Structure of tensor operators in SU3
Energy Technology Data Exchange (ETDEWEB)
Biedenharn, L.C.; Flath, D.E.
1984-03-01
A global algebraic formulation of SU3 tensor operator structure is achieved. A single irreducible unitary representation (irrep), V, of kappa(6, 2) is constructed which contains every SU3 irrep precisely once. An algebra of polynomial differential operators A acting on V is given. The algebra A is shown to consist of linear combinations of all SU3 tensor operators with polynomial invariant operators as coefficients. By carrying out an analysis of A, the multiplicity problem for SU3 tensor operators is resolved.
De Hoop, A.T.; Abubakar, A.; Habashy, T.M.
2009-01-01
The contrast-source stress-velocity integral-equation formulation of three-dimensional time-domain elastodynamic scattering problems is discussed. A novel feature of the formulation is a tensor partitioning of the relevant dynamic stress and the contrast source volume density of deformation rate.
Quadratic third-order tensor optimization problem with quadratic constraints
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Lixing Yang
2014-05-01
Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.
Transversely isotropic higher-order averaged structure tensors
Hashlamoun, Kotaybah; Federico, Salvatore
2017-08-01
For composites or biological tissues reinforced by statistically oriented fibres, a probability distribution function is often used to describe the orientation of the fibres. The overall effect of the fibres on the material response is accounted for by evaluating averaging integrals over all possible directions in space. The directional average of the structure tensor (tensor product of the unit vector describing the fibre direction by itself) is of high significance. Higher-order averaged structure tensors feature in several models and carry similarly important information. However, their evaluation has a quite high computational cost. This work proposes to introduce mathematical techniques to minimise the computational cost associated with the evaluation of higher-order averaged structure tensors, for the case of a transversely isotropic probability distribution of orientation. A component expression is first introduced, using which a general tensor expression is obtained, in terms of an orthonormal basis in which one of the vectors coincides with the axis of symmetry of transverse isotropy. Then, a higher-order transversely isotropic averaged structure tensor is written in an appropriate basis, constructed starting from the basis of the space of second-order transversely isotropic tensors, which is constituted by the structure tensor and its complement to the identity.
Controlling sign problems in spin models using tensor renormalization
Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.; Qin, M. P.; Xiang, T.; Xie, Z. Y.; Yu, J. F.; Zou, Haiyuan
2014-01-01
We consider the sign problem for classical spin models at complex β =1/g02 on L ×L lattices. We show that the tensor renormalization group method allows reliable calculations for larger Imβ than the reweighting Monte Carlo method. For the Ising model with complex β we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the tensor renormalization group method. We check the convergence of the tensor renormalization group method for the O(2) model on L×L lattices when the number of states Ds increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.
Towards overcoming the Monte Carlo sign problem with tensor networks
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Banuls, Mari Carmen; Cirac, J. Ignacio; Kuehn, Stefan [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Saito, Hana [AISIN AW Co., Ltd., Aichi (Japan)
2016-11-15
The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.
Diffusion Tensor Imaging, Structural Connectivity, and Schizophrenia
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Thomas J. Whitford
2011-01-01
Full Text Available A fundamental tenet of the “disconnectivity” theories of schizophrenia is that the disorder is ultimately caused by abnormal communication between spatially disparate brain structures. Given that the white matter fasciculi represent the primary infrastructure for long distance communication in the brain, abnormalities in these fiber bundles have been implicated in the etiology of schizophrenia. Diffusion tensor imaging (DTI is a magnetic resonance imaging (MRI technique that enables the visualization of white matter macrostructure in vivo, and which has provided unprecedented insight into the existence and nature of white matter abnormalities in schizophrenia. The paper begins with an overview of DTI and more commonly used diffusion metrics and moves on to a brief review of the schizophrenia literature. The functional implications of white matter abnormalities are considered, particularly with respect to myelin's role in modulating the transmission velocity of neural discharges. The paper concludes with a speculative hypothesis about the relationship between gray and white matter abnormalities associated with schizophrenia.
Lithospheric Stress Tensor from Gravity and Lithospheric Structure Models
Eshagh, Mehdi; Tenzer, Robert
2017-07-01
In this study we investigate the lithospheric stresses computed from the gravity and lithospheric structure models. The functional relation between the lithospheric stress tensor and the gravity field parameters is formulated based on solving the boundary-value problem of elasticity in order to determine the propagation of stresses inside the lithosphere, while assuming the horizontal shear stress components (computed at the base of the lithosphere) as lower boundary values for solving this problem. We further suppress the signature of global mantle flow in the stress spectrum by subtracting the long-wavelength harmonics (below the degree of 13). This numerical scheme is applied to compute the normal and shear stress tensor components globally at the Moho interface. The results reveal that most of the lithospheric stresses are accumulated along active convergent tectonic margins of oceanic subductions and along continent-to-continent tectonic plate collisions. These results indicate that, aside from a frictional drag caused by mantle convection, the largest stresses within the lithosphere are induced by subduction slab pull forces on the side of subducted lithosphere, which are coupled by slightly less pronounced stresses (on the side of overriding lithospheric plate) possibly attributed to trench suction. Our results also show the presence of (intra-plate) lithospheric loading stresses along Hawaii islands. The signature of ridge push (along divergent tectonic margins) and basal shear traction resistive forces is not clearly manifested at the investigated stress spectrum (between the degrees from 13 to 180).
The Cauchy problem of scalar-tensor theories of gravity
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Salgado, Marcelo [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo. Postal 70-543 Mexico 04510 DF (Mexico)
2006-07-21
The 3 + 1 formulation of scalar-tensor theories of gravity (STT) is obtained in the physical (Jordan) frame departing from the 4 + 0 covariant field equations. Contrary to common belief (folklore), the new system of ADM-like equations shows that the Cauchy problem of STT is well formulated (in the sense that the whole system of evolution equations is of first order in the time derivative). This is the first step towards a full first-order (in time and space) formulation from which a subsequent hyperbolicity analysis (a well-posedness determination) can be performed. Several gauge (lapse and shift) conditions are considered and implemented for STT. In particular, a generalization of the harmonic gauge for STT allows us to prove the well posedness of the STT using a second-order analysis which is very similar to the one employed in general relativity. Several appendices complement the ideas of the main part of the paper.
Controlling sign problems in spin models using tensor renormalization
Energy Technology Data Exchange (ETDEWEB)
Denbleyker, Alan [Iowa U.; Liu, Yuzhi [Colorado U.; Meurice, Y. [Iowa U.; Qin, M. P. [Beijing, Inst. Phys.; Xiang, T. [Beijing, Inst. Phys.; Xie, Z. Y. [Beijing, Inst. Phys.; Yu, J. F. [Beijing, Inst. Phys.; Zou, Haiyuan [Iowa U.
2014-01-09
We consider the sign problem for classical spin models at complex $\\beta =1/g_0^2$ on $L\\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$\\beta$ than the reweighting Monte Carlo method. For the Ising model with complex $\\beta$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $L\\times L$ lattices when the number of states $D_s$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.
Inflationary tensor fossils in large-scale structure
Energy Technology Data Exchange (ETDEWEB)
Dimastrogiovanni, Emanuela [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States); Fasiello, Matteo [Department of Physics, Case Western Reserve University, Cleveland, OH 44106 (United States); Jeong, Donghui [Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 (United States); Kamionkowski, Marc, E-mail: ema@physics.umn.edu, E-mail: mrf65@case.edu, E-mail: duj13@psu.edu, E-mail: kamion@jhu.edu [Department of Physics and Astronomy, 3400 N. Charles St., Johns Hopkins University, Baltimore, MD 21218 (United States)
2014-12-01
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 be 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.
The closest vector problem in tensored root lattices of type A and in their duals
L. Ducas (Léo); W.P.J. van Woerden (Wessel)
2017-01-01
textabstractIn this work we consider the closest vector problem (CVP)—a problem also known as maximum-likelihood decoding—in the tensor of two root lattices of type A ((Formula presented.)), as well as in their duals ((Formula presented.)). This problem is mainly motivated by lattice based
Structure-adaptive sparse denoising for diffusion-tensor MRI.
Bao, Lijun; Robini, Marc; Liu, Wanyu; Zhu, Yuemin
2013-05-01
Diffusion tensor magnetic resonance imaging (DT-MRI) is becoming a prospective imaging technique in clinical applications because of its potential for in vivo and non-invasive characterization of tissue organization. However, the acquisition of diffusion-weighted images (DWIs) is often corrupted by noise and artifacts, and the intensity of diffusion-weighted signals is weaker than that of classical magnetic resonance signals. In this paper, we propose a new denoising method for DT-MRI, called structure-adaptive sparse denoising (SASD), which exploits self-similarity in DWIs. We define a similarity measure based on the local mean and on a modified structure-similarity index to find sets of similar patches that are arranged into three-dimensional arrays, and we propose a simple and efficient structure-adaptive window pursuit method to achieve sparse representation of these arrays. The noise component of the resulting structure-adaptive arrays is attenuated by Wiener shrinkage in a transform domain defined by two-dimensional principal component decomposition and Haar transformation. Experiments on both synthetic and real cardiac DT-MRI data show that the proposed SASD algorithm outperforms state-of-the-art methods for denoising images with structural redundancy. Moreover, SASD achieves a good trade-off between image contrast and image smoothness, and our experiments on synthetic data demonstrate that it produces more accurate tensor fields from which biologically relevant metrics can then be computed. Copyright © 2013 Elsevier B.V. All rights reserved.
Tensor Spectral Clustering for Partitioning Higher-order Network Structures.
Benson, Austin R; Gleich, David F; Leskovec, Jure
2015-01-01
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.
STRUCTURE TENSOR IMAGE FILTERING USING RIEMANNIAN L1 AND L∞ CENTER-OF-MASS
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Jesus Angulo
2014-06-01
Full Text Available Structure tensor images are obtained by a Gaussian smoothing of the dyadic product of gradient image. These images give at each pixel a n×n symmetric positive definite matrix SPD(n, representing the local orientation and the edge information. Processing such images requires appropriate algorithms working on the Riemannian manifold on the SPD(n matrices. This contribution deals with structure tensor image filtering based on Lp geometric averaging. In particular, L1 center-of-mass (Riemannian median or Fermat-Weber point and L∞ center-of-mass (Riemannian circumcenter can be obtained for structure tensors using recently proposed algorithms. Our contribution in this paper is to study the interest of L1 and L∞ Riemannian estimators for structure tensor image processing. In particular, we compare both for two image analysis tasks: (i structure tensor image denoising; (ii anomaly detection in structure tensor images.
Diffusion Tensor Tractography Reveals Disrupted Structural Connectivity during Brain Aging
Lin, Lan; Tian, Miao; Wang, Qi; Wu, Shuicai
2017-10-01
Brain aging is one of the most crucial biological processes that entail many physical, biological, chemical, and psychological changes, and also a major risk factor for most common neurodegenerative diseases. To improve the quality of life for the elderly, it is important to understand how the brain is changed during the normal aging process. We compared diffusion tensor imaging (DTI)-based brain networks in a cohort of 75 healthy old subjects by using graph theory metrics to describe the anatomical networks and connectivity patterns, and network-based statistic (NBS) analysis was used to identify pairs of regions with altered structural connectivity. The NBS analysis revealed a significant network comprising nine distinct fiber bundles linking 10 different brain regions showed altered white matter structures in young-old group compare with middle-aged group (p < .05, family-wise error-corrected). Our results might guide future studies and help to gain a better understanding of brain aging.
Rank classification of linear line structures from images by trifocal tensor determinability.
Zhao, Ming; Chung, Chi-Kit Ronald
2010-07-01
The problem we address is: Given line correspondences over three views, what is the condition of the line correspondences for the spatial relation of the three associated camera positions to be uniquely recoverable? The observed set of lines in space is called critical if there are multiple projectively nonequivalent configurations of the camera positions that can picture the same image triplet of the lines. We tackle the problem from the perspective of trifocal tensor, a quantity that captures the relative pose of the cameras in relation to the captured views. We show that the rank of a matrix that leads to the estimation of the tensor is reduced to 7, 11, 15 if the observed lines come from a line pencil, a line bundle, and a line field, respectively, which are line families belonging to linear line space; and 12, 19, 23 if the lines come from a general linear ruled surface, a general linear line congruence, and a general linear line complex, which are subclasses of linear line structures. We show that the above line structures, with the exception of linear line congruence and linear line complex, ought to be critical line structures. All of these structures are quite typical in reality, and thus, the findings are important to the validity and stability of practically all algorithms related to structure from motion and projective reconstruction using line correspondences.
Tensors, !-graphs, and non-commutative quantum structures
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Aleks Kissinger
2014-12-01
Full Text Available Categorical quantum mechanics (CQM and the theory of quantum groups rely heavily on the use of structures that have both an algebraic and co-algebraic component, making them well-suited for manipulation using diagrammatic techniques. Diagrams allow us to easily form complex compositions of (coalgebraic structures, and prove their equality via graph rewriting. One of the biggest challenges in going beyond simple rewriting-based proofs is designing a graphical language that is expressive enough to prove interesting properties (e.g. normal form results about not just single diagrams, but entire families of diagrams. One candidate is the language of !-graphs, which consist of graphs with certain subgraphs marked with boxes (called !-boxes that can be repeated any number of times. New !-graph equations can then be proved using a powerful technique called !-box induction. However, previously this technique only applied to commutative (or cocommutative algebraic structures, severely limiting its applications in some parts of CQM and (especially quantum groups. In this paper, we fix this shortcoming by offering a new semantics for non-commutative !-graphs using an enriched version of Penrose's abstract tensor notation.
Monitoring the refinement of crystal structures with (15)N solid-state NMR shift tensor data.
Kalakewich, Keyton; Iuliucci, Robbie; Mueller, Karl T; Eloranta, Harriet; Harper, James K
2015-11-21
The (15)N chemical shift tensor is shown to be extremely sensitive to lattice structure and a powerful metric for monitoring density functional theory refinements of crystal structures. These refinements include lattice effects and are applied here to five crystal structures. All structures improve based on a better agreement between experimental and calculated (15)N tensors, with an average improvement of 47.0 ppm. Structural improvement is further indicated by a decrease in forces on the atoms by 2-3 orders of magnitude and a greater similarity in atom positions to neutron diffraction structures. These refinements change bond lengths by more than the diffraction errors including adjustments to X-Y and X-H bonds (X, Y = C, N, and O) of 0.028 ± 0.002 Å and 0.144 ± 0.036 Å, respectively. The acquisition of (15)N tensors at natural abundance is challenging and this limitation is overcome by improved (1)H decoupling in the FIREMAT method. This decoupling dramatically narrows linewidths, improves signal-to-noise by up to 317%, and significantly improves the accuracy of measured tensors. A total of 39 tensors are measured with shifts distributed over a range of more than 400 ppm. Overall, experimental (15)N tensors are at least 5 times more sensitive to crystal structure than (13)C tensors due to nitrogen's greater polarizability and larger range of chemical shifts.
Analyzing vortex breakdown flow structures by assignment of colors to tensor invariants.
Rütten, Markus; Chong, Min S
2006-01-01
Topological methods are often used to describe flow structures in fluid dynamics and topological flow field analysis usually relies on the invariants of the associated tensor fields. A visual impression of the local properties of tensor fields is often complex and the search of a suitable technique for achieving this is an ongoing topic in visualization. This paper introduces and assesses a method of representing the topological properties of tensor fields and their respective flow patterns with the use of colors. First, a tensor norm is introduced, which preserves the properties of the tensor and assigns the tensor invariants to values of the RGB color space. Secondly, the RGB colors of the tensor invariants are transferred to corresponding hue values as an alternative color representation. The vectorial tensor invariants field is reduced to a scalar hue field and visualization of iso-surfaces of this hue value field allows us to identify locations with equivalent flow topology. Additionally highlighting by the maximum of the eigenvalue difference field reflects the magnitude of the structural change of the flow. The method is applied on a vortex breakdown flow structure inside a cylinder with a rotating lid.
Semi-analytic stellar structure in scalar-tensor gravity
Horbatsch, M. W.; Burgess, C. P.
2011-08-01
Precision tests of gravity can be used to constrain the properties of hypothetical very light scalar fields, but these tests depend crucially on how macroscopic astrophysical objects couple to the new scalar field. We study the equations of stellar structure using scalar-tensor gravity, with the goal of seeing how stellar properties depend on assumptions made about the scalar coupling at a microscopic level. In order to make the study relatively easy for different assumptions about microscopic couplings, we develop quasi-analytic approximate methods for solving the stellar-structure equations rather than simply integrating them numerically. (The approximation involved assumes the dimensionless scalar coupling at the stellar center is weak, and we compare our results with numerical integration in order to establish its domain of validity.) We illustrate these methods by applying them to Brans-Dicke scalars, and their generalization in which the scalar-matter coupling slowly runs — or `walks' — as a function of the scalar field: a(phi) simeq as+bsphi. (Such couplings can arise in extra-dimensional applications, for instance.) The four observable parameters that characterize the fields external to a spherically symmetric star are the stellar radius, R, mass, M, scalar `charge', Q, and the scalar's asymptotic value, phi∞. These are subject to two relations because of the matching to the interior solution, generalizing the usual mass-radius, M(R), relation of General Relativity. Since phi∞ is common to different stars in a given region (such as a binary pulsar), all quantities can be computed locally in terms of the stellar masses. We identify how these relations depend on the microscopic scalar couplings, agreeing with earlier workers when comparisons are possible. Explicit analytical solutions are obtained for the instructive toy model of constant-density stars, whose properties we compare to more realistic equations of state for neutron star models.
Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem
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Xuqing Zhang
2013-01-01
Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.
Tensor Factorization for Low-Rank Tensor Completion.
Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao
2018-03-01
Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.
Structural Identification Problem
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Suvorov Aleksei
2016-01-01
Full Text Available The identification problem of the existing structures though the Quasi-Newton and its modification, Trust region algorithms is discussed. For the structural problems, which could be represented by means of the mathematical modelling of the finite element code discussed method is extremely useful. The nonlinear minimization problem of the L2 norm for the structures with linear elastic behaviour is solved by using of the Optimization Toolbox of Matlab. The direct and inverse procedures for the composition of the desired function to minimize are illustrated for the spatial 3D truss structure as well as for the problem of plane finite elements. The truss identification problem is solved with 2 and 3 unknown parameters in order to compare the computational efforts and for the graphical purposes. The particular commands of the Matlab codes are present in this paper.
Keylock, Christopher J.
2017-08-01
A method is presented for deriving random velocity gradient tensors given a source tensor. These synthetic tensors are constrained to lie within mathematical bounds of the non-normality of the source tensor, but we do not impose direct constraints upon scalar quantities typically derived from the velocity gradient tensor and studied in fluid mechanics. Hence, it becomes possible to ask hypotheses of data at a point regarding the statistical significance of these scalar quantities. Having presented our method and the associated mathematical concepts, we apply it to homogeneous, isotropic turbulence to test the utility of the approach for a case where the behavior of the tensor is understood well. We show that, as well as the concentration of data along the Vieillefosse tail, actual turbulence is also preferentially located in the quadrant where there is both excess enstrophy (Q>0 ) and excess enstrophy production (Rtopology implied by the strain eigenvalues and find that for the statistically significant results there is a particularly strong relative preference for the formation of disklike structures in the (Q<0 ,R<0 ) quadrant. With the method shown to be useful for a turbulence that is already understood well, it should be of even greater utility for studying complex flows seen in industry and the environment.
Derevtsov, E. Yu; Louis, A. K.; Maltseva, S. V.; Polyakova, A. P.; Svetov, I. E.
2017-12-01
A problem of reconstruction of 2D vector or symmetric 2-tensor fields by their known ray transforms is considered. Two numerical approaches based on the method of approximate inverse are suggested for solving the problem. The first method allows to recover components of a vector or tensor field, and the second reconstructs its potentials in the sense of feature reconstruction, where the observation operator assigns to a field its potential. Numerical simulations show good results of reconstruction of the sought-for fields or their solenoidal or potential parts from its ray transforms.
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.
Tensor-polarized structure function b1 in the standard convolution description of the deuteron
Cosyn, W.; Dong, Yu-Bing; Kumano, S.; Sargsian, M.
2017-04-01
Tensor-polarized structure functions of a spin-1 hadron are additional observables, which do not exist for the spin-1 /2 nucleon. They could probe novel aspects of the internal hadron structure. Twist-2 tensor-polarized structure functions are b1 and b2, and they are related by the Callan-Gross-like relation in the Bjorken scaling limit. In this work, we theoretically calculate b1 in the standard convolution description for the deuteron. Two different theoretical models, a basic convolution description and a virtual nucleon approximation, are used for calculating b1, and their results are compared with the HERMES measurement. We found large differences between our theoretical results and the data. Although there is still room to improve by considering higher-twist effects and in the experimental extraction of b1 from the spin asymmetry Az z, there is a possibility that the large differences require physics beyond the standard deuteron model for their interpretation. Future b1 studies could shed light on a new field of hadron physics. In particular, detailed experimental studies of b1 will start soon at the Thomas Jefferson National Accelerator Facility. In addition, there are possibilities to investigate tensor-polarized parton distribution functions and b1 at Fermi National Accelerator Laboratory and a future electron-ion collider. Therefore, further theoretical studies are needed for understanding the tensor structure of the spin-1 deuteron, including a new mechanism to explain the large differences between the current data and our theoretical results.
Seismic data filtering using non-local means algorithm based on structure tensor
Yang, Shuai; Chen, Anqing; Chen, Hongde
2017-05-01
Non-Local means algorithm is a new and effective filtering method. It calculates weights of all similar neighborhoods' center points relative to filtering point within searching range by Gaussian weighted Euclidean distance between neighborhoods, then gets filtering point's value by weighted average to complete the filtering operation. In this paper, geometric distance of neighborhood's center point is taken into account in the distance measure calculation, making the non-local means algorithm more reasonable. Furthermore, in order to better protect the geometry structure information of seismic data, we introduce structure tensor that can depict the local geometrical features of seismic data. The coherence measure, which reflects image local contrast, is extracted from the structure tensor, is integrated into the non-local means algorithm to participate in the weight calculation, the control factor of geometry structure similarity is added to form a non-local means filtering algorithm based on structure tensor. The experimental results prove that the algorithm can effectively restrain noise, with strong anti-noise and amplitude preservation effect, improving PSNR and protecting structure information of seismic image. The method has been successfully applied in seismic data processing, indicating that it is a new and effective technique to conduct the structure-preserved filtering of seismic data.
Seismic data filtering using non-local means algorithm based on structure tensor
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Yang Shuai
2017-05-01
Full Text Available Non-Local means algorithm is a new and effective filtering method. It calculates weights of all similar neighborhoods’ center points relative to filtering point within searching range by Gaussian weighted Euclidean distance between neighborhoods, then gets filtering point’s value by weighted average to complete the filtering operation. In this paper, geometric distance of neighborhood’s center point is taken into account in the distance measure calculation, making the non-local means algorithm more reasonable. Furthermore, in order to better protect the geometry structure information of seismic data, we introduce structure tensor that can depict the local geometrical features of seismic data. The coherence measure, which reflects image local contrast, is extracted from the structure tensor, is integrated into the non-local means algorithm to participate in the weight calculation, the control factor of geometry structure similarity is added to form a non-local means filtering algorithm based on structure tensor. The experimental results prove that the algorithm can effectively restrain noise, with strong anti-noise and amplitude preservation effect, improving PSNR and protecting structure information of seismic image. The method has been successfully applied in seismic data processing, indicating that it is a new and effective technique to conduct the structure-preserved filtering of seismic data.
Directly Measuring the Tensor Structure of the Scalar Coupling to Gauge Bosons
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Stolarski, Daniel; Vega-Morales, Roberto
2012-12-01
Kinematic distributions in the decays of the newly discovered resonance to four leptons can provide a direct measurement of the tensor structure of the particle's couplings to gauge bosons. Even if the particle is shown to be a parity even scalar, measuring this tensor structure is a necessary step in determining if this particle is responsible for giving mass to the Z. We consider a Standard Model like coupling as well as coupling via a dimension five operator to either ZZ or Z\\gamma. We show that using full kinematic information from each event allows discrimination between renormalizable and higher dimensional coupling to ZZ at the 95% confidence level with O(50) signal events, and coupling to Z\\gamma can be distinguished with as few as 20 signal events. This shows that these measurements can be useful even with this year's LHC data.
3D reconstruction of tensors and vectors
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Defrise, Michel; Gullberg, Grant T.
2005-02-17
Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields.
Colored Tensor Models - a Review
Directory of Open Access Journals (Sweden)
Razvan Gurau
2012-04-01
Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.
Delineating Neural Structures of Developmental Human Brains with Diffusion Tensor Imaging
Directory of Open Access Journals (Sweden)
Hao Huang
2010-01-01
Full Text Available The human brain anatomy is characterized by dramatic structural changes during fetal development. It is extraordinarily complex and yet its origin is a simple tubular structure. Revealing detailed anatomy at different stages of brain development not only aids in understanding this highly ordered process, but also provides clues to detect abnormalities caused by genetic or environmental factors. However, anatomical studies of human brain development during the fetal period are surprisingly scarce and histology-based atlases have become available only recently. Diffusion tensor imaging (DTI measures water diffusion to delineate the underlying neural structures. The high contrasts derived from DTI can be used to establish the brain atlas. With DTI tractography, coherent neural structures, such as white matter tracts, can be three-dimensionally reconstructed. The primary eigenvector of the diffusion tensor can be further explored to characterize microstructures in the cerebral wall of the developmental brains. In this mini-review, the application of DTI in order to reveal the structures of developmental fetal brains has been reviewed in the above-mentioned aspects. The fetal brain DTI provides a unique insight for delineating the neural structures in both macroscopic and microscopic levels. The resultant DTI database will provide structural guidance for the developmental study of human fetal brains in basic neuroscience, and reference standards for diagnostic radiology of premature newborns.
Julié, Félix-Louis
2018-01-01
Starting from the second post-Keplerian (2PK) Hamiltonian describing the conservative part of the two-body dynamics in massless scalar-tensor (ST) theories, we build an effective-one-body (EOB) Hamiltonian which is a ν deformation (where ν =0 is the test mass limit) of the analytically known ST Hamiltonian of a test particle. This ST-EOB Hamiltonian leads to a simple (yet canonically equivalent) formulation of the conservative 2PK two-body problem, but also defines a resummation of the dynamics which is well-suited to ST regimes that depart strongly from general relativity (GR) and which may provide information on the strong field dynamics; in particular, the ST innermost stable circular orbit location and associated orbital frequency. Results will be compared and contrasted with those deduced from the ST-deformation of the (5PN) GR-EOB Hamiltonian previously obtained in [Phys. Rev. D 95, 124054 (2017), 10.1103/PhysRevD.95.124054].
Collaborative problem structuring using MARVEL
Veldhuis, G.A.; Scheepstal, P.G.M. van; Rouwette, E.A.J.A.; Logtens, T.W.A.
2015-01-01
When faced with wicked and messy problems, practitioners can rely on a variety of problem structuring methods (PSMs). Although previous efforts have been made to combine such methods with simulation, currently, few exist that integrate a simulation capability within problem structuring. Our
Erdtman, Elias; Jönsson, Carl
2012-01-01
This master's thesis addresses numerical methods of computing the typical ranks of tensors over the real numbers and explores some properties of tensors over finite fields. We present three numerical methods to compute typical tensor rank. Two of these have already been published and can be used to calculate the lowest typical ranks of tensors and an approximate percentage of how many tensors have the lowest typical ranks (for some tensor formats), respectively. The third method was developed...
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.
Epifanovsky, Evgeny; Wormit, Michael; Kuś, Tomasz; Landau, Arie; Zuev, Dmitry; Khistyaev, Kirill; Manohar, Prashant; Kaliman, Ilya; Dreuw, Andreas; Krylov, Anna I
2013-10-05
This article presents an open-source object-oriented C++ library of classes and routines to perform tensor algebra.The primary purpose of the library is to enable post-Hartree–Fock electronic structure methods; however, the code is general enough to be applicable in other areas of physical and computational sciences. The library supports tensors of arbitrary order (dimensionality), size, and symmetry. Implemented data structures and algorithms operate on large tensors by splitting them into smaller blocks, storing them both in core memory and in files on disk, and applying divide-and-conquer-type parallel algorithms to perform tensor algebra. The library offers a set of general tensor symmetry algorithms and a full implementation of tensor symmetries typically found in electronic structure theory: permutational, spin, and molecular point group symmetry. The Q-Chem electronic structure software uses this library to drive coupled-cluster, equation-of-motion, and algebraic-diagrammatic construction methods.
Segmentation of the pectoral muscle in breast MR images using structure tensor and deformable model
Lee, Myungeun; Kim, Jong Hyo
2012-02-01
Recently, breast MR images have been used in wider clinical area including diagnosis, treatment planning, and treatment response evaluation, which requests quantitative analysis and breast tissue segmentation. Although several methods have been proposed for segmenting MR images, segmenting out breast tissues robustly from surrounding structures in a wide range of anatomical diversity still remains challenging. Therefore, in this paper, we propose a practical and general-purpose approach for segmenting the pectoral muscle boundary based on the structure tensor and deformable model. The segmentation work flow comprises four key steps: preprocessing, detection of the region of interest (ROI) within the breast region, segmenting the pectoral muscle and finally extracting and refining the pectoral muscle boundary. From experimental results we show that the proposed method can segment the pectoral muscle robustly in diverse patient cases. In addition, the proposed method will allow the application of the quantification research for various breast images.
The Topology of Three-Dimensional Symmetric Tensor Fields
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.
Cartesian tensors an introduction
Temple, G
2004-01-01
This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t
Paniagua, Beatriz; Ehlers, Cindy; Crews, Fulton; Budin, Francois; Larson, Garrett; Styner, Martin; Oguz, Ipek
2011-03-01
Understanding the effects of adolescent binge drinking that persist into adulthood is a crucial public health issue. Adolescent intermittent ethanol exposure (AIE) is an animal model that can be used to investigate these effects in rodents. In this work, we investigate the application of a particular image analysis technique, tensor-based morphometry, for detecting anatomical differences between AIE and control rats using Diffusion Tensor Imaging (DTI). Deformation field analysis is a popular method for detecting volumetric changes analyzing Jacobian determinants calculated on deformation fields. Recent studies showed that computing deformation field metrics on the full deformation tensor, often referred to as tensor-based morphometry (TBM), increases the sensitivity to anatomical differences. In this paper we conduct a comprehensive TBM study for precisely locating differences between control and AIE rats. Using a DTI RARE sequence designed for minimal geometric distortion, 12-directional images were acquired postmortem for control and AIE rats (n=9). After preprocessing, average images for the two groups were constructed using an unbiased atlas building approach. We non-rigidly register the two atlases using Large Deformation Diffeomorphic Metric Mapping, and analyze the resulting deformation field using TBM. In particular, we evaluate the tensor determinant, geodesic anisotropy, and deformation direction vector (DDV) on the deformation field to detect structural differences. This yields data on the local amount of growth, shrinkage and the directionality of deformation between the groups. We show that TBM can thus be used to measure group morphological differences between rat populations, demonstrating the potential of the proposed framework.
Colom, Roberto; Hua, Xue; Martínez, Kenia; Burgaleta, Miguel; Román, Francisco J; Gunter, Jeffrey L; Carmona, Susanna; Jaeggi, Susanne M; Thompson, Paul M
2016-10-01
Tensor-Based Morphometry (TBM) allows the automatic mapping of brain changes across time building 3D deformation maps. This technique has been applied for tracking brain degeneration in Alzheimer's and other neurodegenerative diseases with high sensitivity and reliability. Here we applied TBM to quantify changes in brain structure after completing a challenging adaptive cognitive training program based on the n-back task. Twenty-six young women completed twenty-four training sessions across twelve weeks and they showed, on average, large cognitive improvements. High-resolution MRI scans were obtained before and after training. The computed longitudinal deformation maps were analyzed for answering three questions: (a) Are there differential brain structural changes in the training group as compared with a matched control group? (b) Are these changes related to performance differences in the training program? (c) Are standardized changes in a set of psychological factors (fluid and crystallized intelligence, working memory, and attention control) measured before and after training, related to structural changes in the brain? Results showed (a) greater structural changes for the training group in the temporal lobe, (b) a negative correlation between these changes and performance across training sessions (the greater the structural change, the lower the cognitive performance improvements), and (c) negligible effects regarding the psychological factors measured before and after training. Copyright © 2016 Elsevier Ltd. All rights reserved.
Formalev, V. F.; Kolesnik, S. A.
2017-11-01
The authors are the first to present a closed procedure for numerical solution of inverse coefficient problems of heat conduction in anisotropic materials used as heat-shielding ones in rocket and space equipment. The reconstructed components of the thermal-conductivity tensor depend on temperature (are nonlinear). The procedure includes the formation of experimental data, the implicit gradient-descent method, the economical absolutely stable method of numerical solution of parabolic problems containing mixed derivatives, the parametric identification, construction, and numerical solution of the problem for elements of sensitivity matrices, the development of a quadratic residual functional and regularizing functionals, and also the development of algorithms and software systems. The implicit gradient-descent method permits expanding the quadratic functional in a Taylor series with retention of the linear terms for the increments of the sought functions. This substantially improves the exactness and stability of solution of the inverse problems. Software systems are developed with account taken of the errors in experimental data and disregarding them. On the basis of a priori assumptions of the qualitative behavior of the functional dependences of the components of the thermal-conductivity tensor on temperature, regularizing functionals are constructed by means of which one can reconstruct the components of the thermal-conductivity tensor with an error no higher than the error of the experimental data. Results of the numerical solution of the inverse coefficient problems on reconstruction of nonlinear components of the thermal-conductivity tensor have been obtained and are discussed.
Parrish, Robert M; Hohenstein, Edward G; Schunck, Nicolas F; Sherrill, C David; Martínez, Todd J
2013-09-27
Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the exact tensor hypercontraction method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable tensor factorization of the configuration-space matrix elements. This representation allows for substantial computational savings in chemical, atomic, and nuclear physics simulations, particularly with respect to difficult "exchangelike" contractions.
Problems in structural inorganic chemistry
Li, Wai-Kee; Mak, Thomas Chung Wai; Mak, Kendrew Kin Wah
2013-01-01
This book consists of over 300 problems (and their solutions) in structural inorganic chemistry at the senior undergraduate and beginning graduate level. The topics covered comprise Atomic and Molecular Electronic States, Atomic Orbitals, Hybrid Orbitals, Molecular Symmetry, Molecular Geometry and Bonding, Crystal Field Theory, Molecular Orbital Theory, Vibrational Spectroscopy, and Crystal Structure. The central theme running through these topics is symmetry, molecular or crystalline. The problems collected in this volume originate in examination papers and take-home assignments that have been part of the teaching of the book's two senior authors' at The Chinese University of Hong Kong over the past four decades. The authors' courses include Chemical Bonding, Elementary Quantum Chemistry, Advanced Inorganic Chemistry, X-Ray Crystallography, etc. The problems have been tested by generations of students taking these courses.
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Peng, Bo; Kowalski, Karol
2017-03-01
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 doubles (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.
Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N.
2017-04-01
In this paper, we propose and study two approaches to approximate the solution of the Bethe-Salpeter equation (BSE) by using structured iterative eigenvalue solvers. Both approaches are based on the reduced basis method and low-rank factorizations of the generating matrices. We also propose to represent the static screen interaction part in the BSE matrix by a small active sub-block, with a size balancing the storage for rank-structured representations of other matrix blocks. We demonstrate by various numerical tests that the combination of the diagonal plus low-rank plus reduced-block approximation exhibits higher precision with low numerical cost, providing as well a distinct two-sided error estimate for the smallest eigenvalues of the Bethe-Salpeter operator. The complexity is reduced to O (Nb2) in the size of the atomic orbitals basis set, Nb, instead of the practically intractable O (Nb6) scaling for the direct diagonalization. In the second approach, we apply the quantized-TT (QTT) tensor representation to both, the long eigenvectors and the column vectors in the rank-structured BSE matrix blocks, and combine this with the ALS-type iteration in block QTT format. The QTT-rank of the matrix entities possesses almost the same magnitude as the number of occupied orbitals in the molecular systems, No chain-type molecules, while supporting sufficient accuracy.
Directory of Open Access Journals (Sweden)
Wenchao Qiu
2016-09-01
Full Text Available Purpose: Childhood absence epilepsy (CAE is a common syndrome of idiopathic generalized epilepsy. However, little is known about the brain structural changes in this type of epilepsy, especially in the default mode network (DMN regions. This study aims at using the diffusion tensor imaging (DTI technique to quantify structural abnormalities of DMN nodes in CAE patients. Method: DTI data were acquired in 14 CAE patients (aged 8.64±2.59 years, 7 females and 7 males and 16 age- and sex-matched healthy controls. The data were analyzed using voxel-based analysis (VBA and statistically compared between patients and controls. Pearson correlation was explored between altered DTI metrics and clinical parameters. The difference of brain volumes between patients and controls were also tested using unpaired t-test. Results: Patients showed significant increase of mean diffusivity (MD and radial diffusivity (RD in left medial prefrontal cortex, and decrease of fractional anisotropy (FA in left precuneus and axial diffusivity (AD in both left medial prefrontal cortex and precuneus. In correlation analysis, MD value from left medial prefrontal cortex was positively associated with duration of epilepsy. Neither the disease duration nor the seizure frequency showed significant correlation with FA values. Between-group comparison of brain volumes got no significant difference. Conclusion: The findings indicate that structural impairments exist in DMN regions in children suffering from absence epilepsy and MD values positively correlate with epilepsy duration. This may contribute to understanding the pathological mechanisms of chronic neurological deficits and promote the development of new therapies for this disorder.
Structures and Nuclear Quadrupole Coupling Tensors of a Series of Chlorine-Containing Hydrocarbons
Dikkumbura, Asela S.; Webster, Erica R.; Dorris, Rachel E.; Peebles, Rebecca A.; Peebles, Sean A.; Seifert, Nathan A.; Pate, Brooks
2016-06-01
Rotational spectra for gauche-1,2-dichloroethane (12DCE), gauche-1-chloro-2-fluoroethane (1C2FE) and both anti- and gauche-2,3-dichloropropene (23DCP) have been observed using chirped-pulse Fourier-transform microwave (FTMW) spectroscopy in the 6-18 GHz region. Although the anti conformers for all three species are predicted to be more stable than the gauche forms, they are nonpolar (12DCE) or nearly nonpolar (predicted dipole components for anti-1C2FE: μ_a = 0.11 D, μ_b = 0.02 D and for anti-23DCP: μ_a = 0.25 D, μ_b = 0.02 D); nevertheless, it was also possible to observe and assign the spectrum of anti-23DCP. Assignments of parent spectra and 37Cl and 13C substituted isotopologues utilized predictions at the MP2/6-311++G(2d,2p) level and Pickett's SPCAT/SPFIT programs. For the weak anti-23DCP spectra, additional measurements also utilized a resonant-cavity FTMW spectrometer. Full chlorine nuclear quadrupole coupling tensors for gauche-12DCE and both anti- and gauche-23DCP have been diagonalized to allow comparison of coupling constants. Kraitchman's equations were used to determine r_s coordinates of isotopically substituted atoms and r_0 structures were also deduced for gauche conformers of 12DCE and 1C2FE. Structural details and chlorine nuclear quadrupole coupling constants of all three molecules will be compared, and effects of differing halogen substitution and carbon chain length on molecular properties will be evaluated.
White matter structures associated with creativity: evidence from diffusion tensor imaging.
Takeuchi, Hikaru; Taki, Yasuyuki; Sassa, Yuko; Hashizume, Hiroshi; Sekiguchi, Atsushi; Fukushima, Ai; Kawashima, Ryuta
2010-05-15
Creativity has been essential to the development of human civilization and plays a crucial role in cultural life. However, despite literature that has proposed the importance of structural connectivity in the brain for creativity, the relationship between regional white matter integrity and creativity has never been directly investigated. In this study, we used diffusion tensor imaging and a behavioral creativity test of divergent thinking to investigate the relationship between creativity and structural connectivity. We examined associations between creativity and fractional anisotropy across the brain in healthy young adult (mean age, 21.7 years old; [SD]=1.44) men (n=42) and women (n=13). After controlling for age, sex, and score on Raven's advanced progressive matrices, a test for psychometric measures of intelligence, significant positive relationships between fractional anisotropy and individual creativity as measured by the divergent thinking test were observed in the white matter in or adjacent to the bilateral prefrontal cortices, the body of the corpus callosum, the bilateral basal ganglia, the bilateral temporo-parietal junction and the right inferior parietal lobule. As a whole, these findings indicate that integrated white matter tracts underlie creativity. These pathways involve the association cortices and the corpus callosum, which connect information in distant brain regions and underlie diverse cognitive functions that support creativity. Thus, our results are congruent with the ideas that creativity is associated with the integration of conceptually distant ideas held in different brain domains and architectures and that creativity is supported by diverse high-level cognitive functions, particularly those of the frontal lobe. Copyright (c) 2010 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Yu Sun
Full Text Available Sexual dimorphism in the brain maturation during childhood and adolescence has been repeatedly documented, which may underlie the differences in behaviors and cognitive performance. However, our understanding of how gender modulates the development of structural connectome in healthy adults is still not entirely clear. Here we utilized graph theoretical analysis of longitudinal diffusion tensor imaging data over a five-year period to investigate the progressive gender differences of brain network topology. The brain networks of both genders showed prominent economical "small-world" architecture (high local clustering and short paths between nodes. Additional analysis revealed a more economical "small-world" architecture in females as well as a greater global efficiency in males regardless of scan time point. At the regional level, both increased and decreased efficiency were found across the cerebral cortex for both males and females, indicating a compensation mechanism of cortical network reorganization over time. Furthermore, we found that weighted clustering coefficient exhibited significant gender-time interactions, implying different development trends between males and females. Moreover, several specific brain regions (e.g., insula, superior temporal gyrus, cuneus, putamen, and parahippocampal gyrus exhibited different development trajectories between males and females. Our findings further prove the presence of sexual dimorphism in brain structures that may underlie gender differences in behavioral and cognitive functioning. The sex-specific progress trajectories in brain connectome revealed in this work provide an important foundation to delineate the gender related pathophysiological mechanisms in various neuropsychiatric disorders, which may potentially guide the development of sex-specific treatments for these devastating brain disorders.
Sun, Yu; Lee, Renick; Chen, Yu; Collinson, Simon; Thakor, Nitish; Bezerianos, Anastasios; Sim, Kang
2015-01-01
Sexual dimorphism in the brain maturation during childhood and adolescence has been repeatedly documented, which may underlie the differences in behaviors and cognitive performance. However, our understanding of how gender modulates the development of structural connectome in healthy adults is still not entirely clear. Here we utilized graph theoretical analysis of longitudinal diffusion tensor imaging data over a five-year period to investigate the progressive gender differences of brain network topology. The brain networks of both genders showed prominent economical "small-world" architecture (high local clustering and short paths between nodes). Additional analysis revealed a more economical "small-world" architecture in females as well as a greater global efficiency in males regardless of scan time point. At the regional level, both increased and decreased efficiency were found across the cerebral cortex for both males and females, indicating a compensation mechanism of cortical network reorganization over time. Furthermore, we found that weighted clustering coefficient exhibited significant gender-time interactions, implying different development trends between males and females. Moreover, several specific brain regions (e.g., insula, superior temporal gyrus, cuneus, putamen, and parahippocampal gyrus) exhibited different development trajectories between males and females. Our findings further prove the presence of sexual dimorphism in brain structures that may underlie gender differences in behavioral and cognitive functioning. The sex-specific progress trajectories in brain connectome revealed in this work provide an important foundation to delineate the gender related pathophysiological mechanisms in various neuropsychiatric disorders, which may potentially guide the development of sex-specific treatments for these devastating brain disorders.
