chinese Compound Words Modulates Attentional Blink.

PubMed

Cao, Hongwen; Gao, Min; Yan, Hongmei

2016-01-01

The attentional blink (AB) is the phenomenon in which the identification of the second of two targets (T2) is attenuated if it is presented less than 500 ms after the first target (T1). Although the AB is eliminated in canonical word conditions, it remains unclear whether the character order in compound words affects the magnitude of the AB. Morpheme decomposition and transposition of Chinese two-character compound words can provide an effective means to examine AB priming and to assess combinations of the component representations inherent to visual word identification. In the present study, we examined the processing of consecutive targets in a rapid serial visual presentation (RSVP) paradigm using Chinese two-character compound words in which the two characters were transposed to form meaningful words or meaningless combinations (reversible, transposed, or canonical words). We found that when two Chinese characters that form a compound word, regardless of their order, are presented in an RSVP sequence, the likelihood of an AB for the second character is greatly reduced or eliminated compared to when the two characters constitute separate words rather than a compound word. Moreover, the order of the report for the two characters is more likely to be reversed when the normal order of the two characters in a compound word is reversed, especially when the interval between the presentation of the two characters is extremely short. These findings are more consistent with the cognitive strategy hypothesis than the resource-limited hypothesis during character decomposition and transposition of Chinese two-character compound words. These results suggest that compound characters are perceived as a unit, rather than two separate words. The data further suggest that readers could easily understand the text with character transpositions in compound words during Chinese reading.

Empirical projection-based basis-component decomposition method

NASA Astrophysics Data System (ADS)

Brendel, Bernhard; Roessl, Ewald; Schlomka, Jens-Peter; Proksa, Roland

2009-02-01

Advances in the development of semiconductor based, photon-counting x-ray detectors stimulate research in the domain of energy-resolving pre-clinical and clinical computed tomography (CT). For counting detectors acquiring x-ray attenuation in at least three different energy windows, an extended basis component decomposition can be performed in which in addition to the conventional approach of Alvarez and Macovski a third basis component is introduced, e.g., a gadolinium based CT contrast material. After the decomposition of the measured projection data into the basis component projections, conventional filtered-backprojection reconstruction is performed to obtain the basis-component images. In recent work, this basis component decomposition was obtained by maximizing the likelihood-function of the measurements. This procedure is time consuming and often unstable for excessively noisy data or low intrinsic energy resolution of the detector. Therefore, alternative procedures are of interest. Here, we introduce a generalization of the idea of empirical dual-energy processing published by Stenner et al. to multi-energy, photon-counting CT raw data. Instead of working in the image-domain, we use prior spectral knowledge about the acquisition system (tube spectra, bin sensitivities) to parameterize the line-integrals of the basis component decomposition directly in the projection domain. We compare this empirical approach with the maximum-likelihood (ML) approach considering image noise and image bias (artifacts) and see that only moderate noise increase is to be expected for small bias in the empirical approach. Given the drastic reduction of pre-processing time, the empirical approach is considered a viable alternative to the ML approach.

Extracting the potential-well of a near-field optical trap using the Helmholtz-Hodge decomposition

NASA Astrophysics Data System (ADS)

Zaman, Mohammad Asif; Padhy, Punnag; Hansen, Paul C.; Hesselink, Lambertus

2018-02-01

The non-conservative nature of the force field generated by a near-field optical trap is analyzed. A plasmonic C-shaped engraving on a gold film is considered as the trap. The force field is calculated using the Maxwell stress tensor method. The Helmholtz-Hodge decomposition is used to extract the conservative and the non-conservative component of the force. Due to the non-negligible non-conservative component, it is found that the conventional approach of extracting the potential by direct integration of the force is not accurate. Despite the non-conservative nature of the force field, it is found that the statistical properties of a trapped nanoparticle can be estimated from the conservative component of the force field alone. Experimental and numerical results are presented to support the claims.

Thermal decomposition hazard evaluation of hydroxylamine nitrate.