Energy Technology Data Exchange (ETDEWEB)
Zeng, Dong; Zhang, Xinyu; Bian, Zhaoying, E-mail: zybian@smu.edu.cn, E-mail: jhma@smu.edu.cn; Huang, Jing; Zhang, Hua; Lu, Lijun; Lyu, Wenbing; Feng, Qianjin; Chen, Wufan; Ma, Jianhua, E-mail: zybian@smu.edu.cn, E-mail: jhma@smu.edu.cn [Department of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong 510515, China and Guangdong Provincial Key Laboratory of Medical Image Processing, Southern Medical University, Guangzhou, Guangdong 510515 (China); Zhang, Jing [Department of Radiology, Tianjin Medical University General Hospital, Tianjin 300052 (China)
2016-05-15
Purpose: Cerebral perfusion computed tomography (PCT) imaging as an accurate and fast acute ischemic stroke examination has been widely used in clinic. Meanwhile, a major drawback of PCT imaging is the high radiation dose due to its dynamic scan protocol. The purpose of this work is to develop a robust perfusion deconvolution approach via structure tensor total variation (STV) regularization (PD-STV) for estimating an accurate residue function in PCT imaging with the low-milliampere-seconds (low-mAs) data acquisition. Methods: Besides modeling the spatio-temporal structure information of PCT data, the STV regularization of the present PD-STV approach can utilize the higher order derivatives of the residue function to enhance denoising performance. To minimize the objective function, the authors propose an effective iterative algorithm with a shrinkage/thresholding scheme. A simulation study on a digital brain perfusion phantom and a clinical study on an old infarction patient were conducted to validate and evaluate the performance of the present PD-STV approach. Results: In the digital phantom study, visual inspection and quantitative metrics (i.e., the normalized mean square error, the peak signal-to-noise ratio, and the universal quality index) assessments demonstrated that the PD-STV approach outperformed other existing approaches in terms of the performance of noise-induced artifacts reduction and accurate perfusion hemodynamic maps (PHM) estimation. In the patient data study, the present PD-STV approach could yield accurate PHM estimation with several noticeable gains over other existing approaches in terms of visual inspection and correlation analysis. Conclusions: This study demonstrated the feasibility and efficacy of the present PD-STV approach in utilizing STV regularization to improve the accuracy of residue function estimation of cerebral PCT imaging in the case of low-mAs.
Tubergen, M. J.; Lesarri, A.; Suenram, R. D.; Samuels, A. C.; Jensen, J. O.; Ellzy, M. W.; Lochner, J. M.
2005-10-01
Rotational spectra have been recorded for both the 35Cl and 37Cl isotopic forms of two structural conformations of 2-chloroethyl ethyl sulfide (CEES). The rotational constants of the 35Cl and 37Cl isotopomers were used to identify the conformational isomers. A total of 236 hyperfine transitions have been assigned for 47 rotational transitions of the 35Cl isotope of a GGT conformer, and 146 hyperfine have been assigned for 37 rotational transitions of the 37Cl isotopomer. For the second conformer, a total of 128 (110) hyperfine and 30 (28) rotational transitions have also been assigned to the 35Cl ( 37Cl) isotopes of a TGT conformation. The extensive hyperfine splitting data, measured to high resolution with a compact Fourier transform microwave spectrometer, were used to determine both the diagonal and off-diagonal elements of the 35Cl and 37Cl nuclear quadrupole coupling tensors in the inertial tensor principal axis system. The experimental rotational constant data, as well as the 35Cl and 37Cl nuclear quadrupole coupling tensors, were compared to the results from 27 optimized ab initio (HF/6-311++G ∗∗ and MP2/6-311++G ∗∗) model structures.
Evaluation of bayesian tensor estimation using tensor coherence.
Kim, Dae-Jin; Kim, In-Young; Jeong, Seok-Oh; Park, Hae-Jeong
2009-06-21
Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.
Evaluation of Bayesian tensor estimation using tensor coherence
Kim, Dae-Jin; Kim, In-Young; Jeong, Seok-Oh; Park, Hae-Jeong
2009-06-01
Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.
Decomposing tensors with structured matrix factors reduces to rank-1 approximations
DEFF Research Database (Denmark)
Comon, Pierre; Sørensen, Mikael; Tsigaridas, Elias
2010-01-01
Tensor decompositions permit to estimate in a deterministic way the parameters in a multi-linear model. Applications have been already pointed out in antenna array processing and digital communications, among others, and are extremely attractive provided some diversity at the receiver is availabl...
Exploring the tensor networks/AdS correspondence
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Bhattacharyya, Arpan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Centre For High Energy Physics, Indian Institute of Science,560012 Bangalore (India); Gao, Zhe-Shen [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); State Key Laboratory of Surface Physics and Department of Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Nanjing University,Nanjing, 210093 (China); Liu, Si-Nong [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China)
2016-08-11
In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.
Positivity and conservation of superenergy tensors
Pozo, J M
2002-01-01
Two essential properties of energy-momentum tensors T submu subnu are their positivity and conservation. This is mathematically formalized by, respectively, an energy condition, as the dominant energy condition, and the vanishing of their divergence nabla supmu T submu subnu = 0. The classical Bel and Bel-Robinson superenergy tensors, generated from the Riemann and Weyl tensors, respectively, are rank-4 tensors. But they share these two properties with energy-momentum tensors: the dominant property (DP) and the divergence-free property in the absence of sources (vacuum). Senovilla defined a universal algebraic construction which generates a basic superenergy tensor T left brace A right brace from any arbitrary tensor A. In this construction, the seed tensor A is structured as an r-fold multivector, which can always be done. The most important feature of the basic superenergy tensors is that they satisfy automatically the DP, independently of the generating tensor A. We presented a more compact definition of T...
Non-convex Statistical Optimization for Sparse Tensor Graphical Model.
Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang
2015-01-01
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.
Etingof, Pavel; Nikshych, Dmitri; Ostrik, Victor
2015-01-01
Is there a vector space whose dimension is the golden ratio? Of course not-the golden ratio is not an integer! But this can happen for generalizations of vector spaces-objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This bo
Directory of Open Access Journals (Sweden)
Jie Gao
2017-06-01
Full Text Available Under the condition of the pseudospin symmetry, the approximate analytical solution of the Dirac–Eckart problem with a Hulthén tensor interaction is investigated by working in a complete square integrable basis that supports a tridiagonal matrix representation of the wave operator. The pseudo-centrifugal term is treated with Greene and Aldrich's approximation scheme. The energy eigenvalue equation is obtained by diagonalization of the recursion relation and the corresponding spinor wave functions are presented in terms of Jacobi polynomials or hypergeometric functions.
Vector and tensor analysis with applications
Borisenko, A I; Silverman, Richard A
1979-01-01
Concise and readable, this text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. It also includes a systematic study of the differential and integral calculus of vector and tensor functions of space and time. Worked-out problems and solutions. 1968 edition.
Birman, Joseph L.; Izyumov, Yuri A.
1980-02-01
We formulate the thermodynamic theory of phase transitions in magnetically ordered systems in terms of a tensor, or coupled, order parameter. This basis is constructed by coupling atomic spin and lattice displacement. Symmetry lowering is predicted at the second-order phase transition point (tricritical points are not considered here). Lower-symmetry phases should in general be classified according to the Shubnikov symmetry space group Sh, which will reveal the total broken symmetry due to the coupled order parameter. In case the apparatus is "blind" to one portion of the order parameter: either spin or displacement, the apparent symmetry group will not be Sh, but a related space group, which will reveal "partial information." Comparing this formulation and the usual (uncoupled) theory, new results are obtained here: for example "pseudoscalar order parameters" can arise and different "symmetry-broken" groups. An illustration is given by applying the formulation to the spinel-structure space group: O7h-Fd3m. It is conjectured that for TbNi2 the tensor order parameter Γ1- may be relevant, so that the phase transition which has been identified as O7h-->Sh101166 may actually be O7h-->Sh132227, caused by a pseudoscalar.
Spatio-Temporal Video Object Segmentation via Scale-Adaptive 3D Structure Tensor
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Hai-Yun Wang
2004-06-01
Full Text Available To address multiple motions and deformable objects' motions encountered in existing region-based approaches, an automatic video object (VO segmentation methodology is proposed in this paper by exploiting the duality of image segmentation and motion estimation such that spatial and temporal information could assist each other to jointly yield much improved segmentation results. The key novelties of our method are (1 scale-adaptive tensor computation, (2 spatial-constrained motion mask generation without invoking dense motion-field computation, (3 rigidity analysis, (4 motion mask generation and selection, and (5 motion-constrained spatial region merging. Experimental results demonstrate that these novelties jointly contribute much more accurate VO segmentation both in spatial and temporal domains.
Inference problems in structural biology
DEFF Research Database (Denmark)
Olsson, Simon
The structure and dynamics of biological molecules are essential for their function. Consequently, a wealth of experimental techniques have been developed to study these features. However, while experiments yield detailed information about geometrical features of molecules, this information is of...
Tensor Network Contractions for #SAT
Biamonte, Jacob D.; Morton, Jason; Turner, Jacob
2015-09-01
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g. 2-SAT, which is in ), determining the number of solutions can be #-hard. Recently, computational methods simulating quantum systems experienced advancements due to the development of tensor network algorithms and associated quantum physics-inspired techniques. By these methods, we give an algorithm using an axiomatic tensor contraction language for n-variable #SAT instances with complexity where c is the number of COPY-tensors, g is the number of gates, and d is the maximal degree of any COPY-tensor. Thus, n-variable counting problems can be solved efficiently when their tensor network expression has at most COPY-tensors and polynomial fan-out. This framework also admits an intuitive proof of a variant of the Tovey conjecture (the r,1-SAT instance of the Dubois-Tovey theorem). This study increases the theory, expressiveness and application of tensor based algorithmic tools and provides an alternative insight on these problems which have a long history in statistical physics and computer science.
Son, Shuraku; Kubota, Manabu; Miyata, Jun; Fukuyama, Hidenao; Aso, Toshihiko; Urayama, Shin-ichi; Murai, Toshiya; Takahashi, Hidehiko
2015-05-01
Both creativity and schizotypy are suggested to be manifestations of the hyperactivation of unusual or remote concepts/words. However, the results of studies on creativity in schizophrenia are diverse, possibly due to the multifaceted aspects of creativity and difficulties of differentiating adaptive creativity from pathological schizotypy/positive symptoms. To date, there have been no detailed studies comprehensively investigating creativity, positive symptoms including delusions, and their neural bases in schizophrenia. In this study, we investigated 43 schizophrenia and 36 healthy participants using diffusion tensor imaging. We used idea, design, and verbal (semantic and phonological) fluency tests as creativity scores and Peters Delusions Inventory as delusion scores. Subsequently, we investigated group differences in every psychological score, correlations between fluency and delusions, and relationships between these scores and white matter integrity using tract-based spatial statistics (TBSS). In schizophrenia, idea and verbal fluency were significantly lower in general, and delusion score was higher than in healthy controls, whereas there were no group differences in design fluency. We also found positive correlation between phonological fluency and delusions in schizophrenia. By correlation analyses using TBSS, we found that the anterior part of corpus callosum was the substantially overlapped area, negatively correlated with both phonological fluency and delusion severity. Our results suggest that the anterior interhemispheric dysconnectivity might be associated with executive dysfunction, and disinhibited automatic spreading activation in the semantic network was manifested as uncontrollable phonological fluency or delusions. This dysconnectivity could be one possible neural basis that differentiates pathological positive symptoms from adaptive creativity. Copyright © 2015 Elsevier B.V. All rights reserved.
Chan, Russell W.; Ho, Leon C.; Zhou, Iris Y.; Gao, Patrick P.; Chan, Kevin C.; Wu, Ed X.
2015-01-01
Although pregnancy-induced hormonal changes have been shown to alter the brain at the neuronal level, the exact effects of pregnancy on brain at the tissue level remain unclear. In this study, diffusion tensor imaging (DTI) and resting-state functional MRI (rsfMRI) were employed to investigate and document the effects of pregnancy on the structure and function of the brain tissues. Fifteen Sprague-Dawley female rats were longitudinally studied at three days before mating (baseline) and seventeen days after mating (G17). G17 is equivalent to the early stage of the third trimester in humans. Seven age-matched nulliparous female rats served as non-pregnant controls and were scanned at the same time-points. For DTI, diffusivity was found to generally increase in the whole brain during pregnancy, indicating structural changes at microscopic levels that facilitated water molecular movement. Regionally, mean diffusivity increased more pronouncedly in the dorsal hippocampus while fractional anisotropy in the dorsal dentate gyrus increased significantly during pregnancy. For rsfMRI, bilateral functional connectivity in the hippocampus increased significantly during pregnancy. Moreover, fractional anisotropy increase in the dentate gyrus appeared to correlate with the bilateral functional connectivity increase in the hippocampus. These findings revealed tissue structural modifications in the whole brain during pregnancy, and that the hippocampus was structurally and functionally remodeled in a more marked manner. PMID:26658306
Directory of Open Access Journals (Sweden)
Russell W Chan
Full Text Available Although pregnancy-induced hormonal changes have been shown to alter the brain at the neuronal level, the exact effects of pregnancy on brain at the tissue level remain unclear. In this study, diffusion tensor imaging (DTI and resting-state functional MRI (rsfMRI were employed to investigate and document the effects of pregnancy on the structure and function of the brain tissues. Fifteen Sprague-Dawley female rats were longitudinally studied at three days before mating (baseline and seventeen days after mating (G17. G17 is equivalent to the early stage of the third trimester in humans. Seven age-matched nulliparous female rats served as non-pregnant controls and were scanned at the same time-points. For DTI, diffusivity was found to generally increase in the whole brain during pregnancy, indicating structural changes at microscopic levels that facilitated water molecular movement. Regionally, mean diffusivity increased more pronouncedly in the dorsal hippocampus while fractional anisotropy in the dorsal dentate gyrus increased significantly during pregnancy. For rsfMRI, bilateral functional connectivity in the hippocampus increased significantly during pregnancy. Moreover, fractional anisotropy increase in the dentate gyrus appeared to correlate with the bilateral functional connectivity increase in the hippocampus. These findings revealed tissue structural modifications in the whole brain during pregnancy, and that the hippocampus was structurally and functionally remodeled in a more marked manner.
All-at-once Optimization for Coupled Matrix and Tensor Factorizations
DEFF Research Database (Denmark)
Evrim, Acar Ataman; Kolda, Tamara G.; Dunlavy, Daniel M.
2011-01-01
Joint analysis of data from multiple sources has the potential to improve our understanding of the underlying structures in complex data sets. For instance, in restaurant recommendation systems, recommendations can be based on rating histories of customers. In addition to rating histories.......g., the person by person social network matrix or the restaurant by category matrix, and higher-order tensors, e.g., the "ratings" tensor of the form restaurant by meal by person. In this paper, we are particularly interested in fusing data sets with the goal of capturing their underlying latent structures. We...... formulate this problem as a coupled matrix and tensor factorization (CMTF) problem where heterogeneous data sets are modeled by fitting outer-product models to higher-order tensors and matrices in a coupled manner. Unlike traditional approaches solving this problem using alternating algorithms, we propose...
Welch, K A; Moorhead, T W; McIntosh, A M; Owens, D G C; Johnstone, E C; Lawrie, S M
2013-10-01
Schizophrenia is associated with various brain structural abnormalities, including reduced volume of the hippocampi, prefrontal lobes and thalami. Cannabis use increases the risk of schizophrenia but reports of brain structural abnormalities in the cannabis-using population have not been consistent. We used automated image analysis to compare brain structural changes over time in people at elevated risk of schizophrenia for familial reasons who did and did not use cannabis. Magnetic resonance imaging (MRI) scans were obtained from subjects at high familial risk of schizophrenia at entry to the Edinburgh High Risk Study (EHRS) and approximately 2 years later. Differential grey matter (GM) loss in those exposed (n=23) and not exposed to cannabis (n=32) in the intervening period was compared using tensor-based morphometry (TBM). Cannabis exposure was associated with significantly greater loss of right anterior hippocampal (pcorrected=0.029, t=3.88) and left superior frontal lobe GM (pcorrected=0.026, t=4.68). The former finding remained significant even after the exclusion of individuals who had used other drugs during the inter-scan interval. Using an automated analysis of longitudinal data, we demonstrate an association between cannabis use and GM loss in currently well people at familial risk of developing schizophrenia. This observation may be important in understanding the link between cannabis exposure and the subsequent development of schizophrenia.
Tensor completion for estimating missing values in visual data
Liu, Ji
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 dependant relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between Fa
Hoy, Erik P; Mazziotti, David A
2015-08-14
Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.
Fluid structure interaction problems in large deformation
Le Tallec, Patrick; Gerbeau, Jean-Frédéric; Hauret, Patrice; Vidrascu, Marina
2005-12-01
The present article deals with the simulation of fluid structure interaction problems in large deformation, and discusses two aspects of their numerical solution: (i) the derivation of energy conserving time integration schemes in presence of fluid structure coupling, moving grids, and nonlinear kinematic constraints such as incompressibility and contact, (ii) the introduction of adequate preconditioners efficiently chaining local fluid and structure solvers. Solutions are proposed, analyzed and tested using nonlinear energy correcting terms, and added mass based Dirichlet Neumann preconditioners. Numerical applications include nonlinear impact problems in elastodynamics and blood flows predictions within flexible arteries. To cite this article: P. Le Tallec et al., C. R. Mecanique 333 (2005).
Energy Technology Data Exchange (ETDEWEB)
Wannamaker, P.E.
1994-06-01
We have carried Out an extensive tensor CSAMT survey of the Sulphur Springs geothermal area, Valles Caldera, New Mexico. This survey, consisting of 45 high-quality sites, has been acquired by in support of Continental Scientific Drilling Program (CSDP) drillholes VC-2A and VC-2B. Two independent transmitter dipoles were energized for tensor measurements using a 30 kW generator placed approximately 13 km south of the VC-2B wellhead. The soundings in the Sulphur Springs area were arranged in four profiles to cross major structural features. The electric bipoles parallel to each profile were deployed contiguously to ensure against spatial aliasing of the impedance response corresponding to current flow across structural trends. The frequency range of acquisition was 4096 Hz down to 1 Hz for the central line, but only down to 4 Hz for most sites of the other lines. Data quality is high overall and is established by repeatability of measurements. Agreement between the CSAMT and available natural field MT data is very good over almost all the period range of overlap indicating that we are free of calibration problems and that far-field results are generally being obtained. Non plane-wave effects in the CSAMT around Sulphur Springs are apparent at 1 to 2 Hz, and perhaps slightly even at 4 Hz, however, which is near the bottom of our frequency range. CSAMT and MT data taken outside the Valles Caldera to the west were modeled in an attempt to compare resistivity structure exterior to the caldera to that within. With the availability of tensor CSAMT and MT data both inside and outside Valles Caldera, assumptions and methods of CSAMT are tested. In the Sulphur Springs area, near-coincident CSAMT and MT data near well VC -2B indicate that non-lane-wave effects in the apparent resistivity and impedance phase occure at a frequency near to that predicted from the resistivity structure local to the wester caldera.
Balachandar, R; John, J P; Saini, J; Kumar, K J; Joshi, H; Sadanand, S; Aiyappan, S; Sivakumar, P T; Loganathan, S; Varghese, M; Bharath, S
2015-05-01
Alzheimer's disease (AD) is a progressive neurodegenerative condition where in early diagnosis and interventions are key policy priorities in dementia services and research. We studied the functional and structural connectivity in mild AD to determine the nature of connectivity changes that coexist with neurocognitive deficits in the early stages of AD. Fifteen mild AD subjects and 15 cognitively healthy controls (CHc) matched for age and gender, underwent detailed neurocognitive assessment and magnetic resonance imaging (MRI) of resting state functional MRI (rs-fMRI) and diffusion tensor imaging (DTI). Rest fMRI was analyzed using dual regression approach and DTI by voxel wise statistics. Patients with mild AD had significantly lower functional connectivity (FC) within the default mode network and increased FC within the executive network. The mild AD group scored significantly lower in all domains of cognition compared with CHc. But fractional anisotropy did not significantly (p Resting state functional connectivity alterations are noted during initial stages of cognitive decline in AD, even when there are no significant white matter microstructural changes. Copyright © 2014 John Wiley & Sons, Ltd.
Link prediction via generalized coupled tensor factorisation
DEFF Research Database (Denmark)
Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.
2012-01-01
This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as heterogeneous data, i.e., datasets in the form of matrices...... and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....
DEFF Research Database (Denmark)
Ziegel, Johanna; Nyengaard, Jens Randel; Jensen, Eva B. Vedel
In the present paper, statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles are developed. The focus of this work is on the case where the particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle...... shape and orientation, and stereological estimators of the tensors are derived. It is shown that these estimators can be combined to provide consistent estimators of the moments of the so-called particle cover density. The covariance structure associated with the particle cover density depends...... on the orientation and shape of the particles. For instance, if the distribution of the typical particle is invariant under all rotations, then the covariance matrix is proportional to the identity matrix. A non-parametric test for such isotropy is developed. A flexible L\\'evy-based particle model is proposed, which...
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
Hess, Siegfried
2015-01-01
This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...
Students’ Creativity: Problem Posing in Structured Situation
Amalina, I. K.; Amirudin, M.; Budiarto, M. T.
2018-01-01
This is a qualitative research concerning on students’ creativity on problem posing task. The study aimed at describing the students’ creative thinking ability to pose the mathematics problem in structured situations with varied condition of given problems. In order to find out the students’ creative thinking ability, an analysis of mathematics problem posing test based on fluency, novelty, and flexibility and interview was applied for categorizing students’ responses on that task. The data analysis used the quality of problem posing and categorized in 4 level of creativity. The results revealed from 29 secondary students grade 8, a student in CTL (Creative Thinking Level) 1 met the fluency. A student in CTL 2 met the novelty, while a student in CTL 3 met both fluency and novelty and no one in CTL 4. These results are affected by students’ mathematical experience. The findings of this study highlight that student’s problem posing creativity are dependent on their experience in mathematics learning and from the point of view of which students start to pose problem.
Directory of Open Access Journals (Sweden)
Lingjia Xu
2007-04-01
Full Text Available The interaction of dopamine with adenine and guanine were studied at the Hartree-Fock level theory. The structural and vibrational properties of dopamine-4-N7GUA and dopamine-4-N3ADE were studied at level of HF/6-31G*. Interaction energies (ΔE were calculated to be -11.49 and -11.92 kcal/mol, respectively. Some of bond lengths, angels and tortions are compared. NBO studies were performed to the second-order and perturbative estimates of donor-acceptor interaction have been done. The procedures of gauge-invariant atomic orbital (GIAO and continuous-set-of-gauge-transformation (CSGT were employed to calculate isotropic shielding, chemical shifts anisotropy and chemical shifts anisotropy asymmetry and effective anisotropy using 6-31G* basis set. These calculations yielded molecular geometries in good agreement with available experimental data.
Tensor deep stacking networks.
Hutchinson, Brian; Deng, Li; Yu, Dong
2013-08-01
A novel deep architecture, the tensor deep stacking network (T-DSN), is presented. The T-DSN consists of multiple, stacked blocks, where each block contains a bilinear mapping from two hidden layers to the output layer, using a weight tensor to incorporate higher order statistics of the hidden binary (½0; 1) features. A learning algorithm for the T-DSN’s weight matrices and tensors is developed and described in which the main parameter estimation burden is shifted to a convex subproblem with a closed-form solution. Using an efficient and scalable parallel implementation for CPU clusters, we train sets of T-DSNs in three popular tasks in increasing order of the data size: handwritten digit recognition using MNIST (60k), isolated state/phone classification and continuous phone recognition using TIMIT (1.1 m), and isolated phone classification using WSJ0 (5.2 m). Experimental results in all three tasks demonstrate the effectiveness of the T-DSN and the associated learning methods in a consistent manner. In particular, a sufficient depth of the T-DSN, a symmetry in the two hidden layers structure in each T-DSN block, our model parameter learning algorithm, and a softmax layer on top of T-DSN are shown to have all contributed to the low error rates observed in the experiments for all three tasks.
Tensor rank is not multiplicative under the tensor product
DEFF Research Database (Denmark)
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2018-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection b...
Robust Tensor Preserving Projection for Multispectral Face Recognition
Directory of Open Access Journals (Sweden)
Shaoyuan Sun
2014-01-01
Full Text Available Multiple imaging modalities based face recognition has become a hot research topic. A great number of multispectral face recognition algorithms/systems have been designed in the last decade. How to extract features of different spectrum has still been an important issue for face recognition. To address this problem, we propose a robust tensor preserving projection (RTPP algorithm which represents a multispectral image as a third-order tensor. RTPP constructs sparse neighborhoods and then computes weights of the tensor. RTPP iteratively obtains one spectral space transformation matrix through preserving the sparse neighborhoods. Due to sparse representation, RTPP can not only keep the underlying spatial structure of multispectral images but also enhance robustness. The experiments on both Equinox and DHUFO face databases show that the performance of the proposed method is better than those of related algorithms.
The Topology of Symmetric Tensor Fields
Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval
1997-01-01
Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.
Tensor fields on orbits of quantum states and applications
Energy Technology Data Exchange (ETDEWEB)
Volkert, Georg Friedrich
2010-07-19
On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C{sub 0}-principal bundle H{sub 0} {yields} P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)
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.
Application of tensor analysis
McConnell, Albert Joseph
1957-01-01
Standard work applies tensorial methods to subjects within realm of advanced college mathematics. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor algebra; introduces theory of differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics. 685 exercises, most with answers.
Diffusion Tensor Estimation by Maximizing Rician Likelihood.
Landman, Bennett; Bazin, Pierre-Louis; Prince, Jerry
2007-01-01
Diffusion tensor imaging (DTI) is widely used to characterize white matter in health and disease. Previous approaches to the estimation of diffusion tensors have either been statistically suboptimal or have used Gaussian approximations of the underlying noise structure, which is Rician in reality. This can cause quantities derived from these tensors - e.g., fractional anisotropy and apparent diffusion coefficient - to diverge from their true values, potentially leading to artifactual changes that confound clinically significant ones. This paper presents a novel maximum likelihood approach to tensor estimation, denoted Diffusion Tensor Estimation by Maximizing Rician Likelihood (DTEMRL). In contrast to previous approaches, DTEMRL considers the joint distribution of all observed data in the context of an augmented tensor model to account for variable levels of Rician noise. To improve numeric stability and prevent non-physical solutions, DTEMRL incorporates a robust characterization of positive definite tensors and a new estimator of underlying noise variance. In simulated and clinical data, mean squared error metrics show consistent and significant improvements from low clinical SNR to high SNR. DTEMRL may be readily supplemented with spatial regularization or a priori tensor distributions for Bayesian tensor estimation.
An introduction to linear algebra and tensors
Akivis, M A; Silverman, Richard A
1978-01-01
Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.
Brian Pitts, J.
2012-02-01
It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors as such cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is (nearly) Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix diag(-1,1,1,1), the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and values of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, (densitized) Ogievetsky-Polubarinov spinors form, with the (conformal part of the) metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of
Florez, C.; Romero, M. A.; Ramirez, M. I.; Monsalve, G.
2013-05-01
In the elaboration of a hydrogeological conceptual model in regions of mining exploration where there is significant presence of crystalline massif rocks., the influence of physical and geometrical properties of rock discontinuities must be evaluated. We present the results of a structural analysis of rock discontinuities in a region of the Central Cordillera of Colombia (The upper and middle Bermellon Basin) in order to establish its hydrogeological characteristics for the improvement of the conceptual hydrogeological model for the region. The geology of the study area consists of schists with quartz and mica and porphyritic rocks, in a region of high slopes with a nearly 10 m thick weathered layer. The main objective of this research is to infer the preferential flow directions of groundwater and to estimate the tensor of potential hydraulic conductivity by using surface information and avoiding the use of wells and packer tests. The first step of our methodology is an analysis of drainage directions to detect patterns of structural controls in the run-off; after a field campaign of structural data recollection, where we compile information of strike, dip, continuity, spacing, roughness, aperture and frequency, we built equal area hydro-structural polar diagrams that indicate the potential directions for groundwater flow. These results are confronted with records of Rock Quality Designation (RQD) that have been systematically taken from several mining exploration boreholes in the area of study. By using all this information we estimate the potential tensor of hydraulic conductivity from a cubic law, obtaining the three principal directions with conductivities of the order of 10-5 and 10-6 m/s; the more conductive joint family has a NE strike with a nearly vertical dip.
Zhong, Zhaoxi; Zhao, Tengda; Luo, Jia; Guo, Zhihua; Guo, Meng; Li, Ping; Sun, Jing; He, Yong; Li, Zhanjiang
2014-06-03
Obsessive-compulsive disorder (OCD) is a chronic psychiatric disorder defined by recurrent thoughts, intrusive and distressing impulses, or images and ritualistic behaviors. Although focal diverse regional abnormalities white matter integrity in specific brain regions have been widely studied in populations with OCD, alterations in the structural connectivities among them remain poorly understood. The aim was to investigate the abnormalities in the topological efficiency of the white matter networks and the correlation between the network metrics and Yale-Brown Obsessive-Compulsive Scale scores in unmedicated OCD patients, using diffusion tensor tractography and graph theoretical approaches. This study used diffusion tensor imaging and deterministic tractography to map the white matter structural networks in 26 OCD patients and 39 age- and gender-matched healthy controls; and then applied graph theoretical methods to investigate abnormalities in the global and regional properties of the white matter network in these patients. The patients and control participants both showed small-world organization of the white matter networks. However, the OCD patients exhibited significant abnormal global topology, including decreases in global efficiency (t = -2.32, p = 0.02) and increases in shortest path length, Lp (t = 2.30, p = 0.02), the normalized weighted shortest path length, λ (t = 2.08, p=0.04), and the normalized clustering coefficient, γ (t = 2.26, p = 0.03), of their white matter structural networks compared with healthy controls. Further, the OCD patients showed a reduction in nodal efficiency predominately in the frontal regions, the parietal regions and caudate nucleus. The normalized weighted shortest path length of the network metrics was significantly negatively correlated with obsessive subscale of the Yale-Brown Obsessive-Compulsive Scale (r = -0.57, p = 0.0058). These findings demonstrate the abnormal topological efficiency in the white matter networks
Efficient MATLAB computations with sparse and factored tensors.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)
2006-12-01
In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.
Hyperspectral Image Denoising Based on Tensor Group Sparse Representation
Directory of Open Access Journals (Sweden)
WANG Zhongmei
2017-05-01
Full Text Available A novel algorithm for hyperspectral image (HSI denoising is proposed based on tensor group sparse representation. A HSI is considering as 3 order tensor. First, a HSI is divided into small tensor blocks. Second, similar blocks are gathered into clusters, and then a tensor group sparse representation model is constructed based on every cluster. Through exploiting HSI spectral correlation and nonlocal similarity over space, the model constrained tensor group sparse representation can be decomposed into a series of unconstrained low-rank tensor approximation problems, which can be solved using the tensor decomposition technique. The experiment results on the synthetic and real hyperspectral remote sensing images demonstrate the effectiveness of the proposed approach.
Pre-Service Teachers' Free and Structured Mathematical Problem Posing
Silber, Steven; Cai, Jinfa
2017-01-01
This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing…
Correlators in tensor models from character calculus
Mironov, A.; Morozov, A.
2017-11-01
We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz) character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Correlators in tensor models from character calculus
Directory of Open Access Journals (Sweden)
A. Mironov
2017-11-01
Full Text Available We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Madsen, Niels Kristian; Godtliebsen, Ian H; Losilla, Sergio A; Christiansen, Ove
2018-01-14
A new implementation of vibrational coupled-cluster (VCC) theory is presented, where all amplitude tensors are represented in the canonical polyadic (CP) format. The CP-VCC algorithm solves the non-linear VCC equations without ever constructing the amplitudes or error vectors in full dimension but still formally includes the full parameter space of the VCC[n] model in question resulting in the same vibrational energies as the conventional method. In a previous publication, we have described the non-linear-equation solver for CP-VCC calculations. In this work, we discuss the general algorithm for evaluating VCC error vectors in CP format including the rank-reduction methods used during the summation of the many terms in the VCC amplitude equations. Benchmark calculations for studying the computational scaling and memory usage of the CP-VCC algorithm are performed on a set of molecules including thiadiazole and an array of polycyclic aromatic hydrocarbons. The results show that the reduced scaling and memory requirements of the CP-VCC algorithm allows for performing high-order VCC calculations on systems with up to 66 vibrational modes (anthracene), which indeed are not possible using the conventional VCC method. This paves the way for obtaining highly accurate vibrational spectra and properties of larger molecules.
Chang, Yu-Kai; Tsai, Jack Han-Chao; Wang, Chun-Chih; Chang, Erik Chihhung
2015-07-01
The aim of this study was to use diffusion tensor imaging (DTI) to characterize and compare microscopic differences in white matter integrity in the basal ganglia between elite professional athletes specializing in running and martial arts. Thirty-three young adults with sport-related skills as elite professional runners (n = 11) or elite professional martial artists (n = 11) were recruited and compared with non-athletic and healthy controls (n = 11). All participants underwent health- and skill-related physical fitness assessments. Fractional anisotropy (FA) and mean diffusivity (MD), the primary indices derived from DTI, were computed for five regions of interest in the bilateral basal ganglia, including the caudate nucleus, putamen, globus pallidus internal segment (GPi), globus pallidus external segment (GPe), and subthalamic nucleus. Results revealed that both athletic groups demonstrated better physical fitness indices compared with their control counterparts, with the running group exhibiting the highest cardiovascular fitness and the martial arts group exhibiting the highest muscular endurance and flexibility. With respect to the basal ganglia, both athletic groups showed significantly lower FA and marginally higher MD values in the GPi compared with the healthy control group. These findings suggest that professional sport or motor skill training is associated with changes in white matter integrity in specific regions of the basal ganglia, although these positive changes did not appear to depend on the type of sport-related motor skill being practiced.
Madsen, Niels Kristian; Godtliebsen, Ian H.; Losilla, Sergio A.; Christiansen, Ove
2018-01-01
A new implementation of vibrational coupled-cluster (VCC) theory is presented, where all amplitude tensors are represented in the canonical polyadic (CP) format. The CP-VCC algorithm solves the non-linear VCC equations without ever constructing the amplitudes or error vectors in full dimension but still formally includes the full parameter space of the VCC[n] model in question resulting in the same vibrational energies as the conventional method. In a previous publication, we have described the non-linear-equation solver for CP-VCC calculations. In this work, we discuss the general algorithm for evaluating VCC error vectors in CP format including the rank-reduction methods used during the summation of the many terms in the VCC amplitude equations. Benchmark calculations for studying the computational scaling and memory usage of the CP-VCC algorithm are performed on a set of molecules including thiadiazole and an array of polycyclic aromatic hydrocarbons. The results show that the reduced scaling and memory requirements of the CP-VCC algorithm allows for performing high-order VCC calculations on systems with up to 66 vibrational modes (anthracene), which indeed are not possible using the conventional VCC method. This paves the way for obtaining highly accurate vibrational spectra and properties of larger molecules.
Adaptive stochastic Galerkin FEM with hierarchical tensor representations
Eigel, Martin
2016-01-08
PDE with stochastic data usually lead to very high-dimensional algebraic problems which easily become unfeasible for numerical computations because of the dense coupling structure of the discretised stochastic operator. Recently, an adaptive stochastic Galerkin FEM based on a residual a posteriori error estimator was presented and the convergence of the adaptive algorithm was shown. While this approach leads to a drastic reduction of the complexity of the problem due to the iterative discovery of the sparsity of the solution, the problem size and structure is still rather limited. To allow for larger and more general problems, we exploit the tensor structure of the parametric problem by representing operator and solution iterates in the tensor train (TT) format. The (successive) compression carried out with these representations can be seen as a generalisation of some other model reduction techniques, e.g. the reduced basis method. We show that this approach facilitates the efficient computation of different error indicators related to the computational mesh, the active polynomial chaos index set, and the TT rank. In particular, the curse of dimension is avoided.
Directory of Open Access Journals (Sweden)
Zoë A. Englander
2015-01-01
Full Text Available Cerebral Palsy (CP refers to a heterogeneous group of permanent but non-progressive movement disorders caused by injury to the developing fetal or infant brain (Bax et al., 2005. Because of its serious long-term consequences, effective interventions that can help improve motor function, independence, and quality of life are critically needed. Our ongoing longitudinal clinical trial to treat children with CP is specifically designed to meet this challenge. To maximize the potential for functional improvement, all children in this trial received autologous cord blood transfusions (with order randomized with a placebo administration over 2 years in conjunction with more standard physical and occupational therapies. As a part of this trial, magnetic resonance imaging (MRI is used to improve our understanding of how these interventions affect brain development, and to develop biomarkers of treatment efficacy. In this report, diffusion tensor imaging (DTI and subsequent brain connectome analyses were performed in a subset of children enrolled in the clinical trial (n = 17, who all exhibited positive but varying degrees of functional improvement over the first 2-year period of the study. Strong correlations between increases in white matter (WM connectivity and functional improvement were demonstrated; however no significant relationships between either of these factors with the age of the child at time of enrollment were identified. Thus, our data indicate that increases in brain connectivity reflect improved functional abilities in children with CP. In future work, this potential biomarker can be used to help differentiate the underlying mechanisms of functional improvement, as well as to identify treatments that can best facilitate functional improvement upon un-blinding of the timing of autologous cord blood transfusions at the completion of this study.
Englander, Zoë A; Sun, Jessica; Laura Case; Mikati, Mohamad A; Kurtzberg, Joanne; Song, Allen W
2015-01-01
Cerebral Palsy (CP) refers to a heterogeneous group of permanent but non-progressive movement disorders caused by injury to the developing fetal or infant brain (Bax et al., 2005). Because of its serious long-term consequences, effective interventions that can help improve motor function, independence, and quality of life are critically needed. Our ongoing longitudinal clinical trial to treat children with CP is specifically designed to meet this challenge. To maximize the potential for functional improvement, all children in this trial received autologous cord blood transfusions (with order randomized with a placebo administration over 2 years) in conjunction with more standard physical and occupational therapies. As a part of this trial, magnetic resonance imaging (MRI) is used to improve our understanding of how these interventions affect brain development, and to develop biomarkers of treatment efficacy. In this report, diffusion tensor imaging (DTI) and subsequent brain connectome analyses were performed in a subset of children enrolled in the clinical trial (n = 17), who all exhibited positive but varying degrees of functional improvement over the first 2-year period of the study. Strong correlations between increases in white matter (WM) connectivity and functional improvement were demonstrated; however no significant relationships between either of these factors with the age of the child at time of enrollment were identified. Thus, our data indicate that increases in brain connectivity reflect improved functional abilities in children with CP. In future work, this potential biomarker can be used to help differentiate the underlying mechanisms of functional improvement, as well as to identify treatments that can best facilitate functional improvement upon un-blinding of the timing of autologous cord blood transfusions at the completion of this study.
Energy Technology Data Exchange (ETDEWEB)
Xia Zhicheng; Nguyen, Bao D.; La Mar, Gerd N. [University of California, Department of Chemistry (United States)
2000-06-15
The use of dipolar shifts as important constraints in refining molecular structure of paramagnetic metalloproteins by solution NMR is now well established. A crucial initial step in this procedure is the determination of the orientation of the anisotropic paramagnetic susceptibility tensor in the molecular frame which is generated interactively with the structure refinement. The use of dipolar shifts as constraints demands knowledge of the diamagnetic shift, which, however, is very often not directly and easily accessible. We demonstrate that temperature gradients of dipolar shifts can serve as alternative constraints for determining the orientation of the magnetic axes, thereby eliminating the need to estimate the diamagnetic shifts. This approach is tested on low-spin, ferric sperm whale cyanometmyoglobin by determining the orientation, anisotropies and anisotropy temperature gradients by the alternate routes of using dipolar shifts and dipolar shift gradients as constraints. The alternate routes ultimately lead to very similar orientation of the magnetic axes, magnetic anisotropies and magnetic anisotropy temperature gradients which, by inference, would lead to an equally valid description of the molecular structure. It is expected that the use of the dipolar shift temperature gradients, rather than the dipolar shifts directly, as constraints will provide an accurate shortcut in a solution structure determination of a paramagnetic metalloprotein.
Surgery in colored tensor models
Pérez-Sánchez, Carlos I.
2017-10-01
Rooted in group field theory and matrix models, random tensor models are a recent background-invariant approach to quantum gravity in arbitrary dimensions. Colored tensor models (CTM) generate random triangulated orientable (pseudo)-manifolds. We analyze, in low dimensions, which known spaces are triangulated by specific CTM interactions. As a tool, we develop the graph-encoded surgery that is compatible with the quantum-field-theory-structure and use it to prove that a single model, the complex φ4-interaction in rank- 2, generates all orientable 2-bordisms, thus, in particular, also all orientable, closed surfaces. We show that certain quartic rank- 3 CTM, the φ34 -theory, has as boundary sector all closed, possibly disconnected, orientable surfaces. Hence all closed orientable surfaces are cobordant via manifolds generated by the φ34 -theory.
Diffusion tensor optical coherence tomography
Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.
2018-01-01
In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.
Entangled scalar and tensor fluctuations during inflation
Energy Technology Data Exchange (ETDEWEB)
Collins, Hael; Vardanyan, Tereza [Department of Physics, Carnegie Mellon University,5000 Forbes Avenue, Pittsburgh, Pennsylvania (United States)
2016-11-29
We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with a simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.
Tensors and their applications
Islam, Nazrul
2006-01-01
About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces
Tensor network models of multiboundary wormholes
Peach, Alex; Ross, Simon F.
2017-05-01
We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement structure in holography. We extend this by quotienting the plane by discrete isometries to obtain models of the multiboundary states. We show that there are networks where the entanglement structure is purely bipartite, extending results obtained in the large temperature limit. We analyse the entanglement structure in a range of examples.
Orthogonal tensor decompositions
Energy Technology Data Exchange (ETDEWEB)
Tamara G. Kolda
2000-03-01
The authors explore the orthogonal decomposition of tensors (also known as multi-dimensional arrays or n-way arrays) using two different definitions of orthogonality. They present numerous examples to illustrate the difficulties in understanding such decompositions. They conclude with a counterexample to a tensor extension of the Eckart-Young SVD approximation theorem by Leibovici and Sabatier [Linear Algebra Appl. 269(1998):307--329].
Structuring and assessing large and complex decision problems using MCDA
DEFF Research Database (Denmark)
Barfod, Michael Bruhn
This paper presents an approach for the structuring and assessing of large and complex decision problems using multi-criteria decision analysis (MCDA). The MCDA problem is structured in a decision tree and assessed using the REMBRANDT technique featuring a procedure for limiting the number of pair...
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
Tensor Field Visualization in Geomechanics Applications
Hotz, I.; Feng, L.; Hamann, B.; Joy, K.; Manaker, D.; Billen, M. I.; Kellogg, L. H.
2004-12-01
, indicating compression, we obtain a dense compressed texture. By animating the various parameters of our technique, the impression of stretching, compressing and bending can be enhanced, or used to represent time-varying data sets. The method is based on two steps: first, we define a positive definite metric with the same topological structure as the tensor field; second, we visualize the resulting metric. Every principal direction is represented using line-integral convolution (LIC). Here, a white-noise texture is blurred according to the tensor field, resulting in a high correlation of pixels along the principal lines, whereas almost no correlation appears in directions perpendicular to these lines. The resulting visualizations are highly effective depictions of the principal direction behavior over the entire field. In each LIC image, the eigenvalues of every eigenvector field are used to define the free parameters of the underlaying noise image (density, spot size) and the convolution (length of a filter kernel). In addition to these three ``structural'' parameters, color intensity can be used to enhance the impression of compression and stretching. We use a continuous color mapping, ranging from red for the smallest negative eigenvalues, white for zero eigenvalues, to green for largest positive eigenvalues. Finally, the resulting LIC images are overlaid to generate the fabric-like texture.
Gong, Changfei; Han, Ce; Gan, Guanghui; Deng, Zhenxiang; Zhou, Yongqiang; Yi, Jinling; Zheng, Xiaomin; Xie, Congying; Jin, Xiance
2017-04-01
Dynamic myocardial perfusion CT (DMP-CT) imaging provides quantitative functional information for diagnosis and risk stratification of coronary artery disease by calculating myocardial perfusion hemodynamic parameter (MPHP) maps. However, the level of radiation delivered by dynamic sequential scan protocol can be potentially high. The purpose of this work is to develop a pre-contrast normal-dose scan induced structure tensor total variation regularization based on the penalized weighted least-squares (PWLS) criteria to improve the image quality of DMP-CT with a low-mAs CT acquisition. For simplicity, the present approach was termed as ‘PWLS-ndiSTV’. Specifically, the ndiSTV regularization takes into account the spatial-temporal structure information of DMP-CT data and further exploits the higher order derivatives of the objective images to enhance denoising performance. Subsequently, an effective optimization algorithm based on the split-Bregman approach was adopted to minimize the associative objective function. Evaluations with modified dynamic XCAT phantom and preclinical porcine datasets have demonstrated that the proposed PWLS-ndiSTV approach can achieve promising gains over other existing approaches in terms of noise-induced artifacts mitigation, edge details preservation, and accurate MPHP maps calculation.
Roy, Bhaswati; Trivedi, Richa; Garg, Ravindra K; Gupta, Pradeep K; Tyagi, Ritu; Gupta, Rakesh K
2015-06-01
Vitamin B12 deficiency may cause neural tissue damage. Even in advanced stages, conventional imaging of brain usually appears normal in vitamin B12 deficient patients. The aim of this study was to assess the structural and functional changes in brain of patients with vitamin B12 deficiency before and after six weeks of vitamin B12 supplementation using diffusion tensor imaging and pseudo-continuous arterial spin labelling (PCASL). MR imaging including DTI and PCASL and neuropsychological tests (NPT) were performed in 16 patients with vitamin B12 deficiency and 16 controls before and after 6weeks of therapy. Cerebral blood flow (CBF) derived from PCASL and DTI indices was calculated in brain of patients with vitamin B12 deficiency and controls. Patient with vitamin B12 deficiency showed altered neuropsychological scores and altered CBF as well as fractional anisotropy (FA) values in various brain regions as compared with controls. Both CBF values and neuropsychological scores showed complete reversibility at 6weeks post therapy. Though FA values showed significant recovery, it failed to show complete recovery. Our results suggest that micro-structural recovery lags behind functional recovery in patients with vitamin B12 deficiency following therapy and CBF change may be used as an early predictor of complete recovery in patients with B12 deficiency. Copyright © 2015. Published by Elsevier Inc.
Problems in large-scale structural optimization
Arora, J. S.; Belegundu, A. D.
1984-01-01
A general design optimization model for large complex systems is defined. Major features of the model that challenge various optimization algorithms are discussed. Requirements of a model optimization algorithm are identified. Objectives of the study of various algorithms are defined and a basis for conducting such a study is developed. Primal as well as transformation methods are analytically studied and a unified viewpoint of various methods is presented. Several numerical examples are solved using different methods to study their performance. Conclusions drawn from the study are presented and discussed. Areas of future research in nonlinear programming as well as structural optimization are identified and discussed.
Constructibility Problems in Blast Resistant, Reinforced Concrete Structures
1992-08-01
34CONSTRUCTIBILITY PROBLEMS IN BLAST RESISTANT, REINFORCED CONCRETE STRUCTURES " Darrell D. Barker and Mark G. Whitney Wilfred Baker Engineering...Blast Resistant, Reinforced Concrete Structures 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER... concrete structures , problems result from an attempt to minimize element thickness by increasing bar sizes and decreasing spacing. This is normally done
Tensor calculus for engineers and physicists
de Souza Sánchez Filho, Emil
2016-01-01
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of N dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without need...
Directory of Open Access Journals (Sweden)
K. F. Komkov
2014-01-01
Full Text Available The mathematical model proposed earlier by the author for materials tensor which is due to nonlinearity of plastic changes, loss of the internal relations and the accumulation of damage to the structure, shows the consent of the theory with experimental data, for example, gray cast iron. The model was not able to accurately reflect the peculiarity of aluminum and other materials, which are anomalously high values of the ratio of the transverse deformation at plastic strength. Mentioned alloys currently attract the attention of many scientists who give with the help of metallographic analysis convincing evidence of the fact that internal processes include mechanisms "self-healing " defects.The objective is to improve the original model for gelatinous plastic materials. The analysis of experimental researches have shown that the tensor nonlinearity these environments attributed to the strong dependence of the volume deformations and medium voltage, as the level of strain and stress. For their description from the original equations (Reiner already allocated other equations for dilatancy. The latter, as a component of the volumetric strain, can be both positive and negative. This preserves the nonlinear coupling between the deviators. For more accurate descriptions of all the strains and stresses imposed additional options, since the dependence of the main characteristics and dilatancy of stress vary significantly. The material functions and all constants are defined makroelementa.It is shown that the parameter characterizing the process of self-organization patterns, is rapidly increasing function of the deformation. Changes also mean stress, reflecting the nonlinear growth of the number of additional connection with the decrease in volume deformations. It is possible to assume that such behavior of dilatancy in strain, close to destroy, can cause loss of balance between the dissipative process and the process of its self-organization and
Measuring Nematic Susceptibilities from the Elastoresistivity Tensor
Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian
The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.
Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.
Iwasaki, Tohru; Furukawa, Tetsuo
2016-05-01
In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.
Deep learning and the electronic structure problem
Mills, Kyle; Spanner, Michael; Tamblyn, Isaac
In the past decade, the fields of artificial intelligence and computer vision have progressed remarkably. Supported by the enthusiasm of large tech companies, as well as significant hardware advances and the utilization of graphical processing units to accelerate computations, deep neural networks (DNN) are gaining momentum as a robust choice for many diverse machine learning applications. We have demonstrated the ability of a DNN to solve a quantum mechanical eigenvalue equation directly, without the need to compute a wavefunction, and without knowledge of the underlying physics. We have trained a convolutional neural network to predict the total energy of an electron in a confining, 2-dimensional electrostatic potential. We numerically solved the one-electron Schrödinger equation for millions of electrostatic potentials, and used this as training data for our neural network. Four classes of potentials were assessed: the canonical cases of the harmonic oscillator and infinite well, and two types of randomly generated potentials for which no analytic solution is known. We compare the performance of the neural network and consider how these results could lead to future advances in electronic structure theory.
Tensor analysis for physicists
Schouten, J A
1989-01-01
This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...
Martino, M; Magioncalda, P; Saiote, C; Conio, B; Escelsior, A; Rocchi, G; Piaggio, N; Marozzi, V; Huang, Z; Ferri, F; Amore, M; Inglese, M; Northoff, G
2016-10-01
The objective of the study was to investigate the relationship between structural connectivity (SC) and functional connectivity (FC) in the cingulum in bipolar disorder (BD) and its various phases. We combined resting-state functional magnetic resonance imaging and probabilistic tractographic diffusion tensor imaging to investigate FC and SC of the cingulum and its portions, the SC-FC relationship, and their correlations with clinical and neurocognitive measures on sustained attention in manic (n = 21), depressed (n = 20), and euthymic (n = 20) bipolar patients and healthy controls (HC) (n = 42). First, we found decreased FC between the anterior and posterior parts of the cingulum in manic patients when compared to depressed patients and HC. Second, we observed decreased SC of the cingulum bundle, particularly in its anterior part, in manic patients when compared to HC. Finally, alterations in the cingulum FC (but not SC) correlated with clinical severity scores while changes in the cingulum SC (but not FC) were related with neurocognitive deficits in sustained attention in BD. We demonstrate for the first time a reduction in FC and concomitantly in SC of the cingulum in mania, which correlated with psychopathological and neurocognitive parameters, respectively, in BD. This supports the central role of cingulum connectivity specifically in mania. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Tensors, relativity, and cosmology
Dalarsson, Mirjana
2015-01-01
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...
Structural qualia: a solution to the hard problem of consciousness
Directory of Open Access Journals (Sweden)
Kristjan eLoorits
2014-03-01
Full Text Available The hard problem of consciousness has been often claimed to be unsolvable by the methods of traditional empirical sciences. It has been argued that all the objects of empirical sciences can be fully analyzed in structural terms but that consciousness is (or has something over and above its structure. However, modern neuroscience has introduced a theoretical framework in which also the apparently non-structural aspects of consciousness, namely the so called qualia or qualitative properties, can be analyzed in structural terms. That framework allows us to see qualia as something compositional with internal structures that fully determine their qualitative nature. Moreover, those internal structures can be identified which certain neural patterns. Thus consciousness as a whole can be seen as a complex neural pattern that misperceives some of its own highly complex structural properties as monadic and qualitative. Such neural pattern is analyzable in fully structural terms and thereby the hard problem is solved.
Scalable Tensor Factorizations with Missing Data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G.
2010-01-01
is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram...
Topology optimization of fluid-structure-interaction problems in poroelasticity
DEFF Research Database (Denmark)
Andreasen, Casper Schousboe; Sigmund, Ole
2013-01-01
This paper presents a method for applying topology optimization to fluid-structure interaction problems in saturated poroelastic media. The method relies on a multiple-scale method applied to periodic media. The resulting model couples the Stokes flow in the pores of the structure with the deform......This paper presents a method for applying topology optimization to fluid-structure interaction problems in saturated poroelastic media. The method relies on a multiple-scale method applied to periodic media. The resulting model couples the Stokes flow in the pores of the structure...... with the deformation of the elastic skeleton through a macroscopic Darcy-type flow law. The method allows to impose pressure loads for static problems through a one way coupling, while transient problems are fully coupled modeling the interaction between fluid and solid. The material distribution is determined...
Directory of Open Access Journals (Sweden)
Chetsadaporn Promteangtrong
Full Text Available ABSTRACT The authors make a complete review of the potential clinical applications of traditional and novel magnetic resonance imaging (MRI techniques in the evaluation of patients with Alzheimer's disease, including structural MRI, functional MRI, diffusion tension imaging and magnetization transfer imaging.
TENSOR MODELING BASED FOR AIRBORNE LiDAR DATA CLASSIFICATION
Directory of Open Access Journals (Sweden)
N. Li
2016-06-01
Full Text Available Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on tensor decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the “raw” data attributes. Then, the feature rasters of LiDAR data are stored as a tensor, and tensor decomposition is used to select component features. This tensor representation could keep the initial spatial structure and insure the consideration of the neighborhood. Based on a small number of component features a k nearest neighborhood classification is applied.
Specificity and structure of regional security control information support problem
Masloboev A. V.; Putilov V. A.
2015-01-01
The paper deals with system analysis of problems of regional economy information security and methods for their solutions at various stages of the crisis situation life-cycle. Specificity and structure of control problems of regional security in the economy as an object of information support have been considered. A set of decision-making information support problems occurred at the strategic, tactical and operational levels of regional security management has been defined. The information su...
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables....... Exploiting this duality, we propose necessary and sufficient conditions for the existence of such a decomposition of a given rank, using the properties of Hankel (and quasi-Hankel) matrices, derived from multivariate polynomials and normal form computations. This leads to the resolution of systems...
Applicability Problem in Optimum Reinforced Concrete Structures Design
Directory of Open Access Journals (Sweden)
Ashara Assedeq
2016-01-01
Full Text Available Optimum reinforced concrete structures design is very complex problem, not only considering exactness of calculus but also because of questionable applicability of existing methods in practice. This paper presents the main theoretical mathematical and physical features of the problem formulation as well as the review and analysis of existing methods and solutions considering their exactness and applicability.
Stability Operations: Ill-Structured Problems, Stakeholders, and Gaining Consensus
2011-05-19
Tom Ritchey , “Wicked Problems: Structuring Social Messes with Morphological Analysis,” Swedish Morphological Society, http://www.swemorph.com/wp.html...six coping techniques for dealing with wicked problems. 54 50 Tom Ritchey , “General...a continuous assessment of the environment is required to analyze possible unintended effects elsewhere in the environment. 51 Ritchey , “Wicked
The tensor network theory library
Al-Assam, S.; Clark, S. R.; Jaksch, D.
2017-09-01
In this technical paper we introduce the tensor network theory (TNT) library—an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org.
Optimal neighbor graph-based orthogonal tensor locality preserving projection for image recognition
Yuan, Sen; Mao, Xia
2016-11-01
As a typical multilinear dimensionality reduction (DR) method, tensor locality preserving projection (TLPP) has been successfully applied in many practical problems. However, TLPP depends mainly on preserving its local neighbor graph which often suffers from the following issues: (1) the neighbor graph is constructed with the Euclidean distance which fails to consider the relationships among different coordinates for tensor data; (2) the affinity matrix only focuses on the local structure information of samples while ignoring the existing label information; (3) the projection matrices are nonorthogonal, thus it is difficult to preserve the local manifold structure. To address these problems, a multilinear DR algorithm called optimal neighbor graph-based orthogonal tensor locality preserving projection (OG-OTLPP) is proposed. In OG-OTLPP, an optimal neighbor graph is first built according to tensor distance. Then the affinity matrix of data is defined by utilizing both the label information and the intrinsic local geometric properties of the data. Finally, in order to improve the manifold preserving ability, an efficient and stable scheme is designed to iteratively learn the orthogonal projections. We evaluate the proposed algorithm by applying it to image recognition. The experimental results on five public image databases demonstrate the effectiveness of our algorithm.
Aligning Structured and Unstructured Medical Problems Using UMLS.
Carlo, Lorena; Chase, Herbert S; Weng, Chunhua
2010-11-13
This paper reports a pilot study to align medical problems in structured and unstructured EHR data using UMLS. A total of 120 medical problems in discharge summaries were extracted using NLP software (MedLEE) and aligned with 87 ICD-9 diagnoses for 19 non-overlapping hospital visits of 4 patients. The alignment accuracy was evaluated by a medical doctor. The average overlap of medical problems between the two data sources obtained by our automatic alignment method was 23.8%, which was about half of the manual review result, 43.56%. We discuss the implications for related research in integrating structured and unstructured EHR data.
Energy Technology Data Exchange (ETDEWEB)
Huber, M. [Institut fuer Organische Chemie, FU Berlin, Berlin (Germany); Toerring, J.T.; Plato, M.; Moebius, K. [Institut fuer Experimentalphysik, FU Berlin, Berlin (Germany); Fink, U.; Lubitz, W. [Max-Volmer Institut, TU Berlin, Berlin (Germany); Feick, R. [Max-Planck-Institut fuer Biochemie, Martinsried (Germany); Schenck, C.C. [Department of Biochemistry, Colorado State University, Fort Collins (United States)
1995-08-01
Cation radicals of the primary electron donor (D{sup +}) in bacterial photosynthesis were investigated by high field, high frequency (95 GHz) EPR. Measurements on frozen solutions of D{sup +}, a dimeric {pi}-cation radical, of various organisms (Rps. viridis, Rb. sphaeroides, Chloroflexus aurantiacus and a heterodimer mutant) are reported, revealing differences in the principal values of the G-tensor. Elements of a theory relating the magnitudes of G principal values to the electronic structure are discussed
Specificity and structure of regional security control information support problem
Directory of Open Access Journals (Sweden)
Masloboev A. V.
2015-09-01
Full Text Available The paper deals with system analysis of problems of regional economy information security and methods for their solutions at various stages of the crisis situation life-cycle. Specificity and structure of control problems of regional security in the economy as an object of information support have been considered. A set of decision-making information support problems occurred at the strategic, tactical and operational levels of regional security management has been defined. The information support problem-solving unified methodological and instrumental framework of regional security has been proposed
Jenkins, Samantha; Blancafort, Lluís; Kirk, Steven R; Bearpark, Michael J
2014-04-21
New insights into the double bond isomerization of fulvene in the ground and excited electronic states are provided by newly developed QTAIM and stress tensor tools. The S0 and S1 states follow the 'biradical' torsion model, but the double bond is stiffer in the S0 state; by contrast, the S2 state follows the 'zwitterionic' torsion. Differences are explained in terms of the ellipticity and bond critical point (BCP) stiffness for both QTAIM and the stress tensor. Overall, the wave-function based analysis is found to be in agreement with the work of Bonačić-Koutecký and Michl that the bond-twisted species can have biradical or zwitterionic character, depending on the state. Using QTAIM and the stress tensor a new understanding of bond torsion is revealed; the electronic charge density around the twisted bond is found not to rotate in concert with the nuclei of the rotated -CH2 methylene group. The ability to visualize how the bond stiffness varies between individual electronic states and how this correlates with the QTAIM and stress tensor bond stiffness is highlighted. In addition, the most and least preferred morphologies of bond-path torsion are visualized. Briefly we discuss the prospects for using this new QTAIM and stress tensor analysis for excited state chemistry.
Energy Technology Data Exchange (ETDEWEB)
Alsing, Paul M; McDonald, Jonathan R [Information Directorate, Air Force Research Laboratory, Rome, NY 13441 (United States); Miller, Warner A, E-mail: jonathan.mcdonald.ctr@rl.af.mil [Department of Physics, Florida Atlantic University, Boca Raton, FL 33431 (United States)
2011-08-07
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area-an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.
Black holes with surrounding matter in scalar-tensor theories.
Cardoso, Vitor; Carucci, Isabella P; Pani, Paolo; Sotiriou, Thomas P
2013-09-13
We uncover two mechanisms that can render Kerr black holes unstable in scalar-tensor gravity, both associated with the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar. Our results highlight the importance of understanding the structure of spacetime in realistic, astrophysical black holes in scalar-tensor theories.
Heller, Patricia; Hollabaugh, Mark
1992-07-01
A supportive environment based on cooperative grouping was developed to foster students' learning of an effective problem-solving strategy. Experiments to adapt the technique of cooperative grouping to physics problem solving were carried out in two diverse settings: a large introductory course at state university, and a small modern physics class at a community college. Groups were more likely to use an effective problem-solving strategy when given context-rich problems to solve than when given standard textbook problems. Well-functioning cooperative groups were found to result from specific structural and management procedures governing group members' interactions. Group size, the gender and ability composition of groups, seating arrangement, role assignment, textbook use, and group as well as individual testing were all found to contribute to the problem-solving performance of cooperative groups.
Chen, Yasheng; Zhu, Hongtu; An, Hongyu; Armao, Diane; Shen, Dinggang; Gilmore, John H; Lin, Weili
2014-03-01
The aim of this study was to characterize the maturational changes of the three eigenvalues (λ1 ≥ λ2 ≥ λ3) of diffusion tensor imaging (DTI) during early postnatal life for more insights into early brain development. In order to overcome the limitations of using presumed growth trajectories for regression analysis, we employed Multivariate Adaptive Regression Splines (MARS) to derive data-driven growth trajectories for the three eigenvalues. We further employed Generalized Estimating Equations (GEE) to carry out statistical inferences on the growth trajectories obtained with MARS. With a total of 71 longitudinal datasets acquired from 29 healthy, full-term pediatric subjects, we found that the growth velocities of the three eigenvalues were highly correlated, but significantly different from each other. This paradox suggested the existence of mechanisms coordinating the maturations of the three eigenvalues even though different physiological origins may be responsible for their temporal evolutions. Furthermore, our results revealed the limitations of using the average of λ2 and λ3 as the radial diffusivity in interpreting DTI findings during early brain development because these two eigenvalues had significantly different growth velocities even in central white matter. In addition, based upon the three eigenvalues, we have documented the growth trajectory differences between central and peripheral white matter, between anterior and posterior limbs of internal capsule, and between inferior and superior longitudinal fasciculus. Taken together, we have demonstrated that more insights into early brain maturation can be gained through analyzing eigen-structural elements of DTI.
McKenna, Benjamin S; Theilmann, Rebecca J; Sutherland, Ashley N; Eyler, Lisa T
2015-05-01
Evidence for abnormal brain function as measured with diffusion tensor imaging (DTI) and functional magnetic resonance imaging (fMRI) and cognitive dysfunction have been observed in inter-episode bipolar disorder (BD) patients. We aimed to create a joint statistical model of white matter integrity and functional response measures in explaining differences in working memory and processing speed among BD patients. Medicated inter-episode BD (n=26; age=45.2±10.1 years) and healthy comparison (HC; n=36; age=46.3±11.5 years) participants completed 51-direction DTI and fMRI while performing a working memory task. Participants also completed a processing speed test. Tract-based spatial statistics identified common white matter tracts where fractional anisotropy was calculated from atlas-defined regions of interest. Brain responses within regions of interest activation clusters were also calculated. Least angle regression was used to fuse fMRI and DTI data to select the best joint neuroimaging predictors of cognitive performance for each group. While there was overlap between groups in which regions were most related to cognitive performance, some relationships differed between groups. For working memory accuracy, BD-specific predictors included bilateral dorsolateral prefrontal cortex from fMRI, splenium of the corpus callosum, left uncinate fasciculus, and bilateral superior longitudinal fasciculi from DTI. For processing speed, the genu and splenium of the corpus callosum and right superior longitudinal fasciculus from DTI were significant predictors of cognitive performance selectively for BD patients. BD patients demonstrated unique brain-cognition relationships compared to HC. These findings are a first step in discovering how interactions of structural and functional brain abnormalities contribute to cognitive impairments in BD.
Spacetime Encodings III - Second Order Killing Tensors
Brink, Jeandrew
2009-01-01
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 of 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...
On some fundamental properties of structural topology optimization problems
DEFF Research Database (Denmark)
Stolpe, Mathias
2010-01-01
We study some fundamental mathematical properties of discretized structural topology optimization problems. Either compliance is minimized with an upper bound on the volume of the structure, or volume is minimized with an upper bound on the compliance. The design variables are either continuous...... or 0–1. We show, by examples which can be solved by hand calculations, that the optimal solutions to the problems in general are not unique and that the discrete problems possibly have inactive volume or compliance constraints. These observations have immediate consequences on the theoretical...... convergence properties of penalization approaches based on material interpolation models. Furthermore, we illustrate that the optimal solutions to the considered problems in general are not symmetric even if the design domain, the external loads, and the boundary conditions are symmetric around an axis...
Gogny interactions with tensor terms
Energy Technology Data Exchange (ETDEWEB)
Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)
2016-07-15
We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)
The damper placement problem for large flexible space structures
Kincaid, Rex K.
1992-01-01
The damper placement problem for large flexible space truss structures is formulated as a combinatorial optimization problem. The objective is to determine the p truss members of the structure to replace with active (or passive) dampers so that the modal damping ratio is as large as possible for all significant modes of vibration. Equivalently, given a strain energy matrix with rows indexed on the modes and the columns indexed on the truss members, we seek to find the set of p columns such that the smallest row sum, over the p columns, is maximized. We develop a tabu search heuristic for the damper placement problems on the Controls Structures Interaction (CSI) Phase 1 Evolutionary Model (10 modes and 1507 truss members). The resulting solutions are shown to be of high quality.
Multidimensional seismic data reconstruction using tensor analysis
Kreimer, Nadia
Exploration seismology utilizes the seismic wavefield for prospecting oil and gas. The seismic reflection experiment consists on deploying sources and receivers in the surface of an area of interest. When the sources are activated, the receivers measure the wavefield that is reflected from different subsurface interfaces and store the information as time-series called traces or seismograms. The seismic data depend on two source coordinates, two receiver coordinates and time (a 5D volume). Obstacles in the field, logistical and economical factors constrain seismic data acquisition. Therefore, the wavefield sampling is incomplete in the four spatial dimensions. Seismic data undergoes different processes. In particular, the reconstruction process is responsible for correcting sampling irregularities of the seismic wavefield. This thesis focuses on the development of new methodologies for the reconstruction of multidimensional seismic data. This thesis examines techniques based on tensor algebra and proposes three methods that exploit the tensor nature of the seismic data. The fully sampled volume is low-rank in the frequency-space domain. The rank increases when we have missing traces and/or noise. The methods proposed perform rank reduction on frequency slices of the 4D spatial volume. The first method employs the Higher-Order Singular Value Decomposition (HOSVD) immersed in an iterative algorithm that reinserts weighted observations. The second method uses a sequential truncated SVD on the unfoldings of the tensor slices (SEQ-SVD). The third method formulates the rank reduction problem as a convex optimization problem. The measure of the rank is replaced by the nuclear norm of the tensor and the alternating direction method of multipliers (ADMM) minimizes the cost function. All three methods have the interesting property that they are robust to curvature of the reflections, unlike many reconstruction methods. Finally, we present a comparison between the methods
Topology optimization of coated structures and material interface problems
DEFF Research Database (Denmark)
Clausen, Anders; Aage, Niels; Sigmund, Ole
2015-01-01
This paper presents a novel method for including coated structures and prescribed material interface properties into the minimum compliance topology optimization problem. Several elements of the method are applicable to a broader range of interface problems. The approach extends the standard SIMP...... method by including the normalized norm of the spatial gradient of the design field into the material interpolation function, enforcing coating material at interfaces by attributing particular properties. The length scales of the base structure and the coating are separated by introducing a two...
Brown, Eric
2008-10-01
Some of the most beautiful and complex theories in physics are formulated in the language of tensors. While powerful, these methods are sometimes daunting to the uninitiated. I will introduce the use of Clifford Algebra as a practical alternative to the use of tensors. Many physical quantities can be represented in an indexless form. The boundary between the classical and the quantum worlds becomes a little more transparent. I will review some key concepts, and then talk about some of the things that I am doing with this interesting and powerful tool. Of note to some will be the development of rigid body dynamics for a game engine. Others may be interested in expressing the connection on a spin bundle. My intent is to prove to the audience that there exists an accessible mathematical tool that can be employed to probe the most difficult of topics in physics.
A Memetic Algorithm for 3-D Protein Structure Prediction Problem.
Correa, Leonardo; Borguesan, Bruno; Farfan, Camilo; Inostroza-Ponta, Mario; Dorn, Marcio
2016-12-02
Memetic Algorithms are population-based metaheuristics intrinsically concerned with exploiting all available knowledge about the problem under study. The incorporation of problem domain knowledge is not an optional mechanism, but a fundamental feature of the Memetic Algorithms. In this paper, we present a Memetic Algorithm to tackle the three-dimensional protein structure prediction problem. The method uses a structured population and incorporates a Simulated Annealing algorithm as a local search strategy, as well as ad-hoc crossover and mutation operators to deal with the problem. It takes advantage of structural knowledge stored in the Protein Data Bank, by using an Angle Probability List that helps to reduce the search space and to guide the search strategy. The proposed algorithm was tested on nineteen protein sequences of amino acid residues, and the results show the ability of the algorithm to find native-like protein structures. Experimental results have revealed that the proposed algorithm can find good solutions regarding root-mean-square deviation and global distance total score test in comparison with the experimental protein structures. We also show that our results are comparable in terms of folding organization with state-of-the-art prediction methods, corroborating the effectiveness of our proposal.
Alsing, Paul M; Miller, Warner A; 10.1088/0264-9381/28/15/155007
2011-01-01
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-linear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher-dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of ...
Sparse tensor discriminant analysis.
Lai, Zhihui; Xu, Yong; Yang, Jian; Tang, Jinhui; Zhang, David
2013-10-01
The classical linear discriminant analysis has undergone great development and has recently been extended to different cases. In this paper, a novel discriminant subspace learning method called sparse tensor discriminant analysis (STDA) is proposed, which further extends the recently presented multilinear discriminant analysis to a sparse case. Through introducing the L1 and L2 norms into the objective function of STDA, we can obtain multiple interrelated sparse discriminant subspaces for feature extraction. As there are no closed-form solutions, k-mode optimization technique and the L1 norm sparse regression are combined to iteratively learn the optimal sparse discriminant subspace along different modes of the tensors. Moreover, each non-zero element in each subspace is selected from the most important variables/factors, and thus STDA has the potential to perform better than other discriminant subspace methods. Extensive experiments on face databases (Yale, FERET, and CMU PIE face databases) and the Weizmann action database show that the proposed STDA algorithm demonstrates the most competitive performance against the compared tensor-based methods, particularly in small sample sizes.
Quantum engineering of superconducting structures: Principles, promise and problems
Zagoskin, Alexandre
2017-07-01
Quantum technologies went through an explosive development since the beginning of the century. The progress in the field of superconducting quantum structures was especially fast. As the result, the design and characterization of large quantum coherent structures became an engineering problem. We will discuss the current status of the emerging discipline of quantum engineering and possible ways of meeting its main challenge, the fundamental impossibility of an efficient modelling of a quantum system using classical means.
Solution of Confined Seepage Problems below Hydraulic Structures ...
African Journals Online (AJOL)
Confined seepage problems below hydraulic structures using finite element method are investigated. The foundations are assumed to be infinite with homogeneous and isotropic conditions. Three different types of elements with varying mesh sizes are used for comparing the finite element results with those of exact ...
Structural analysis for diagnosis with application to ship propulsion problem
DEFF Research Database (Denmark)
Izadi-Zamanabadi, Roozbeh; Blanke, Mogens
2002-01-01
Aiming at design of algorithms for fault diagnosis, structural analysis of systems offers concise yet easy overall analysis. Graph-based matching, which is the essential tech-nique to obtain redundant information for diagnosis, is reconsidered in this paper. Matching is reformulated as a problem...
Structural Analysis for Diagnosis - the Matching Problem Revisited
DEFF Research Database (Denmark)
Izadi-Zamanabadi, Roozbeh; Blanke, Mogens
2002-01-01
Aiming at design of algorithms for fault diagnosis, structural analysis of systems offers concise yet easy overall analysis. Graph-based matching, which is the essential technique to obtain redundant information for diagnosis, is re-considered in this paper. Matching is re-formulated as a problem...
Structured Sparsity Regularization Approach to the EEG Inverse Problem
DEFF Research Database (Denmark)
Montoya-Martinez, Jair; Artes-Rodriguez, Antonio; Hansen, Lars Kai
2012-01-01
Localization of brain activity involves solving the EEG inverse problem, which is an undetermined ill-posed problem. We propose a novel approach consisting in estimating, using structured sparsity regularization techniques, the Brain Electrical Sources (BES) matrix directly in the spatio......-temporal source space. We use proximal splitting optimization methods, which are efficient optimization techniques, with good convergence rates and with the ability to handle large nonsmooth convex problems, which is the typical scenario in the EEG inverse problem. We have evaluated our approach under a simulated...... scenario, consisting in estimating a synthetic BES matrix with 5124 sources. We report results using ℓ1 (LASSO), ℓ1/ℓ2 (Group LASSO) and ℓ1 + ℓ1/ℓ2 (Sparse Group LASSO) regularizers....
Quantum inferring acausal structures and the Monty Hall problem
Kurzyk, Dariusz; Glos, Adam
2016-12-01
This paper presents a quantum version of the Monty Hall problem based upon the quantum inferring acausal structures, which can be identified with generalization of Bayesian networks. Considered structures are expressed in formalism of quantum information theory, where density operators are identified with quantum generalization of probability distributions. Conditional relations between quantum counterpart of random variables are described by quantum conditional operators. Presented quantum inferring structures are used to construct a model inspired by scenario of well-known Monty Hall game, where we show the differences between classical and quantum Bayesian reasoning.
Structural problems of mining region innovative development (Kuzbass, Western Siberia
Directory of Open Access Journals (Sweden)
Dotsenko Elena
2017-01-01
Full Text Available At present, the issues of overcoming the negative structural shift in Russian economy, accelerating economic growth, reducing technological and social- and-economic gap between Russia and the developed countries are strategically important. Modern structure of Russian economy which had been developed as a part of market model does not generate the innovative type of development. In this situation, mining regions, the structure of which was formed in the early 20th century and is represented by the extractive industries, are undergoing the greatest problems of innovative development. Therefore, despite high urbanization and industrial development level the economy of Kuzbass (Western Siberia, Russia is characterized by significant structural problems. They are associated with primary extractive nature of the regional industry, in which coal and iron ore, metallurgical and chemical industries dominate. They highly depend on Russian and global market of raw materials, widely use low-productive technologies, and they are characterized by high level of fixed capital depreciation and insufficient pace of innovative infrastructure development. The solution of the structural problems of economic development of mining region is connected with technological modernization of extractive industries and use of modern materials for the production of high-tech products.
Finite element solution of transient fluid-structure interaction problems
Everstine, Gordon C.; Cheng, Raymond S.; Hambric, Stephen A.
1991-01-01
A finite element approach using NASTRAN is developed for solving time-dependent fluid-structure interaction problems, with emphasis on the transient scattering of acoustic waves from submerged elastic structures. Finite elements are used for modeling both structure and fluid domains to facilitate the graphical display of the wave motion through both media. For the liquid, the use of velocity potential as the fundamental unknown results in a symmetric matrix equation. The approach is illustrated for the problem of transient scattering from a submerged elastic spherical shell subjected to an incident tone burst. The use of an analogy between the equations of elasticity and the wave equation of acoustics, a necessary ingredient to the procedure, is summarized.
Model reduction for optimization of structural-acoustic coupling problems
DEFF Research Database (Denmark)
Creixell Mediante, Ester; Jensen, Jakob Søndergaard; Brunskog, Jonas
2016-01-01
-acoustic coupling, for which two different approaches to constructing a modal reduction base are discussed. The efficiency and accuracy of the CMS and the MMR methods are strongly model-dependent; in this paper, they are compared for two optimization problems in the hearing aid context, where the MMR technique......Fully coupled structural-acoustic models of complex systems, such as those used in the hearing aid field, may have several hundreds of thousands of nodes. When there is a strong structure-acoustic interaction, performing optimization on one part requires the complete model to be taken into account......, which becomes highly time consuming since many iterations may be required. The use of model reduction techniques to speed up the computations is studied in this work. The Component Mode Synthesis (CMS) method and the Multi-Model Reduction (MMR) method are adapted for problems with structure...
Visualizing Tensor Normal Distributions at Multiple Levels of Detail.
Abbasloo, Amin; Wiens, Vitalis; Hermann, Max; Schultz, Thomas
2016-01-01
Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.
Dark energy in scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Moeller, J.
2007-12-15
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
A framework for solving ill-structured community problems
Keller, William Cotesworth
A multifaceted protocol for solving ill-structured community problems has been developed. It embodies the lessons learned from the past by refining and extending features of previous models from the systems thinkers, and the fields of behavioral decision making and creative problem solving. The protocol also embraces additional features needed to address the unique aspects of community decision situations. The essential elements of the protocol are participants from the community, a problem-solving process, a systems picture, a facilitator, a modified Delphi method of communications, and technical expertise. This interdisciplinary framework has been tested by a quasi experiment with a real world community problem (the high cost of electrical power on Long Island, NY). Results indicate the protocol can enable members of the community to understand a complicated, ill-structured problem and guide them to action to solve the issue. However, the framework takes time (over one year in the test case) and will be inappropriate for crises where quick action is needed.
Data Structures: Sequence Problems, Range Queries, and Fault Tolerance
DEFF Research Database (Denmark)
Jørgensen, Allan Grønlund
The focus of this dissertation is on algorithms, in particular data structures that give provably ecient solutions for sequence analysis problems, range queries, and fault tolerant computing. The work presented in this dissertation is divided into three parts. In Part I we consider algorithms for...... to assume that the algorithms themselves are in charge for dealing with memory faults. We investigate searching, sorting and counting algorithms and data structures that provably returns sensible information in spite of memory corruptions.......The focus of this dissertation is on algorithms, in particular data structures that give provably ecient solutions for sequence analysis problems, range queries, and fault tolerant computing. The work presented in this dissertation is divided into three parts. In Part I we consider algorithms...... by the constraints. Many variants and similar problems have been proposed leading to several dierent approaches and algorithms. We consider problems where the function is the sum of the elements in the sequence and the constraints only bound the length of the subsequences considered. We give optimal algorithms...
Mathematical theory of a relaxed design problem in structural optimization
Kikuchi, Noboru; Suzuki, Katsuyuki
1990-01-01
Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.
Malecki, A.; Potdevin, G.; Biernath, T.; Eggl, E.; Willer, K.; Lasser, T.; Maisenbacher, J.; Gibmeier, J.; Wanner, A.; Pfeiffer, F.
2014-02-01
Here we introduce a new concept for x-ray computed tomography that yields information about the local micro-morphology and its orientation in each voxel of the reconstructed 3D tomogram. Contrary to conventional x-ray CT, which only reconstructs a single scalar value for each point in the 3D image, our approach provides a full scattering tensor with multiple independent structural parameters in each volume element. In the application example shown in this study, we highlight that our method can visualize sub-pixel fiber orientations in a carbon composite sample, hence demonstrating its value for non-destructive testing applications. Moreover, as the method is based on the use of a conventional x-ray tube, we believe that it will also have a great impact in the wider range of material science investigations and in future medical diagnostics. The authors declare no competing financial interests.
The geomagnetic field gradient tensor
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Olsen, Nils
2012-01-01
of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination......We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...
Tensor norms and operator ideals
Defant, A; Floret, K
1992-01-01
The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer
Tensor Fusion Network for Multimodal Sentiment Analysis
Zadeh, Amir; Chen, Minghai; Poria, Soujanya; Cambria, Erik; Morency, Louis-Philippe
2017-01-01
Multimodal sentiment analysis is an increasingly popular research area, which extends the conventional language-based definition of sentiment analysis to a multimodal setup where other relevant modalities accompany language. In this paper, we pose the problem of multimodal sentiment analysis as modeling intra-modality and inter-modality dynamics. We introduce a novel model, termed Tensor Fusion Network, which learns both such dynamics end-to-end. The proposed approach is tailored for the vola...
Overview of recent advances in numerical tensor algebra
Bergqvist G.; Larsson E.G.
2010-01-01
We present a survey of some recent developments for decompositions of multi-way arrays or tensors, with special emphasis on results relevant for applications and modeling in signal processing. A central problem is how to find lowrank approximations of tensors, and we describe some new results, including numerical methods, algorithms and theory, for the higher order singular value decomposition (HOSVD) and the parallel factors expansion or canonical decomposition (CP expansion).
Asymptotic tensor rank of graph tensors: beyond matrix multiplication
M. Christandl (Matthias); P. Vrana (Péter); J. Zuiddam (Jeroen)
2016-01-01
textabstractWe present an upper bound on the exponent of the asymptotic behaviour of the tensor rank of a family of tensors defined by the complete graph on $k$ vertices. For $k\\geq4$, we show that the exponent per edge is at most 0.77, outperforming the best known upper bound on the exponent per
On some fundamental properties of structural topology optimization problems
DEFF Research Database (Denmark)
Stolpe, Mathias
2009-01-01
We study some fundamental mathematical properties of classical structural topology optimization problems. Either compliance is minimized with an upper bound on the volume of the structure, or volume is minimized with an upper bound on the compliance. The design variables are either continuous or 0......--1. We show, by examples which can be solved by hand calculations, that the optimal solutions in general are not unique and possibly do not have an active volume constraint. These observations have immediate consequences on the theoretical convergence properties of penalization approaches. Furthermore...
STRUCTURAL PROBLEMS IN HUNGARIAN AGRICULTURE AFTER THE POLITICAL TURNOVER
Directory of Open Access Journals (Sweden)
B VIZVÁRI
2003-10-01
Full Text Available The so-called socialist regime collapsed in Hungary in May 1990 with the first free elections. The new government immediately started to reorganize the country's agriculture, but unfortunately on a mainly ideological basis. The agriculture of Hungary had been a successful branch of the national economy in the 1970's and 1980's, because its structure, including the co-operation of large farms and smallholders, was very effectively adapted to the technological conditions and market opportunities of the time. The measures introduced in the early nineties by the new government destroyed this structure. The arable land was split up and became the property of many owners, and this way a lot of new farms of very small size emerged. International supermarket chains also appeared on the Hungarian market. They are a new factor of agri-business earlier unknown in Hungary, causing a lot of fears and several problems. Hungarian agriculture still lacks a stable structure, i.e. the sizes and owners of farms keep changing, the applied farming technology is not adapted to the new situation, the products possible to grow in a profitable way are not clearly identified, though it would be necessary in order to solve the problem of high unemployment experienced in rural areas. All these problems are analyzed in this paper and suggestions for the solution are made.
Tensor-based dynamic reconstruction method for electrical capacitance tomography
Lei, J.; Mu, H. P.; Liu, Q. B.; Li, Z. H.; Liu, S.; Wang, X. Y.
2017-03-01
Electrical capacitance tomography (ECT) is an attractive visualization measurement method, in which the acquisition of high-quality images is beneficial for the understanding of the underlying physical or chemical mechanisms of the dynamic behaviors of the measurement objects. In real-world measurement environments, imaging objects are often in a dynamic process, and the exploitation of the spatial-temporal correlations related to the dynamic nature will contribute to improving the imaging quality. Different from existing imaging methods that are often used in ECT measurements, in this paper a dynamic image sequence is stacked into a third-order tensor that consists of a low rank tensor and a sparse tensor within the framework of the multiple measurement vectors model and the multi-way data analysis method. The low rank tensor models the similar spatial distribution information among frames, which is slowly changing over time, and the sparse tensor captures the perturbations or differences introduced in each frame, which is rapidly changing over time. With the assistance of the Tikhonov regularization theory and the tensor-based multi-way data analysis method, a new cost function, with the considerations of the multi-frames measurement data, the dynamic evolution information of a time-varying imaging object and the characteristics of the low rank tensor and the sparse tensor, is proposed to convert the imaging task in the ECT measurement into a reconstruction problem of a third-order image tensor. An effective algorithm is developed to search for the optimal solution of the proposed cost function, and the images are reconstructed via a batching pattern. The feasibility and effectiveness of the developed reconstruction method are numerically validated.
Snap-Through Buckling Problem of Spherical Shell Structure
Directory of Open Access Journals (Sweden)
Sumirin Sumirin
2014-12-01
Full Text Available This paper presents results of a numerical study on the nonlinear behavior of shells undergoing snap-through instability. This research investigates the problem of snap-through buckling of spherical shells applying nonlinear finite element analysis utilizing ANSYS Program. The shell structure was modeled by axisymmetric thin shell of finite elements. Shells undergoing snap-through buckling meet with significant geometric change of their physical configuration, i.e. enduring large deflections during their deformation process. Therefore snap-through buckling of shells basically is a nonlinear problem. Nonlinear numerical operations need to be applied in their analysis. The problem was solved by a scheme of incremental iterative procedures applying Newton-Raphson method in combination with the known line search as well as the arc- length methods. The effects of thickness and depth variation of the shell is taken care of by considering their geometrical parameter l. The results of this study reveal that spherical shell structures subjected to pressure loading experience snap-through instability for values of l≥2.15. A form of ‘turn-back’ of the load-displacement curve took place at load levels prior to the achievement of the critical point. This phenomenon was observed for values of l=5.0 to l=7.0.
Structure of Matter An Introductory Course with Problems and Solutions
Rigamonti, Attilio
2007-01-01
This is the second edition of this textbook, the original of which was published in 2007. Initial undergraduate studies in physics are usually in an organized format devoted to elementary aspects, which is then followed by advanced programmes in specialized fields. A difficult task is to provide a formative introduction in the early period, suitable as a base for courses more complex, thus bridging the wide gap between elementary physics and topics pertaining to research activities. This textbook remains an endeavour toward that goal, and is based on a mixture of simplified institutional theory and solved problems. In this way, the hope is to provide physical insight, basic knowledge and motivation, without impeding advanced learning. The choice has been to limit the focus to key concepts and to those aspects most typical of atoms, molecules and compounds, by looking at the basic, structural components, without paying detailed attention to the properties possessed by them. Problems are intertwined with formal...
Structure of Matter An Introductory Course with Problems and Solutions
Rigamonti, Attilio
2009-01-01
This is the second edition of this textbook, the original of which was published in 2007. Initial undergraduate studies in physics are usually in an organized format devoted to elementary aspects, which is then followed by advanced programmes in specialized fields. A difficult task is to provide a formative introduction in the early period, suitable as a base for courses more complex, thus bridging the wide gap between elementary physics and topics pertaining to research activities. This textbook remains an endeavour toward that goal, and is based on a mixture of simplified institutional theory and solved problems. In this way, the hope is to provide physical insight, basic knowledge and motivation, without impeding advanced learning. The choice has been to limit the focus to key concepts and to those aspects most typical of atoms, molecules and compounds, by looking at the basic, structural components, without paying detailed attention to the properties possessed by them. Problems are intertwined with formal...
Batch derivation of piezoresistive coefficient tensor by matrix algebra
Bao, Minhang; Huang, Yiping
2004-03-01
To commemorate the important discovery of the piezoresistance effect of germanium and silicon by C S Smith half a century ago, we present a new method of deriving the piezoresistive (PR) coefficient tensor for diamond structure material using matrix algebra. Using this method, all the components of the PR coefficient tensor (of the fourth rank) in an arbitrary Cartesian coordinate system can be obtained in a batch and the relation between the components is clearly shown.
Model reduction for optimization of structural-acoustic coupling problems
DEFF Research Database (Denmark)
Creixell Mediante, Ester; Jensen, Jakob Søndergaard; Brunskog, Jonas
2016-01-01
Fully coupled structural-acoustic models of complex systems, such as those used in the hearing aid field, may have several hundreds of thousands of nodes. When there is a strong structure-acoustic interaction, performing optimization on one part requires the complete model to be taken into account......-acoustic coupling, for which two different approaches to constructing a modal reduction base are discussed. The efficiency and accuracy of the CMS and the MMR methods are strongly model-dependent; in this paper, they are compared for two optimization problems in the hearing aid context, where the MMR technique...... is found to be the most efficient, speeding up the optimizations up to 6 times compared to the full model....
Structure of matter an introductory course with problems and solutions
Rigamonti, Attilio
2015-01-01
This textbook, now in its third edition, provides a formative introduction to the structure of matter that will serve as a sound basis for students proceeding to more complex courses, thus bridging the gap between elementary physics and topics pertaining to research activities. The focus is deliberately limited to key concepts of atoms, molecules and solids, examining the basic structural aspects without paying detailed attention to the related properties. For many topics the aim has been to start from the beginning and to guide the reader to the threshold of advanced research. This edition includes four new chapters dealing with relevant phases of solid matter (magnetic, electric and superconductive) and the related phase transitions. The book is based on a mixture of theory and solved problems that are integrated into the formal presentation of the arguments. Readers will find it invaluable in enabling them to acquire basic knowledge in the wide and wonderful field of condensed matter and to understand how ...