PubMed

Wei, Chunyang; Rogers, William J; Mannan, M Sam

2006-03-17

Hydroxylamine nitrate (HAN) is an important member of the hydroxylamine family and it is a liquid propellant when combined with alkylammonium nitrate fuel in an aqueous solution. Low concentrations of HAN are used primarily in the nuclear industry as a reductant in nuclear material processing and for decontamination of equipment. Also, HAN has been involved in several incidents because of its instability and autocatalytic decomposition behavior. This paper presents calorimetric measurement for the thermal decomposition of 24 mass% HAN/water. Gas phase enthalpy of formation of HAN is calculated using both semi-empirical methods with MOPAC and high-level quantum chemical methods of Gaussian 03. CHETAH is used to estimate the energy release potential of HAN. A Reactive System Screening Tool (RSST) and an Automatic Pressure Tracking Adiabatic Calorimeter (APTAC) are used to characterize thermal decomposition of HAN and to provide guidance about safe conditions for handling and storing of HAN.

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).

Microbial community assembly and metabolic function during mammalian corpse decomposition.

PubMed

Metcalf, Jessica L; Xu, Zhenjiang Zech; Weiss, Sophie; Lax, Simon; Van Treuren, Will; Hyde, Embriette R; Song, Se Jin; Amir, Amnon; Larsen, Peter; Sangwan, Naseer; Haarmann, Daniel; Humphrey, Greg C; Ackermann, Gail; Thompson, Luke R; Lauber, Christian; Bibat, Alexander; Nicholas, Catherine; Gebert, Matthew J; Petrosino, Joseph F; Reed, Sasha C; Gilbert, Jack A; Lynne, Aaron M; Bucheli, Sibyl R; Carter, David O; Knight, Rob

2016-01-08

Vertebrate corpse decomposition provides an important stage in nutrient cycling in most terrestrial habitats, yet microbially mediated processes are poorly understood. Here we combine deep microbial community characterization, community-level metabolic reconstruction, and soil biogeochemical assessment to understand the principles governing microbial community assembly during decomposition of mouse and human corpses on different soil substrates. We find a suite of bacterial and fungal groups that contribute to nitrogen cycling and a reproducible network of decomposers that emerge on predictable time scales. Our results show that this decomposer community is derived primarily from bulk soil, but key decomposers are ubiquitous in low abundance. Soil type was not a dominant factor driving community development, and the process of decomposition is sufficiently reproducible to offer new opportunities for forensic investigations. Copyright © 2016, American Association for the Advancement of Science.

In-situ and self-distributed: A new understanding on catalyzed thermal decomposition process of ammonium perchlorate over Nd{sub 2}O{sub 3}

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

Zou, Min, E-mail: zoumin3362765@163.com; Wang, Xin, E-mail: wangx@mail.njust.edu.cn; Jiang, Xiaohong, E-mail: jxh0668@sina.com

2014-05-01

Catalyzed thermal decomposition process of ammonium perchlorate (AP) over neodymium oxide (Nd{sub 2}O{sub 3}) was investigated. Catalytic performances of nanometer-sized Nd{sub 2}O{sub 3} and micrometer-sized Nd{sub 2}O{sub 3} were evaluated by differential scanning calorimetry (DSC). In contrast to universal concepts, catalysts in different sizes have nearly similar catalytic activities. Based on structural and morphological variation of the catalysts during the reaction, combined with mass spectrum analyses and studies of unmixed style, a new understanding of this catalytic process was proposed. We believed that the newly formed chloride neodymium oxide (NdOCl) was the real catalytic species in the overall thermal decompositionmore » of AP over Nd{sub 2}O{sub 3}. Meanwhile, it was the “self-distributed” procedure which occurred within the reaction that also worked for the improvement of overall catalytic activities. This work is of great value in understanding the roles of micrometer-sized catalysts used in heterogeneous reactions, especially the solid–solid reactions which could generate a large quantity of gaseous species. - Graphical abstract: In-situ and self-distributed reaction process in thermal decomposition of AP catalyzed by Nd{sub 2}O{sub 3}. - Highlights: • Micro- and nano-Nd{sub 2}O{sub 3} for catalytic thermal decomposition of AP. • No essential differences on their catalytic performances. • Structural and morphological variation of catalysts digs out catalytic mechanism. • This catalytic process is “in-situ and self-distributed” one.« less

Analytical separations of mammalian decomposition products for forensic science: a review.