Obtaining orthotropic elasticity tensor using entries zeroing method.
Gierlach, Bartosz; Danek, Tomasz
2017-04-01
A generally anisotropic elasticity tensor obtained from measurements can be represented by a tensor belonging to one of eight material symmetry classes. Knowledge of symmetry class and orientation is helpful for describing physical properties of a medium. For each non-trivial symmetry class except isotropic this problem is nonlinear. A common method of obtaining effective tensor is a choosing its non-trivial symmetry class and minimizing Frobenius norm between measured and effective tensor in the same coordinate system. Global optimization algorithm has to be used to determine the best rotation of a tensor. In this contribution, we propose a new approach to obtain optimal tensor, with the assumption that it is orthotropic (or at least has a similar shape to the orthotropic one). In orthotropic form tensor 24 out of 36 entries are zeros. The idea is to minimize the sum of squared entries which are supposed to be equal to zero through rotation calculated with optimization algorithm - in this case Particle Swarm Optimization (PSO) algorithm. Quaternions were used to parametrize rotations in 3D space to improve computational efficiency. In order to avoid a choice of local minima we apply PSO several times and only if we obtain similar results for the third time we consider it as a correct value and finish computations. To analyze obtained results Monte-Carlo method was used. After thousands of single runs of PSO optimization, we obtained values of quaternion parts and plot them. Points concentrate in several points of the graph following the regular pattern. It suggests the existence of more complex symmetry in the analyzed tensor. Then thousands of realizations of generally anisotropic tensor were generated - each tensor entry was replaced with a random value drawn from normal distribution having a mean equal to measured tensor entry and standard deviation of the measurement. Each of these tensors was subject of PSO based optimization delivering quaternion for optimal
Potentials and problems in space applications of smart structures technology
Eaton, D. C.; Bashford, D. P.
1994-09-01
The well known addage 'don't run before you can walk emerging materials. It typically takes ten years before a material is sufficiently well characterized for commercial aerospace application. Much has to be learnt not only about the material properties and their susceptibility to the effects of their working environment but also about the manufacturing process and the most effective configuration related application. No project will accept a product which has no proven reliability and attractive cost effectiveness in its application. The writers firmly believe that smart structures and their related technologies must follow a similar development pattern. Indeed, faced with a range of interdisciplinary problems it seems likely that 'partially smart' techniques may well be the first applications. These will place emphasis on the more readily realizable features for any structural application. Prior use may well have been achieved in other engineering sectors. Because ground based applications are more readily accessible to check and maintain, these are generally the front runners of smart technology usage. Nevertheless, there is a strong potential for the use of smart techniques in space applications if their capabilities can be advantageously introduced when compared with traditional solutions. This paper endeavors to give a critical appraisal of the possibilities and the accompanying problems. A sample overview of related developing space technology is included. The reader is also referred to chapters 90 to 94 in ESA's Structural Materials Handbook (ESA PSS 03 203, issue 1.). It is envisaged that future space applications may include the realization and maintenance of large deployable reflector profiles, the dimensional stability of optical payloads, active noise and vibration control and in orbit health monitoring and control for largely unmanned spacecraft. The possibility of monitoring the health of items such as large cryogenic fuel tanks is a typical longer
A linear support higher-order tensor machine for classification.
Hao, Zhifeng; He, Lifang; Chen, Bingqian; Yang, Xiaowei
2013-07-01
There has been growing interest in developing more effective learning machines for tensor classification. At present, most of the existing learning machines, such as support tensor machine (STM), involve nonconvex optimization problems and need to resort to iterative techniques. Obviously, it is very time-consuming and may suffer from local minima. In order to overcome these two shortcomings, in this paper, we present a novel linear support higher-order tensor machine (SHTM) which integrates the merits of linear C-support vector machine (C-SVM) and tensor rank-one decomposition. Theoretically, SHTM is an extension of the linear C-SVM to tensor patterns. When the input patterns are vectors, SHTM degenerates into the standard C-SVM. A set of experiments is conducted on nine second-order face recognition datasets and three third-order gait recognition datasets to illustrate the performance of the proposed SHTM. The statistic test shows that compared with STM and C-SVM with the RBF kernel, SHTM provides significant performance gain in terms of test accuracy and training speed, especially in the case of higher-order tensors.
Generalized Slow Roll for Tensors
Hu, Wayne
2014-01-01
The recent BICEP2 detection of degree scale CMB B-mode polarization, coupled with a deficit of observed power in large angle temperature anisotropy, suggest that the slow-roll parameter $\\epsilon_H$, the fractional variation in the Hubble rate per efold, is both relatively large and may evolve from an even larger value on scales greater than the horizon at recombination. The relatively large tensor contribution implied also requires finite matching features in the tensor power spectrum for an...
The Role of Problem Structure in a Deductive Reasoning Task.
Griggs, Richard A.; Newstead, Stephen E.
1982-01-01
Four experiments were conducted to determine the source of difficulty of Wason's THOG problem. The THOG problem permits examination of the way people tackle a novel hypothetico-deductive problem. The results are interpreted as demonstrating the importance of problem presentation in problem solving. (Author/PN)
Numerical Methods of Solving Cauchy Problems with Contrast Structures
Directory of Open Access Journals (Sweden)
A. A. Belov
2016-01-01
Full Text Available Modern numerical methods allowing to solve contrast structure problems in the most efficient way are described. These methods include explicit-implicit Rosenbrock schemes with complex coefficients and fully implicit backward optimal Runge–Kutta schemes. As an integration argument, it is recommended to choose the length of the integral curve arc. This argument provides high reliability of the calculation and sufficiently decreases the complexity of computations for low-order systems. In order to increase the efficiency, we propose an automatic step selection algorithm based on curvature of the integral curve. This algorithm is as efficient as standard algorithms and has sufficiently larger reliability. We show that along with such an automatic step selection it is possible to calculate a posteriori asymptotically precise error estimation. Standard algorithms do not provide such estimations and their actual error quite often exceeds the user-defined tolerance by several orders. The applicability limitations of numerical methods are investigated. In solving superstiff problems, they sometimes do not provide satisfactory results. In such cases, it is recommended to imply approximate analytical methods. Consequently, numerical and analytical methods are complementary.
Development of the Tensoral Computer Language
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.
Direct solution of the Chemical Master Equation using quantized tensor trains.
Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph
2014-03-01
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 hp-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 storage
Direct solution of the Chemical Master Equation using quantized tensor trains.
Directory of Open Access Journals (Sweden)
Vladimir Kazeev
2014-03-01
Full Text Available 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 hp-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
Scalable tensor factorizations for incomplete data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; KOlda, Tamara G.
2011-01-01
experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 × 1000 × 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP......-WOPT on two real-world applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process....
Structuring students’ analogical reasoning in solving algebra problem
Lailiyah, S.; Nusantara, T.; Sa’dijah, C.; Irawan, E. B.; Kusaeri; Asyhar, A. H.
2018-01-01
The average achievement of Indonesian students’ mathematics skills according to Benchmark International Trends in Mathematics and Science Study (TIMSS) is ranked at the 38th out of 42 countries and according to the survey result in Program for International Student Assessment (PISA) is ranked at the 64th out of 65 countries. The low mathematics skill of Indonesian student has become an important reason to research more deeply about reasoning and algebra in mathematics. Analogical reasoning is a very important component in mathematics because it is the key to creativity and it can make the learning process in the classroom become effective. The major part of the analogical reasoning is about structuring including the processes of inferencing and decision-making happens. Those processes involve base domain and target domain. Methodologically, the subjects of this research were 42 students from class XII. The sources of data were derived from the results of thinks aloud, the transcribed interviews, and the videos taken while the subject working on the instruments and interviews. The collected data were analyzed using qualitative techniques. The result of this study described the structuring characteristics of students’ analogical reasoning in solving algebra problems from all the research subjects.
Research Projects in Physics: A Mechanism for Teaching Ill-Structured Problem Solving
Milbourne, Jeff; Bennett, Jonathan
2017-10-01
Physics education research has a tradition of studying problem solving, exploring themes such as physical intuition and differences between expert and novice problem solvers. However, most of this work has focused on traditional, or well-structured, problems, similar to what might appear in a textbook. Less work has been done with open-ended, or ill-structured, problems, similar to the types of problems students might face in their professional lives. Given the national discourse on educational system reform aligned with 21st century skills, including problem solving, it is critical to provide educational experiences that help students learn to solve all types of problems, including ill-structured problems.
Tensor renormalization group methods for spin and gauge models
Zou, Haiyuan
The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.
DEFF Research Database (Denmark)
Yoon, Gil Ho; Jensen, Jens Stissing; Sigmund, Ole
2007-01-01
The paper presents a gradient-based topology optimization formulation that allows to solve acoustic-structure (vibro-acoustic) interaction problems without explicit boundary interface representation. In acoustic-structure interaction problems, the pressure and displacement fields are governed...
A tensor-based dictionary learning approach to tomographic image reconstruction
DEFF Research Database (Denmark)
Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian
2016-01-01
with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images...
Akinobu, DOTE; Yoshiko, KANADA-EN'YO; Hisashi, HORIUCHI; Yoshinori, AKAISHI; Kiyomi, IKEDA; High Energy Accelerator Research Organization (KEK); Yukawa Institute for Theoretical Physics; Department of Physics, Kyoto University; College of Science and Technology, Nihon University; The Institute of Physical and Chemical Research (RIKEN)
2006-01-01
In order to treat the tensor force explicitly, we propose a microscopic model of nuclear structure based on antisymmetrized molecular dynamics (AMD). It is found that some extensions of the AMD method are effective for incorporating the tensor correlation into wave functions. Calculating the wave functions for deuteron, triton and He^4 with the extended version of AMD, we obtained solutions for which the contribution of the tensor force is large. By analyzing the wave function of He^4, it is ...
Seismic data interpolation and denoising by learning a tensor tight frame
Liu, Lina; Plonka, Gerlind; Ma, Jianwei
2017-10-01
Seismic data interpolation and denoising plays a key role in seismic data processing. These problems can be understood as sparse inverse problems, where the desired data are assumed to be sparsely representable within a suitable dictionary. In this paper, we present a new method based on a data-driven tight frame (DDTF) of Kronecker type (KronTF) that avoids the vectorization step and considers the multidimensional structure of data in a tensor-product way. It takes advantage of the structure contained in all different modes (dimensions) simultaneously. In order to overcome the limitations of a usual tensor-product approach we also incorporate data-driven directionality. The complete method is formulated as a sparsity-promoting minimization problem. It includes two main steps. In the first step, a hard thresholding algorithm is used to update the frame coefficients of the data in the dictionary; in the second step, an iterative alternating method is used to update the tight frame (dictionary) in each different mode. The dictionary that is learned in this way contains the principal components in each mode. Furthermore, we apply the proposed KronTF to seismic interpolation and denoising. Examples with synthetic and real seismic data show that the proposed method achieves better results than the traditional projection onto convex sets method based on the Fourier transform and the previous vectorized DDTF methods. In particular, the simple structure of the new frame construction makes it essentially more efficient.
Pitts, J Brian
2011-01-01
It is a commonplace that any theory can be written in any coordinates via tensor calculus. But it is claimed that spinors as such cannot be represented in coordinates in a curved space-time. What general covariance means for theories with fermions is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov (OP) constructed spinors in coordinates in 1965, helping to spawn nonlinear group representations. Locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient. The tetrad formalism is de-Ockhamized, with 6 extra fields and 6 compensating gauge symmetries. OP spinors, as developed nonperturbatively by Bilyalov, admit any coordinates at a point, but "time" must be listed first: the product of the metric components and the matrix diag(-1,1,1,1) must have no negative eigenvalues to yield a real symmetric square root function of the metric. Thus the admissible coordinates depend o...
Octupolar tensors for liquid crystals
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.
DEFF Research Database (Denmark)
Nielsen, Søren Føns Vind; Mørup, Morten
2014-01-01
Non-negative Tensor Factorization (NTF) has become a prominent tool for analyzing high dimensional multi-way structured data. In this paper we set out to analyze gene expression across brain regions in multiple subjects based on data from the Allen Human Brain Atlas [1] with more than 40 % data...... from all subjects the model based predictions are useful. When analyzing the structure of the components derived for one of the best predicting model orders the components identified in general constitute localized regions of the brain. Non-negative tensor factorization based on marginalization thus...... missing in our problem. Our analysis is based on the non-negativity constrained Canonical Polyadic (CP) decomposition where we handle the missing data using marginalization considering three prominent alternating least squares procedures; multiplicative updates, column-wise, and row-wise updating...
Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem
Aickelin, Uwe; Dowsland, Kathryn
2008-01-01
There is considerable interest in the use of genetic algorithms to solve problems arising in the areas of scheduling and timetabling. However, the classical genetic algorithm paradigm is not well equipped to handle the conflict between objectives and constraints that typically occurs in such problems. In order to overcome this, successful implementations frequently make use of problem specific knowledge. This paper is concerned with the development of a GA for a nurse rostering problem at a m...
Using Digital Mapping Tool in Ill-Structured Problem Solving
Bai, Hua
2013-01-01
Scaffolding students' problem solving and helping them to improve problem solving skills are critical in instructional design courses. This study investigated the effects of students' uses of a digital mapping tool on their problem solving performance in a design case study. It was found that the students who used the digital mapping tool…
Problem of Auroral Oval Mapping and Multiscale Auroral Structures
Antonova, Elizaveta; Stepanova, Marina; Kirpichev, Igor; Vovchenko, Vadim; Vorobjev, Viachislav; Yagodkina, Oksana
The problem of the auroral oval mapping to the equatorial plane is reanalyzed taking into account the latest results of the analysis of plasma pressure distribution at low altitudes and at the equatorial plane. Statistical pictures of pressure distribution at low latitudes are obtained using data of DMSP observations. We obtain the statistical pictures of pressure distribution at the equatorial plane using data of THEMIS mission. Results of THEMIS observations demonstrate the existence of plasma ring surrounding the Earth at geocentric distances from ~6 till ~12Re. Plasma pressure in the ring is near to isotropic and its averaged values are larger than 0.2 nPa. We take into account that isotropic plasma pressure is constant along the field line and that the existence of field-aligned potential drops in the region of the acceleration of auroral electrons leads to pressure decrease at low altitudes. We show that most part of quite time auroral oval does not map to the real plasma sheet. It maps to the surrounding the Earth plasma ring. We also show that transverse currents in the plasma ring are closed inside the magnetosphere forming the high latitude continuation of the ordinary ring current. The obtained results are used for the explanation of ring like form of the auroral oval. We also analyze the processes of the formation of multiscale auroral structures including thin auroral arcs and discuss the difficulties of the theories of alfvenic acceleration of auroral electrons.
Spectral Tensor-Train Decomposition
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.
2016-01-01
.e., the “cores”) comprising the functional TT decomposition. This result motivates an approximation scheme employing polynomial approximations of the cores. For functions with appropriate regularity, the resulting spectral tensor-train decomposition combines the favorable dimension-scaling of the TT......The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT...
Semantic Annotation of Complex Text Structures in Problem Reports
Malin, Jane T.; Throop, David R.; Fleming, Land D.
2011-01-01
Text analysis is important for effective information retrieval from databases where the critical information is embedded in text fields. Aerospace safety depends on effective retrieval of relevant and related problem reports for the purpose of trend analysis. The complex text syntax in problem descriptions has limited statistical text mining of problem reports. The presentation describes an intelligent tagging approach that applies syntactic and then semantic analysis to overcome this problem. The tags identify types of problems and equipment that are embedded in the text descriptions. The power of these tags is illustrated in a faceted searching and browsing interface for problem report trending that combines automatically generated tags with database code fields and temporal information.
One-loop tensor Feynman integral reduction with signed minors
DEFF Research Database (Denmark)
Fleischer, Jochem; Riemann, Tord; Yundin, Valery
2012-01-01
of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically......We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms...... of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application...
Tensor calculus for physics a concise guide
Neuenschwander, Dwight E
2015-01-01
Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...
The Lunar Internal Structure Model: Problems and Solutions
Nefedyev, Yuri; Gusev, Alexander; Petrova, Natalia; Varaksina, Natalia
The report is devoted the problems of the internal structure and gravitational field of the Moon. New data received from 14 newest instruments installed on low-orbit satellite Kaguya essentially enriched our knowledge of the Moon. Chinese satellite ChagE-1 and Indian Chandrayan-1 have demonstrated strong potential of China and India in the field of lunar research and obtained new data on gravitational field, mascons, crust, and geochemical composition of the circumlunar space. Internal structure of the Moon: There are some essential arguments in favor of existence of a small-sized Moon’s core made of metallic iron alloyed with a small amount of sulfur and/or oxygen, and availability of hot viscous lower mantle. Structure of gravitational field of the Moon, determined by the comparison of high-precision trajectory measurements by Lunar Prospector (1998- 1999) with the results of laser altimetry obtained by Clementine (1994), as well as with data sets of laser ranging of the Moon (1970-2006), assumes the presence of a metal core. Interpretation of the polar moment value within the framework of chemical, thermal and density models of lunar crust and mantle informed conclusions about the weight and size of the core. LLR analysis of dissipation of rotation of the Moon points at two possible sources of dissipation: monthly solid-state inflows and liquid core, rotation of which differs from viscous-elastic mantle. Liquid (melted) core has its unique impact on the Moon’s rotation. In particular, there are two force moments due to topographical and phase interaction at the boundary between liquid core and elastic mantle (CMB). Liquid core can rotate independently from solid mantle Selenoid satellites (SS) open new and most perspective opportunities in the study of gravitational field and the Moon’s figure. SSs “Moon 10”, “Apollo”, “Clementine”, “Lunar Prospector” trajectory tracking data processing has allowed for identification of coefficients in
De Corte, E.; And Others
One important finding from recent research on multiplication word problems is that children's performances are strongly affected by the nature of the multiplier (whether it is an integer, decimal larger than 1 or a decimal smaller than 1). On the other hand, the size of the multiplicand has little or no effect on problem difficulty. The aim of the…
The space generated by metric and torsion tensors, derivation of Einstein-Hilbert equation
Directory of Open Access Journals (Sweden)
Николай Иванович Яременко
2014-11-01
Full Text Available This paper is devoted to the derivation of field equations in space with the geometric structure generated by metric and torsion tensors. We also study the geometry of the space are generated jointly and agreed by the metric tensor and the torsion tensor. We showed that in such space the structure of the curvature tensor has special features and for this tensor obtained analog Ricci - Jacobi identity; was evaluated gap that occurs at the transition from the original to the image and vice versa, in the case of an infinitely small contours. We have researched the geodesic lines equation. We introduce the tensor π_αβ which is similar to the second fundamental tensor of hypersurfaces Y^n-1, but the structure of this tensor is substantially different from the case of Riemannian spaces with zero torsion. Then we obtained formulas which characterize the change of vectors in accompanying basis relative to this basis itself in the small. Taking into considerations our results about the structure of such space we derived from the variation principle the general field equations (electromagnetic and gravitational.
Hong, Jee Yun; Kim, Min Kyeong
2016-01-01
Ill-structured problems can be regarded as one of the measures that meet recent social needs emphasizing students' abilities to solve real-life problems. This study aimed to analyze the mathematical abstraction process in solving such problems, and to identify the mathematical abstraction level ([I] Recognition of mathematical structure through…
Interactive Volume Rendering of Diffusion Tensor Data
Energy Technology Data Exchange (ETDEWEB)
Hlawitschka, Mario; Weber, Gunther; Anwander, Alfred; Carmichael, Owen; Hamann, Bernd; Scheuermann, Gerik
2007-03-30
As 3D volumetric images of the human body become an increasingly crucial source of information for the diagnosis and treatment of a broad variety of medical conditions, advanced techniques that allow clinicians to efficiently and clearly visualize volumetric images become increasingly important. Interaction has proven to be a key concept in analysis of medical images because static images of 3D data are prone to artifacts and misunderstanding of depth. Furthermore, fading out clinically irrelevant aspects of the image while preserving contextual anatomical landmarks helps medical doctors to focus on important parts of the images without becoming disoriented. Our goal was to develop a tool that unifies interactive manipulation and context preserving visualization of medical images with a special focus on diffusion tensor imaging (DTI) data. At each image voxel, DTI provides a 3 x 3 tensor whose entries represent the 3D statistical properties of water diffusion locally. Water motion that is preferential to specific spatial directions suggests structural organization of the underlying biological tissue; in particular, in the human brain, the naturally occuring diffusion of water in the axon portion of neurons is predominantly anisotropic along the longitudinal direction of the elongated, fiber-like axons [MMM+02]. This property has made DTI an emerging source of information about the structural integrity of axons and axonal connectivity between brain regions, both of which are thought to be disrupted in a broad range of medical disorders including multiple sclerosis, cerebrovascular disease, and autism [Mos02, FCI+01, JLH+99, BGKM+04, BJB+03].
Automated hydraulic tensor for Total Knee Arthroplasty.
Marmignon, C; Leimnei, A; Lavallée, S; Cinquin, P
2005-12-01
To obtain a long lifespan of knee prosthesis, it is necessary to restore the alignment of the lower limb. In some cases of severe arthrosis, the ligament envelope of the joint may be deformed, inducing an asymmetric laxity once the lower limb is realigned. Because there is not yet unanimity regarding how to optimally measure or implement soft tissue balance, we provide a means to acquire a variety of measurements. In traditional surgery, the surgeon sometimes uses a "tensor", which acts like a forceps. This system was redesigned, instrumented, actuated, and integrated into a navigation system for orthopaedic surgery. Improving the perception of the surgeon, it helps him to address the ligament balancing problem. Our first prototype has been tested on sawbones before being validated in an experiment on two cadavers. In our first attempt, the surgeon was able to assess soft tissue balance but judged the device not powerful enough, which led us to develop a new more powerful hydraulic system. In this paper, we present our approach and the first results of the new hydraulic tensor which is currently in an integration process. Copyright 2005 John Wiley & Sons, Ltd.
Site symmetry and crystal symmetry: a spherical tensor analysis
Energy Technology Data Exchange (ETDEWEB)
Brouder, Christian; Juhin, Amelie; Bordage, Amelie; Arrio, Marie-Anne [Institut de Mineralogie et de Physique des Milieux Condenses, CNRS UMR 7590, Universites Paris 6 et 7, IPGP, 140 rue de Lourmel, 75015 Paris (France)], E-mail: christian.brouder@impmc.jussieu.fr
2008-11-12
The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of the electric dipole and quadrupole transitions in x-ray absorption spectroscopy. The main application of the formalism is the reduction of computation time in the calculation of the properties of crystals by band-structure methods. The general approach is illustrated by the examples of substitutional chromium in spinel and substitutional vanadium in garnet.
Testing a time-domain regional momtent tensor inversion program for large worldwide earthquakes
Richter, G.; Hoffmann, M.; Hanka, W.; Saul, J.
2009-04-01
After gaining an accurate source location and magnitude estimate of large earthquakes the direction of plate movement is the next important information for reliable hazard assessment. For this purpose rapid moment tensor inversions are necessary. In this study the time-domain moment tensor inversion program by Dreger (2001) is tested. This program for regional moment tensor solutions is applied to seismic data from regional stations of the GEOFON net and international cooperating partner networks (InaTEWS, IRIS, GEOFON Extended Virtual Network) to obtain moment tensor solutions for large earthquakes worldwide. The motivation of the study is to have rapid information on the plate motion direction for the verification of tsunami generation hazard by earthquakes. A special interest lies on the application in the Indonesian archipelago to integrate the program in German-Indonesian Tsunami Early Warning System (GITEWS). Performing the inversion on a single CPU of a normal PC most solutions are achieved within half an hour after origin time. The program starts automatically for large earthquakes detected by the seismic analysis tool SeisComP3 (Hanka et al, 2008). The data from seismic stations in the distance range up to 2000 km are selected, prepared and quality controlled. First the program searches the best automatic solution by varying the source depth. Testing different stations combinations for the inversion enables to identify the stability of the solution. For further optimization of the solution the interactive selection of available stations is facilitated. The results of over 200 events are compared to centroid moment tensor solutions from the Global CMT-Project, from MedNet/INGV and NEID to evaluate the accuracy of the results. The inversion in the time-domain is sensitive to uncertainties in the velocity model and in the source location. These resolution limits are visible in the waveform fits. Another reason for misfits are strong structural inhomogeneities
Representation of light pressure resultant force and moment as a tensor series
Nerovny, Nikolay; Zimin, Vladimir; Fedorchuk, Sergey; Golubev, Evgeny
2017-08-01
In this article, we address the problem of the determination of light pressure upon space structures with a complex geometric shape. For each surface element, we enforce a condition that it can interact with light only from its front side, a condition represented in the form of series of Chebyshev polynomials of the first kind. This Chebyshev expansion enables the use of a series of tensors of increasing rank for determination of the force and moment acting on the sail. We obtain expressions for the determination of light pressure on space structures of complex geometry, taking into account self-shadowing and reflections within the structure. We also give the expressions for tensor parametrization using the specularity coefficient in case of specular -diffuse reflection. For these expressions, we calculated the principal moment and force upon two-sided flat solar sail, spherical and cylindrical bodies, and approximated light pressure upon the proposed space-based observatory Millimetron. The proposed expressions can be used in the ballistic analysis of solar sails and other space objects significantly affected by radiation pressure. Also, these results can be used to analyze the dynamics of large-scale space structures around their center of gravity under light pressure.
Stress Energy Tensor in c=0 Logarithmic Conformal Field Theory
Kogan, I. I.; Nichols, A.
2002-01-01
We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. We analyze the OPE for T, \\bar{T} and the logarithmic partners t and \\bar{t} for c=0 theories.
Holographic duality from random tensor networks
Energy Technology Data Exchange (ETDEWEB)
Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)
2016-11-02
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main
A combinatorial enumeration problem of RNA secondary structures
African Journals Online (AJOL)
use
2011-12-21
Dec 21, 2011 ... In 1978, M.S. Waterman firstly gave a mathematical definition of RNA secondary structures (Stein and. Waterman 1978). And in order to satisfy the need of research, RNA secondary structures are usually modeled by some discrete mathematic objects, which establish a connection between Discrete ...
Hyperinvariant Tensor Networks and Holography
Evenbly, Glen
2017-10-01
We propose a new class of tensor network state as a model for the AdS /CFT correspondence and holography. This class is demonstrated to retain key features of the multiscale entanglement renormalization ansatz (MERA), in that they describe quantum states with algebraic correlation functions, have free variational parameters, and are efficiently contractible. Yet, unlike the MERA, they are built according to a uniform tiling of hyperbolic space, without inherent directionality or preferred locations in the holographic bulk, and thus circumvent key arguments made against the MERA as a model for AdS /CFT . Novel holographic features of this tensor network class are examined, such as an equivalence between the causal cones C (R ) and the entanglement wedges E (R ) of connected boundary regions R .
Structural analysis of complex ecological economic optimal control problems
Kiseleva, T.
2011-01-01
This thesis demonstrates the importance and effectiveness of methods of bifurcation theory applied to studying non-convex optimal control problems. It opens up a new methodological approach to investigation of parameterized economic models. While standard analytical methods are not efficient and
Features for Exploiting Black-Box Optimization Problem Structure
DEFF Research Database (Denmark)
Tierney, Kevin; Malitsky, Yuri; Abell, Tinus
2013-01-01
Black-box optimization (BBO) problems arise in numerous scientic and engineering applications and are characterized by compu- tationally intensive objective functions, which severely limit the number of evaluations that can be performed. We present a robust set of features that analyze the tness...
The solution of location problems with certain existing facility structures
DEFF Research Database (Denmark)
Juel, Henrik; Love, Robert F.
1983-01-01
It is known that in the Euclidean distance case, the optimal minisum location of a new facility in relation to four existing facilities is at the intersection of the two lines joining two pairs of the facilities. The authors extend this concept to minisum problems having any even number of existing...... facilities and characterized by generalized distance norms...
Bonner, L. R.; Schultz, Adam
2017-01-01
Ground level electric fields arising from geomagnetic disturbances (GMDs) are used by the electric power industry to calculate geomagnetically induced currents (GICs) in the power grid. Current industry practice is limited to electric fields associated with 1-D ground electrical conductivity structure, yet at any given depth in the crust and mantle lateral (3-D) variations in conductivity can span at least 3 orders of magnitude, resulting in large deviations in electric fields relative to 1-D models. Solving Maxwell's equations for electric fields associated with GMDs above a 3-D Earth is computationally burdensome and currently impractical for industrial applications. A computationally light algorithm is proposed as an alternative. Real-time data from magnetic observatories are projected through multivariate transfer functions to locations of previously occupied magnetotelluric (MT) stations. MT time series and impedance tensors, such as those publically available from the NSF EarthScope Program, are used to scale the projected magnetic observatory data into local electric field predictions that can then be interpolated onto points along power grid transmission lines to actively improve resilience through GIC modeling. Preliminary electric field predictions are tested against previously recorded time series, idealized transfer function cases, and existing industry methods to assess the validity of the algorithm for potential adoption by the power industry. Some limitations such as long-period diurnal drift are addressed, and solutions are suggested to further improve the method before direct comparisons with actual GIC measurements are made.
Economic action and social structure: The problem of embeddedness
Granovetter, M.
1985-01-01
Metadata only record The origin of the concept of "embeddedness", this article has been highly influential in guiding how social scientists conceptualize the interplay between markets and social relations. Rejecting the extremes of an "under" and "over" socialized approach, the article casts the market as "embedded in a network of social relations that do not determine, but certainly influence how individuals behave." This model is explored in the context of malfeasance and the problem of ...
Structural dialectical approach in psychology: problems and research results
Veraksa, Nikolay; Belolutskaya, Anastasiya; Vorobyeva, Irina; Krasheninnikov, Eugene; Rachkova, Elena; Shiyan, Igor; Shiyan, Olga
2013-01-01
In this article dialectical thinking is regarded as one of the central cognitive processes. Because of this cognitive function we can analyze the development of processes and objects. It also determines the possibilities for the creative transformation of some content and for solving problems. The article presents a description and the results of experimental studies. This evidence proves that dialectical thinking is a specific line of cognitive development in children and adults. This line c...
Gurtman, Michael B.
1995-01-01
The empirical structure of the item set from the Inventory of Interpersonal Problems was examined in the context of the interpersonal circumplex and Big Five factors of personality using results from 1,093 undergraduates. Results support using a theoretically guided empirical analysis rather than blind analysis of empirical methods. (SLD)
Shape anisotropy: tensor distance to anisotropy measure
Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S.
2011-03-01
Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.
Research Projects in Physics: A Mechanism for Teaching Ill-Structured Problem Solving
Milbourne, Jeff; Bennett, Jonathan
2017-01-01
Physics education research has a tradition of studying problem solving, exploring themes such as physical intuition and differences between expert and novice problem solvers. However, most of this work has focused on traditional, or well-structured, problems, similar to what might appear in a textbook. Less work has been done with open-ended, or…
Family Structure and Its Effect on Behavioral and Emotional Problems in Young Adolescents.
Lee, Valerie E.; And Others
1994-01-01
Investigated the relationship between school-related emotional and behavioral problems and variation in family structure in a sample of eighth graders. Found that among those who exhibited behavioral problems, such problems were two to four times as likely to occur in single-parent or step-families as in intact families and that gender was also a…
Fusion proteins as alternate crystallization paths to difficult structure problems
Carter, Daniel C.; Rueker, Florian; Ho, Joseph X.; Lim, Kap; Keeling, Kim; Gilliland, Gary; Ji, Xinhua
1994-01-01
The three-dimensional structure of a peptide fusion product with glutathione transferase from Schistosoma japonicum (SjGST) has been solved by crystallographic methods to 2.5 A resolution. Peptides or proteins can be fused to SjGST and expressed in a plasmid for rapid synthesis in Escherichia coli. Fusion proteins created by this commercial method can be purified rapidly by chromatography on immobilized glutathione. The potential utility of using SjGST fusion proteins as alternate paths to the crystallization and structure determination of proteins is demonstrated.
Structural dialectical approach in psychology: problems and research results
Directory of Open Access Journals (Sweden)
Veraksa, Nikolay E.
2013-06-01
Full Text Available In this article dialectical thinking is regarded as one of the central cognitive processes. Because of this cognitive function we can analyze the development of processes and objects. It also determines the possibilities for the creative transformation of some content and for solving problems. The article presents a description and the results of experimental studies. This evidence proves that dialectical thinking is a specific line of cognitive development in children and adults. This line can degrade during school time if the educational program follows formal logical principles, or it can become significantly stronger if the pedagogy is based on dialectical methodology.
DEFF Research Database (Denmark)
Niss, Martin
2017-01-01
This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called structuring for mathematization, where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report...... the results of an analysis of four protocols from task-based interviews with university students working on physics problems in pairs who fail when solving the problems. The obstacles encountered by the students are shown to be related to how the students approach the structuring for mathematization...
DEFF Research Database (Denmark)
Quaglia, Alberto; Sarup, Bent; Sin, Gürkan
2013-01-01
structure for efficient formulation of enterprise-wide optimization problems is presented. Through the integration of the described data structure in our synthesis and design framework, the problem formulation workflow is automated in a software tool, reducing time and resources needed to formulate large...
Niss, Martin
2017-01-01
This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called "structuring for mathematization," where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report the results of an analysis of four…
solution of confined seepage problems below hydraulic structures ...
African Journals Online (AJOL)
user
1985-09-01
Sep 1, 1985 ... compared with those results obtained by exact solutions for the case of standard profiles like, horizontal floor with a central pile and floor with two piles. Finally using the optimum number of elements thus evolved, complicated boundary forms of hydraulic structures are considered for the solution of confined.
solution of confined seepage problems below hydraulic structures ...
African Journals Online (AJOL)
user
1985-09-01
Sep 1, 1985 ... parametric quadrilateral elements which are best suited for inclined boundaries are used ... Consequently the design of control structures .... iso-parametric quadrilateral element is considered in such cases as shown in Fig. 3. The field variable model selected to represent the variation of the unknown over ...
State Confessional Relations: Problem of the Subject Structure
Directory of Open Access Journals (Sweden)
Alexandra A. Dorskaya
2014-06-01
Full Text Available In the article various existing definitions of the concept "state and confessional relations" are analyzed, also author's definition is offered. Three levels of the state and confessional relations are revealed: conceptual, legislative and administrative-managerial. In the article it is shown that in Russia a tradition of only two subjects of the state and confessional relations – government bodies and the religious organizations allocation exists. It is revealed that at the present stage many researchers are dissatisfied with such situation. Scientific sources of the problem of the state and church relations within the psychological school of the law, which are addressed to the personality and experiences in the legal sphere are studied and revealed. Special attention is paid to scientific heritage of the M.A. Reysner, who was one of the first to begin study of this problem. In the article the question of the school of three subjects of the state and confessional relations allocation formation, what adds the faithful or faithless personality in addition to two traditional subjects is analyzed. The state and confessional relations are considered in the context of the human rights development. The question of new type of the believer possessing high education level and knowledge formation is considered. In the article it is shown that at the present stage relations of any regulation between the state and religious organizations is based on the basis of international legal standards, domestic legislation and norms of canon law.
Sharpe, Louise; Walker, Michael; Coughlan, Maree-Jo; Enersen, Kirsten; Blaszczynski, Alex
2005-01-01
This study aimed to evaluate the effectiveness of three proposed modifications to the structural characteristics of electronic gaming machines as harm minimisation strategies for non-problem and probable problem gamblers. Structural changes included reducing the maximum bet size, reducing reel spin and removing large note acceptors. Behavioural patterns of play were observed in 779 participants attending clubs and hotels. Observations were conducted in the gaming venue during regular gaming sessions. Eight experimental machines were designed to represent every combination of the modifications. 210 participants played at least one modified and one unmodified machine. Following play, the South Oaks Gambling Screen (SOGS) was administered. More problem than non-problem gamblers used high denomination bill acceptors and bet over one-dollar per wager. Machines modified to accept the one-dollar maximum bet were played for less time and were associated with smaller losses, fewer individual wagers and lower levels of alcohol consumption and smoking. It was concluded that the reduction of maximum bet levels was the only modification likely to be effective as a harm minimization strategy for problem gamblers.
Bartel, J.; Bencheikh, K.; Meyer, J.
2008-02-01
For a one-body Hamiltonian obtained from the energy-density functional associated with a Skyrme effective interaction, including a tensor force, semiclassical functional densities are derived in the framework of the Extended Thomas-Fermi method, in spherical symmetry, for the kinetic energy and spin-orbit density. The structure of the self-consistent mean-field potentials constructed with such semiclassical functionals is studied. The impact of the tensor force in particular on the spin-orbit form factor clearly indicates the necessity of including such tensor-force terms in the theoretical description of atomic nuclei and their possible influence on the shell structure of exotic nuclei.
Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification.
Li, Qun; Schonfeld, Dan
2014-12-01
In the past decade, great efforts have been made to extend linear discriminant analysis for higher-order data classification, generally referred to as multilinear discriminant analysis (MDA). Existing examples include general tensor discriminant analysis (GTDA) and discriminant analysis with tensor representation (DATER). Both the two methods attempt to resolve the problem of tensor mode dependency by iterative approximation. GTDA is known to be the first MDA method that converges over iterations. However, its performance relies highly on the tuning of the parameter in the scatter difference criterion. Although DATER usually results in better classification performance, it does not converge, yet the number of iterations executed has a direct impact on DATER's performance. In this paper, we propose a closed-form solution to the scatter difference objective in GTDA, namely, direct GTDA (DGTDA) which also gets rid of parameter tuning. We demonstrate that DGTDA outperforms GTDA in terms of both efficiency and accuracy. In addition, we propose constrained multilinear discriminant analysis (CMDA) that learns the optimal tensor subspace by iteratively maximizing the scatter ratio criterion. We prove both theoretically and experimentally that the value of the scatter ratio criterion in CMDA approaches its extreme value, if it exists, with bounded error, leading to superior and more stable performance in comparison to DATER.
A Unified Approach to Substructuring and Structural Modification Problems
Directory of Open Access Journals (Sweden)
Walter D’Ambrogio
2004-01-01
Full Text Available Substructures coupling is still an important tool in several applications of modal analysis, especially structural modification and structures assembling. The subject is particularly relevant in virtual prototyping of complex systems and responds to actual industrial needs. This paper analyzes the possibility of assembling together different substructures' models. The important role of rotational DoFs is highlighted, underlying the difficulty of assembling theoretical and experimental models, for which, usually, the rotational DoFs are not available. Expansion techniques can be used to provide this information as well as appropriate modelling of joints. With this information FRF models, modal models and FE models can be appropriately combined together and solutions for several cases of practical interest are presented. The analyzed procedures are tested on purpose-built benchmarks, showing limits and capabilities of each of them.
Convex programming for detection in structured communication problems
Morsy, T.; Götze, J.; Nassar, H.
2010-12-01
The generalized Minimum Mean Squared Error (GMMSE) detector has a bit error rate performance, which is similar to the MMSE detector. The advantage of the GMMSE detector is that it does not require the knowledge of the noise power. However, the computational complexity of the GMMSE detector is significantly higher than the computational complexity of the MMSE detector. In this paper, the complexity of the GMMSE detector is reduced by taking into account the structure of the system matrix (Toeplitz). Furthermore, by using circular approximation of the structured system matrix an approximate GMMSE detector is presented, whose computational complexity is only slightly higher than MMSE, i.e.~only an iterative gradient descent algorithm based on the inversion of diagonal matrices is additionally required.
Anisotropic diffusion tensor applied to temporal mammograms
DEFF Research Database (Denmark)
Karemore, Gopal; Brandt, Sami; Sporring, Jon
2010-01-01
Breast density is considered a structural property of a mammogram that can change in various ways explaining different effects of medicinal treatments. The aim of the present work is to provide a framework for obtaining more accurate and sensitive measurements of breast density...... changes related to specific effects like Hormonal Replacement Therapy (HRT) and aging. Given effect-grouped patient data, we demonstrated how anisotropic diffusion tensor and its coherence features computed in an anatomically oriented breast coordinate system followed by statistical learning...
An Introduction to the Problem of Dynamic Structural Damping,
1978-01-01
INTRODUCTION TO THE P ROBLEM OF DYNAMIC STRUCTURAL DAMPING by PSa n t ini , A.Castellan i and A.Nappi (stituto di Tecnologia Aerospaziale deIl’Unive rsità di...obtain information s on typical values of ~ to be used in each of the analyses described under Art . 2. It is generally agreed, in fac t , that the...clearly indicate that experimental validation of the results is of vital importance. No safe prediction of the phenomena listed under Art . 2 can be
CISM International Advanced School on Stability Problems of Steel Structures
Skaloud, M
1992-01-01
This volume strives to give complete information about the main aspect of the stability behaviour of steel structures and their members. In following this objective, the volume presents a complete scientific background (profiting from the fact that the authors of the individual parts of the publication have personally been very active in the corresponding field of research for an extended period of time now), but also establishes recommendations, procedures and formulae for practical design. The significance of the volume may be seen in its challenging current concepts of stability analysis, encouraging progress in the field and thereby establishing an advanced basis for more reliable and economical design.
Tensor power spectrum and disformal transformations
Fumagalli, Jacopo; Postma, Marieke
2016-01-01
In a general effective theory description of inflation a disformal transformation can be used to set the tensor sound speed to one. After the transformation, the tensor power spectrum then automatically only depends on the Hubble parameter. We show that this disformal transformation, however, is nothing else than a change of units. It is a very useful tool for simplifying and interpreting computations, but it cannot change any physics. While the apparent parametrical dependence of the tensor power spectrum does change under a disformal transformation, the physics described is frame invariant. We further illustrate the frame invariance of the tensor power spectrum by writing it exclusively in terms of separately invariant quantities.
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
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.
Manipulation of logical structure of chemistry problems and its effect on student performance
Niaz, Mansoor; Robinson, William R.
It has been shown previously that manipulation of the M demand (amount of information needed for processing) of chemistry problems affects student performance, which suggests that manipulation of logical structure of chemistry problems could also lead to significant changes in performance. The objective of this study is to investigate the following: Given the opportunity for training, what is the effect of increasing (manipulation) the complexity of logical structure of chemistry problems on student performance, and to what extent can cognitive variables explain changes in performance. Results obtained show that (a) even a small increase in the logical structure of a problem can change the role of cognitive variables (mental capacity and formal reasoning) to the extent that increase in logical complexity outweighs the advantage students may have gained through training on a similar problem; (b) the use of algorithms and training on particular types of chemistry problems could lead to a situation in which formal reasoning is the only cognitive variable that explains variance in performance significantly; and (c) after having solved very similar problems on two different occasions with improving performance, the improvement is not retained if the logical structure of a third problem increases considerably. It is concluded that when dealing with significant changes in logical complexity of chemistry problems, developmental level of students is the most consistent predictor of success. A model for the qualitative analysis of logical complexity of chemistry problems is presented.
Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian
2011-01-01
The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... considerable effect on the final estimations of the method, in particular on the coefficient of variation of the estimated failure probability. Based on these observations, a simple optimization algorithm is proposed which distributes the support points so that the coefficient of variation of the method...... is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high...
DEFF Research Database (Denmark)
Larsen, Jesper
2002-01-01
Two ideas for using structural information for solving the Vehicle Routing Problem with Time Windows (VRPTW) is presented. The VRPTW is a generalization of the well known capacity constrained Vehicle Routing Problem (VRP). Both techniques are based on solving the VRPTW using a Branch-and-Price ap......Two ideas for using structural information for solving the Vehicle Routing Problem with Time Windows (VRPTW) is presented. The VRPTW is a generalization of the well known capacity constrained Vehicle Routing Problem (VRP). Both techniques are based on solving the VRPTW using a Branch...
A Simplified Algorithm for Inverting Higher Order Diffusion Tensors
Directory of Open Access Journals (Sweden)
Laura Astola
2014-11-01
Full Text Available In Riemannian geometry, a distance function is determined by an inner product on the tangent space. In Riemann–Finsler geometry, this distance function can be determined by a norm. This gives more freedom on the form of the so-called indicatrix or the set of unit vectors. This has some interesting applications, e.g., in medical image analysis, especially in diffusion weighted imaging (DWI. An important application of DWI is in the inference of the local architecture of the tissue, typically consisting of thin elongated structures, such as axons or muscle fibers, by measuring the constrained diffusion of water within the tissue. From high angular resolution diffusion imaging (HARDI data, one can estimate the diffusion orientation distribution function (dODF, which indicates the relative diffusivity in all directions and can be represented by a spherical polynomial. We express this dODF as an equivalent spherical monomial (higher order tensor to directly generalize the (second order diffusion tensor approach. To enable efficient computation of Riemann–Finslerian quantities on diffusion weighted (DW-images, such as the metric/norm tensor, we present a simple and efficient algorithm to invert even order spherical monomials, which extends the familiar inversion of diffusion tensors, i.e., symmetric matrices.
Tensor models, Kronecker coefficients and permutation centralizer algebras
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.
Numerical evaluation of tensor Feynman integrals in Euclidean kinematics
Energy Technology Data Exchange (ETDEWEB)
Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2010-10-15
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)
Shakir, Ali; AL-Khateeb, Belal; Shaker, Khalid; Jalab, Hamid A.
2014-12-01
The design of course timetables for academic institutions is a very difficult job due to the huge number of possible feasible timetables with respect to the problem size. This process contains lots of constraints that must be taken into account and a large search space to be explored, even if the size of the problem input is not significantly large. Different heuristic approaches have been proposed in the literature in order to solve this kind of problem. One of the efficient solution methods for this problem is tabu search. Different neighborhood structures based on different types of move have been defined in studies using tabu search. In this paper, different neighborhood structures on the operation of tabu search are examined. The performance of different neighborhood structures is tested over eleven benchmark datasets. The obtained results of every neighborhood structures are compared with each other. Results obtained showed the disparity between each neighborhood structures and another in terms of penalty cost.
A Multi-Model Reduction Technique for Optimization of Coupled Structural-Acoustic Problems
DEFF Research Database (Denmark)
Creixell Mediante, Ester; Jensen, Jakob Søndergaard; Brunskog, Jonas
2016-01-01
Finite Element models of structural-acoustic coupled systems can become very large for complex structures with multiple connected parts. Optimization of the performance of the structure based on harmonic analysis of the system requires solving the coupled problem iteratively and for several...
A tensor-based subspace approach for bistatic MIMO radar in spatial colored noise.
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.
A Tensor-Based Subspace Approach for Bistatic MIMO Radar in Spatial Colored Noise
Directory of Open Access Journals (Sweden)
Xianpeng Wang
2014-02-01
Full Text Available 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.
A Tensor-Based Subspace Approach for Bistatic MIMO Radar in Spatial Colored Noise
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
An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU
Lyakh, Dmitry I.
2015-04-01
An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typically appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the naïve scattering algorithm (no memory access optimization). The tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).
Advanced fit of the diffusion kurtosis tensor by directional weighting and regularization.
Kuder, Tristan A; Stieltjes, Bram; Bachert, Peter; Semmler, Wolfhard; Laun, Frederik B
2012-05-01
The diffusional kurtosis is an indicator for diffusion restrictions in biological tissue. It is observed experimentally that the kurtosis is largest for directions perpendicular to the fiber direction in white matter. The directional dependence of the kurtosis can be described by the diffusion kurtosis tensor. Since the intention of diffusion kurtosis imaging is to detect diffusion restrictions, the fit of the kurtosis tensor should be dominated by directions perpendicular to the fibers. In this work, it is shown that the basic approach, which is solving the occurring linear system by a pseudoinverse matrix, may completely fail in this regard if the diffusion is highly anisotropic. This problem is solved by adapting the weights of the fit--and thus emphasizing directions of restricted water motion--using a direct fit of the kurtosis tensor to the measured kurtosis values. Moreover, due to its large number of degrees of freedom, the kurtosis tensor can assume complicated shapes resulting in a fit which is sensitive to noise. This article demonstrates that the quality of the kurtosis tensor calculation can be further improved if the fit is regularized by suppressing too large and too small kurtosis tensor values and thus restricting the possible tensor shapes. Copyright © 2011 Wiley Periodicals, Inc.
DEFF Research Database (Denmark)
Stolpe, Mathias; Stidsen, Thomas K.
2007-01-01
of minimizing the weight of a structure subject to displacement and local design-dependent stress constraints. The method iteratively treats a sequence of problems of increasing size of the same type as the original problem. The problems are defined on a design mesh which is initially coarse......In this paper, we present a hierarchical optimization method for finding feasible true 0-1 solutions to finite-element-based topology design problems. The topology design problems are initially modelled as non-convex mixed 0-1 programs. The hierarchical optimization method is applied to the problem...... and then successively refined as needed. At each level of design mesh refinement, a neighbourhood optimization method is used to treat the problem considered. The non-convex topology design problems are equivalently reformulated as convex all-quadratic mixed 0-1 programs. This reformulation enables the use of methods...
DEFF Research Database (Denmark)
Stolpe, Mathias; Stidsen, Thomas K.
2005-01-01
of minimizing the weight of a structure subject to displacement and local design-dependent stress constraints. The method iteratively solves a sequence of problems of increasing size of the same type as the original problem. The problems are defined on a design mesh which is initially coarse......In this paper we present a hierarchical optimization method for finding feasible true 0-1 solutions to finite element based topology design problems. The topology design problems are initially modeled as non-convex mixed 0-1 programs. The hierarchical optimization method is applied to the problem...... and then successively refined as needed. At each level of design mesh refinement, a neighborhood optimization method is used to solve the problem considered. The non-convex topology design problems are equivalently reformulated as convex all-quadratic mixed 0-1 programs. This reformulation enables the use of methods...
Moret-Hartman, Margriet; van der Wilt, Gert Jan; Grin, John
2007-01-01
The practical significance of health technology assessment (HTA) in policy decisions or clinical practice has been challenged. Possibly, problem definitions underlying HTA do not concur sufficiently with the problem definitions held by policy makers or clinicians. We performed an in-depth case study on mebeverine, a drug prescribed to patients with irritable bowel syndrome, to explore this hypothesis. The theoretical framework was provided by the theory of argumentative policy analysis. We analyzed documents and held semistructured interviews to collect data. We reconstructed interpretative frames to analyze actors' argumentation. The funding and usage problems relating to mebeverine were ill-structured. Actors disagreed on the information needed and the norms at stake. As a result, the problem definition shifted, and the resulting problem definitions failed to correspond with the problems perceived by the target populations. To ensure that future studies on healthcare problems are useful, it is imperative that policy makers take the problem definitions of potential users into account.
An Optimization Problem for Predicting the Maximal Effect of Degradation of Mechanical Structures
DEFF Research Database (Denmark)
Achtziger, W.; Bendsøe, Martin P.; Taylor, J. E.
2000-01-01
-product, this gives insight in terms of a mechanical interpretation of the optimization problem. We derive an equivalent convex problem formulation and a convex dual problem, and for dyadic matrices A(i) a quadratic programming problem formulation is developed. A nontrivial numerical example is included, based......This paper deals with a nonlinear nonconvex optimization problem that models prediction of degradation in discrete or discretized mechanical structures. The mathematical difficulty lies in equality constraints of the form Σ(i=1)(m) 1/yi A(i) x=b, where A(i) are symmetric and positive semidefinite...
Complete stress tensor determination by microearthquake analysis
Slunga, R.
2010-12-01
Jones 1984 found that half of the shallow strike-slip EQ in California had at least one M>2 foreshock. By the Gutenberg law this means at least 3-20 M>0 (low b-value 0.4-0.8). deformations within the crust. This was confirmed by observations in Iceland after 1990 when anew seismic network in Iceland operated by IMO started. Like the Parkfield project in California the SIL network in Iceland was established in an area predicted (Einarsson et al 1981, Stefansson and Halldorsson 1988) to be struck by major EQs within decades of years. The area of main interest have a detection threshold of M=0. A physical approach was chosen to the earthquake warning problem (Stefansson et al 1993) and therefore all microearthquakes were analyzed for FPS by the spectral amplitude method (Slunga 1981). As the shear slip is caused by the in situ stress it is logical to investigate what bounds the FPS puts on the stress tensor. McKenzie 1969 assumed that the earthquake takes place in a crust containing only one fracture, the fault plane. He found that in s uch a case only very weak constraints could be put on the stress. This was widely accepted t o be valid also for microearthquakes in the real crust and lead to methods (Angelier 1978, G ephart and Forsythe 1984 etc) to put four constraints on the stress tensor by assuming that the same stress tensor is causing the slip on four or more different fractures. Another and more realistic approach is to assume that the crust have frequent fractures with almost all orientations. In such a case one can rely on Coulomb's failure criterion for isotropic mat erial (gives four constraints) instead of the weaker Bolt's criterion (giving only one const raint). One obvious fifth constraint is to require the vertical stress to equal the lithosta tic pressure. A sixth constraint is achieved by requiring that the deviatoric elastic energy is minimized. The water pressure is also needed for the fourth constraint by Coulomb (CFS=0 ). It can be related to
A few cosmological implications of tensor nonlocalities
Ferreira, Pedro G.; Maroto, Antonio L.
2013-12-01
We consider nonlocal gravity theories that include tensor nonlocalities. We show that in the cosmological context, the tensor nonlocalities, unlike scalar ones, generically give rise to growing modes. An explicit example with quadratic curvature terms is studied in detail. Possible consequences for recent nonlocal cosmological models proposed in the literature are also discussed.
Directory of Open Access Journals (Sweden)
Kuang-dai Leng
2012-01-01
Full Text Available Fabric tensor has proved to be an effective tool statistically characterizing directional data in a smooth and frame-indifferent form. Directional data arising from microscopic physics and mechanics can be summed up as tensor-valued orientation distribution functions (ODFs. Two characterizations of the tensor-valued ODFs are proposed, using the asymmetric and symmetric fabric tensors respectively. The later proves to be nonconvergent and less accurate but still an available solution for where fabric tensors are required in full symmetry. Analytic solutions of the two types of fabric tensors characterizing centrosymmetric and anticentrosymmetric tensor-valued ODFs are presented in terms of orthogonal irreducible decompositions in both two- and three-dimensional (2D and 3D spaces. Accuracy analysis is performed on normally distributed random ODFs to evaluate the approximation quality of the two characterizations, where fabric tensors of higher orders are employed. It is shown that the fitness is dominated by the dispersion degree of the original ODFs rather than the orders of fabric tensors. One application of tensor-valued ODF and fabric tensor in continuum damage mechanics is presented.
Elasticity $\\mathscr{M}$-tensors and the Strong Ellipticity Condition
Ding, Weiyang; Liu, Jinjie; Qi, Liqun; Yan, Hong
2017-01-01
In this paper, we propose a class of tensors satisfying the strong ellipticity condition. The elasticity $\\mathscr{M}$-tensor is defined with respect to the M-eigenvalues of elasticity tensors. We prove that any nonsingular elasticity $\\mathscr{M}$-tensor satisfies the strong ellipticity condition by employing a Perron-Frobenius-type theorem for M-spectral radii of nonnegative elasticity tensors. We also establish other equivalent definitions of nonsingular elasticity $\\mathscr{M}$-tensors.
On large N limit of symmetric traceless tensor models
Klebanov, Igor R.; Tarnopolsky, Grigory
2017-10-01
For some theories where the degrees of freedom are tensors of rank 3 or higher, there exist solvable large N limits dominated by the melonic diagrams. Simple examples are provided by models containing one rank 3 tensor in the tri-fundamental representation of the O( N)3 symmetry group. When the quartic interaction is assumed to have a special tetrahedral index structure, the coupling constant g must be scaled as N -3/2 in the melonic large N limit. In this paper we consider the combinatorics of a large N theory of one fully symmetric and traceless rank-3 tensor with the tetrahedral quartic interaction; this model has a single O( N ) symmetry group. We explicitly calculate all the vacuum diagrams up to order g 8, as well as some diagrams of higher order, and find that in the large N limit where g 2 N 3 is held fixed only the melonic diagrams survive. While some non-melonic diagrams are enhanced in the O( N ) symmetric theory compared to the O( N )3 one, we have not found any diagrams where this enhancement is strong enough to make them comparable with the melonic ones. Motivated by these results, we conjecture that the model of a real rank-3 symmetric traceless tensor possesses a smooth large N limit where g 2 N 3 is held fixed and all the contributing diagrams are melonic. A feature of the symmetric traceless tensor models is that some vacuum diagrams containing odd numbers of vertices are suppressed only by N -1/2 relative to the melonic graphs.
Structural Variables That Determine Problem-Solving Difficulty in Computer Assisted Instruction
Loftus, Elizabeth F.; Suppes, Patrick
1972-01-01
Analysis showed that a word problem is difficult to solve if: it is of a different type from the problem that preceded it; its solution requires a large number of different operations; its surface structure is complex; it has a large number of words; or it requires a conversion of units. (Authors)
2-Sat Sub-Clauses and the Hypernodal Structure of the 3-Sat Problem
Powell, D. B.
2004-01-01
Like simpler graphs, nested (hypernodal) graphs consist of two components: a set of nodes and a set of edges, where each edge connects a pair of nodes. In the hypernodal graph model, however, a node may contain other graphs, so that a node may be contained in a graph that it contains. The inherently recursive structure of the hypernodal graph model aptly characterizes both the structure and dynamic of the 3-sat problem, a broadly applicable, though intractable, computer science problem. In th...
Fitting alignment tensor components to experimental RDCs, CSAs and RQCs.
Wirz, Lukas N; Allison, Jane R
2015-05-01
Residual dipolar couplings, chemical shift anisotropies and quadrupolar couplings provide information about the orientation of inter-spin vectors and the anisotropic contribution of the local environment to the chemical shifts of nuclei, respectively. Structural interpretation of these observables requires parameterization of their angular dependence in terms of an alignment tensor. We compare and evaluate two algorithms for generating the optimal alignment tensor for a given molecular structure and set of experimental data, namely SVD (Losonczi et al. in J Magn Reson 138(2):334-342, 1999), which scales as [Formula: see text], and the linear least squares algorithm (Press et al. in Numerical recipes in C. The art of scientific computing, 2nd edn. Cambridge University Press, Cambridge, 1997), which scales as [Formula: see text].
STRUCTURAL STUDY AND INVESTIGATION OF NMR TENSORS ...
African Journals Online (AJOL)
60 cells or human glioblastoma cell lines [9] by copper-mediated oxidation of DA [10] or by oxidation of DA with prostaglandin H synthase [11, 12]. We hypothesize that oxidation of DA to its quinone and subsequent reaction with DNA cause DNA damage via formation of specific depurinating adducts, and the mutations ...
Data fusion in metabolomics using coupled matrix and tensor factorizations
DEFF Research Database (Denmark)
Evrim, Acar Ataman; Bro, Rasmus; Smilde, Age Klaas
2015-01-01
With a goal of identifying biomarkers/patterns related to certain conditions or diseases, metabolomics focuses on the detection of chemical substances in biological samples such as urine and blood using a number of analytical techniques, including nuclear magnetic resonance (NMR) spectroscopy...... vast amounts of data using different analytical methods, data fusion remains a challenging task, in particular, when the goal is to capture the underlying factors and use them for interpretation, e.g., for biomarker identification. Furthermore, many data fusion applications require joint analysis...... of heterogeneous (i.e., in the form of higher order tensors and matrices) data sets with shared/unshared factors. In order to jointly analyze such heterogeneous data sets, we formulate data fusion as a coupled matrix and tensor factorization (CMTF) problem, which has already proved useful in many data mining...
Depth inpainting by tensor voting.
Kulkarni, Mandar; Rajagopalan, Ambasamudram N
2013-06-01
Depth maps captured by range scanning devices or by using optical cameras often suffer from missing regions due to occlusions, reflectivity, limited scanning area, sensor imperfections, etc. In this paper, we propose a fast and reliable algorithm for depth map inpainting using the tensor voting (TV) framework. For less complex missing regions, local edge and depth information is utilized for synthesizing missing values. The depth variations are modeled by local planes using 3D TV, and missing values are estimated using plane equations. For large and complex missing regions, we collect and evaluate depth estimates from self-similar (training) datasets. We align the depth maps of the training set with the target (defective) depth map and evaluate the goodness of depth estimates among candidate values using 3D TV. We demonstrate the effectiveness of the proposed approaches on real as well as synthetic data.
Hand-waving and interpretive dance: an introductory course on tensor networks
Bridgeman, Jacob C.; Chubb, Christopher T.
2017-06-01
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this difficulty in both the numerical and analytic regimes. These notes form the basis for a seven lecture course, introducing the basics of a range of common tensor networks and algorithms. In particular, we cover: introductory tensor network notation, applications to quantum information, basic properties of matrix product states, a classification of quantum phases using tensor networks, algorithms for finding matrix product states, basic properties of projected entangled pair states, and multiscale entanglement renormalisation ansatz states. The lectures are intended to be generally accessible, although the relevance of many of the examples may be lost on students without a background in many-body physics/quantum information. For each lecture, several problems are given, with worked solutions in an ancillary file.
Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell; Ramanujam, J.; Sadayappan, P.
2009-09-01
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations, such as minimization of cache misses and utilization of multimedia vector instructions, are discussed. A library for efficient index permutation of multidimensional tensors is described, and experimental performance data is provided that demonstrates its effectiveness.
Energy Technology Data Exchange (ETDEWEB)
Saur, R. [Sektion fuer Experimentelle Kernspinresonanz des ZNS, Abt. Neuroradiologie, Universitaetsklinikum Tuebingen (Germany); Augenklinik des Universitaetsklinikums Tuebingen (Germany); Klinik fuer Psychiatrie und Psychotherapie des Universitaetsklinikums Tuebingen (Germany); Gharabaghi, A. [Klinik fuer Neurochirurgie des Universitaetsklinikums Tuebingen (Germany); Erb, M. [Sektion fuer Experimentelle Kernspinresonanz des ZNS, Abt. Neuroradiologie, Universitaetsklinikum Tuebingen (Germany)
2007-07-01
Knowledge about integrity and location of fibre tracts arising from eloquent cortical areas is important to plan neurosurgical interventions and to allow maximization of resection of pathological tissue while preserving vital white matter tracts. Diffusion Tensor Imaging (DTI) is so far the only method to get preoperatively an impression of the individual complexity of nerve bundles. Thereby nerve fibres are not mapped directly. They are derived indirectly by analysis of the directional distribution of diffusion of water molecules which is influenced mainly by large fibre tracts. From acquisition to reconstruction and visualisation of the fibre tracts many representational stages and working steps have to be passed. Exact knowledge about problems of Diffusion Imaging is important for interpretation of the results. Particularly, brain tumor edema, intraoperative brain shift, MR-artefacts and limitations of the mathematical models and algorithms challenge DTI-developers and applicants. (orig.)
On the (1,1)-tensor bundle with Cheeger–Gromoll type metric
Indian Academy of Sciences (India)
[2] Cengiz N and Salimov A A, Complete lifts of derivations to tensor bundles, Bol. Soc. Mat. Mexicana (3) 8(1) (2002) 75–82. [3] Cheeger J and Gromoll D, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. 96 (1972) 413–443. [4] Gezer A and Salimov A, Diagonal lifts of tensor fields of type (1,1) ...
The Role of Content Knowledge in Ill-Structured Problem Solving for High School Physics Students
Milbourne, Jeff; Wiebe, Eric
2017-03-01
While Physics Education Research has a rich tradition of problem-solving scholarship, most of the work has focused on more traditional, well-defined problems. Less work has been done with ill-structured problems, problems that are better aligned with the engineering and design-based scenarios promoted by the Next Generation Science Standards. This study explored the relationship between physics content knowledge and ill-structured problem solving for two groups of high school students with different levels of content knowledge. Both groups of students completed an ill-structured problem set, using a talk-aloud procedure to narrate their thought process as they worked. Analysis of the data focused on identifying students' solution pathways, as well as the obstacles that prevented them from reaching "reasonable" solutions. Students with more content knowledge were more successful reaching reasonable solutions for each of the problems, experiencing fewer obstacles. These students also employed a greater variety of solution pathways than those with less content knowledge. Results suggest that a student's solution pathway choice may depend on how she perceives the problem.
Opportunity Structure for Gambling and Problem Gambling among Employees in the Transport Industry
Revheim, Tevje; Buvik, Kristin
2009-01-01
Working conditions for employees in the transport sector might present an opportunity structure for gambling by providing access to gambling during the workday. This study investigates connections between opportunity structure, gambling during the workday, and gambling problems among employees in the transport sector. Data has been collected from…
Conformal field theories and tensor categories. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics
2014-08-01
First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Chao, Lo-Hsin; Tsai, Meng-Che; Liang, Ya-Lun; Strong, Carol; Lin, Chung-Ying
2018-01-01
Childhood adversity (CA) is associated with problem behaviors in adolescence, but the mediators, that is, those factors that help build resilience and prevent some children who experience CA from engaging in problem behaviors, await more exploration, including social integration. The aim of this study was to identify the association between CA and adolescent problem behaviors, and to further examine the mediating role of social integration distinctly as psychological and structural integration. Data used were from the Taiwan Education Panel Survey, a core panel of 4,261 students (age 13) surveyed in 2001 and followed for three more waves until age 18. For psychological integration, an average score was calculated to represent adolescents' feelings about their school. Structural integration was constructed using several items about adolescents' school and extracurricular activities. We used structural equation modeling with the diagonally weighted least squares method to examine the effect of CA on the primary outcome: adolescent problem behaviors via social integration. The hypothesized structural equation model specifying the path from CA to adolescent problem behavior had good fit. Respondents with one CA were indirectly linked to problem behaviors via psychological but not structural integration (e.g. the level of participation in school and non-school activities). On mediation analysis, psychological integration significantly mediated the paths from one CA to all six problem behaviors (all P integration; two or more CA were not associated with significant paths to problem behaviors. The contribution of social integration is crucial to an adolescent's development from CA to problem behaviors. To form supportive social relationships to achieve better health, we suggest that those adolescents who have been exposed to CA should be helped to join more teams and take part in more activities, thereby increasing their opportunities for social interaction, and improving
Directory of Open Access Journals (Sweden)
Eloy Guerrero Seide
2004-11-01
Full Text Available This article summarizes the results obtained in an exploratory and comparative study of two ways of structuring the mathematical content of a B.S. program in Agronomic Engineering at Guantanamo University, Cuba: the formal systematization of the presentation of the knowledge, and an organization through problems. The sign test is used in the proof of the hypothesis. In a preliminary form, at least, it was demonstrated that the variant of systemic structuring of knowledge through problems is more conducive to the efficiency of the knowledge acquired by students than the structure presented by means of the logical exposition of achieved knowledge.
Local Tensor Radiation Conditions For Elastic Waves
DEFF Research Database (Denmark)
Krenk, S.; Kirkegaard, Poul Henning
2001-01-01
A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point....... The tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves. The effectiveness of the local tensor radiation condition...
Explicit Determination of Piezoelectric Eshelby Tensors for a Spheroidal Inclusion
Energy Technology Data Exchange (ETDEWEB)
Yozo Mikata
2001-06-21
In this paper, by systematically treating the integrals involved in the piezoelectric inclusion problem, explicit results were obtained for the piezoelectric Eshelby tensors for a spheroidal inclusion aligned along the axis of the anisotropy in a transversely isotropic piezoelectric material. This problem was first treated by Dunn and Wienecke (1996) using a Green's function approach, which closely follows Withers' approach (1989) for an ellipsoidal inclusion problem in a transversely isotropic elastic medium. The same problem was recently treated by Michelitsch and Levin (2000) also using a Green's function approach. In this paper, a different method was used to obtain the explicit results for the piezoelectric Eshelby tensors for a spheroidal inclusion. The method is a direct extension of a more unified approach, which has been recently developed by Mikata (2000), which is based on Deeg's results (1980) on a piezoelectric inclusion problem. The main advantage of this method is that it is more straightforward and simpler than Dunn and Wienecke (1996), or Michelitsch and Levin (2000), and the results are a little bit more explicit than their solutions. The key step of this paper is an analytical closed form evaluation of several integrals, which was made possible after a careful treatment of a certain bi-cubic equation.
Smartphone dependence classification using tensor factorization.
Choi, Jingyun; Rho, Mi Jung; Kim, Yejin; Yook, In Hye; Yu, Hwanjo; Kim, Dai-Jin; Choi, In Young
2017-01-01
Excessive smartphone use causes personal and social problems. To address this issue, we sought to derive usage patterns that were directly correlated with smartphone dependence based on usage data. This study attempted to classify smartphone dependence using a data-driven prediction algorithm. We developed a mobile application to collect smartphone usage data. A total of 41,683 logs of 48 smartphone users were collected from March 8, 2015, to January 8, 2016. The participants were classified into the control group (SUC) or the addiction group (SUD) using the Korean Smartphone Addiction Proneness Scale for Adults (S-Scale) and a face-to-face offline interview by a psychiatrist and a clinical psychologist (SUC = 23 and SUD = 25). We derived usage patterns using tensor factorization and found the following six optimal usage patterns: 1) social networking services (SNS) during daytime, 2) web surfing, 3) SNS at night, 4) mobile shopping, 5) entertainment, and 6) gaming at night. The membership vectors of the six patterns obtained a significantly better prediction performance than the raw data. For all patterns, the usage times of the SUD were much longer than those of the SUC. From our findings, we concluded that usage patterns and membership vectors were effective tools to assess and predict smartphone dependence and could provide an intervention guideline to predict and treat smartphone dependence based on usage data.
Smartphone dependence classification using tensor factorization.
Directory of Open Access Journals (Sweden)
Jingyun Choi
Full Text Available Excessive smartphone use causes personal and social problems. To address this issue, we sought to derive usage patterns that were directly correlated with smartphone dependence based on usage data. This study attempted to classify smartphone dependence using a data-driven prediction algorithm. We developed a mobile application to collect smartphone usage data. A total of 41,683 logs of 48 smartphone users were collected from March 8, 2015, to January 8, 2016. The participants were classified into the control group (SUC or the addiction group (SUD using the Korean Smartphone Addiction Proneness Scale for Adults (S-Scale and a face-to-face offline interview by a psychiatrist and a clinical psychologist (SUC = 23 and SUD = 25. We derived usage patterns using tensor factorization and found the following six optimal usage patterns: 1 social networking services (SNS during daytime, 2 web surfing, 3 SNS at night, 4 mobile shopping, 5 entertainment, and 6 gaming at night. The membership vectors of the six patterns obtained a significantly better prediction performance than the raw data. For all patterns, the usage times of the SUD were much longer than those of the SUC. From our findings, we concluded that usage patterns and membership vectors were effective tools to assess and predict smartphone dependence and could provide an intervention guideline to predict and treat smartphone dependence based on usage data.
Smartphone dependence classification using tensor factorization
Kim, Yejin; Yook, In Hye; Yu, Hwanjo; Kim, Dai-Jin
2017-01-01
Excessive smartphone use causes personal and social problems. To address this issue, we sought to derive usage patterns that were directly correlated with smartphone dependence based on usage data. This study attempted to classify smartphone dependence using a data-driven prediction algorithm. We developed a mobile application to collect smartphone usage data. A total of 41,683 logs of 48 smartphone users were collected from March 8, 2015, to January 8, 2016. The participants were classified into the control group (SUC) or the addiction group (SUD) using the Korean Smartphone Addiction Proneness Scale for Adults (S-Scale) and a face-to-face offline interview by a psychiatrist and a clinical psychologist (SUC = 23 and SUD = 25). We derived usage patterns using tensor factorization and found the following six optimal usage patterns: 1) social networking services (SNS) during daytime, 2) web surfing, 3) SNS at night, 4) mobile shopping, 5) entertainment, and 6) gaming at night. The membership vectors of the six patterns obtained a significantly better prediction performance than the raw data. For all patterns, the usage times of the SUD were much longer than those of the SUC. From our findings, we concluded that usage patterns and membership vectors were effective tools to assess and predict smartphone dependence and could provide an intervention guideline to predict and treat smartphone dependence based on usage data. PMID:28636614
PHYSLIB: A C++ tensor class library
Energy Technology Data Exchange (ETDEWEB)
Budge, K.G.
1991-10-09
C++ is the first object-oriented programming language which produces sufficiently efficient code for consideration in computation-intensive physics and engineering applications. In addition, the increasing availability of massively parallel architectures requires novel programming techniques which may prove to be relatively easy to implement in C++. For these reasons, Division 1541 at Sandia National Laboratories is devoting considerable resources to the development of C++ libraries. This document describes the first of these libraries to be released, PHYSLIB, which defines classes representing Cartesian vectors and (second-order) tensors. This library consists of the header file physlib.h, the inline code file physlib.inl, and the source file physlib.C. The library is applicable to both three-dimensional and two-dimensional problems; the user selects the 2-D version of the library by defining the symbol TWO D in the header file physlib.h and recompiling physlib.C and his own code. Alternately, system managers may wish to provide duplicate header and object modules of each dimensionality. This code was produced under the auspices of Sandia National Laboratories, a federally-funded research center administered for the United States Department of Energy on a non-profit basis by AT T. This code is available to US citizens, and institutions under research, government use and/or commercial license agreements.
Directory of Open Access Journals (Sweden)
Milev Jordan
2016-01-01
Full Text Available The main purpose of the paper is to present practical application of Eurocodes in the field of RC structures design. The selected examples represent the main problems in practical application of Eurocodes for seismic analysis and design of RC Structures in Bulgarian construction practice. The analysis is focused on some structural and economic problems as well as on some contradictions in Eurocode 8 itself. Special attention is paid to the practical solution of the following problems: recognition of torsionally flexible systems, stiffness reduction of RC elements for linear analysis dimensions and detailing of confined boundary areas of shear walls, detailing of wall structures, etc. Those problems appear during the practical design of some buildings in Bulgaria. Several proposals for solving some problems defined in the paper are presented through some practical examples. Some conclusions are made for further application of Eurocode 8 in the design and construction practice. The importance of some rules and procedures in Eurocode 8 is supported by the examples of damaged RC members during the past earthquakes. The problems of Eurocode 8 and their solutions are illustrated through the experience of Bulgarian construction practice.
Near-wall diffusion tensor of an axisymmetric colloidal particle
Lisicki, Maciej; Wajnryb, Eligiusz
2016-01-01
Hydrodynamic interactions with confining boundaries often lead to drastic changes in the diffusive behaviour of microparticles in suspensions. For axially symmetric particles, earlier numerical studies have suggested a simple form of the near-wall diffusion matrix which depends on the distance and orientation of the particle with respect to the wall, which is usually calculated numerically. In this work, we derive explicit analytical formulae for the dominant correction to the bulk diffusion tensor of an axially symmetric colloidal particle due to the presence of a nearby no-slip wall. The relative correction scales as powers of inverse wall-particle distance and its angular structure is represented by simple polynomials in sines and cosines of the particle's inclination angle to the wall. We analyse the correction for translational and rotational motion, as well as the translation-rotation coupling. Our findings provide a simple approximation to the anisotropic diffusion tensor near a wall, which completes a...
One-loop tensor Feynman integral reduction with signed minors
Energy Technology Data Exchange (ETDEWEB)
Fleischer, J. [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, V. [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center
2011-12-15
We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically in a systematic way. The final expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions. (orig.)
The nonabelian tensor square of a crystallographic group with quaternion point group of order eight
Afiqah Mohammad, Siti; Haniza Sarmin, Nor; Izzati Mat Hassim, Hazzirah
2017-10-01
A crystallographic group is a discrete subgroup of the set of isometries of Euclidean space where the quotient space is compact. A torsion free crystallographic group, or also known as a Bieberbach group has the symmetry structure that will reveal its algebraic properties. One of the algebraic properties is its nonabelian tensor square. The nonabelian tensor square is a special case of the nonabelian tensor product where the product is defined if the two groups act on each other in a compatible way and their action is taken to be conjugation. Meanwhile, Bieberbach group with quaternion point group of order eight is a polycyclic group. In this paper, by using the polycyclic method, the computation of the nonabelian tensor square of this group will be shown.
Kinetics of Fluid Demixing in Complex Plasmas: Domain Growth Analysis using Minkowski Tensors
Böbel, Alexander
2016-01-01
A molecular dynamics simulation of the demixing process of a binary complex plasma is analysed and the role of distinct interaction potentials is discussed by using morphological Minkowski tensor analysis of the minority phase domain growth in a demixing simulated binary complex plasma. These Minkowski tensor methods are compared with previous results that utilized a power spectrum method based on the time-dependent average structure factor. It is shown that the Minkowski tensor methods are superior to the previously used power spectrum method in the sense of higher sensitivity to changes in domain size. By analysis of the slope of the temporal evolution of Minkowski tensor measures qualitative differences between the case of particle interaction with a single length scale compared to particle interactions with two different length scales (dominating long range interaction) are revealed. After proper scaling the graphs for the two length scale scenario coincide, pointing towards universal behaviour. The quali...
Poincare Algebra Extension with Tensor Generator
Soroka, Dmitrij V.; Soroka, Vyacheslav A.
2005-01-01
A tensor extension of the Poincar\\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... 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...
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-06
In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Calculus of tensors and differential forms
Sinha, Rajnikant
2014-01-01
Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.
Tensor extension of the Poincare algebra
Energy Technology Data Exchange (ETDEWEB)
Soroka, Dmitrij V. [Kharkov Institute of Physics and Technology, 61108 Kharkov (Ukraine)]. E-mail: dsoroka@kipt.kharkov.ua; Soroka, Vyacheslav A. [Kharkov Institute of Physics and Technology, 61108 Kharkov (Ukraine)]. E-mail: vsoroka@kipt.kharkov.ua
2005-02-10
A tensor extension of the Poincare algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions D=2,3,4.
The energy–momentum tensor(s) in classical gauge theories
Energy Technology Data Exchange (ETDEWEB)
Blaschke, Daniel N., E-mail: dblaschke@lanl.gov [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Gieres, François, E-mail: gieres@ipnl.in2p3.fr [Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Bat. P. Dirac, 4 rue Enrico Fermi, F-69622 Villeurbanne (France); Reboud, Méril, E-mail: meril.reboud@ens-lyon.fr [Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Bat. P. Dirac, 4 rue Enrico Fermi, F-69622 Villeurbanne (France); Ecole Normale Supérieure de Lyon, 46 allée d' Italie, F-69364 Lyon CEDEX 07 (France); Schweda, Manfred, E-mail: mschweda@tph.tuwien.ac.at [Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna (Austria)
2016-11-15
We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
The energy–momentum tensor(s in classical gauge theories
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2016-11-01
Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Calibration of magnetic gradient tensor measurement array in magnetic anomaly detection
Chen, Jinfei; Zhang, Qi; Pan, Mengchun; Weng, Feibing; Chen, Dixiang; Pang, Hongfeng
2013-01-01
Magnetic anomaly detection based on magnetic gradient tensor has become more and more important in civil and military applications. Compared with methods based on magnetic total field or components measurement, magnetic gradient tensor has some unique advantages. Usually, a magnetic gradient tensor measurement array is constituted by four three-axis magnetometers. The prominent problem of magnetic gradient tensor measurement array is the misalignment of sensors. In order to measure the magnetic gradient tensor accurately, it is quite essential to calibrate the measurement array. The calibration method, which is proposed in this paper, is divided into two steps. In the first step, each sensor of the measurement array should be calibrated, whose error is mainly caused by constant biases, scale factor deviations and nonorthogonality of sensor axes. The error of measurement array is mainly caused by the misalignment of sensors, so that triplets' deviation in sensors array coordinates is calibrated in the second step. In order to verify the effectiveness of the proposed method, simulation was taken and the result shows that the proposed method improves the measurement accuracy of magnetic gradient tensor greatly.
Directory of Open Access Journals (Sweden)
Liu Xiaogang
2013-01-01
Full Text Available When the computational point is approaching the poles, the variance and covariance formulae of the disturbing gravity gradient tensors tend to be infinite, and this is a singular problem. In order to solve the problem, the authors deduced the practical non-singular computational formulae of the first-and second-order derivatives of the Legendre functions and two kinds of spherical harmonic functions, and then constructed the nonsingular formulae of variance and covariance function of disturbing gravity gradient tensors.
Solving probabilistic and statistical problems: a matter of information structure and question form.
Girotto, V; Gonzalez, M
2001-03-01
Is the human mind inherently unable to reason probabilistically, or is it able to do so only when problems tap into a module for reasoning about natural frequencies? We suggest an alternative possibility: naive individuals are able to reason probabilistically when they can rely on a representation of subsets of chances or frequencies. We predicted that naive individuals solve conditional probability problems if they can infer conditional probabilities from the subset relations in their representation of the problems, and if the question put to them makes it easy to consider the appropriate subsets. The results of seven studies corroborated these predictions: when the form of the question and the structure of the problem were framed so as to activate intuitive principles based on subset relations, naive individuals solved problems, whether they were stated in terms of probabilities or frequencies. Otherwise, they failed with both sorts of information. The results contravene the frequentist hypothesis and the evolutionary account of probabilistic reasoning.
An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics
Directory of Open Access Journals (Sweden)
A. Barari
2008-01-01
Full Text Available Variational iteration method (VIM is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iteration method (VIM. The results reveal that this method is very effective and simple, and that it yields the exact solutions. It was shown that this method can be used effectively for solving linear and nonlinear boundary value problems.
THE PROBLEM OF THE FEASIBILITY STUDY IN RESPECT OF DESIGN OF JOINTS OF METAL STRUCTURES
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Morozova Dina Vol'demarovna
2012-12-01
It is noteworthy that this problem enjoyed much attention back in the past when the country suffered from steel deficit, and metal processing plants could not keep up with the needs of consumers. This problem was dealt with by Y.M. Lihtarnikov, a Soviet scientist, who published his work "Variant design and optimization of steel structures" in 1979. The authors employ the theoretical base developed by the scientist to perform their research into the optimum solutions to the problems of several types of metal joints.
Exploring Interface Problems in Taiwan’s Construction Projects Using Structural Equation Modeling
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Chien-Liang Lin
2017-05-01
Full Text Available Construction projects are complex systems that inherently contain complex interface problems. This study explored the root causes of interface problems in construction projects using structural equation modeling. This technique is a systematic approach that combines factor analysis and path analysis to investigate the causal relationships among multidimensional factors. The literature on construction interface problems was reviewed, and a questionnaire survey was conducted in Taiwan to identify 27 initial factors that cause interface problems in three dimensions: owner, design, and construction. Then, a series of structural equation models (SEMs was developed to further explore the root causes of the interface problems and their causal relationships. This study has three main findings: (1 poor design causes interface problems; (2 ineffective communication and coordination among the owner, design, and construction dimensions are the main factors that cause construction interface problems; and (3 a lack of communication and coordination has a greater influence on the construction dimension than on the owner and design dimensions. The above findings can be used as important references and sustainable management strategies for academia and decision-makers in the construction industry.
Approximation of High-Dimensional Rank One Tensors
Bachmayr, Markus
2013-11-12
Many real world problems are high-dimensional in that their solution is a function which depends on many variables or parameters. This presents a computational challenge since traditional numerical techniques are built on model classes for functions based solely on smoothness. It is known that the approximation of smoothness classes of functions suffers from the so-called \\'curse of dimensionality\\'. Avoiding this curse requires new model classes for real world functions that match applications. This has led to the introduction of notions such as sparsity, variable reduction, and reduced modeling. One theme that is particularly common is to assume a tensor structure for the target function. This paper investigates how well a rank one function f(x 1,...,x d)=f 1(x 1)⋯f d(x d), defined on Ω=[0,1]d can be captured through point queries. It is shown that such a rank one function with component functions f j in W∞ r([0,1]) can be captured (in L ∞) to accuracy O(C(d,r)N -r) from N well-chosen point evaluations. The constant C(d,r) scales like d dr. The queries in our algorithms have two ingredients, a set of points built on the results from discrepancy theory and a second adaptive set of queries dependent on the information drawn from the first set. Under the assumption that a point z∈Ω with nonvanishing f(z) is known, the accuracy improves to O(dN -r). © 2013 Springer Science+Business Media New York.
Harder, Valerie S; Mutiso, Victoria N; Khasakhala, Lincoln I; Burke, Heather M; Rettew, David C; Ivanova, Masha Y; Ndetei, David M
2014-12-01
Data on youth emotional and behavioral problems from societies in Sub-Saharan Africa are lacking. This may be due to the fact that few youth mental health assessments have been tested for construct validity of syndrome structure across multicultural societies that include developing countries, and almost none have been tested in Sub-Saharan Africa. The Youth Self-Report (YSR), for example, has shown great consistency of its syndrome structure across many cultures, yet data from only one developing country in Sub-Saharan Africa have been included. In this study, we test the factor structure of YSR syndromes among Kenyan youth ages 11-18 years from an informal settlement in Nairobi, Kenya and examine sex-differences in levels of emotional and behavioral problems. We find the eight syndrome structure of the YSR to fit these data well (Root Mean Square Error of Approximation=.049). While Kenyan girls have significantly higher internalizing (Anxious/Depressed, Withdrawn/Depressed, Somatic) problem scores than boys, these differences are of similar magnitude to published multicultural findings. The results support the generalizability of the YSR syndrome structure to Kenyan youth and are in line with multicultural findings supporting the YSR as an assessment of emotional and behavioral problems in diverse societies.
Bayesian approach to magnetotelluric tensor decomposition
Directory of Open Access Journals (Sweden)
Michel Menvielle
2010-05-01
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Magnetotelluric directional analysis and impedance tensor decomposition are basic tools to validate a local/regional composite electrical model of the underlying structure. Bayesian stochastic methods approach the problem of the parameter estimation and their uncertainty characterization in a fully probabilistic fashion, through the use of posterior model probabilities.We use the standard GroomBailey 3D local/2D regional composite model in our bayesian approach. We assume that the experimental impedance estimates are contamined with the Gaussian noise and define the likelihood of a particular composite model with respect to the observed data. We use noninformative, flat priors over physically reasonable intervals for the standard GroomBailey decomposition parameters. We apply two numerical methods, the Markov chain Monte Carlo procedure based on the Gibbs sampler and a singlecomponent adaptive Metropolis algorithm. From the posterior samples, we characterize the estimates and uncertainties of the individual decomposition parameters by using the respective marginal posterior probabilities. We conclude that the stochastic scheme performs reliably for a variety of models, including the multisite and multifrequency case with up to
Ultrasound elastic tensor imaging: comparison with MR diffusion tensor imaging in the myocardium
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 0.05, unpaired, one-tailed t-test, N = 10). In
On the Landau-de Gennes Elastic Energy of a Q-Tensor Model for Soft Biaxial Nematics
Mucci, Domenico; Nicolodi, Lorenzo
2017-12-01
In the Landau-de Gennes theory of liquid crystals, the propensities for alignments of molecules are represented at each point of the fluid by an element Q of the vector space S_0 of 3× 3 real symmetric traceless matrices, or Q-tensors. According to Longa and Trebin (1989), a biaxial nematic system is called soft biaxial if the tensor order parameter Q satisfies the constraint tr(Q^2) = {const}. After the introduction of a Q-tensor model for soft biaxial nematic systems and the description of its geometric structure, we address the question of coercivity for the most common four-elastic-constant form of the Landau-de Gennes elastic free-energy (Iyer et al. 2015) in this model. For a soft biaxial nematic system, the tensor field Q takes values in a four-dimensional sphere S^4_ρ of radius ρ ≤ √{2/3} in the five-dimensional space S_0 with inner product = tr(QP). The rotation group it{SO}(3) acts orthogonally on S_0 by conjugation and hence induces an action on S^4_ρ \\subset {S}_0. This action has generic orbits of codimension one that are diffeomorphic to an eightfold quotient S^3/H of the unit three-sphere S^3, where H={± 1, ± i, ± j, ± k} is the quaternion group, and has two degenerate orbits of codimension two that are diffeomorphic to the projective plane RP^2. Each generic orbit can be interpreted as the order parameter space of a constrained biaxial nematic system and each singular orbit as the order parameter space of a constrained uniaxial nematic system. It turns out that S^4_ρ is a cohomogeneity one manifold, i.e., a manifold with a group action whose orbit space is one-dimensional. Another important geometric feature of the model is that the set Σ _ρ of diagonal Q-tensors of fixed norm ρ is a (geodesic) great circle in S^4_ρ which meets every orbit of S^4_ρ orthogonally and is then a section for S^4_ρ in the sense of the general theory of canonical forms. We compute necessary and sufficient coercivity conditions for the elastic energy by
Hoffmann, Michael; Borenstein, Jason
2014-03-01
As a committee of the National Academy of Engineering recognized, ethics education should foster the ability of students to analyze complex decision situations and ill-structured problems. Building on the NAE's insights, we report about an innovative teaching approach that has two main features: first, it places the emphasis on deliberation and on self-directed, problem-based learning in small groups of students; and second, it focuses on understanding ill-structured problems. The first innovation is motivated by an abundance of scholarly research that supports the value of deliberative learning practices. The second results from a critique of the traditional case-study approach in engineering ethics. A key problem with standard cases is that they are usually described in such a fashion that renders the ethical problem as being too obvious and simplistic. The practitioner, by contrast, may face problems that are ill-structured. In the collaborative learning environment described here, groups of students use interactive and web-based argument visualization software called "AGORA-net: Participate - Deliberate!". The function of the software is to structure communication and problem solving in small groups. Students are confronted with the task of identifying possible stakeholder positions and reconstructing their legitimacy by constructing justifications for these positions in the form of graphically represented argument maps. The argument maps are then presented in class so that these stakeholder positions and their respective justifications become visible and can be brought into a reasoned dialogue. Argument mapping provides an opportunity for students to collaborate in teams and to develop critical thinking and argumentation skills.