PubMed

Swann, L M; Forbes, S L; Lewis, S W

2010-12-03

The study of mammalian soft tissue decomposition is an emerging area in forensic science, with a major focus of the research being the use of various chemical and biological methods to study the fate of human remains in the environment. Decomposition of mammalian soft tissue is a postmortem process that, depending on environmental conditions and physiological factors, will proceed until complete disintegration of the tissue. The major stages of decomposition involve complex reactions which result in the chemical breakdown of the body's main constituents; lipids, proteins, and carbohydrates. The first step to understanding this chemistry is identifying the compounds present in decomposition fluids and determining when they are produced. This paper provides an overview of decomposition chemistry and reviews recent advances in this area utilising analytical separation science. Copyright © 2010 Elsevier B.V. All rights reserved.

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.

Non-convex Statistical Optimization for Sparse Tensor Graphical Model

PubMed Central

Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang

2016-01-01

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies. PMID:28316459

Traffic Speed Data Imputation Method Based on Tensor Completion

PubMed Central

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

2015-01-01

Traffic speed data plays a key role in Intelligent Transportation Systems (ITS); however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS). In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC), an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS) database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches. PMID:25866501

A General Sparse Tensor Framework for Electronic Structure Theory

DOE PAGES

Manzer, Samuel; Epifanovsky, Evgeny; Krylov, Anna I.; ...

2017-01-24

Linear-scaling algorithms must be developed in order to extend the domain of applicability of electronic structure theory to molecules of any desired size. But, the increasing complexity of modern linear-scaling methods makes code development and maintenance a significant challenge. A major contributor to this difficulty is the lack of robust software abstractions for handling block-sparse tensor operations. We therefore report the development of a highly efficient symbolic block-sparse tensor library in order to provide access to high-level software constructs to treat such problems. Our implementation supports arbitrary multi-dimensional sparsity in all input and output tensors. We then avoid cumbersome machine-generatedmore » code by implementing all functionality as a high-level symbolic C++ language library and demonstrate that our implementation attains very high performance for linear-scaling sparse tensor contractions.« less

Spacetime encodings. III. Second order Killing tensors

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

Brink, Jeandrew

2010-01-15

This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture ofmore » what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing tensors.« less

Heterogeneous decomposition of silane in a fixed bed reactor

NASA Technical Reports Server (NTRS)

Iya, S. K.; Flagella, R. N.; Dipaolo, F. S.

1982-01-01

Heterogeneous decomposition of silane in a fluidized bed offers an attractive route for the low-cost production of silicon for photovoltaic application. To obtain design data for a fluid bed silane pyrolysis reactor, deposition experiments were conducted in a small-scale fixed bed apparatus. Data on the decomposition mode, plating rate, and deposition morphology were obtained in the temperature range 600-900 C. Conditions favorable for heterogeneous decomposition with good deposition morphology were identified. The kinetic rate data showed the reaction to be first order with an activation energy of 38.8 kcal/mol, which agrees well with work done by others. The results are promising for the development of an economically attractive fluid bed process.

Renormalization group contraction of tensor networks in three dimensions

NASA Astrophysics Data System (ADS)

García-Sáez, Artur; Latorre, José I.

2013-02-01

We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then, performing a controlled truncation of the resulting tensor. We benchmark this approximation procedure in two dimensions against an exact contraction. We then apply the same idea to a three-dimensional quantum system. The underlying rational for emphasizing the exact coarse graining renormalization group step prior to truncation is related to monogamy of entanglement.

Identification of the full anisotropic flow resistivity tensor for multiple glass wool and melamine foam samples.

PubMed

Van der Kelen, Christophe; Göransson, Peter

2013-12-01

The flow resistivity tensor, which is the inverse of the viscous permeability tensor, is one of the most important material properties for the acoustic performance of porous materials used in acoustic treatments. Due to the manufacturing processes involved, these porous materials are most often geometrically anisotropic on a microscopic scale, and for demanding applications, there is a need for improved characterization methods. This paper discusses recent refinements of a method for the identification of the anisotropic flow resistivity tensor. The inverse estimation is verified for three fictitious materials with different degrees of anisotropy. Measurements are performed on nine glass wool samples and seven melamine foam samples, and the anisotropic flow resistivity tensors obtained are validated by comparison to measurements performed on uni-directional cylindrical samples, extracted from the same, previously measured cubic samples. The variability of flow resistivity in the batch of material from which the glass wool is extracted is discussed. The results for the melamine foam suggest that there is a relation between the direction of highest flow resistivity, and the rise direction of the material.

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.

Diffusion tensor optical coherence tomography

NASA Astrophysics Data System (ADS)

Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.

2018-01-01

In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.

Topology in colored tensor models via crystallization theory

NASA Astrophysics Data System (ADS)

Casali, Maria Rita; Cristofori, Paola; Dartois, Stéphane; Grasselli, Luigi

2018-07-01

The aim of this paper is twofold. On the one hand, it provides a review of the links between random tensor models, seen as quantum gravity theories, and the PL-manifolds representation by means of edge-colored graphs (crystallization theory). On the other hand, the core of the paper is to establish results about the topological and geometrical properties of the Gurau-degree (or G-degree) of the represented manifolds, in relation with the motivations coming from physics. In fact, the G-degree appears naturally in higher dimensional tensor models as the quantity driving their 1 / N expansion, exactly as it happens for the genus of surfaces in the two-dimensional matrix model setting. In particular, the G-degree of PL-manifolds is proved to be finite-to-one in any dimension, while in dimension 3 and 4 a series of classification theorems are obtained for PL-manifolds represented by graphs with a fixed G-degree. All these properties have specific relevance in the tensor models framework, showing a direct fruitful interaction between tensor models and discrete geometry, via crystallization theory.

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.

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.…

Wood decomposition as influenced by invertebrates.

PubMed

Ulyshen, Michael D

2016-02-01

The diversity and habitat requirements of invertebrates associated with dead wood have been the subjects of hundreds of studies in recent years but we still know very little about the ecological or economic importance of these organisms. The purpose of this review is to examine whether, how and to what extent invertebrates affect wood decomposition in terrestrial ecosystems. Three broad conclusions can be reached from the available literature. First, wood decomposition is largely driven by microbial activity but invertebrates also play a significant role in both temperate and tropical environments. Primary mechanisms include enzymatic digestion (involving both endogenous enzymes and those produced by endo- and ectosymbionts), substrate alteration (tunnelling and fragmentation), biotic interactions and nitrogen fertilization (i.e. promoting nitrogen fixation by endosymbiotic and free-living bacteria). Second, the effects of individual invertebrate taxa or functional groups can be accelerative or inhibitory but the cumulative effect of the entire community is generally to accelerate wood decomposition, at least during the early stages of the process (most studies are limited to the first 2-3 years). Although methodological differences and design limitations preclude meta-analysis, studies aimed at quantifying the contributions of invertebrates to wood decomposition commonly attribute 10-20% of wood loss to these organisms. Finally, some taxa appear to be particularly influential with respect to promoting wood decomposition. These include large wood-boring beetles (Coleoptera) and termites (Termitoidae), especially fungus-farming macrotermitines. The presence or absence of these species may be more consequential than species richness and the influence of invertebrates is likely to vary biogeographically. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

[Decomposition of corpses--a microbial degradation process with special reference to mummification, formation of adipocere and incomplete putrified corpes].