Directory of Open Access Journals (Sweden)
Samir Dey
2015-07-01
Full Text Available This paper proposes a new multi-objective intuitionistic fuzzy goal programming approach to solve a multi-objective nonlinear programming problem in context of a structural design. Here we describe some basic properties of intuitionistic fuzzy optimization. We have considered a multi-objective structural optimization problem with several mutually conflicting objectives. The design objective is to minimize weight of the structure and minimize the vertical deflection at loading point of a statistically loaded three-bar planar truss subjected to stress constraints on each of the truss members. This approach is used to solve the above structural optimization model based on arithmetic mean and compare with the solution by intuitionistic fuzzy goal programming approach. A numerical solution is given to illustrate our approach.
Parallel Tensor Compression for Large-Scale Scientific Data.
Energy Technology Data Exchange (ETDEWEB)
Kolda, Tamara G. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Ballard, Grey [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Austin, Woody Nathan [Univ. of Texas, Austin, TX (United States)
2015-10-01
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 memory 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.
Social problem solving among depressed adolescents is enhanced by structured psychotherapies
Dietz, Laura J.; Marshal, Michael P.; Burton, Chad M.; Bridge, Jeffrey A.; Birmaher, Boris; Kolko, David; Duffy, Jamira N.; Brent, David A.
2014-01-01
Objective Changes in adolescent interpersonal behavior before and after an acute course of psychotherapy were investigated as outcomes and mediators of remission status in a previously described treatment study of depressed adolescents. Maternal depressive symptoms were examined as moderators of the association between psychotherapy condition and changes in adolescents’ interpersonal behavior. Method Adolescents (n = 63, mean age = 15.6 years, 77.8% female, 84.1% Caucasian) engaged in videotaped interactions with their mothers before randomization to cognitive behavior therapy (CBT), systemic behavior family therapy (SBFT), or nondirective supportive therapy (NST), and after 12–16 weeks of treatment. Adolescent involvement, problem solving and dyadic conflict were examined. Results Improvements in adolescent problem solving were significantly associated with CBT and SBFT. Maternal depressive symptoms moderated the effect of CBT, but not SBFT, on adolescents’ problem solving; adolescents experienced increases in problem solving only when their mothers had low or moderate levels of depressive symptoms. Improvements in adolescents’ problem solving were associated with higher rates of remission across treatment conditions, but there were no significant indirect effects of SBFT on remission status through problem solving. Exploratory analyses revealed a significant indirect effect of CBT on remission status through changes in adolescent problem solving, but only when maternal depressive symptoms at study entry were low. Conclusions Findings provide preliminary support for problem solving as an active treatment component of structured psychotherapies for depressed adolescents and suggest one Pathway by which maternal depression may disrupt treatment efficacy for depressed adolescents treated with CBT. PMID:24491077
Social problem solving among depressed adolescents is enhanced by structured psychotherapies.
Dietz, Laura J; Marshal, Michael P; Burton, Chad M; Bridge, Jeffrey A; Birmaher, Boris; Kolko, David; Duffy, Jamira N; Brent, David A
2014-04-01
Changes in adolescent interpersonal behavior before and after an acute course of psychotherapy were investigated as outcomes and mediators of remission status in a previously described treatment study of depressed adolescents. Maternal depressive symptoms were examined as moderators of the association between psychotherapy condition and changes in adolescents' interpersonal behavior. Adolescents (n = 63, mean age = 15.6 years, 77.8% female, 84.1% White) engaged in videotaped interactions with their mothers before randomization to cognitive behavior therapy (CBT), systemic behavior family therapy (SBFT), or nondirective supportive therapy (NST) and after 12-16 weeks of treatment. Adolescent involvement, problem solving, and dyadic conflict were examined. Improvements in adolescent problem solving were significantly associated with CBT and SBFT. Maternal depressive symptoms moderated the effect of CBT, but not SBFT, on adolescents' problem solving; adolescents experienced increases in problem solving only when their mothers had low or moderate levels of depressive symptoms. Improvements in adolescents' problem solving were associated with higher rates of remission across treatment conditions, but there were no significant indirect effects of SBFT on remission status through problem solving. Exploratory analyses revealed a significant indirect effect of CBT on remission status through changes in adolescent problem solving, but only when maternal depressive symptoms at study entry were low. Findings provide preliminary support for problem solving as an active treatment component of structured psychotherapies for depressed adolescents and suggest one pathway by which maternal depression may disrupt treatment efficacy for depressed adolescents treated with CBT.
Jikang, Zhang; Yuanyuan, Liang
2006-01-01
This paper examines the structural characteristics of China's inter-bank foreign exchange market and evaluates the prospects for the renminbi to become a regional lead currency. While China has made considerable progress in reforming her foreign exchange market and thereby set the preconditions for gradually moving toward more flexibility in her exchange regime, the foreign exchange market is still hampered by several structural and institutional problems that will continue to put a constrain...
Scalar, vector and tensor harmonics on the three-sphere
Lindblom, Lee; Taylor, Nicholas W.; Zhang, Fan
2017-11-01
Scalar, vector and tensor harmonics on the three-sphere were introduced originally to facilitate the study of various problems in gravitational physics. These harmonics are defined as eigenfunctions of the covariant Laplace operator which satisfy certain divergence and trace identities, and ortho-normality conditions. This paper provides a summary of these properties, along with a new notation that simplifies and clarifies some of the key expressions. Practical methods are described for accurately and efficiently computing these harmonics numerically, and test results are given that illustrate how well the analytical identities are satisfied by the harmonics computed numerically in this way.
Poya, Roman; Gil, Antonio J.; Ortigosa, Rogelio
2017-07-01
The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.
Cho, Siu-Yeung; Chi, Zheru; Siu, Wan-Chi; Tsoi, Ah Chung
2003-01-01
Many researchers have explored the use of neural-network representations for the adaptive processing of data structures. One of the most popular learning formulations of data structure processing is backpropagation through structure (BPTS). The BPTS algorithm has been successful applied to a number of learning tasks that involve structural patterns such as logo and natural scene classification. The main limitations of the BPTS algorithm are attributed to slow convergence speed and the long-term dependency problem for the adaptive processing of data structures. In this paper, an improved algorithm is proposed to solve these problems. The idea of this algorithm is to optimize the free learning parameters of the neural network in the node representation by using least-squares-based optimization methods in a layer-by-layer fashion. Not only can fast convergence speed be achieved, but the long-term dependency problem can also be overcome since the vanishing of gradient information is avoided when our approach is applied to very deep tree structures.
Staal, I I E; van den Brink, H A G; Hermanns, J M A; Schrijvers, A J P; van Stel, H F
2011-07-01
Assessment of (early signs of) parenting and developmental problems in young children by preventive child health care (CHC) workers is recommended, but no validated instruments exist. The aim of this project was to develop and test an instrument for early detection and assessment of problems in toddlers, using the perspectives and experience of both the parent and the professional. Using an iterative process, we adapted and expanded a structured interview on need for parenting support into the Structured Problem Analysis of Raising Kids (SPARK). The SPARK consists of 16 subject areas, ranging from somatic health to family issues. The SPARK was tested in daily practice for feasibility and discriminative capacity. The sample consisted of all toddlers aged 18 months living in Zeeland, a province of the Netherlands, during the study period (n= 1140). The response rate was 97.8%. Although the median level of support needed according to the SPARK was low, 4.5% of the toddlers and their parents required intensive help or immediate action. The risk assessment showed 2.9% high, 16.5% increased and 80.6% low risk for parenting and developmental problems. The risk assessment of the CHC professional was associated with known risk factors for child maltreatment. This study shows that a structured interview, named the SPARK, is feasible in daily practice and clarifies risks and care needs for parenting and developmental problems in toddlers. © 2011 Blackwell Publishing Ltd.
Tensor network state correspondence and holography
Singh, Sukhwinder
2018-01-01
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.
Scheifes, Arlette; Egberts, Toine C G|info:eu-repo/dai/nl/162850050; Stolker, Joost Jan; Nijman, Henk L I; Heerdink, Eibert R.
2016-01-01
Background: Polypharmacy and chronic drug use are common in people with intellectual disability and behavioural problems, although evidence of effectiveness and safety in this population is lacking. This study examined the effects of a structured medication review and aimed to improve
Wibawa, Kadek Adi; Nusantara, Toto; Subanji; Parta, I. Nengah
2017-01-01
This study aims to reveal the fragmentation of thinking structure's students in solving the problems of application definite integral in area. Fragmentation is a term on the computer (storage) that is highly relevant correlated with theoretical constructions that occur in the human brain (memory). Almost every student has a different way to…
Topological Design for Acoustic-Structure Interaction Problems with a Mixed Finite Element Method
DEFF Research Database (Denmark)
Yoon, Gil Ho; Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
to subdomain interfaces evolving during the optimization process. In this paper, we propose to use a mixed finite element formulation with displacements and pressure as primary variables (u/p formulation) which eliminates the need for explicit boundary representation. In order to describe the Helmholtz...... acoustic-structure interaction problems are optimized to show the validity of the proposed method....
Problem-Based Learning and Structural Redesign in a Choral Methods Course
Freer, Patrick
2017-01-01
This article describes the process of structural redesign of an undergraduate music education choral methods course. A framework incorporating Problem-based Learning was developed to promote individualized student learning. Ten students participated in the accompanying research study, contributing an array of written and spoken comments as well as…
Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem
Raman, Aaswath
2010-02-26
We formulate the photonic band structure calculation of any lossless dispersive photonic crystal and optical metamaterial as a Hermitian eigenvalue problem. We further show that the eigenmodes of such lossless systems provide an orthonormal basis, which can be used to rigorously describe the behavior of lossy dispersive systems in general. © 2010 The American Physical Society.
Modeling the evolution of lithium-ion particle contact distributions using a fabric tensor approach
Energy Technology Data Exchange (ETDEWEB)
Stershic, Andrew [Duke University; Simunovic, Srdjan [ORNL; Nanda, Jagjit [ORNL
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 positive 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.
Detecting brain dynamics during resting state: a tensor based evolutionary clustering approach
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.
On the Validation of a Numerical Model for the Analysis of Soil-Structure Interaction Problems
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Jorge Luis Palomino Tamayo
Full Text Available Abstract Modeling and simulation of mechanical response of structures, relies on the use of computational models. Therefore, verification and validation procedures are the primary means of assessing accuracy, confidence and credibility in modeling. This paper is concerned with the validation of a three dimensional numerical model based on the finite element method suitable for the dynamic analysis of soil-structure interaction problems. The soil mass, structure, structure's foundation and the appropriate boundary conditions can be represented altogether in a single model by using a direct approach. The theory of porous media of Biot is used to represent the soil mass as a two-phase material which is considered to be fully saturated with water; meanwhile other parts of the system are treated as one-phase materials. Plasticity of the soil mass is the main source of non-linearity in the problem and therefore an iterative-incremental algorithm based on the Newton-Raphson procedure is used to solve the nonlinear equilibrium equations. For discretization in time, the Generalized Newmark-β method is used. The soil is represented by a plasticity-based, effective-stress constitutive model suitable for liquefaction. Validation of the present numerical model is done by comparing analytical and centrifuge test results of soil and soil-pile systems with those results obtained with the present numerical model. A soil-pile-structure interaction problem is also presented in order to shown the potentiality of the numerical tool.
Roldan-Valadez, Ernesto; Rios, Camilo; Cortez-Conradis, David; Favila, Rafael; Moreno-Jimenez, Sergio
2014-01-01
Background Histological behavior of glioblastoma multiforme suggests it would benefit more from a global rather than regional evaluation. A global (whole-brain) calculation of diffusion tensor imaging (DTI) derived tensor metrics offers a valid method to detect the integrity of white matter structures without missing infiltrated brain areas not seen in conventional sequences. In this study we calculated a predictive model of brain infiltration in patients with glioblastoma using global tensor metrics. Methods Retrospective, case and control study; 11 global DTI-derived tensor metrics were calculated in 27 patients with glioblastoma multiforme and 34 controls: mean diffusivity, fractional anisotropy, pure isotropic diffusion, pure anisotropic diffusion, the total magnitude of the diffusion tensor, linear tensor, planar tensor, spherical tensor, relative anisotropy, axial diffusivity and radial diffusivity. The multivariate discriminant analysis of these variables (including age) with a diagnostic test evaluation was performed. Results The simultaneous analysis of 732 measures from 12 continuous variables in 61 subjects revealed one discriminant model that significantly differentiated normal brains and brains with glioblastoma: Wilks’ λ = 0.324, χ2 (3) = 38.907, p < .001. The overall predictive accuracy was 92.7%. Conclusions We present a phase II study introducing a novel global approach using DTI-derived biomarkers of brain impairment. The final predictive model selected only three metrics: axial diffusivity, spherical tensor and linear tensor. These metrics might be clinically applied for diagnosis, follow-up, and the study of other neurological diseases. PMID:24991202
Effect of Physics Problem Solving on Structures Schemes and Knowledge Associations
Setyowidodo, I.; Jatmiko, B.; Susantini, E.; Widodo, S.; Shofwan, A.
2017-09-01
This study aims to develop learners’ thinking structures through associations, case based, and schematic method so that different knowledge structures have a role in influencing the structure of creative thinking. The learners have low mastery of physics materials since they are not given sufficient opportunity to build their own knowledge. They should be directed to approach each new problem or task with their prior knowledge, assimilate new information, and construct their own understanding. The design of this research was a quasi-experiment using purposive sampling. Data were analyzed using variance analysis. The design of this research was a quasi-experiment using purposive sampling. Data were analyzed using variance analysis. The learning process of problemsolving consists of: 1) identifying problems, 2) planning projects, 3) creating projects, 4) presenting projects, and 5) evaluating projects. From the results of this research, it can be concluded that problem-solving method can provide strong supports in developing the learners’ creative thinking skills as they can share their knowledge and interact with their friends and the environment. This learning activity also constitutes an appropriate technique to help the learners to develop problem solving knowledge and skills.
Scheifes, Arlette; Egberts, Toine C G; Stolker, Joost Jan; Nijman, Henk L I; Heerdink, Eibert R
2016-07-01
Polypharmacy and chronic drug use are common in people with intellectual disability and behavioural problems, although evidence of effectiveness and safety in this population is lacking. This study examined the effects of a structured medication review and aimed to improve pharmacotherapy in inpatients with intellectual disability. In a treatment facility for people with mild to borderline intellectual disability and severe behavioural problems, a structured medication review was performed. Prevalence and type of drug-related problems (DRPs) and of the recommended and executed actions were calculated. In a total of 55 patients with intellectual disability and behavioural problems, 284 medications were prescribed, in which a DRP was seen in 106 (34%). No indication/unclear indication was the most prevalent DRP (70). Almost 60% of the recommended actions were also executed. This high prevalence of DRPs is worrying. The structured medication review is a valuable instrument to optimize pharmacotherapy and to support psychiatrists in adequate prescribing of both psychotropic and somatic drugs. © 2015 John Wiley & Sons Ltd.
Huf, P. A.; Carminati, J.
2015-09-01
In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment.
The Racah-Wigner algebra and coherent tensors
Rowe, D. J.; Repka, J.
1996-05-01
We present a set of tensors which are shift tensors (Wigner tensors) in accordance with the definitions of Biedenharn and Louck and satisfy the coherence conditions of Flath and Towber. Our tensors are defined for all connected compact Lie groups and for finite-dimensional representations of connected reductive Lie groups. Thus, we have a realization of the coherent tensors in a rather general setting. Moreover, this realization enables us to confirm most of the conjectures of Flath and Towber concerning the properties of coherent tensors.
Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.
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.
Permittivity and permeability tensors for cloaking applications
Choudhury, Balamati; Jha, Rakesh Mohan
2016-01-01
This book is focused on derivations of analytical expressions for stealth and cloaking applications. An optimal version of electromagnetic (EM) stealth is the design of invisibility cloak of arbitrary shapes in which the EM waves can be controlled within the cloaking shell by introducing a prescribed spatial variation in the constitutive parameters. The promising challenge in design of invisibility cloaks lies in the determination of permittivity and permeability tensors for all the layers. This book provides the detailed derivation of analytical expressions of the permittivity and permeability tensors for various quadric surfaces within the eleven Eisenhart co-ordinate systems. These include the cylinders and the surfaces of revolutions. The analytical modeling and spatial metric for each of these surfaces are provided along with their tensors. This mathematical formulation will help the EM designers to analyze and design of various quadratics and their hybrids, which can eventually lead to design of cloakin...
The pressure tensor in tangential equilibria
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F. Mottez
2004-09-01
Full Text Available The tangential equilibria are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. Such equilibria can be spatially periodic (like waves, or they can separate two regions with asymptotic uniform conditions (like MHD tangential discontinuities. It is possible to compute the velocity moments of the particle distribution function. Even in very simple cases, the pressure tensor is not isotropic and not gyrotropic. The differences between a scalar pressure and the pressure tensor derived in the frame of the Maxwell-Vlasov theory are significant when the gradient scales are of the order of the Larmor radius; they concern mainly the ion pressure tensor.
Quantum Critical Scaling of the Geometric Tensors
Campos Venuti, Lorenzo; Zanardi, Paolo
2007-08-01
Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this Letter we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.
Spectral analysis of the full gravity tensor
Rummel, R.; van Gelderen, M.
1992-10-01
It is shown that, when the five independent components of the gravity tensor are grouped into (Gamma-zz), (Gamma-xz, Gamma-yz), and (Gamma-xx - Gamma-yy, 2Gamma-xy) sets and expanded into an infinite series of pure-spin spherical harmonic tensors, it is possible to derive simple eigenvalue connections between these three sets and the spherical harmonic expansion of the gravity potential. The three eigenvalues are (n + 1)(n + 2), -(n + 2) sq rt of n(n + 1), and sq rt of (n - 1)n(n + 1)(n + 2). The joint ESA and NASA Aristoteles mission is designed to measure with high precision the tensor components Gamma-zz, Gamma-yz, and Gamma-yy, which will make it possible to determine the global gravity field in six months time with a high precision.
Delvaux, D.
2012-04-01
The Win-Tensor program is an interactive computer program for fracture analysis and crustal stress reconstruction, freely distributed to the scientific and academic community and widely used by structural geologists. It was developed with a constant feed-back from the users and is regularly upgraded. Version 4.0 released in January 2012 provides as a new feature the standard deviation of the horizontal stress axes (SHmax/SHmin) and the stress regime Index R'. The latter expresses the relative stress magnitudes and the nature of the vertical stress in a continuous scale, ranging from 1 to 3. Computation of the standard deviations is based on the examination of all possible reduced stress tensors for a particular stress solution obtained from the inversion of fault-slip or focal mechanism data. They are defined by combining the possible values of each individual stress axes (sigma 1, sigma 2, sigma 3) and the stress ratio R = (sigma2-sigma3)/(sigma1-sigma3). For each possible reduced tensors, the horizontal paleostress directions (SHmax/SHmin) and regime (R') are computed and the related 1 sigma standard deviations determined. This way, the 4 dimensions of the reduced stress tensor are reduced to a two dimensional expression with is commonly used to depict the horizontal stress trajectories as in the World Stress Map project. This procedure has been implemented for the three different methods for reconstructing the reduced stress tensors in Win-Tensor: PBT Right Dihedron and Rotational Optimisation. The advantages of this statistical expression of stress parameters are demonstrated using practical examples. Win-Tensor program can be downloaded from the Tensor web site: http://www.damiendelvaux.be/Tensor/tensor-index.html
Nguyen, Duc T.
1990-01-01
Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process where one starts with an initial design, a finite element structure analysis is then performed to calculate the response of the system (such as displacements, stresses, eigenvalues, etc.). Based upon the sensitivity information on the objective and constraint functions, an optimizer such as ADS or IDESIGN, can be used to find the new, improved design. For the structural analysis phase, the equation solver for the system of simultaneous, linear equations plays a key role since it is needed for either static, or eigenvalue, or dynamic analysis. For practical, large-scale structural analysis-synthesis applications, computational time can be excessively large. Thus, it is necessary to have a new structural analysis-synthesis code which employs new solution algorithms to exploit both parallel and vector capabilities offered by modern, high performance computers such as the Convex, Cray-2 and Cray-YMP computers. The objective of this research project is, therefore, to incorporate the latest development in the parallel-vector equation solver, PVSOLVE into the widely popular finite-element production code, such as the SAP-4. Furthermore, several nonlinear unconstrained optimization subroutines have also been developed and tested under a parallel computer environment. The unconstrained optimization subroutines are not only useful in their own right, but they can also be incorporated into a more popular constrained optimization code, such as ADS.
Knol, Anne B; Briggs, David J; Lebret, Erik
2010-06-15
Many environmental risks are multi-faceted and their health consequences can be far-ranging in both time and space. It can be a challenging task to develop informed policies for such risks. Integrated environmental health impact assessment aims to support policy by assessing environmental health effects in ways that take into account the complexities and uncertainties involved. For such assessment to be successful, a clear and agreed conceptual framework is needed, which defines the issue under consideration and sets out the principles on which the assessment is based. Conceptual frameworks facilitate involvement of stakeholders, support harmonized discussions, help to make assumptions explicit, and provide a framework for data analysis and interpretation. Various conceptual frameworks have been developed for different purposes, but as yet no clear taxonomy exists. We propose a three-level taxonomy of conceptual frameworks for use in environmental health impact assessment. At the first level of the taxonomy, structural frameworks show the wide context of the issues at hand. At the second level, relational frameworks describe how the assessment variables are causally related. At the third level, this causal structure is translated into an operational model, which serves as a basis for analysis. The different types of frameworks are complementary and all play a role in the assessment process. The taxonomy is illustrated using a hypothetical assessment of urban brownfield development for residential uses. We suggest that a better understanding of types of conceptual frameworks and their potential roles in the different phases of assessment will contribute to more informed assessments and policies. Copyright 2010 Elsevier B.V. All rights reserved.
Analysis and control of Boolean networks a semi-tensor product approach
Cheng, Daizhan; Li, Zhiqiang
2010-01-01
This book presents a new approach to the investigation of Boolean control networks, using the semi-tensor product (STP), which can express a logical function as a conventional discrete-time linear system. This makes it possible to analyze basic control problems.
The gravitational wave stress–energy (pseudo)-tensor in modified gravity
Saffer, Alexander; Yunes, Nicolás; Yagi, Kent
2018-03-01
The recent detections of gravitational waves by the advanced LIGO and Virgo detectors open up new tests of modified gravity theories in the strong-field and dynamical, extreme gravity regime. Such tests rely sensitively on the phase evolution of the gravitational waves, which is controlled by the energy–momentum carried by such waves out of the system. We here study four different methods for finding the gravitational wave stress–energy pseudo-tensor in gravity theories with any combination of scalar, vector, or tensor degrees of freedom. These methods rely on the second variation of the action under short-wavelength averaging, the second perturbation of the field equations in the short-wavelength approximation, the construction of an energy complex leading to a Landau–Lifshitz tensor, and the use of Noether’s theorem in field theories about a flat background. We apply these methods in general relativity, Jordan–Fierz–Brans–Dicky theoy, and Einstein-Æther theory to find the gravitational wave stress–energy pseudo-tensor and calculate the rate at which energy and linear momentum is carried away from the system. The stress–energy tensor and the rate of linear momentum loss in Einstein-Æther theory are presented here for the first time. We find that all methods yield the same rate of energy loss, although the stress–energy pseudo-tensor can be functionally different. We also find that the Noether method yields a stress–energy tensor that is not symmetric or gauge-invariant, and symmetrization via the Belinfante procedure does not fix these problems because this procedure relies on Lorentz invariance, which is spontaneously broken in Einstein-Æther theory. The methods and results found here will be useful for the calculation of predictions in modified gravity theories that can then be contrasted with observations.
Traffic Volume Data Outlier Recovery via Tensor Model
Directory of Open Access Journals (Sweden)
Huachun Tan
2013-01-01
Full Text Available Traffic volume data is already collected and used for a variety of purposes in intelligent transportation system (ITS. However, the collected data might be abnormal due to the problem of outlier data caused by malfunctions in data collection and record systems. To fully analyze and operate the collected data, it is necessary to develop a validate method for addressing the outlier data. Many existing algorithms have studied the problem of outlier recovery based on the time series methods. In this paper, a multiway tensor model is proposed for constructing the traffic volume data based on the intrinsic multilinear correlations, such as day to day and hour to hour. Then, a novel tensor recovery method, called ADMM-TR, is proposed for recovering outlier data of traffic volume data. The proposed method is evaluated on synthetic data and real world traffic volume data. Experimental results demonstrate the practicability, effectiveness, and advantage of the proposed method, especially for the real world traffic volume data.
Improving Tensor Based Recommenders with Clustering
DEFF Research Database (Denmark)
Leginus, Martin; Dolog, Peter; Zemaitis, Valdas
2012-01-01
Social tagging systems (STS) model three types of entities (i.e. tag-user-item) and relationships between them are encoded into a 3-order tensor. Latent relationships and patterns can be discovered by applying tensor factorization techniques like Higher Order Singular Value Decomposition (HOSVD),...... of the recommendations and execution time are improved and memory requirements are decreased. The clustering is motivated by the fact that many tags in a tag space are semantically similar thus the tags can be grouped. Finally, promising experimental results are presented...
Blue running of the primordial tensor spectrum
Energy Technology Data Exchange (ETDEWEB)
Gong, Jinn-Ouk, E-mail: jinn-ouk.gong@apctp.org [Asia Pacific Center for Theoretical Physics, Pohang 790-784 (Korea, Republic of)
2014-07-01
We examine the possibility of positive spectral index of the power spectrum of the primordial tensor perturbation produced during inflation in the light of the detection of the B-mode polarization by the BICEP2 collaboration. We find a blue tilt is in general possible when the slow-roll parameter decays rapidly. We present two known examples in which a positive spectral index for the tensor power spectrum can be obtained. We also briefly discuss other consistency tests for further studies on inflationary dynamics.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based...
Tensor analysis methods for activity characterization in spatiotemporal data
Energy Technology Data Exchange (ETDEWEB)
Haass, Michael Joseph; Van Benthem, Mark Hilary; Ochoa, Edward M
2014-03-01
Tensor (multiway array) factorization and decomposition offers unique advantages for activity characterization in spatio-temporal datasets because these methods are compatible with sparse matrices and maintain multiway structure that is otherwise lost in collapsing for regular matrix factorization. This report describes our research as part of the PANTHER LDRD Grand Challenge to develop a foundational basis of mathematical techniques and visualizations that enable unsophisticated users (e.g. users who are not steeped in the mathematical details of matrix algebra and mulitway computations) to discover hidden patterns in large spatiotemporal data sets.
Triangular Alignment (TAME). A Tensor-based Approach for Higher-order Network Alignment
Energy Technology Data Exchange (ETDEWEB)
Mohammadi, Shahin [Purdue Univ., West Lafayette, IN (United States); Gleich, David F. [Purdue Univ., West Lafayette, IN (United States); Kolda, Tamara G. [Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Grama, Ananth [Purdue Univ., West Lafayette, IN (United States)
2015-11-01
Network alignment is an important tool with extensive applications in comparative interactomics. Traditional approaches aim to simultaneously maximize the number of conserved edges and the underlying similarity of aligned entities. We propose a novel formulation of the network alignment problem that extends topological similarity to higher-order structures and provide a new objective function that maximizes the number of aligned substructures. This objective function corresponds to an integer programming problem, which is NP-hard. Consequently, we approximate this objective function as a surrogate function whose maximization results in a tensor eigenvalue problem. Based on this formulation, we present an algorithm called Triangular AlignMEnt (TAME), which attempts to maximize the number of aligned triangles across networks. We focus on alignment of triangles because of their enrichment in complex networks; however, our formulation and resulting algorithms can be applied to general motifs. Using a case study on the NAPABench dataset, we show that TAME is capable of producing alignments with up to 99% accuracy in terms of aligned nodes. We further evaluate our method by aligning yeast and human interactomes. Our results indicate that TAME outperforms the state-of-art alignment methods both in terms of biological and topological quality of the alignments.
Key Labeling Technologies to Tackle Sizeable Problems in RNA Structural Biology
Directory of Open Access Journals (Sweden)
Kwaku T. Dayie
2008-07-01
Full Text Available The ability to adopt complex three-dimensional (3D structures that can rapidly interconvert between multiple functional states (folding and dynamics is vital for the proper functioning of RNAs. Consequently, RNA structure and dynamics necessarily determine their biological function. In the post-genomic era, it is clear that RNAs comprise a larger proportion (>50% of the transcribed genome compared to proteins (Ã¢Â‰Â¤ 2%. Yet the determination of the 3D structures of RNAs lags considerably behind those of proteins and to date there are even fewer investigations of dynamics in RNAs compared to proteins. Site specific incorporation of various structural and dynamic probes into nucleic acids would likely transform RNA structural biology. Therefore, various methods for introducing probes for structural, functional, and biotechnological applications are critically assessed here. These probes include stable isotopes such as 2H, 13C, 15N, and 19F. Incorporation of these probes using improved RNA ligation strategies promises to change the landscape of structural biology of supramacromolecules probed by biophysical tools such as nuclear magnetic resonance (NMR spectroscopy, X-ray crystallography and Raman spectroscopy. Finally, some of the structural and dynamic problems that can be addressed using these technological advances are outlined.
Features of inverse problem arise from structure of a general pure Mueller matrix
Savenkov, Sergey N.; Oberemok, Yevgen A.; Nikonov, Vladimir N.
2009-08-01
Changes in the state of polarization of a beam of radiation occurring without depolarization can be described by means of a pure Mueller matrix. Pure Mueller matrix can be expressed in terms of the elements of a 2x2 Jones matrix. This results in that the pure Mueller matrix has a simple and elegant structure, which is embodied by interrelations between matrix elements. All possible interrelations for the elements of a general pure Mueller matrix are derived by Hovenier (Appl. Opt., Vol.33, No.36, pp. 8318-8324, 1994). The structure of the pure Mueller matrix enables to solve the inverse problem basing not on all sixteen matrix elements but only on certain part of them. We show that four elements which are formed each of columns and rows of the pure Mueller matrix considering them individually are dependent and the inverse problem can be solved in general case basing only on the rest of twelve matrix elements.
THE APPLICATION OF WAVELET-MULTIFRACTAL ANALYSIS IN PROBLEMS OF METAL STRUCTURE
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VOLCHUK V. N.
2015-09-01
Full Text Available Raising of problem. In order to obtain acceptable results of the evaluation of the metal structure developed methodology should include the use of both classical and modern methods of its evaluation and the properties of the produced goods. Thus, to establish the relationship between mechanical properties and structural elements of metal to use multifractal theory. The proposed method is the most appropriate to quantify the majority of real structures, which are integral approximation figures Euclid introduces some uncertainty, and therefore not always acceptable in practical problems of modern materials science. According to the proposed method, each of heterogeneous objects, which are the structures most metals can be characterized by variety of statistical Renyi dimensions. The range of dimensions multifractals interpreted as some of the physical laws, which have a separate statistical properties that make it possible to their financial performance. Application of statistical dimensions of the structural elements for the assessment of qualitative characteristics of metal contributes to their formalization as a function of the fractal dimension. This in turn makes it possible to identify and anticipate the physical and mechanical properties of the metal without producing special mechanical tests. Purpose obtain information about the possible application of wavelet-multifractal analysis to assess the microstructure of the metal. Conclusion. Using the methods of wavelet multifractal analysis, a statistical evaluation of the structural elements of steel St3ps. An analysis of the characteristics of uniformity, consistency and regularity of the structural elements has shown that most of the change observed in the samples subjected to accelerated cooling water in the temperature range of the intermediate (bainitic conversion 550 – 4500С, less - in samples cooled in the temperature range 650 pearlite transformation 6000С and the smallest
Applications of tensor (multiway array) factorizations and decompositions in data mining
DEFF Research Database (Denmark)
Mørup, Morten
2011-01-01
Tensor (multiway array) factorization and decomposition has become an important tool for data mining. Fueled by the computational power of modern computer researchers can now analyze large-scale tensorial structured data that only a few years ago would have been impossible. Tensor factorizations...... have several advantages over two-way matrix factorizations including uniqueness of the optimal solution and component identification even when most of the data is missing. Furthermore, multiway decomposition techniques explicitly exploit the multiway structure that is lost when collapsing some...... of the modes of the tensor in order to analyze the data by regular matrix factorization approaches. Multiway decomposition is being applied to new fields every year and there is no doubt that the future will bring many exciting new applications. The aim of this overview is to introduce the basic concepts...
A Semi-Automated Approach for Structuring Multi Criteria Decision Problems
Maier, Konradin; Stix, Volker
2013-01-01
This article seeks to enhance multi criteria decision making by providing a scientic approach for decomposing and structuring decision problems. We propose a process, based on concept mapping, which integrates group creativity techniques, card sorting procedures, quantitative data analysis and algorithmic automatization to construct meaningful and complete hierarchies of criteria. The algorithmic aspect is covered by a newly proposed recursive cluster algorithm, which automatically generat...
Yıldırım, Emre Alper; Koca, Esra
2012-01-01
Motivated by the spare parts distribution system of a major automotive manufacturer in Turkey, we consider a multicommodity distribution problem from a central depot to a number of geographically dispersed demand points. The distribution of the items is carried out by a set of identical vehicles. The demand of each demand point can be satisfied by several vehicles and a single vehicle is allowed to serve multiple demand points. For a given vehicle, the cost structure is dictated by the farthe...
On the structure of 3-dimensional 2-body problem solutions in Wheeler-Feynman electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Klimenko, S. [Institute for High Energy Physics, Protvino (Russian Federation); Nikitin, I. [National Research Center for Information Technology, St. Augustin (Germany)
2001-09-01
The problem of the relativistic 3-dimensional motion of 2 oppositely charged equally massive particles in classical electrodynamics with half-retarded/half-advanced interactions is investigated. It is shown that at a certain critical energy value the topological structure of phase space is changed, leading to bifurcation (splitting) of solutions, appearance of extra non-Newtonian degrees of freedom and break of reflectional symmetries.
Zhu, Yanjie; Peng, Xi; Wu, Yin; Wu, Ed X; Ying, Leslie; Liu, Xin; Zheng, Hairong; Liang, Dong
2017-02-01
To develop a new model-based method with spatial and parametric constraints (MB-SPC) aimed at accelerating diffusion tensor imaging (DTI) by directly estimating the diffusion tensor from highly undersampled k-space data. The MB-SPC method effectively incorporates the prior information on the joint sparsity of different diffusion-weighted images using an L1-L2 norm and the smoothness of the diffusion tensor using a total variation seminorm. The undersampled k-space datasets were obtained from fully sampled DTI datasets of a simulated phantom and an ex-vivo experimental rat heart with acceleration factors ranging from 2 to 4. The diffusion tensor was directly reconstructed by solving a minimization problem with a nonlinear conjugate gradient descent algorithm. The reconstruction performance was quantitatively assessed using the normalized root mean square error (nRMSE) of the DTI indices. The MB-SPC method achieves acceptable DTI measures at an acceleration factor up to 4. Experimental results demonstrate that the proposed method can estimate the diffusion tensor more accurately than most existing methods operating at higher net acceleration factors. The proposed method can significantly reduce artifact, particularly at higher acceleration factors or lower SNRs. This method can easily be adapted to MR relaxometry parameter mapping and is thus useful in the characterization of biological tissue such as nerves, muscle, and heart tissue. © 2016 American Association of Physicists in Medicine.
Diffractometric measurement of the temperature dependence of piezoelectric tensor in GMO monocrystal
Breczko, Teodor; Lempaszek, Andrzej
2007-04-01
Functional materials, of which an example is ferroelectric, ferroelastic monocrystal of molybdate (III) gadolinium (VI), are often used in the micro-motor operators (micro-servo motors) working in changeable environment conditions. Most frequently this change refers to temperature. That is why the important practical problem is the precise measurement of the value of piezoelectric tensor elements in dependence on the temperature of a particular monocrystal. In the presented article for this kind of measurements, the use of X-ray diffractometer has been shown. The advantage of the method presented is that, apart from precise dependence measurement between the temperature of a monocrystal and the value of piezoelectric tensor elements, it enables synchronous measurement of the value of thermal expansion tensor elements for a monocrystal.
Observations About the Projective Tensor Product of Banach Spaces
African Journals Online (AJOL)
, 46B, 46E, 47B. Keywords: tensor, Banach, banach space, tensor product, projective norm, greatest crossnorm, semi-embedding, Radon-Nikodym property, absolutely p-summable sequence, strongly p-summable sequence, topological linear ...
Directory of Open Access Journals (Sweden)
Irappa Basappa Hunagund
2018-10-01
Full Text Available In this article, we propose Simulated Annealing (SA heuristic to solve Unequal Area Dynamic Facility Layout Problem (FBS with Flexible Bay Structure (UA-DFLPs with FBS. The UA-DFLP with FBS is the problem of determining the facilities dimension and their location coordinates with flexible bays formation in the layout for various periods of the planning horizon. The UA-DFLP with FBS is more constrained than general UA-DFLP and it is an NP-complete problem. The proposed SA is tested with the available UA-DFLPs instances in the literature. The proposed SA heuristic has given new best solution or the same solution for FBS based problems as compared with the best-known reported in the UA-DFLPs with FBS literature. The proposed SA heuristic is also tested on standard UA-DFLPs used in non-FBS approaches. The SA heuristic solution is not significantly different from the best solution reported in the literature for non-FBS approaches. Equal area DFLP instances are also solved with the proposed SA and the results obtained are promising with the solutions reported in the literature. Hence the results obtained indicate that the proposed SA for UA-DFLP with FBS is effective and versatile for both equal and unequal area dynamic facility layout problems. The computational efficiency of the proposed SA heuristic is very much competitive as compared to other meta-heuristics computational timings reported in the literature.
Coelho, V N; Coelho, I M; Souza, M J F; Oliveira, T A; Cota, L P; Haddad, M N; Mladenovic, N; Silva, R C P; Guimarães, F G
2016-01-01
This article presents an Evolution Strategy (ES)--based algorithm, designed to self-adapt its mutation operators, guiding the search into the solution space using a Self-Adaptive Reduced Variable Neighborhood Search procedure. In view of the specific local search operators for each individual, the proposed population-based approach also fits into the context of the Memetic Algorithms. The proposed variant uses the Greedy Randomized Adaptive Search Procedure with different greedy parameters for generating its initial population, providing an interesting exploration-exploitation balance. To validate the proposal, this framework is applied to solve three different [Formula: see text]-Hard combinatorial optimization problems: an Open-Pit-Mining Operational Planning Problem with dynamic allocation of trucks, an Unrelated Parallel Machine Scheduling Problem with Setup Times, and the calibration of a hybrid fuzzy model for Short-Term Load Forecasting. Computational results point out the convergence of the proposed model and highlight its ability in combining the application of move operations from distinct neighborhood structures along the optimization. The results gathered and reported in this article represent a collective evidence of the performance of the method in challenging combinatorial optimization problems from different application domains. The proposed evolution strategy demonstrates an ability of adapting the strength of the mutation disturbance during the generations of its evolution process. The effectiveness of the proposal motivates the application of this novel evolutionary framework for solving other combinatorial optimization problems.
Effective field theory approaches for tensor potentials
Energy Technology Data Exchange (ETDEWEB)
Jansen, Maximilian
2016-11-14
Effective field theories are a widely used tool to study physical systems at low energies. We apply them to systematically analyze two and three particles interacting via tensor potentials. Two examples are addressed: pion interactions for anti D{sup 0}D{sup *0} scattering to dynamically generate the X(3872) and dipole interactions for two and three bosons at low energies. For the former, the one-pion exchange and for the latter, the long-range dipole force induce a tensor-like structure of the potential. We apply perturbative as well as non-perturbative methods to determine low-energy observables. The X(3872) is of major interest in modern high-energy physics. Its exotic characteristics require approaches outside the range of the quark model for baryons and mesons. Effective field theories represent such methods and provide access to its peculiar nature. We interpret the X(3872) as a hadronic molecule consisting of neutral D and D{sup *} mesons. It is possible to apply an effective field theory with perturbative pions. Within this framework, we address chiral as well as finite volume extrapolations for low-energy observables, such as the binding energy and the scattering length. We show that the two-point correlation function for the D{sup *0} meson has to be resummed to cure infrared divergences. Moreover, next-to-leading order coupling constants, which were introduced by power counting arguments, appear to be essential to renormalize the scattering amplitude. The binding energy as well as the scattering length display a moderate dependence on the light quark masses. The X(3872) is most likely deeper bound for large light quark masses. In a finite volume on the other hand, the binding energy significantly increases. The dependence on the light quark masses and the volume size can be simultaneously obtained. For bosonic dipoles we apply a non-perturbative, numerical approach. We solve the Lippmann-Schwinger equation for the two-dipole system and the Faddeev
STATEMENT ON THE ISSUE OF THE PROBLEM IDENTIFICATION OF FRACTAL METAL STRUCTURES
Directory of Open Access Journals (Sweden)
BOLSHAKOV V. I.
2016-05-01
Full Text Available Summary. To study the structure of metals and alloys and its influence on their properties are widely used traditional methods of macro- and microanalysis, X-ray, spectral, thermal and inspection (X-ray, magnetic, ultrasonic. They have their own threshold, often narrowly focused and applied directly depending on the purpose of the research object (pipe, forming rolls, metal, etc.. Currently existing mathematical models of forecasting the qualitative characteristics of metal products based only on an analysis of statistical data do not provide physical-chemical interpretation of the processes that occur during the formation of the structure or who could definitely take into account the effect of the chemical composition and other parameters of the technology. Therefore, the forecast results can not always meet the requirements. In order to obtain acceptable quality results produced by the product specifications developed by the forecast methodology should include the use of both classical and modern methods of structure evaluation. So, to determine the relationship between mechanical properties and structure elements of cast iron roll is planned to use the theory of fractals and multifractal. The proposed method is the most appropriate to quantify the majority of real structures, which the integer approximation of the figures of Euclid introduces some uncertainty, and therefore not always acceptable in practical problems of modern materials. In this regard, it is assumed conducting special experiments, the analysis of which allows to develop a qualitative evaluation of the mechanical properties of the investigated steels and cast iron. As a result of analysis of the production technology of steel and iron and research work aimed at solving the problem of evaluating the mechanical properties of the formulated problem statement of operational forecasting of these properties and the basic ways of its solution.
Revitalizing problem based learning: student and tutor attitudes towards a structured tutorial.
Espey, Eve; Ogburn, Tony; Kalishman, Summers; Zsemlye, Meggan; Cosgrove, Ellen
2007-03-01
The pre-clinical curriculum at the University of New Mexico School of Medicine is a hybrid model that includes small group, problem-based learning (PBL) tutorials and didactic lectures. A structured tutorial format was piloted for the human sexuality/reproduction organ system block for the PBL component. The objective of this study was to compare the acceptability of the structured format and its effectiveness with that of a traditional PBL tutorial. Students were surveyed after the renal/endocrinology block of 2004 (traditional tutorial format) and after the human sexuality/reproduction block of 2004 (structured tutorial format) (n = 70). Survey questions covered the quality of learning and of tutorial. Students (n = 132) and tutors (n = 24) who participated in human sexuality/reproduction in 2004 and 2005 were surveyed for attitudes about the structured tutorial overall and specific components. Means of responses were compared using t-tests. Students indicated that the structured tutorial format supported a greater improvement in their basic science and clinical knowledge and their ability to evaluate information (p < 0.05). The majority of students and tutors recommended the structured format for tutorials in other blocks. We demonstrated the acceptability of a structured tutorial format to students and faculty. Faculty members perceived greater depth of learning and participation by the students.
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-03-05
In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
... ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is constructed. It is used to derive Einstein's planetary equation of motion and photon equation of motion in the vicinity of the rotating homogeneous spherical mass.
Families of twisted tensor product codes
Giuzzi, Luca; Pepe, Valentina
2011-01-01
Using geometric properties of the variety $\\cV_{r,t}$, the image under the Grassmannian map of a Desarguesian $(t-1)$-spread of $\\PG(rt-1,q)$, we introduce error correcting codes related to the twisted tensor product construction, producing several families of constacyclic codes. We exactly determine the parameters of these codes and characterise the words of minimum weight.
Tensors in image processing and computer vision
De Luis García, Rodrigo; Tao, Dacheng; Li, Xuelong
2009-01-01
Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the developments in this branch of signal processing, offering research and discussions by experts in the area. It is suitable for advanced students working in the area of computer vision and image processing.