PubMed

Schoenen, Dirk

2013-01-01

Decomposition of the human body is a microbial process. It is influenced by the environmental situation and it depends to a high degree on the exchange of substances between the corpse and the environment. Mummification occurs at low humidity or frost. Adipocere arises from lack of oxygen, incomplete putrified corpses develop when there is no exchange of air or water between the corpse and the environment.

Waveform-based Bayesian full moment tensor inversion and uncertainty determination for the induced seismicity in an oil/gas field

NASA Astrophysics Data System (ADS)

Gu, Chen; Marzouk, Youssef M.; Toksöz, M. Nafi

2018-03-01

Small earthquakes occur due to natural tectonic motions and are induced by oil and gas production processes. In many oil/gas fields and hydrofracking processes, induced earthquakes result from fluid extraction or injection. The locations and source mechanisms of these earthquakes provide valuable information about the reservoirs. Analysis of induced seismic events has mostly assumed a double-couple source mechanism. However, recent studies have shown a non-negligible percentage of non-double-couple components of source moment tensors in hydraulic fracturing events, assuming a full moment tensor source mechanism. Without uncertainty quantification of the moment tensor solution, it is difficult to determine the reliability of these source models. This study develops a Bayesian method to perform waveform-based full moment tensor inversion and uncertainty quantification for induced seismic events, accounting for both location and velocity model uncertainties. We conduct tests with synthetic events to validate the method, and then apply our newly developed Bayesian inversion approach to real induced seismicity in an oil/gas field in the sultanate of Oman—determining the uncertainties in the source mechanism and in the location of that event.

General tensor discriminant analysis and gabor features for gait recognition.

PubMed

Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J

2007-10-01

The traditional image representations are not suited to conventional classification methods, such as the linear discriminant analysis (LDA), because of the under sample problem (USP): the dimensionality of the feature space is much higher than the number of training samples. Motivated by the successes of the two dimensional LDA (2DLDA) for face recognition, we develop a general tensor discriminant analysis (GTDA) as a preprocessing step for LDA. The benefits of GTDA compared with existing preprocessing methods, e.g., principal component analysis (PCA) and 2DLDA, include 1) the USP is reduced in subsequent classification by, for example, LDA; 2) the discriminative information in the training tensors is preserved; and 3) GTDA provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of GTDA converges, while that of 2DLDA does not. We use human gait recognition to validate the proposed GTDA. The averaged gait images are utilized for gait representation. Given the popularity of Gabor function based image decompositions for image understanding and object recognition, we develop three different Gabor function based image representations: 1) the GaborD representation is the sum of Gabor filter responses over directions, 2) GaborS is the sum of Gabor filter responses over scales, and 3) GaborSD is the sum of Gabor filter responses over scales and directions. The GaborD, GaborS and GaborSD representations are applied to the problem of recognizing people from their averaged gait images.A large number of experiments were carried out to evaluate the effectiveness (recognition rate) of gait recognition based on first obtaining a Gabor, GaborD, GaborS or GaborSD image representation, then using GDTA to extract features and finally using LDA for classification. The proposed methods achieved good performance for gait recognition based on image sequences from the USF HumanID Database. Experimental comparisons are made with nine

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.

Elliptic Relaxation of a Tensor Representation for the Redistribution Terms in a Reynolds Stress Turbulence Model

NASA Technical Reports Server (NTRS)

Carlson, J. R.; Gatski, T. B.

2002-01-01

A formulation to include the effects of wall proximity in a second-moment closure model that utilizes a tensor representation for the redistribution terms in the Reynolds stress equations is presented. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. Direct numerical simulation data and Reynolds stress solutions using a full differential approach are compared for the case of fully developed channel flow.

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

Motion Detection in Ultrasound Image-Sequences Using Tensor Voting

NASA Astrophysics Data System (ADS)

Inba, Masafumi; Yanagida, Hirotaka; Tamura, Yasutaka

2008-05-01

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