Fermionic topological quantum states as tensor networks
Wille, C.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.
Visualization and processing of tensor fields
Weickert, Joachim
2007-01-01
Presents information on the visualization and processing of tensor fields. This book serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as a textbook for specialized classes and seminars for graduate and doctoral students.
Magnetotelluric impedance tensor analysis for identification of ...
Indian Academy of Sciences (India)
We present the results of magnetotelluric (MT) impedance tensors analyses of 18 sites located along a profile cutting various faults in the uplifted Wagad block of the Kachchh basin. The MT time series of 4–5 days recording duration have been processed and the earth response functions are estimated in broad frequency ...
Radiation Forces and Torques without Stress (Tensors)
Bohren, Craig F.
2011-01-01
To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…
Introduction to vector and tensor analysis
Wrede, Robert C
1972-01-01
A broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.
Tensor B mode and stochastic Faraday mixing
Giovannini, Massimo
2014-01-01
This paper investigates the Faraday effect as a different source of B mode polarization. The E mode polarization is Faraday rotated provided a stochastic large-scale magnetic field is present prior to photon decoupling. In the first part of the paper we discuss the case where the tensor modes of the geometry are absent and we argue that the B mode recently detected by the Bicep2 collaboration cannot be explained by a large-scale magnetic field rotating, through the Faraday effect, the well established E mode polarization. In this case, the observed temperature autocorrelations would be excessively distorted by the magnetic field. In the second part of the paper the formation of Faraday rotation is treated as a stationary, random and Markovian process with the aim of generalizing a set of scaling laws originally derived in the absence of the tensor modes of the geometry. We show that the scalar, vector and tensor modes of the brightness perturbations can all be Faraday rotated even if the vector and tensor par...
Holographic coherent states from random tensor networks
Qi, Xiao-Liang; Yang, Zhao; You, Yi-Zhuang
2017-08-01
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we generalize the random tensor network approach to allow quantum superposition of different spatial geometries. We setup a framework in which all possible bulk spatial geometries, characterized by weighted adjacient matrices of all possible graphs, are mapped to the boundary Hilbert space and form an overcomplete basis of the boundary. We name such an overcomplete basis as holographic coherent states. A generic boundary state can be expanded in this basis, which describes the state as a superposition of different spatial geometries in the bulk. We discuss how to define distinct classical geometries and small fluctuations around them. We show that small fluctuations around classical geometries define "code subspaces" which are mapped to the boundary Hilbert space isometrically with quantum error correction properties. In addition, we also show that the overlap between different geometries is suppressed exponentially as a function of the geometrical difference between the two geometries. The geometrical difference is measured in an area law fashion, which is a manifestation of the holographic nature of the states considered.
Flaga, Kazimierz; Furtak, Kazimierz
2015-03-01
Steel-concrete composite structures have been used in bridge engineering from decades. This is due to rational utilisation of the strength properties of the two materials. At the same time, the reinforced concrete (or prestressed) deck slab is more favourable than the orthotropic steel plate used in steel bridges (higher mass, better vibration damping, longer life). The most commonly found in practice are composite girder bridges, particularly in highway bridges of small and medium spans, but the spans may reach over 200 m. In larger spans steel truss girders are applied. Bridge composite structures are also employed in cable-stayed bridge decks of the main girder spans of the order of 600, 800 m. The aim of the article is to present the cionstruction process and strength analysis problems concerning of this type of structures. Much attention is paid to the design and calculation of the shear connectors characteristic for the discussed objects. The authors focused mainly on the issues of single composite structures. The effect of assembly states on the stresses and strains in composite members are highlighted. A separate part of problems is devoted to the influence of rheological factors, i.e. concrete shrinkage and creep, as well as thermal factors on the stresses and strains and redistribution of internal forces.
Directory of Open Access Journals (Sweden)
Neculai Curteanu
2012-10-01
Full Text Available In this paper we point out some difficult problems of thesaurus-dictionary entry parsing, relying on the parsing technology of SCD (Segmentation-Cohesion-Dependency configurations, successfully applied on six largest thesauri -- Romanian (2, French, German (2, and Russian. \\textbf{Challenging Problems:} \\textbf{(a}~Intricate and~/~or recursive structures of the lexicographic segments met in the entries of certain thesauri; \\textbf{(b}~Cyclicity (recursive calls of some sense marker classes on marker sequences; \\textbf{(c}~Establishing the hypergraph-driven dependencies between all the atomic and non-atomic sense definitions. Classical approach to solve these parsing problems is hard mainly because of depth-first search of sense definitions and markers, the substantial complexity of entries, and the sense tree dynamic construction embodied within these parsers. \\textbf{SCD-based Parsing Solutions:} \\textbf{(a}~The SCD parsing method is a procedural tool, completely formal grammar-free, handling the recursive structure of the lexicographic segments by procedural non-recursive calls performed on the SCD parsing configurations of the entry structure. \\textbf{(b}~For dealing with cyclicity (recursive calls between secondary sense markers and the sense enumeration markers, we proposed the Enumeration Closing Condition, sometimes coupled with New{\\_}Paragraphs typographic markers transformed into numeral sense enumeration. \\textbf{(c}~These problems, their lexicographic modeling and parsing solutions are addressed to both dictionary parser programmers to experience the SCD-based parsing method, as well as to lexicographers and thesauri designers for tailoring balanced lexical-semantics granularities and sounder sense tree definitions of the dictionary entries.
The operator tensor formulation of quantum theory.
Hardy, Lucien
2012-07-28
In this paper, we provide what might be regarded as a manifestly covariant presentation of discrete quantum theory. A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation (e.g. B(b(2)a(3))(a(1))) can have zero or more quantum systems inputted into it and zero or more quantum systems outputted from it. The operation B(b(2)a(3))(a(1)) has one system of type a inputted, and one system of type b and one system of type a outputted. We can wire together operations to form circuits, for example, A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Each repeated integer label here denotes a wire connecting an output to an input of the same type. As each operation in a circuit has an outcome associated with it, a circuit represents a set of outcomes that can happen in a run of the experiment. In the operator tensor formulation of quantum theory, each operation corresponds to an operator tensor. For example, the operation B(b(2)a(3))(a(1)) corresponds to the operator tensor B(b(2)a(3))(a(1)). Further, the probability for a general circuit is given by replacing operations with corresponding operator tensors as in Prob(A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3))) = Â(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Repeated integer labels indicate that we multiply in the associated subspace and then take the partial trace over that subspace. Operator tensors must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).
Using concept mapping to evaluate knowledge structure in problem-based learning.
Hung, Chia-Hui; Lin, Chen-Yung
2015-11-27
Many educational programs incorporate problem-based learning (PBL) to promote students' learning; however, the knowledge structure developed in PBL remains unclear. The aim of this study was to use concept mapping to generate an understanding of the use of PBL in the development of knowledge structures. Using a quasi-experimental study design, we employed concept mapping to illustrate the effects of PBL by examining the patterns of concepts and differences in the knowledge structures of students taught with and without a PBL approach. Fifty-two occupational therapy undergraduates were involved in the study and were randomly divided into PBL and control groups. The PBL group was given two case scenarios for small group discussion, while the control group continued with ordinary teaching and learning. Students were asked to make concept maps after being taught about knowledge structure. A descriptive analysis of the morphology of concept maps was conducted in order to compare the integration of the students' knowledge structures, and statistical analyses were done to understand the differences between groups. Three categories of concept maps were identified as follows: isolated, departmental, and integrated. The students in the control group constructed more isolated maps, while the students in the PBL group tended toward integrated mapping. Concept Relationships, Hierarchy Levels, and Cross Linkages in the concept maps were significantly greater in the PBL group; however, examples of concept maps did not differ significantly between the two groups. The data indicated that PBL had a strong effect on the acquisition and integration of knowledge. The important properties of PBL, including situational learning, problem spaces, and small group interactions, can help students to acquire more concepts, achieve an integrated knowledge structure, and enhance clinical reasoning.
Beiki, Majid
2011-01-01
Gravity gradient tensor (GGT) data contains the second derivatives of the Earth’s gravitational potential in three orthogonal directions. GGT data can be measured either using land, airborne, marine or space platforms. In the last two decades, the applications of GGT data in hydrocarbon exploration, mineral exploration and structural geology have increased considerably. This work focuses on developing new interpretation techniques for GGT data as well as pseudo-gravity gradient tensor (PGGT) ...
Identifying key nodes in multilayer networks based on tensor decomposition
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.
Real-time MR diffusion tensor and Q-ball imaging using Kalman filtering.
Poupon, Cyril; Roche, Alexis; Dubois, Jessica; Mangin, Jean-François; Poupon, Fabrice
2008-10-01
Diffusion magnetic resonance imaging (dMRI) has become an established research tool for the investigation of tissue structure and orientation. In this paper, we present a method for real-time processing of diffusion tensor and Q-ball imaging. The basic idea is to use Kalman filtering framework to fit either the linear tensor or Q-ball model. Because the Kalman filter is designed to be an incremental algorithm, it naturally enables updating the model estimate after the acquisition of any new diffusion-weighted volume. Processing diffusion models and maps during ongoing scans provides a new useful tool for clinicians, especially when it is not possible to predict how long a subject may remain still in the magnet. First, we introduce the general linear models corresponding to the two diffusion tensor and analytical Q-ball models of interest. Then, we present the Kalman filtering framework and we focus on the optimization of the diffusion orientation sets in order to speed up the convergence of the online processing. Last, we give some results on a healthy volunteer for the online tensor and the Q-ball model, and we make some comparisons with the conventional offline techniques used in the literature. We could achieve full real-time for diffusion tensor imaging and deferred time for Q-ball imaging, using a single workstation.
Kubo, Atsuki; Fukuyama, Eiichi; Kawai, Hiroyuki; Nonomura, Ken'ichi
2002-10-01
We have examined the quality of the National Research Institute for Earth Science and Disaster Prevention (NIED) seismic moment tensor (MT) catalogue obtained using a regional broadband seismic network (FREESIA). First, we examined using synthetic waveforms the robustness of the solutions with regard to data noise as well as to errors in the velocity structure and focal location. Then, to estimate the reliability, robustness and validity of the catalogue, we compared it with the Harvard centroid moment tensor (CMT) catalogue as well as the Japan Meteorological Agency (JMA) focal mechanism catalogue. We found out that the NIED catalogue is consistent with Harvard and JMA catalogues within the uncertainty of 0.1 in moment magnitude, 10 km in depth, and 15° in direction of the stress axes. The NIED MT catalogue succeeded in reducing to 3.5 the lower limit of moment magnitude above which the moment tensor could be reliably estimated. Finally, we estimated the stress tensors in several different regions by using the NIED MT catalogue. This enables us to elucidate the stress/deformation field in and around the Japanese islands to understand the mode of deformation and applied stress. Moreover, we identified a region of abnormal stress in a swarm area from stress tensor estimates.
Traveling salesman problems with PageRank Distance on complex networks reveal community structure
Jiang, Zhongzhou; Liu, Jing; Wang, Shuai
2016-12-01
In this paper, we propose a new algorithm for community detection problems (CDPs) based on traveling salesman problems (TSPs), labeled as TSP-CDA. Since TSPs need to find a tour with minimum cost, cities close to each other are usually clustered in the tour. This inspired us to model CDPs as TSPs by taking each vertex as a city. Then, in the final tour, the vertices in the same community tend to cluster together, and the community structure can be obtained by cutting the tour into a couple of paths. There are two challenges. The first is to define a suitable distance between each pair of vertices which can reflect the probability that they belong to the same community. The second is to design a suitable strategy to cut the final tour into paths which can form communities. In TSP-CDA, we deal with these two challenges by defining a PageRank Distance and an automatic threshold-based cutting strategy. The PageRank Distance is designed with the intrinsic properties of CDPs in mind, and can be calculated efficiently. In the experiments, benchmark networks with 1000-10,000 nodes and varying structures are used to test the performance of TSP-CDA. A comparison is also made between TSP-CDA and two well-established community detection algorithms. The results show that TSP-CDA can find accurate community structure efficiently and outperforms the two existing algorithms.
Directory of Open Access Journals (Sweden)
Eugenio Aulisa
2009-04-01
Full Text Available Solving complex coupled processes involving fluid-structure-thermal interactions is a challenging problem in computational sciences and engineering. Currently there exist numerous public-domain and commercial codes available in the area of Computational Fluid Dynamics (CFD, Computational Structural Dynamics (CSD and Computational Thermodynamics (CTD. Different groups specializing in modelling individual process such as CSD, CFD, CTD often come together to solve a complex coupled application. Direct numerical simulation of the non-linear equations for even the most simplified fluid-structure-thermal interaction (FSTI model depends on the convergence of iterative solvers which in turn rely heavily on the properties of the coupled system. The purpose of this paper is to introduce a flexible multilevel algorithm with finite elements that can be used to study a coupled FSTI. The method relies on decomposing the complex global domain, into several local sub-domains, solving smaller problems over these sub-domains and then gluing back the local solution in an efficient and accurate fashion to yield the global solution. Our numerical results suggest that the proposed solution methodology is robust and reliable.
Shulga, Dmytro; Morozov, Oleksii; Hunziker, Patrick
2017-04-01
Optical Diffusion Tomography (ODT) is a modern non-invasive medical imaging modality which requires mathematical modelling of near-infrared light propagation in tissue. Solving the ODT forward problem equation accurately and efficiently is crucial. Typically, the forward problem is represented by a Diffusion PDE and is solved using the Finite Element Method (FEM) on a mesh, which is often unstructured. Tensor B-spline signal processing has the attractive features of excellent interpolation and approximation properties, multiscale properties, fast algorithms and does not require meshing. This paper introduces Tensor B-spline methodology with arbitrary spline degree tailored to solve the ODT forward problem in an accurate and efficient manner. We show that our Tensor B-spline formulation induces efficient and highly parallelizable computational algorithms. Exploitation of B-spline properties for integration over irregular domains proved valuable. The Tensor B-spline solver was tested on standard problems and on synthetic medical data and compared to FEM, including state-of-the art ODT forward solvers. Results show that 1) a significantly higher accuracy can be achieved with the same number of nodes, 2) fewer nodes are required to achieve a prespecified accuracy, 3) the algorithm converges in significantly fewer iterations to a given error. These findings support the value of Tensor B-spline methodology for high-performance ODT implementations. This may translate into advances in ODT imaging for biomedical research and clinical application.
Evaluation of full seismic moment tensor from isotropic, LCVD and double-couple components
Czech Academy of Sciences Publication Activity Database
Kolář, Petr
2006-01-01
Roč. 3, č. 4 (2006), s. 105-107 ISSN 1214-9705 R&D Projects: GA AV ČR IAA300120502 Institutional research plan: CEZ:AV0Z30120515 Keywords : evaluation * full seismic moment tensor * point source representation Subject RIV: DC - Siesmology, Volcanology, Earth Structure
Locally self-consistent Green’s function approach to the electronic structure problem
DEFF Research Database (Denmark)
Abrikosov, I.A.; Simak, S.I.; Johansson, B.
1997-01-01
The locally self-consistent Green's function (LSGF) method is an order-N method for calculation of the electronic structure of systems with an arbitrary distribution of atoms of different kinds on an underlying crystal lattice. For each atom Dyson's equation is used to solve the electronic multiple...... scattering problem in a local interaction zone (LIZ) embedded in an effective medium judiciously chosen to minimize the size of the, LIZ. The excellent real-space convergence of the LSGF calculations and the reliability of its results are demonstrated for a broad spectrum of metallic alloys with different...
Teaching ill-structured problem solving using occupational therapy practice epistemology.
Mitchell, Anita Witt
2013-01-01
ABSTRACT Epistemic and ontological cognition (EOC) have to do with an individual's beliefs about knowledge and knowing. Research has shown that EOC have an influence on learning and achievement. EOC may be discipline-specific with a profession being defined by its practice epistemology. If an individual's EOC is inconsistent with the profession's practice epistemology, the student or practitioner may struggle with effectively solving ill-structured occupational performance problems. The purpose of this paper is to increase awareness of the constructs of EOC, to describe its importance to occupational therapy education and practice, and to provide recommendations for educators and researchers. Specific examples are detailed and recommendations for future research are proposed.
Numerical Modeling of Inverse Problems under Uncertainty for Damage Detection in Aircraft Structures
2013-08-01
Filtro de Kalman para um Problema Inverso de AFOSR/SOARD Grant FA9550-10-1-0103. Report 2010-13. PI: Dr. Ariosto B Jorge. Numerical Modeling of...Inverse Problems under Uncertainty for Damage Detection in Aircraft Structures. 15 Localização e Detecção de Dano em Problema 2-D). Type of monograph...Parameter Identification and Global Optimization Techniques (in Portuguese) (Modelagem de Problema Inverso de Detecção de Danos por Técnicas de
Hussain, Nur Farahin Mee; Zahid, Zalina
2014-12-01
Nowadays, in the job market demand, graduates are expected not only to have higher performance in academic but they must also be excellent in soft skill. Problem-Based Learning (PBL) has a number of distinct advantages as a learning method as it can deliver graduates that will be highly prized by industry. This study attempts to determine the satisfaction level of engineering students on the PBL Approach and to evaluate their determinant factors. The Structural Equation Modeling (SEM) was used to investigate how the factors of Good Teaching Scale, Clear Goals, Student Assessment and Levels of Workload affected the student satisfaction towards PBL approach.
Algebraic and computational aspects of real tensor ranks
Sakata, Toshio; Miyazaki, Mitsuhiro
2016-01-01
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...
Moment tensor inversions using strong motion waveforms of Taiwan TSMIP data, 1993–2009
Chang, Kaiwen; Chi, Wu-Cheng; Gung, Yuancheng; Dreger, Douglas; Lee, William H K.; Chiu, Hung-Chie
2011-01-01
Earthquake source parameters are important for earthquake studies and seismic hazard assessment. Moment tensors are among the most important earthquake source parameters, and are now routinely derived using modern broadband seismic networks around the world. Similar waveform inversion techniques can also apply to other available data, including strong-motion seismograms. Strong-motion waveforms are also broadband, and recorded in many regions since the 1980s. Thus, strong-motion data can be used to augment moment tensor catalogs with a much larger dataset than that available from the high-gain, broadband seismic networks. However, a systematic comparison between the moment tensors derived from strong motion waveforms and high-gain broadband waveforms has not been available. In this study, we inverted the source mechanisms of Taiwan earthquakes between 1993 and 2009 by using the regional moment tensor inversion method using digital data from several hundred stations in the Taiwan Strong Motion Instrumentation Program (TSMIP). By testing different velocity models and filter passbands, we were able to successfully derive moment tensor solutions for 107 earthquakes of Mw >= 4.8. The solutions for large events agree well with other available moment tensor catalogs derived from local and global broadband networks. However, for Mw = 5.0 or smaller events, we consistently over estimated the moment magnitudes by 0.5 to 1.0. We have tested accelerograms, and velocity waveforms integrated from accelerograms for the inversions, and found the results are similar. In addition, we used part of the catalogs to study important seismogenic structures in the area near Meishan Taiwan which was the site of a very damaging earthquake a century ago, and found that the structures were dominated by events with complex right-lateral strike-slip faulting during the recent decade. The procedures developed from this study may be applied to other strong-motion datasets to compliment or fill
Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J.
2017-01-01
Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D, observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄. When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model. PMID:28989561
Band connectivity for topological quantum chemistry: Band structures as a graph theory problem
Bradlyn, Barry; Elcoro, L.; Vergniory, M. G.; Cano, Jennifer; Wang, Zhijun; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei
2018-01-01
The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature (London) 547, 298 (2017), 10.1038/nature23268], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local k .p band structures across the Brillouin zone in terms of graph theory. In this paper, we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.
Arias, E.; Florez, E.; Pérez-Torres, J. F.
2017-06-01
A new algorithm for the determination of equilibrium structures suitable for metal nanoclusters is proposed. The algorithm performs a stochastic search of the minima associated with the nuclear potential energy function restricted to a sphere (similar to the Thomson problem), in order to guess configurations of the nuclear positions. Subsequently, the guessed configurations are further optimized driven by the total energy function using the conventional gradient descent method. This methodology is equivalent to using the valence shell electron pair repulsion model in guessing initial configurations in the traditional molecular quantum chemistry. The framework is illustrated in several clusters of increasing complexity: Cu7, Cu9, and Cu11 as benchmark systems, and Cu38 and Ni9 as novel systems. New equilibrium structures for Cu9, Cu11, Cu38, and Ni9 are reported.
Directory of Open Access Journals (Sweden)
N.R.Yusupbekov
2014-07-01
Full Text Available This paper provides a new approach for solving a problem of modeling and structural syntheses of information networks of automated control systems by applying fuzzy sets theory, fuzzy logic and genetic algorithms. The procedure of formalizing structural syntheses of multi-level dispersed information networks of automated control systems is proposed. Also, the paper proposes a conceptual model of evolutionary syntheses based on genetic algorithms, which do not require additional information about the characteristics and features of target function. Modified genetic operators of crossover, mutation and algorithms of evolutionary syntheses of information networks systems are developed. Finally, the results of computational experiments on researching the influence of probability of the use of crossover and mutation operators, method of choosing parental pairs, and the size of initial population on the speed and precision of final results are provided.
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
2009-01-01
This paper reports on the work carried out supporting a rural community in Denmark under the LEADER+ programme. This is a programme that supports development in particularly vulnerable rural regions of the European countries members of EU. It supports creative and innovative projects that can...... contribute to long-term and sustainable development in these regions. The main tasks have been the organisation and facilitation of conferences and workshops to structure the problematic situation of identifying and designing innovative projects for the development of the community and to support decision...... making processes related to the agreement on action plans. Learning to design, plan, manage and facilitate conferences and workshops have also being another central activity. The main purpose of these conferences and workshops was not only problem structuring and decision making in connection...
STUDY THE PROBLEMS OF OPTIMIZING THE CAPITAL STRUCTURE OF THE COMPANY
Directory of Open Access Journals (Sweden)
Olga Gaydarzhyyska
2016-11-01
Full Text Available The aim of this work is to study the problem of optimizing the capital structure of the company. Optimization of capital structure is a necessary condition of adaptation the enterprises regardless of the branch of economy to which a company belongs, to changes in the economy in its development. Methods and criteria of optimisation of the capital structure of the enterprise. The method of determining the optimal capital structure of the enterprise according to the criteria of maximizing financial profitability. Technique. The study is based on the theoretical analysis of scientific works and practical activity of enterprises. Results. It is proved that in the process of optimizing the capital structure necessary to take into account the predictable result of economic activity of the enterprise, that is, financial result from usual activity before taxation. The study of problems of optimization of capital structure aimed at opening opportunities for the effective organization of business enterprises, providing conditions for disclosure for businesses achieving the goals of any order, and the creation of opportunities for enterprise maximum level of profit. The principle of optimization is to select the solution that best would take into account internal possibilities and external terms of activity of the enterprise. Optimization is the choice of a certain economic indicator that would allow to compare the effectiveness of any solutions. Also it is advisable to pay attention to the use of different types of loan capital to business enterprises, to know that helps to speed up circulation of funds and increase returns on invested capital, increase the efficiency of financial activities of a business entity. Value. Today, the economic activities of enterprises has a significant impact on the development of trade and economy. The achievement of dynamic growth of the basic indicators of work of enterprises of any sector of the economy, is the basic
Tensor modes on the string theory landscape
Energy Technology Data Exchange (ETDEWEB)
Westphal, Alexander
2012-06-15
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Estimate of the limit displacement wave amplitude in the dynamic problem on an out-of-plane crack
Petrov, Yu. V.; Smirnov, V. I.
2017-07-01
The paper presents several results of structural fracture macromechanics used to study the integrity of continuum under impulse loading conditions. The dynamic problem on a semi-infinite steady-state crack of longitudinal shear is considered. Exact analytical expressions for the stress tensor and displacement vector components on the crack line are obtained. The values of the threshold displacement amplitude on the wave front are determined for several structural materials.
Numerical CP Decomposition of Some Difficult Tensors
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Phan, A. H.; Cichocki, A.
2017-01-01
Roč. 317, č. 1 (2017), s. 362-370 ISSN 0377-0427 R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : Small matrix multiplication * Canonical polyadic tensor decomposition * Levenberg-Marquardt method Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0468385. pdf
Vector-tensor interaction of gravitation
Energy Technology Data Exchange (ETDEWEB)
Zhang Yuan-zhong; Guo han-ying
1982-11-01
In the paper, by using the equation of motion a particle, we show that the antigravity exist in the vector-tensor model of gravitation. Thus the motion of a particle deviates from the geodesic equation. In Newtonian approximation and weak gravitational field, acceleration of a particle in a spherically symmetric and astatic gravitation field is zero. The result is obviously not in agreement with gravitational phenomena.
Monte Carlo Volcano Seismic Moment Tensors
Waite, G. P.; Brill, K. A.; Lanza, F.
2015-12-01
Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.
The Impact of EU Structural Fund Support and Problems of its Absorption
Directory of Open Access Journals (Sweden)
Daiva Jurevičienė
2013-06-01
Full Text Available Targeted allocation of EU support in Lithuania can help resolving a number of problems and achieving significant results in a variety of areas. However, rush to absorb support may lead to a little, zero or even negative impact on national economy. In addition, EU support opportunities may distort investment motivation. This paper deals with issues related to the impact of EU support and problems of its absorption. The impact of EU support on the national economy has been established in three areas: attraction of foreign direct investment state investments into capital formation, and experience of companies, which are EU support beneficiaries. The paper proposes using regression analysis in search and evaluation of relations while obtaining more information about programmes, priorities and the impact of structural support on different indicators. In addition, it focuses on ascertaining the effectiveness of governmental and company spending. Furthermore, as companies – EU support beneficiaries – are engaged in different economic activities, their experience cannot be ascertained from statistical data; consequently, findings of an expert survey are presented to demonstrate the experience acquired by business companies as well as problems they face. Limitation of research was a short period of time to evaluate (only four years of the current funding period
Forbes, Miriam K; Schniering, Carolyn A
2013-01-01
Sexual dysfunctions, depression, and anxiety disorders have high rates of comorbidity. The aim of this study was to empirically evaluate an expanded model of internalizing psychopathology (Krueger, 1999) that includes sexual problems, based on these patterns of comorbidity. Responses to an online survey from a sexually active community sample (n = 563) were analyzed using structural equation modeling to compare the fit of four alternative models for males and females. An expanded model of the internalizing spectrum that included sexual problems was a good fit for the pattern of interrelationships in the female data. However, the weak relationships between the observed variables in the male data meant that none of the models provided an adequate fit for men. This study offers preliminary evidence for the utility of a model of the internalizing spectrum that includes sexual problems for women, which could facilitate a better understanding of the role of common underlying psychopathological processes between disorders and offer a first step towards effective diagnosis and treatment. Future research should focus on clinical and representative samples, using other measurement methods.
Structuring policy problems for plastics, the environment and human health: reflections from the UK
Shaxson, Louise
2009-01-01
How can we strengthen the science–policy interface for plastics, the environment and human health? In a complex policy area with multiple stakeholders, it is important to clarify the nature of the particular plastics-related issue before trying to understand how to reconcile the supply and demand for evidence in policy. This article proposes a simple problem typology to assess the fundamental characteristics of a policy issue and thus identify appropriate processes for science–policy interactions. This is illustrated with two case studies from one UK Government Department, showing how policy and science meet over the environmental problems of plastics waste in the marine environment and on land. A problem-structuring methodology helps us understand why some policy issues can be addressed through relatively linear flows of science from experts to policymakers but why others demand a more reflexive approach to brokering the knowledge between science and policy. Suggestions are given at the end of the article for practical actions that can be taken on both sides. PMID:19528061
Mapping the MMPI-2-RF Specific Problems Scales Onto Extant Psychopathology Structures.
Sellbom, Martin
2017-01-01
A main objective in developing the Minnesota Multiphasic Personality Inventory-2-Restructured Form (MMPI-2-RF; Ben-Porath & Tellegen, 2008 ) was to link the hierarchical structure of the instrument's scales to contemporary psychopathology and personality models for greater enhancement of construct validity. Initial evidence published with the Restructured Clinical scales has indicated promising results in that the higher order structure of these measures maps onto those reported in the extant psychopathology literature. This study focused on evaluating the internal structure of the Specific Problems and Interest scales, which have not yet been examined in this manner. Two large, mixed-gender outpatient and correctional samples were used. Exploratory factor analyses revealed consistent evidence for a 4-factor structure representing somatization, negative affect, externalizing, and social detachment. Convergent and discriminant validity analyses in the outpatient sample yielded a pattern of results consistent with expectations. These findings add further evidence to indicate that the MMPI-2-RF hierarchy of scales map onto extant psychopathology literature, and also add support to the notion that somatization and detachment should be considered important higher order domains in the psychopathology literature.
Tensor integrand reduction via Laurent expansion
Energy Technology Data Exchange (ETDEWEB)
Hirschi, Valentin [SLAC, National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025-7090 (United States); Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom)
2016-06-09
We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MADLOOP, which is part of the public MADGRAPH5{sub A}MC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CUTTOOLS, SAMURAI, IREGI, PJFRY++ and GOLEM95. We find that Ninja outperforms traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool GOLEM95 which is however more limited and slower than Ninja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.
Georgievskii, D. V.; Israilov, M. Sh.
2015-07-01
In the problems of common vibrations of extended underground structures (pipelines and tunnels) and soil, an approach of the one-dimensional deformation of the medium is developed; this approach is based on the assumption that the soil deformation in the direction of seismic wave propagation coinciding with the pipeline axis is prevailing. The analytic solutions are obtained in the cases where the wave velocity in the soil is respectively less or greater than the wave velocity in the pipeline. The parameters influencing the pipeline fracture are revealed and methods for increasing the seismic stability of such structures are given. The possibility of the pipeline fatigue fracture is pointed out. The statements and solutions of parabolic problems modeling the physical phenomena in soils in the case of discontinuous velocity on the boundaries at the initial time are given. The notion of generalized vorticity diffusion is introduced and the cases of self-similarity existence are classified. A detailed analysis is performed for the non-Newtonian polynomial fluid, the medium close in properties to the rigidly ideally plastic body, and the viscoplastic Shvedov—Bingham body. In the case of physically linear medium, new self-similar solutions are obtained which describe the process of unsteady axially symmetric shear in spherical coordinates. The first approximation to the asymptotic solution of the problem of the vortex sheet diffusion is constructed in a medium with small polynomial nonlinearity. The solutions polynomially decreasing to zero as the self-similar variable increases are proposed in the class of two-constant fluids.
Climate-Change Problem Solving: Structured Approaches Based on Real-World Experiences
Rood, R. B.; Briley, L. J.; Brown, D. A.
2012-12-01
Nearly two decades of experience using both seasonal and long-term climate model projections has led to the identification of a set of characteristics of the successful use of climate knowledge in planning and adaptation applications. These characteristics include end-to-end knowledge systems, co-generation or co-production of solution approaches by scientists and practitioners, and tailoring climate model information to the decision-making processes of the specific application. Glisaclimate.org strives to apply the growing body of research into the successful use of climate knowledge using a set of prototype, real-world applications. We describe an online problem-solving environment whose design is based on the characteristics of the successful use of climate predictions and projections by practitioners such as resource managers, urban planners, public health professionals, and policy makers. Design features of Glisaclimate.org include: Based on principles extracted from social science studies of the use of climate information. Anchored on structured templates of problem solving with the identification of common steps in problem solving that are repeated in one application to the next. Informed by interviews with real-world users who desire to incorporate climate-science knowledge into their decision making. Built with open-source tools to allow participation of a community of developers and to facilitate the sustainability of the effort. A structured approach to problem solving is described by four functions of information management. At the foundation of problem solving is the collection of existing information, an inventory stage. Following the collection of the information there are analysis and evaluation stages. In the analysis stage interfaces are described and knowledge gaps are identified. The evaluation stage assesses the quality of the information and the relevance of the information to the specific attributes of the problem. The development of plans
Extended Nonnegative Tensor Factorisation Models for Musical Sound Source Separation
Directory of Open Access Journals (Sweden)
Derry FitzGerald
2008-01-01
Full Text Available Recently, shift-invariant tensor factorisation algorithms have been proposed for the purposes of sound source separation of pitched musical instruments. However, in practice, existing algorithms require the use of log-frequency spectrograms to allow shift invariance in frequency which causes problems when attempting to resynthesise the separated sources. Further, it is difficult to impose harmonicity constraints on the recovered basis functions. This paper proposes a new additive synthesis-based approach which allows the use of linear-frequency spectrograms as well as imposing strict harmonic constraints, resulting in an improved model. Further, these additional constraints allow the addition of a source filter model to the factorisation framework, and an extended model which is capable of separating mixtures of pitched and percussive instruments simultaneously.
Emergent gravity from vanishing energy-momentum tensor
Carone, Christopher D.; Erlich, Joshua; Vaman, Diana
2017-03-01
A constraint of vanishing energy-momentum tensor is motivated by a variety of perspectives on quantum gravity. We demonstrate in a concrete example how this constraint leads to a metric-independent theory in which quantum gravity emerges as a nonperturbative artifact of regularization-scale physics. We analyze a scalar theory similar to the Dirac-Born-Infeld (DBI) theory with vanishing gauge fields, with the DBI Lagrangian modulated by a scalar potential. In the limit of a large number of scalars, we explicitly demonstrate the existence of a composite massless spin-2 graviton in the spectrum that couples to matter as in Einstein gravity. We comment on the cosmological constant problem and the generalization to theories with fermions and gauge fields.
Economic Structure and Problems of Trout Enterprises: A Case of Fethiye
Directory of Open Access Journals (Sweden)
Hicran Ekmekci
2017-01-01
Full Text Available In this study, economic structure and problems of trout enterprise were analysed in Fethiye district. It was aimed to determine the input of enterprises engaged in aquaculture at the Fethiye district, calculation of the economic situation, investigation of the market situation and determine problems. In addition possible solutions were tried to be to problems. In the district, it was interviewed with 17 trout enterprises. Data were collected with interviewing face to face by questionnaires. These data was analysed by MS Excel and SPSS programmes. 52.9% of the enterprises were established in the foothill, 35.3% were in open field and 11.8% were established in between valleys. 58.8% of these enterprises were individual enterprises, %17.6 was simple partnership and 23.5% were commercial partnership. The most shares in the active capital were constituted working capital with a rate of 70.3% whereas the share of landlord’s capital was 29.7%. The share of own capital in passive capital was 93.9% and the usage of foreign capital was low (6.1%. The share of variable cost was 83.6% while fixed cost was 16.4% in the total production cost. The main problem of enterprises was the rise of feed costs. A feed cost was found to constitute 63.4% of total production costs. Producers should be given support in terms of technical knowledge and efforts to raise awareness of local people and consumers should be made.
A Research on Structural Characteristics and Problems of Goat Breeding in Nigde
Directory of Open Access Journals (Sweden)
Ayhan Ceyhan
2014-09-01
Full Text Available This study was carried out to reveal the present status of goat farms in Nigde, to detect basic priority problems and to offer some solutions to these problems. For this purpose, a survey was conducted to the goat breeders face to face in randomly selected total 38 goat farms.The survey questions; goat farms and growing core business activities of enterprises that reveals the overall structure, and also the level of satisfaction with the priority issues of breeders are designed to measure. Analyze the results was shown that a large portion of goat breeders (85.0% were primary school graduates, 5.3%secondery school and also 5.3% high school graduates, goat farms have whole hair goat breed. Goat enterprises have rate of 44.7%, more than 500 goat, 92.1% of goat enterprises go out to highlands, also provided 73.7% of the shepherd's family. In addition, operating revenues were determined come from 50% of goat's milk. Goat breeders were evaluated only 39.5% the form of cheese production, as 60.5% of the cheese, butter, yogurt, and the sale of raw milk of the total milk yield. All business was assessed that owners a profitable goat farming as an occupation and the first five main problems were member alliance, ownership sufficient technical knowledge, serving the technical staff, buck mating and breeding presses, goat shelter, respectively. In addition, it was seen that according to Likert scale, at least the first five issues were satisfied that such as feed, labor, and electricity inputs, product marketing price, sold animals the price, market opportunities related to the sale of manufactured products and finacial supply, respectively. As a result, it could be said that the most important problem for goat enterprises in Nigde province is high production costs and low product prices.
De Kruijf, J.
2007-01-01
Water management issues are often complex, unstructured problems. They are complex, because they are part of a natural and human system wich consists of many diverse, interdependent elements, e.g. upstream events influence the water system downstream, different interdependent goverment layers,
Energy Technology Data Exchange (ETDEWEB)
D' Auvergne, Edward J. [Max Planck Institute for Biophysical Chemistry, Department of NMR-based Structural Biology (Germany)], E-mail: edward@nmr-relax.com; Gooley, Paul R. [University of Melbourne, Department of Biochemistry and Molecular Biology, Bio21 Institute of Biotechnology and Molecular Science (Australia)
2008-02-15
Finding the dynamics of an entire macromolecule is a complex problem as the model-free parameter values are intricately linked to the Brownian rotational diffusion of the molecule, mathematically through the autocorrelation function of the motion and statistically through model selection. The solution to this problem was formulated using set theory as an element of the universal set U-the union of all model-free spaces (d'Auvergne EJ and Gooley PR (2007) Mol BioSyst 3(7), 483-494). The current procedure commonly used to find the universal solution is to initially estimate the diffusion tensor parameters, to optimise the model-free parameters of numerous models, and then to choose the best model via model selection. The global model is then optimised and the procedure repeated until convergence. In this paper a new methodology is presented which takes a different approach to this diffusion seeded model-free paradigm. Rather than starting with the diffusion tensor this iterative protocol begins by optimising the model-free parameters in the absence of any global model parameters, selecting between all the model-free models, and finally optimising the diffusion tensor. The new model-free optimisation protocol will be validated using synthetic data from Schurr JM et al. (1994) J Magn Reson B 105(3), 211-224 and the relaxation data of the bacteriorhodopsin (1-36)BR fragment from Orekhov VY (1999) J Biomol NMR 14(4), 345-356. To demonstrate the importance of this new procedure the NMR relaxation data of the Olfactory Marker Protein (OMP) of Gitti R et al. (2005) Biochem 44(28), 9673-9679 is reanalysed. The result is that the dynamics for certain secondary structural elements is very different from those originally reported.
Directory of Open Access Journals (Sweden)
Josef HRUSAK
2005-06-01
Full Text Available An extraordinary generality, conceptual simplicity and practical usefulness of the Tellegen's theorem is well known in the field of electrical engineering [1]. It is one of few general theoretical results that apply in non-linear and time-varying situations, too. For standard linear electrical network models with constant parameters many classical results of electrical circuits theory can be derived as direct consequences of it. In the paper a more general class of abstract strictly causal system representations is addressed. A new problem, that of the abstract state space system representation structure reconstruc-tion has been formulated in [3], and partially solved in [3] and [4]. In this paper a new approach based on a generalized form of the classical Tellegen's principle, providing an equivalence class of physically as well as mathematically correct solutions is developed and some well-known, as well as new results are shown to be straightforward consequences of the derived struc-ture. Some connections of dissipativity, conservativity, state and parameter minimality, instability and chaos with system representation structures are investigated from this point of view. Analytical results are illustrated by a number of typical examples and visualized by simulations.
Аn example of different AHP structuring in a forest management problem
Directory of Open Access Journals (Sweden)
Lakićević Milena D.
2016-01-01
Full Text Available The paper investigates how different hierarchy structuring in analytic hierarchy process (AHP may affect the final results in the decision-making process. This problem is analyzed in a case study of the Rila monastery forest stands in Bulgaria. There were three similar and mutually overlapped hierarchies defined. A decision maker evaluated all of them and after analyzing final results and consistency performance, he selected and revised the most appropriate hierarchy structure. Consistency check assisted in detecting the judgments which have strongly violated evaluation procedure. These mistakes are interpreted as a consequence of a large number of required pair-wise comparisons. The paper emphases the importance of properly defining hierarchy structure and recommends using consistency analysis as a guide and not as a directive for the revision of judgments. [Projekat Ministarstva nauke Republike Srbije, br. 174003: Theory and application of analytic hierarchy process (AHP in multi-criteria decision making under conditions of risk and uncertainty (individual and group context
Nguyen, D. T.; Al-Nasra, M.; Zhang, Y.; Baddourah, M. A.; Agarwal, T. K.; Storaasli, O. O.; Carmona, E. A.
1991-01-01
Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.
Directory of Open Access Journals (Sweden)
Nordmyr Johanna
2016-09-01
Full Text Available AIMS – This study aims to explore associations between structural and functional aspects of social networks and relationships (here labelled social ties among individuals exhibiting problematic alcohol use and problem gambling, respectively.
Wu, Bian; Wang, Minhong; Spector, J. Michael; Yang, Stephen J. H.
2013-01-01
Problem solving has been increasingly used as an important approach to learning especially in ill-structured domains. It is assumed that knowledge can be better consolidated and extended through problem-solving experience. However, many learners do not have the ability to separate general knowledge from specific cases, which inhibits successful…
On structure and open problems in topological theories coupled to topological gravity
Energy Technology Data Exchange (ETDEWEB)
Losev, A. [Inst. of Theoretical and Experimental Physics, Moscow (Russian Federation)
1995-01-01
The structure of topological theory coupled to topological gravity is studied. We show that in this theory Q-exact terms do not decouple. This not decoupling in the action of the theory is connected with the existence of boundaries of the moduli space and leads to problems in defining the topological gravity for massive topological theories. Not decoupling of Q-exact observables leads to filtration of the gravitational descendants constructed from matter fields. Two a priori different preferred splittings of this filtration are constructed (one connected with the massive deformation of the theory and the other connected with the flatness of the connection on the space of theories). It is conjectured that they coincide.
Graph theory approach to the eigenvalue problem of large space structures
Reddy, A. S. S. R.; Bainum, P. M.
1981-01-01
Graph theory is used to obtain numerical solutions to eigenvalue problems of large space structures (LSS) characterized by a state vector of large dimensions. The LSS are considered as large, flexible systems requiring both orientation and surface shape control. Graphic interpretation of the determinant of a matrix is employed to reduce a higher dimensional matrix into combinations of smaller dimensional sub-matrices. The reduction is implemented by means of a Boolean equivalent of the original matrices formulated to obtain smaller dimensional equivalents of the original numerical matrix. Computation time becomes less and more accurate solutions are possible. An example is provided in the form of a free-free square plate. Linearized system equations and numerical values of a stiffness matrix are presented, featuring a state vector with 16 components.
An Objective Structured Clinical Examination to Assess Problem-Based Learning
O'Connell, Mary Beth; Garwood, Candice L.; Lehr, Victoria Tutag; Abdallah, Karina
2012-01-01
Objectives. To compare pharmacy students’ performance on an objective structured clinical examination (OSCE) to their performance on a written examination for the assessment of problem-based learning (PBL); and to determine students’ and faculty members’ perceptions of OSCEs for PBL evaluations. Design. Four OSCEs were added to the written examination to assess 4 PBL cases in a third-year pharmacotherapy course. OSCE scores were compared to written examination scores. Faculty members evaluated student performance. Assessment. OSCE performance did not correlate with the written-examination scores. Most students (≥ 75%) agreed that OSCEs reflected their learning from PBL and measured knowledge, communication, and clinical skills. A majority of faculty members (≥75%) agreed that OSCEs should be part of PBL assessment. Conclusions. Addition of an OSCE to written examinations was valued and provided a more comprehensive assessment of the PBL experience. PMID:22544961
Flux-corrected transport algorithms preserving the eigenvalue range of symmetric tensor quantities
Lohmann, Christoph
2017-12-01
This paper presents a new approach to constraining the eigenvalue range of symmetric tensors in numerical advection schemes based on the flux-corrected transport (FCT) algorithm and a continuous finite element discretization. In the context of element-based FEM-FCT schemes for scalar conservation laws, the numerical solution is evolved using local extremum diminishing (LED) antidiffusive corrections of a low order approximation which is assumed to satisfy the relevant inequality constraints. The application of a limiter to antidiffusive element contributions guarantees that the corrected solution remains bounded by the local maxima and minima of the low order predictor. The FCT algorithm to be presented in this paper guarantees the LED property for the maximal and minimal eigenvalues of the transported tensor at the low order evolution step. At the antidiffusive correction step, this property is preserved by limiting the antidiffusive element contributions to all components of the tensor in a synchronized manner. The definition of the element-based correction factors for FCT is based on perturbation bounds for auxiliary tensors which are constrained to be positive semidefinite to enforce the generalized LED condition. The derivation of sharp bounds involves calculating the roots of polynomials of degree up to 3. As inexpensive and numerically stable alternatives, limiting techniques based on appropriate estimates are considered. The ability of the new limiters to enforce local bounds for the eigenvalue range is confirmed by numerical results for 2D advection problems.
Some late-time asymptotics of general scalar-tensor cosmologies
Energy Technology Data Exchange (ETDEWEB)
Barrow, John D [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Shaw, Douglas J [Astronomy Unit, Queen Mary University, Mile End Rd., London E1 4NS (United Kingdom)
2008-04-21
We study the asymptotic behaviour of isotropic and homogeneous universes in general scalar-tensor gravity theories containing a p = -{rho} vacuum fluid stress and other sub-dominant matter stresses. It is shown that in order for there to be an approach to a de Sitter spacetime at large 4-volumes the coupling function, {omega}({phi}), which defines the scalar-tensor theory, must diverge faster than |{phi}{sub {infinity}} - {phi}|{sup -1+{epsilon}} for all {epsilon} > 0 as {phi} {yields} {phi}{sub {infinity}} {ne} 0 for large values of the time. Thus, for a given theory, specified by {omega}({phi}), there must exist some {phi}{sub {infinity}} element of (0, {infinity}) such that {omega} {yields} {infinity} and {omega}'/{omega}{sup 2+{epsilon}} {yields} 0 as {phi} {yields} {phi}{sub {infinity}} in order for cosmological solutions of the theory to approach de Sitter expansion at late times. We also classify the possible asymptotic time variations of the gravitation 'constant' G(t) at late times in scalar-tensor theories. We show that (unlike in general relativity) the problem of a profusion of 'Boltzmann brains' at late cosmological times can be avoided in scalar-tensor theories, including Brans-Dicke theory, in which {phi} {yields} {infinity} and {omega} {approx}o({phi}{sup 1/2}) at asymptotically late times.
Cognitive structures of good and poor novice problem solvers in physics
Jong, de, AJM Ton; Ferguson-Hessler, MGM Monica
1986-01-01
The way knowledge is organized in memory is generally expected to relate to the degree of success in problem solving. In the present study, we investigated whether good novice problem solvers have their knowledge arranged around problem types to a greater extent than poor problem solvers have. In the subject of physics (electricity and magnetism), 12 problem types were distinguished according to their underlying physics principles. For each problem type, a set of elements of knowledge contain...
Visualizing Dataflow Graphs of Deep Learning Models in TensorFlow.
Wongsuphasawat, Kanit; Smilkov, Daniel; Wexler, James; Wilson, Jimbo; Mane, Dandelion; Fritz, Doug; Krishnan, Dilip; Viegas, Fernanda B; Wattenberg, Martin
2018-01-01
We present a design study of the TensorFlow Graph Visualizer, part of the TensorFlow machine intelligence platform. This tool helps users understand complex machine learning architectures by visualizing their underlying dataflow graphs. The tool works by applying a series of graph transformations that enable standard layout techniques to produce a legible interactive diagram. To declutter the graph, we decouple non-critical nodes from the layout. To provide an overview, we build a clustered graph using the hierarchical structure annotated in the source code. To support exploration of nested structure on demand, we perform edge bundling to enable stable and responsive cluster expansion. Finally, we detect and highlight repeated structures to emphasize a model's modular composition. To demonstrate the utility of the visualizer, we describe example usage scenarios and report user feedback. Overall, users find the visualizer useful for understanding, debugging, and sharing the structures of their models.
Petraglia, Riccardo; Nicolaï, Adrien; Wodrich, Matthew D; Ceriotti, Michele; Corminboeuf, Clemence
2016-01-05
Computational studies of organic systems are frequently limited to static pictures that closely align with textbook style presentations of reaction mechanisms and isomerization processes. Of course, in reality chemical systems are dynamic entities where a multitude of molecular conformations exists on incredibly complex potential energy surfaces (PES). Here, we borrow a computational technique originally conceived to be used in the context of biological simulations, together with empirical force fields, and apply it to organic chemical problems. Replica-exchange molecular dynamics (REMD) permits thorough exploration of the PES. We combined REMD with density functional tight binding (DFTB), thereby establishing the level of accuracy necessary to analyze small molecular systems. Through the study of four prototypical problems: isomer identification, reaction mechanisms, temperature-dependent rotational processes, and catalysis, we reveal new insights and chemistry that likely would be missed using static electronic structure computations. The REMD-DFTB methodology at the heart of this study is powered by i-PI, which efficiently handles the interface between the DFTB and REMD codes. © 2015 Wiley Periodicals, Inc.
Directory of Open Access Journals (Sweden)
Олена Миколаївна Євтушенко
2016-04-01
Full Text Available Aim: The research object was the definition of problems and tendencies of pharmaceutical market development of Sudan as the country which in recent years tries to pull through the consequence of political and economic crisis and to build the socially oriented model of the state.Methods: In the researches it has been used the marketing and economic analysis methods as well as the historical, logical, comparative and graphic methods.Results: The authors represented the marketing analysis results of pharmaceutical market of Sudan. It has been identified the main problems and tendencies of it development. It has been made the macroeconomic indexes analysis which has the influence to the availability level of the pharmaceutical assistance to the population of the country. It has been studied the spending dynamics of the medical and pharmaceutical provision per capita in the country, the tendencies of the amounts changes in the pharmaceutical market, the branded market structure. It has been established the position of Sudan according to the national systems division of the public health and pharmaceutical assistance of population depending on the macroeconomic indexes of region development.Conclusions: It has been established the positive and negative tendencies indicative to the modern state of the county. After the research results it has been distinguished the further development directions especially the actions for the rational model creation for the population assistance in public health
An introduction to tensors and group theory for physicists
Jeevanjee, Nadir
2011-01-01
An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Exercises and examples are provided throughout for go...
Redberry: a computer algebra system designed for tensor manipulation
Poslavsky, Stanislav; Bolotin, Dmitry
2015-05-01
In this paper we focus on the main aspects of computer-aided calculations with tensors and present a new computer algebra system Redberry which was specifically designed for algebraic tensor manipulation. We touch upon distinctive features of tensor software in comparison with pure scalar systems, discuss the main approaches used to handle tensorial expressions and present the comparison of Redberry performance with other relevant tools.
Sijtsema, J J; Oldehinkel, A J; Veenstra, R; Verhulst, F C; Ormel, J
2014-06-01
Both structural (i.e., SES, familial psychopathology, family composition) and dynamic (i.e., parental warmth and rejection) family characteristics have been associated with aggressive and depressive problem development. However, it is unclear to what extent (changes in) dynamic family characteristics have an independent effect on problem development while accounting for stable family characteristics and comorbid problem development. This issue was addressed by studying problem development in a large community sample (N = 2,230; age 10-20) of adolescents using Linear Mixed models. Paternal and maternal warmth and rejection were assessed via the Egna Minnen Beträffande Uppfostran for Children (EMBU-C). Aggressive and depressive problems were assessed via subscales of the Youth/Adult Self-Report. Results showed that dynamic family characteristics independently affected the development of aggressive problems. Moreover, maternal rejection in preadolescence and increases in paternal rejection were associated with aggressive problems, whereas decreases in maternal rejection were associated with decreases in depressive problems over time. Paternal and maternal warmth in preadolescence was associated with fewer depressive problems during adolescence. Moreover, increases in paternal warmth were associated with fewer depressive problems over time. Aggressive problems were a stable predictor of depressive problems over time. Finally, those who increased in depressive problems became more aggressive during adolescence, whereas those who decreased in depressive problems became also less aggressive. Besides the effect of comorbid problems, problem development is to a large extent due to dynamic family characteristics, and in particular to changes in parental rejection, which leaves much room for parenting-based interventions.
Regional, Local, and In-mine Moment Tensors for the 2013 Rudna Mine collapse
Whidden, K. M.; Rudzinski, L.; Lizurek, G.; Pankow, K. L.
2013-12-01
On March 19, 2013, the room-and-pillar Rudna copper mine in southwest Poland experienced a collapse (mb 4.7) that trapped 19 miners who were all rescued hours later. News outlets reported that the collapse occurred as the result of an earthquake on a fault. We use three different moment tensor methods and seismic networks to study the source of this event. The velocity structure at regional distances is complex. To the southwest are the Sudetic Mountains and to the north and east a deep sedimentary basin extends towards the Baltic Sea. A single 1-D velocity model is unlikely to adequately account for the paths to all stations. Regional moment tensors were calculated for this event using two sets of velocity models: 1) those used for routine regional moment tensor calculation in Utah, with slight modifications for stations in the deepest part of the basin, and 2) velocity models derived from the POLONAISE'97 seismic refraction experiment (Janik et al. 2002, Sroda et al. 2002, Grad et al. 2003). All models were validated for use in Poland by calculating a moment tensor for the M4.4 earthquake on 2004/11/03 in southeast Poland that has regional moment tensor estimates from two different agencies (see International Seismological Centre event 7443851 for solutions by the Swiss Seismological Service and MedNet Regional Centroid Moment Tensors). Both sets of velocity models were able to generate synthetics that were a good match to the data for the 2004 earthquake, and the resulting moment tensor solutions closely match those from previous investigators, confirming that the velocity models used in the analysis are adequate. A full waveform moment tensor using the velocity models described above and a broadband regional network with event to station distances of 75 to 220 km reveals a source with a dominant and statistically significant implosive component. A local network consisting of four short-period three axial sensors, with event to station distances of 3.5 to 7 km
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
Some remarks on the genesis of scalar-tensor theories
Goenner, Hubert
2012-01-01
Between 1941 and 1962, scalar-tensor theories of gravitation were suggested four times by different scientists in four different countries. The earliest originator, the Swiss mathematician W. Scherrer, was virtually unknown until now whereas the chronologically latest pair gave their names to a multitude of publications on Brans-Dicke theory. P. Jordan, one of the pioneers of quantum mechanics theory, and Y. Thiry, a student of the mathematician A. Lichnerowicz, known by his book on celestial mechanics, complete the quartet. Diverse motivations for and conceptual interpretations of their theories will be discussed as well as relations among them. Also, external factors like language, citation habits, or closeness to the mainstream are considered. It will become clear why Brans-Dicke theory, although structurally a d\\'ej\\`a-vu, superseded all the other approaches.
Quantum-chemical insights from deep tensor neural networks
Schütt, Kristof T.; Arbabzadah, Farhad; Chmiela, Stefan; Müller, Klaus R.; Tkatchenko, Alexandre
2017-01-01
Learning from data has led to paradigm shifts in a multitude of disciplines, including web, text and image search, speech recognition, as well as bioinformatics. Can machine learning enable similar breakthroughs in understanding quantum many-body systems? Here we develop an efficient deep learning approach that enables spatially and chemically resolved insights into quantum-mechanical observables of molecular systems. We unify concepts from many-body Hamiltonians with purpose-designed deep tensor neural networks, which leads to size-extensive and uniformly accurate (1 kcal mol-1) predictions in compositional and configurational chemical space for molecules of intermediate size. As an example of chemical relevance, the model reveals a classification of aromatic rings with respect to their stability. Further applications of our model for predicting atomic energies and local chemical potentials in molecules, reliable isomer energies, and molecules with peculiar electronic structure demonstrate the potential of machine learning for revealing insights into complex quantum-chemical systems.
Measurement of Deuteron Tensor Polarization in Elastic Electron Scattering
Energy Technology Data Exchange (ETDEWEB)
Gustafsson, Kenneth K. [Univ. of Maryland, College Park, MD (United States)
2000-01-01
Nuclear physics traces it roots back to the very beginning of the last century. The concept of the nuclear atom was introduced by Rutherford around 1910. The discovery of the neutron Chadwick in 1932 gave us the concept of two nucleons: the proton and the neutron. The Jlab electron accelerator with its intermediate energy high current continuous wave beam combined with the Hall C high resolution electron spectrometer and a deutron recoil polarimeter provided experiment E94018 with the opportunity to study the deuteron electomagnetic structure, in particular to measure the tensor polarization observable t_{20}, at high four momentum transfers than ever before. This dissertation presents results of JLab experiment E94018.
Symmetric Topological Phases and Tensor Network States
Jiang, Shenghan
Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.
CONSTRUCTION A CORING FROM TENSOR PRODUCT OF BIALGEBRA
Directory of Open Access Journals (Sweden)
Nikken Prima Puspita
2015-01-01
Full Text Available In this Paper introduced a coring from tensor product of bialgebra. An algebra with compatible coalgebrastructure are known as bialgebra. For any bialgebra B we can obtained tensor product between B anditself. Defined a right and left B -action on the tensor product of bialgebra B such that we have tensorproduct of B and itself is a bimodule over B. In this note we expect that the tensor product B anditself becomes a B -coring with comultiplication and counit.Keywords : action, algebra, coalgebra, coring.
3D Inversion of SQUID Magnetic Tensor Data
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2012-01-01
Developments in SQUID-based technology have enabled direct measurement of magnetic tensor data for geophysical exploration. For quantitative interpretation, we introduce 3D regularized inversion for magnetic tensor data. For mineral exploration-scale targets, our model studies show that magnetic...... tensor data have significantly improved resolution compared to magnetic vector data for the same model. We present a case study for the 3D regularized inversion of magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D regularized inversion agree...
p-Norm SDD tensors and eigenvalue localization
Directory of Open Access Journals (Sweden)
Qilong Liu
2016-07-01
Full Text Available Abstract We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors, which is a subclass of strong H $\\mathcal{H}$ -tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016 in some case. Based on this set, we give a checkable sufficient condition for the positive (semidefiniteness of an even-order symmetric tensor.
TENSOR MODELING BASED FOR AIRBORNE LiDAR DATA CLASSIFICATION
Li, N.; Liu, C; Pfeifer, N; Yin, J. F.; Liao, Z.Y.; Zhou, Y
2016-01-01
Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on tensor decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the “raw” data attributes. Then, the feature rasters of LiDAR data are stored as a tensor, and tensor decomposition is used to select component features. This tensor representation could kee...
Mathematical conformity problems in the dynamic modeling of seismic stability structures
Directory of Open Access Journals (Sweden)
Mogiljuk Zhanna
2017-01-01
Full Text Available The article discusses the problems of field studies and dynamic stability of construction objects at design stage. It highlights the analysis results of various mathematical model approaches for seismic stability of construction structures. The mathematical aspects of their dynamic properties are represented as amplitude-frequency responses and transfer functions. The results of the study as well as the comparative analysis of the mathematical conformity of modeling dynamic properties of a construction object by the Fourier method and the Laplace method are represented. The article considers the uncertainty in the estimates of the dynamic coefficient of structures when using amplitude-frequency response of the object. Furthermore, it is identified that there is a dependence between this coefficient and the instantaneous spectrum of seismic impact when using the Fourier method. The article gives the results of the studies on causes of virtual dependence of the amplitude-frequency response and on the dynamic coefficient from the Fourier transform basis function. The Fourier transform basis function is proved to fall a long way short of the field data and represents itself some abstract description of seismic loads that do not exist in the real nature. The diagrams are given in the article, that proves the comparative estimates of the mathematical conformity and metrological validity of the construction’s dynamic models when using the Fourier method and the Laplace method.od.
Status and problems of wind turbine structural health monitoring techniques in China
Energy Technology Data Exchange (ETDEWEB)
Liu, Wenyi; Tang, Baoping; Jiang, Yonghua [The State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030 (China)
2010-07-15
Wind energy is an important renewable energy source because of its reliability due to the maturity of the technology, good infrastructure and relative cost competitiveness. Rich wind resources and strong support in regulations by the Chinese government have enabled the wind power industry to grow at a fast speed and the primary market scale has been achieved, making it the second largest wind power market in the world. There has also been an increase in wind energy research in various regions in China during the last few years. As utility-size wind turbines increase in size, and correspondingly their initial capital investment cost, there is an increasing need to monitor the health of these structures. However, most of the research papers in China are about the manufacture and production, such as the simulation of the wind turbine generator system model, the systematic resonance and stability for the world turbine, the wind speed, wind power and pitch adjustment simulation model, and so on. Few papers focus on the structural health monitoring (SHM) techniques of the wind turbine. In this paper, we review the status of the current SHM techniques in wind turbine and analyze the problems of them in China. The aims of this paper are to let more scholars and experts know the status of the current SHM techniques and to do something for building a successful industry in China. (author)
Tensor Decompositions for Learning Latent Variable Models
2012-12-08
for several popular latent variable models Tensor Decompositions for Learning Latent Variable Models Anima Anandkumar1, Rong Ge2, Daniel Hsu3, Sham M...the ARO Award W911NF-12-1-0404. References [AFH+12] A. Anandkumar, D. P. Foster, D. Hsu, S. M. Kakade, and Y.-K. Liu . A spectral algorithm for latent...volume 13. Cambridge University Press, 2005. [PSX11] A. Parikh, L. Song , and E. P. Xing. A spectral algorithm for latent tree graphical models. In
A Case of Tensor Fasciae Suralis Muscle
Miyauchi, Ryosuke; Kurihara, Kazushige; Tachibana, Gen
1985-01-01
An anomalous muscle was found on the dorsum of the right lower limb of a 67-year-old Japanese male. It originated by two heads from the semitendinosus and long head of the biceps femoris and ran distally to insert into the deep surface of the sural fascia. The origin, insertion and location of the muscle were compared with those of the various supernumerary muscles hitherto published. The muscle is consequently regarded as being the tensor fasciae suralis. This is the fifth case in Japan.
Radiation forces and torques without stress (tensors)
Energy Technology Data Exchange (ETDEWEB)
Bohren, Craig F, E-mail: bohren@meteo.psu.edu [Department of Meteorology, Pennsylvania State University, University Park, PA 16802 (United States)
2011-11-15
To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce within illuminated objects. This can be shown directly by deriving the radiation force and torque resulting from normal-incidence illumination of a planar interface between free space and an arbitrary medium. Every point of the medium contributes to the total force and torque, which are therefore not localized.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
2016-01-01
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise...
Strodl, Johannes; Doerner, Karl F.; Tricoire, Fabien; Hartl, Richard F.
In this paper we study the impact of different index structures used within hybrid solution approaches for vehicle routing problems with hard feasibility checks. We examine the case of the vehicle routing problem with two-dimensional loading constraints, which combines the loading of freight into the vehicles and the routing of the vehicles to satisfy the demands of the customers. The problem is solved by a variable neighborhood search for the routing part, in which we embed an exact procedure for the loading subproblem. The contribution of the paper is threefold: i) Four different index mechanisms for managing the subproblems are implemented and tested. It is shown that simple index structures tend to lead to better solutions than more powerful albeit complex ones, when using the same runtime limits. ii) The problem of balancing the CPU budget between exploration of different solutions and exact solution of the loading subproblem is investigated; experiments show that solving exactly hard subproblems can lead to better solution quality over the whole solution process. iii) New best results are presented on existing benchmark instances.
Cognitive Structures of Good and Poor Novice Problem Solvers in Physics
de Jong, Anthonius J.M.; Ferguson-Hessler, Monica G.M.
1986-01-01
The way knowledge is organized in memory is generally expected to relate to the degree of success in problem solving. In the present study, we investigated whether good novice problem solvers have their knowledge arranged around problem types to a greater extent than poor problem solvers have. In
Dentinal tubules revealed with X-ray tensor tomography.
Jud, Christoph; Schaff, Florian; Zanette, Irene; Wolf, Johannes; Fehringer, Andreas; Pfeiffer, Franz
2016-09-01
Dentin is a mineralized material making up most of the tooth bulk. A system of microtubules, so called dentinal tubules, transverses it radially from the pulp chamber to the outside. This highly oriented structure leads to anisotropic mechanical properties directly connected to the tubules orientation and density: the ultimate tensile strength as well as the fracture toughness and the shear strength are largest perpendicular to dentinal tubules. Consequently, the fatigue strength depends on the direction of dentinal tubules, too. However, none of the existing techniques used to investigate teeth provide access to orientation and density of dentinal tubules for an entire specimen in a non-destructive way. In this paper, we measure a third molar human tooth both with conventional micro-CT and X-ray tensor tomography (XTT). While the achievable resolution in micro-CT is too low to directly resolve the dentinal tubules, we provide strong evidence that the direction and density of dentinal tubules can be indirectly measured by XTT, which exploits small-angle X-ray scattering to retrieve a 3D map of scattering tensors. We show that the mean directions of scattering structures correlate to the orientation of dentinal tubules and that the mean effective scattering strength provides an estimation of the relative density of dentinal tubules. Thus, this method could be applied to investigate the connection between tubule orientation and fatigue or tensile properties of teeth for a full sample without cutting one, non-representative peace of tooth out of the full sample. Copyright © 2016 The Academy of Dental Materials. All rights reserved.
Biocomputing: numerical simulation of glioblastoma growth using diffusion tensor imaging
Bondiau, Pierre-Yves; Clatz, Olivier; Sermesant, Maxime; Marcy, Pierre-Yves; Delingette, Herve; Frenay, Marc; Ayache, Nicholas
2008-02-01
Glioblastoma multiforma (GBM) is one of the most aggressive tumors of the central nervous system. It can be represented by two components: a proliferative component with a mass effect on brain structures and an invasive component. GBM has a distinct pattern of spread showing a preferential growth in the white fiber direction for the invasive component. By using the architecture of white matter fibers, we propose a new model to simulate the growth of GBM. This architecture is estimated by diffusion tensor imaging in order to determine the preferred direction for the diffusion component. It is then coupled with a mechanical component. To set up our growth model, we make a brain atlas including brain structures with a distinct response to tumor aggressiveness, white fiber diffusion tensor information and elasticity. In this atlas, we introduce a virtual GBM with a mechanical component coupled with a diffusion component. These two components are complementary, and can be tuned independently. Then, we tune the parameter set of our model with an MRI patient. We have compared simulated growth (initialized with the MRI patient) with observed growth six months later. The average and the odd ratio of image difference between observed and simulated images are computed. Displacements of reference points are compared to those simulated by the model. The results of our simulation have shown a good correlation with tumor growth, as observed on an MRI patient. Different tumor aggressiveness can also be simulated by tuning additional parameters. This work has demonstrated that modeling the complex behavior of brain tumors is feasible and will account for further validation of this new conceptual approach.
CSIR Research Space (South Africa)
Suliman, Ridhwaan
2012-07-01
Full Text Available This work details the development of a computational tool that can accurately model strongly-coupled fluid-structure interaction (FSI) problems, with a particular focus on thin-walled structures undergoing large, non-linear deformations. The first...
Tensor-vector-scalar-modified gravity: from small scale to cosmology.
Bekenstein, Jacob D
2011-12-28
The impressive success of the standard cosmological model has suggested to many that its ingredients are all that one needs to explain galaxies and their systems. I summarize a number of known problems with this programme. They might signal the failure of standard gravity theory on galaxy scales. The requisite hints as to the alternative gravity theory may lie with the modified Newtonian dynamics (MOND) paradigm, which has proved to be an effective summary of galaxy phenomenology. A simple nonlinear modified gravity theory does justice to MOND at the non-relativistic level, but cannot be consistently promoted to relativistic status. The obstacles were first side-stepped with the formulation of tensor-vector-scalar theory (TeVeS), a covariant-modified gravity theory. I review its structure, its MOND and Newtonian limits, and its performance in the face of galaxy phenomenology. I also summarize features of TeVeS cosmology and describe the confrontation with data from strong and weak gravitational lensing.
Continuity equations for bound electromagnetic field and the electromagnetic energy-momentum tensor
Energy Technology Data Exchange (ETDEWEB)
Kholmetskii, A L [Department of Physics, Belarusian State University, 4 Nezavisimosti Avenue, 220030 Minsk (Belarus); Missevitch, O V [Institute for Nuclear Problems, Belarusian State University, 11 Bobruiskaya Street, 220030 Minsk (Belarus); Yarman, T, E-mail: khol123@yahoo.com [Department of Engineering, Okan University, Akfirat, Istanbul, Turkey and Savronik, Eskisehir (Turkey)
2011-05-01
We analyze the application of the Poynting theorem to the bound (velocity-dependent) electromagnetic (EM) field and show that an often-used arbitrary elimination of the term of self-interaction in the product j{center_dot}E (where j is the current density and E the electric field) represents, in general, an illegitimate operation, which leads to incorrect physical consequences. We propose correct ways of eliminating the terms of self-interaction from the Poynting theorem to transform it into the form that is convenient for problems with bound EM field, which yield the continuity equations for the proper EM energy density, the interaction part of EM energy density and the total EM energy density of bound fields, respectively. These equations indicate the incompleteness of the common EM energy-momentum tensor, and in our analysis, we find a missed term in its structure, which makes its trace non-vanished. Some implications of these results are discussed, in particular, in view of the notion of EM mass of charged particles.
Improving Functional MRI Registration Using Whole-Brain Functional Correlation Tensors.
Zhou, Yujia; Yap, Pew-Thian; Zhang, Han; Zhang, Lichi; Feng, Qianjin; Shen, Dinggang
2017-09-01
Population studies of brain function with resting-state functional magnetic resonance imaging (rs-fMRI) largely rely on the accurate inter-subject registration of functional areas. This is typically achieved through registration of the corresponding T1-weighted MR images with more structural details. However, accumulating evidence has suggested that such strategy cannot well-align functional regions which are not necessarily confined by the anatomical boundaries defined by the T1-weighted MR images. To mitigate this problem, various registration algorithms based directly on rs-fMRI data have been developed, most of which have utilized functional connectivity (FC) as features for registration. However, most of the FC-based registration methods usually extract the functional features only from the thin and highly curved cortical grey matter (GM), posing a great challenge in accurately estimating the whole-brain deformation field. In this paper, we demonstrate that the additional useful functional features can be extracted from brain regions beyond the GM, particularly, white-matter (WM) based on rs-fMRI, for improving the overall functional registration. Specifically, we quantify the local anisotropic correlation patterns of the blood oxygenation level-dependent (BOLD) signals, modeled by functional correlation tensors (FCTs), in both GM and WM. Functional registration is then performed based on multiple components of the whole-brain FCTs using a multichannel Large Deformation Diffeomorphic Metric Mapping (mLDDMM) algorithm. Experimental results show that our proposed method achieves superior functional registration performance, compared with other conventional registration methods.
Nearest-neighbor interaction systems in the tensor-train format
Gelß, Patrick; Klus, Stefan; Matera, Sebastian; Schütte, Christof
2017-07-01
Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods anymore due to the so-called curse of dimensionality. This requires techniques to handle linear operators defined on extremely large state spaces and to solve the resulting systems of linear equations or eigenvalue problems. In this paper, we present a systematic tensor-train decomposition for nearest-neighbor interaction systems which is applicable to a host of different problems. With the aid of this decomposition, it is possible to reduce the memory consumption as well as the computational costs significantly. Furthermore, it can be shown that in some cases the rank of the tensor decomposition does not depend on the network size. The format is thus feasible even for high-dimensional systems. We will illustrate the results with several guiding examples such as the Ising model, a system of coupled oscillators, and a CO oxidation model.
Higher order singular value decomposition of tensors for fusion of registered images
Thomason, Michael G.; Gregor, Jens
2011-01-01
This paper describes a computational method using tensor math for higher order singular value decomposition (HOSVD) of registered images. Tensor decomposition is a rigorous way to expose structure embedded in multidimensional datasets. Given a dataset of registered 2-D images, the dataset is represented in tensor format and HOSVD of the tensor is computed to obtain a set of 2-D basis images. The basis images constitute a linear decomposition of the original dataset. HOSVD is data-driven and does not require the user to select parameters or assign thresholds. A specific application uses the basis images for pixel-level fusion of registered images into a single image for visualization. The fusion is optimized with respect to a measure of mean squared error. HOSVD and image fusion are illustrated empirically with four real datasets: (1) visible and infrared data of a natural scene, (2) MRI and x ray CT brain images, and in nondestructive testing (3) x ray, ultrasound, and eddy current images, and (4) x ray, ultrasound, and shearography images.
Gaussian Mixtures on Tensor Fields for Segmentation: Applications to Medical Imaging
de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos
2012-01-01
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. PMID:20932717
A new method to derive white matter conductivity from diffusion tensor MRI.
Wang, Kun; Zhu, Shanan; Mueller, Bryon A; Lim, Kelvin O; Liu, Zhongming; He, Bin
2008-10-01
We propose a new algorithm to derive the anisotropic conductivity of the cerebral white matter (WM) from the diffusion tensor MRI (DT-MRI) data. The transportation processes for both water molecules and electrical charges are described through a common multicompartment model that consists of axons, glia, or the cerebrospinal fluid (CSF). The volume fraction (VF) of each compartment varies from voxel to voxel and is estimated from the measured diffusion tensor. The conductivity tensor at each voxel is then computed from the estimated VF values and the decomposed eigenvectors of the diffusion tensor. The proposed VF algorithm was applied to the DT-MRI data acquired from two healthy human subjects. The extracted anisotropic conductivity distribution was compared with those obtained by using two existing algorithms, which were based upon a linear conductivity-to-diffusivity relationship and a volume constraint, respectively. The present results suggest that the VF algorithm is capable of incorporating the partial volume effects of the CSF and the intravoxel fiber crossing structure, both of which are not addressed altogether by existing algorithms. Therefore, it holds potential to provide a more accurate estimate of the WM anisotropic conductivity, and may have important applications to neuroscience research or clinical applications in neurology and neurophysiology.
Fast and Analytical EAP Approximation from a 4th-Order Tensor
Directory of Open Access Journals (Sweden)
Aurobrata Ghosh
2012-01-01
Full Text Available Generalized diffusion tensor imaging (GDTI was developed to model complex apparent diffusivity coefficient (ADC using higher-order tensors (HOTs and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP. Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF, since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.
Review. Supporting problem structuring with computer-based tools in participatory forest planning
Directory of Open Access Journals (Sweden)
T. Hujala
2013-07-01
Full Text Available Aim of study: This review presents the state-of-art of using computerized techniques for problem structuring (PS in participatory forest planning. Frequency and modes of using different computerized tool types and their contribution for planning processes as well as critical observations are described, followed by recommendations on how to better integrate PS with the use of forest decision support systems.Area of study: The reviewed research cases are from Asia, Europe, North-America, Africa and Australia.Materials and methods: Via Scopus search and screening of abstracts, 32 research articles from years 2002–2011 were selected for review. Explicit and implicit evidence of using computerized tools for PS was recorded and assessed with content-driven qualitative analysis.Main results: GIS and forest-specific simulation tools were the most prevalent software types whereas cognitive modelling software and spreadsheet and calculation tools were less frequently used, followed by multi-criteria and interactive tools. The typical use type was to provide outputs of simulation–optimization or spatial analysis to negotiation situations or to compile summaries or illustrations afterwards; using software during group negotiation to foster interaction was observed only in a few cases.Research highlights: Expertise in both decision support systems and group learning is needed to better integrate PS and computerized decision analysis. From the knowledge management perspective, it is recommended to consider how the results of PS – e.g. conceptual models – could be stored into a problem perception database, and how PS and decision making could be streamlined by retrievals from such systems.Keywords: facilitated modeling; group negotiation; knowledge management; natural resource management; PSM; soft OR; stakeholders.
Review. Supporting problem structuring with computer-based tools in participatory forest planning
Energy Technology Data Exchange (ETDEWEB)
Hujala, T.; Khadka, C.; Wolfslehner, B.; Vacik, H.
2013-09-01
Aim of study: This review presents the state-of-art of using computerized techniques for problem structuring (PS) in participatory forest planning. Frequency and modes of using different computerized tool types and their contribution for planning processes as well as critical observations are described, followed by recommendations on how to better integrate PS with the use of forest decision support systems. Area of study: The reviewed research cases are from Asia, Europe, North-America, Africa and Australia. Material and methods: Via Scopus search and screening of abstracts, 32 research articles from years 2002-2011 were selected for review. Explicit and implicit evidence of using computerized tools for PS was recorded and assessed with content-driven qualitative analysis. Main results: GIS and forest-specific simulation tools were the most prevalent software types whereas cognitive modelling software and spreadsheet and calculation tools were less frequently used, followed by multi-criteria and interactive tools. The typical use type was to provide outputs of simulation–optimization or spatial analysis to negotiation situations or to compile summaries or illustrations afterwards; using software during group negotiation to foster interaction was observed only in a few cases. Research highlights: Expertise in both decision support systems and group learning is needed to better integrate PS and computerized decision analysis. From the knowledge management perspective, it is recommended to consider how the results of PS —e.g. conceptual models— could be stored into a problem perception database, and how PS and decision making could be streamlined by retrievals from such systems. (Author)
Black holes in vector-tensor theories
Heisenberg, Lavinia; Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji
2017-08-01
We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.
Lyubetsky, Vassily; Gershgorin, Roman; Gorbunov, Konstantin
2017-12-06
Chromosome structure is a very limited model of the genome including the information about its chromosomes such as their linear or circular organization, the order of genes on them, and the DNA strand encoding a gene. Gene lengths, nucleotide composition, and intergenic regions are ignored. Although highly incomplete, such structure can be used in many cases, e.g., to reconstruct phylogeny and evolutionary events, to identify gene synteny, regulatory elements and promoters (considering highly conserved elements), etc. Three problems are considered; all assume unequal gene content and the presence of gene paralogs. The distance problem is to determine the minimum number of operations required to transform one chromosome structure into another and the corresponding transformation itself including the identification of paralogs in two structures. We use the DCJ model which is one of the most studied combinatorial rearrangement models. Double-, sesqui-, and single-operations as well as deletion and insertion of a chromosome region are considered in the model; the single ones comprise cut and join. In the reconstruction problem, a phylogenetic tree with chromosome structures in the leaves is given. It is necessary to assign the structures to inner nodes of the tree to minimize the sum of distances between terminal structures of each edge and to identify the mutual paralogs in a fairly large set of structures. A linear algorithm is known for the distance problem without paralogs, while the presence of paralogs makes it NP-hard. If paralogs are allowed but the insertion and deletion operations are missing (and special constraints are imposed), the reduction of the distance problem to integer linear programming is known. Apparently, the reconstruction problem is NP-hard even in the absence of paralogs. The problem of contigs is to find the optimal arrangements for each given set of contigs, which also includes the mutual identification of paralogs. We proved that these
Li, Chih-Ying; Waid-Ebbs, Julia; Velozo, Craig A; Heaton, Shelley C
2016-01-01
Social problem-solving deficits characterise individuals with traumatic brain injury (TBI), and poor social problem solving interferes with daily functioning and productive lifestyles. Therefore, it is of vital importance to use the appropriate instrument to identify deficits in social problem solving for individuals with TBI. This study investigates factor structure and item-level psychometrics of the Social Problem Solving Inventory-Revised: Short Form (SPSI-R:S), for adults with moderate and severe TBI. Secondary analysis of 90 adults with moderate and severe TBI who completed the SPSI-R:S was performed. An exploratory factor analysis (EFA), principal components analysis (PCA) and Rasch analysis examined the factor structure and item-level psychometrics of the SPSI-R:S. The EFA showed three dominant factors, with positively worded items represented as the most definite factor. The other two factors are negative problem-solving orientation and skills; and negative problem-solving emotion. Rasch analyses confirmed the three factors are each unidimensional constructs. It was concluded that the total score interpretability of the SPSI-R:S may be challenging due to the multidimensional structure of the total measure. Instead, we propose using three separate SPSI-R:S subscores to measure social problem solving for the TBI population.
Cho, ChangSoo
2015-04-01
Moment tensor inversion method using waveform is not widely used in identification of fault direction for earthquake but also in identification of explosion experiment such as north korea nuclear test. TDMT inversion code as open source was used for 1-D focal mechanism to moderate earthquake. But TDMT code caused some problems to fit waveform data of earthquake. This software was modified and improved with using the extraction bandwidth for event data and using waveform fitting of maximum cross-correlation with limit of shifting time. Improved algorithm was applied to moderate earthquakes occurred in and around the korean peninsula and showed the result of good data fitting in deriving focal mechanism. CMT centeroid locations were calculated with this algorithm. Earthquakes occurred rarely in the korean peninsula and instrumental recording started from 1990's late. But quality of measurement ground motion is very good after the beginning of instrumental recording. 61 moderate earthquakes occurred analyzed between 2000 to present were analyzed. most of all focal mechanism of earthquake showed strike slip or reverse fault as intraplate earthquake. The horizontal direction of tectonic stress of the korean peninsula is ENE-WSW derived with focal mechanisms that were calculated with 1D moment tensor inversion for moderate earthquake by Zoback(1992)'s method of tectonic stress. 3D-moment tensor inversion method was also developed with simulation code of 3-D viscoelastic finite difference method with ADE(auxiliary differential equation)-PML(perfectly matched layer) and applied to main moderate earthquakes. Forward modeling of 3D seismic wave propagation for moment tensor inversion require much time and expensive cost. Forward simulation with domain decomposition of having only thin model between source and receiver in moment tensor inversion could reduce much time, memory and computational cost in 3D moment tensor inversion even though this method was not more effective
Narasingharao, Kumar; Pradhan, Balaram; Navaneetham, Janardhana
2017-03-01
Autism Spectrum Disorder (ASD) is a neuro developmental disorder which appears at early childhood age between 18 and 36 months. Apart from behaviour problems ASD children also suffer from sleep and Gastrointestinal (GI) problems. Major behaviour problems of ASD children are lack of social communication and interaction, less attention span, repetitive and restrictive behaviour, lack of eye to eye contact, aggressive and self-injurious behaviours, sensory integration problems, motor problems, deficiency in academic activities, anxiety and depression etc. Our hypothesis is that structured yoga intervention will brings significant changes in the problems of ASD children. The aim of this study was to find out efficacy of structured yoga intervention for sleep problems, gastrointestinal problems and behaviour problems of ASD children. It was an exploratory study with pre-test and post-test control design. Three sets of questionnaires having 61 questions developed by researchers were used to collect data pre and post yoga intervention. Questionnaires were based on three problematic areas of ASD children as mentioned above and were administered to parents by teachers under the supervision of researcher and clinical psychologists. Experimental group was given yoga intervention for a period of 90 days and control group continued with school curriculum. Both children and parents participated in this intervention. Significant changes were seen post yoga intervention in three areas of problems as mentioned above. Statistical analysis also showed significance value of 0.001 in the result. Structured yoga intervention can be conducted for a large group of ASD children with parent's involvement. Yoga can be used as alternative therapy to reduce the severity of symptoms of ASD children.
Energy Technology Data Exchange (ETDEWEB)
Sigrist, J.F
2004-11-15
The present work deals with the numerical simulation of a coupled fluid/structure problem with fluid free surface. A generic coupled fluid/structure system is defined, on which a linear problem (modal analysis) and a non-linear problem (temporal analysis) are stated. In the linear case, a strong coupled method is used. It is based on a finite element approach of the structure problem and a finite or a boundary element approach of the fluid problem. The coupled problem is formulated in terms of pressure and displacement, leading to a non-symmetric problem which is solved with an appropriate algorithm. In the non-linear case, the structure problem is described with non-linear equations of motion, whereas the fluid problem is modeled with the Stokes equations. The numerical resolution of the coupled problem is based on a weak coupling procedure. The fluid problem is solved with a finite volume technique, using a moving mesh technique to adjust the structure motion, a VOF method for the description of the free surface and the PISO algorithm for the time integration. The structure problem is solved with a finite element technique, using an explicit/implicit time integration algorithm. A procedure is developed in order to handle the coupling in space (fluid forces and structure displacement exchanges between fluid and structure mesh, fluid re-meshing) and in time (staggered explicit algorithm, dynamic filtering of numerical oscillations). The non linear coupled problem is solved using a CFD code, whose use for FSI problem is validated with a benchmark presented in this work. A comparison is proposed between numerical results and analytical solution for two elementary fluid problems. The validation process can be applied for any CFD numerical code. A numerical study is then proposed on the generic coupled case in order to describe the fluid/structure interaction phenomenon (added mass, displaced mass, mode coupling, influence of structural non-linearity). An industrial
Moret-Hartman, M.; Wilt, G.J. van der; Grin, J.
2007-01-01
OBJECTIVES: The practical significance of health technology assessment (HTA) in policy decisions or clinical practice has been challenged. Possibly, problem definitions underlying HTA do not concur sufficiently with the problem definitions held by policy makers or clinicians. We performed an
van Scheppingen, Corinne; Lettinga, Ant T.; Duipmans, Jose C.; Maathuis, Care G. B.; Jonkman, Marcel F.
2008-01-01
The objective of this study was to identify and specify the problems of children with epidermolysis bullosa. The questions explored were: (i) What do children with epidermolysis bullosa experience as the most difficult problems; (it) What is the impact of these problems on their daily life; and
2010-06-15
demonstrate that in a number of image inverse problems, including inpainting , zooming, and deblurring, the same algorithm produces either equal, often...inverse problems, including inpainting , zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small...problems often named inpainting or interpolation, zooming and deblurring. Estimating f requires some prior information on the image, or equivalently image
Soliman, Sylvain
2012-05-29
We present a way to compute the minimal semi-positive invariants of a Petri net representing a biological reaction system, as resolution of a Constraint Satisfaction Problem. The use of Petri nets to manipulate Systems Biology models and make available a variety of tools is quite old, and recently analyses based on invariant computation for biological models have become more and more frequent, for instance in the context of module decomposition. In our case, this analysis brings both qualitative and quantitative information on the models, in the form of conservation laws, consistency checking, etc. thanks to finite domain constraint programming. It is noticeable that some of the most recent optimizations of standard invariant computation techniques in Petri nets correspond to well-known techniques in constraint solving, like symmetry-breaking. Moreover, we show that the simple and natural encoding proposed is not only efficient but also flexible enough to encompass sub/sur-invariants, siphons/traps, etc., i.e., other Petri net structural properties that lead to supplementary insight on the dynamics of the biochemical system under study. A simple implementation based on GNU-Prolog's finite domain solver, and including symmetry detection and breaking, was incorporated into the BIOCHAM modelling environment and in the independent tool Nicotine. Some illustrative examples and benchmarks are provided.
Directory of Open Access Journals (Sweden)
Soliman Sylvain
2012-05-01
Full Text Available Abstract Background We present a way to compute the minimal semi-positive invariants of a Petri net representing a biological reaction system, as resolution of a Constraint Satisfaction Problem. The use of Petri nets to manipulate Systems Biology models and make available a variety of tools is quite old, and recently analyses based on invariant computation for biological models have become more and more frequent, for instance in the context of module decomposition. Results In our case, this analysis brings both qualitative and quantitative information on the models, in the form of conservation laws, consistency checking, etc. thanks to finite domain constraint programming. It is noticeable that some of the most recent optimizations of standard invariant computation techniques in Petri nets correspond to well-known techniques in constraint solving, like symmetry-breaking. Moreover, we show that the simple and natural encoding proposed is not only efficient but also flexible enough to encompass sub/sur-invariants, siphons/traps, etc., i.e., other Petri net structural properties that lead to supplementary insight on the dynamics of the biochemical system under study. Conclusions A simple implementation based on GNU-Prolog's finite domain solver, and including symmetry detection and breaking, was incorporated into the BIOCHAM modelling environment and in the independent tool Nicotine. Some illustrative examples and benchmarks are provided.
Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery
2013-08-16
drawn uniformly at random (by the command orth(randn(·, ·)) in Matlab ). The observed entries are chosen uniformly with ratio ρ. We increase the...and 4d pre-stack seismic data completion using tensor nuclear norm (tnn). preprint, 2013. [GQ12] D. Goldfarb and Z. Qin. Robust low-rank tensor
Cosmic no-hair conjecture in scalar–tensor theories
Indian Academy of Sciences (India)
In fact, during inflation there is no difference between scalar–tensor theories, Lyra's manifold and general relativity (GR). Keywords. Scalar–tensor theories; cosmic no-hair. PACS Nos 04.20.jb; 98.80.Hw. 1. Introduction. With regard to the question whether the Universe evolves to a homogeneous and isotropic state during ...
Secoond order parallel tensors on some paracontact manifolds | Liu ...
African Journals Online (AJOL)
The object of the present paper is to study the symmetric and skewsymmetric properties of a second order parallel tensor on paracontact metric (k;μ)- spaces and almost β-para-Kenmotsu (k;μ)-spaces. In this paper, we prove that if there exists a second order symmetric parallel tensor on a paracontact metric (k;μ)- space M, ...
Kanazawa, Takahiko; Yasuda, Keiichiro
Metaheuristics is a new paradigm that aims to obtain an approximate solution within a feasible computation time. To design the effective metaheuristics, strategies of intensification and diversification are essential. This paper proposes an algorithm that has long term policy for realizing intensification and diversification based on higher level structure in solution space. In order to verify the performance, the proposed algorithm is applied to some traveling salesman problems which are typical combinatorial optimization problems.
Energy Technology Data Exchange (ETDEWEB)
Malhotra, M. [Stanford Univ., CA (United States)
1996-12-31
Finite-element discretizations of time-harmonic acoustic wave problems in exterior domains result in large sparse systems of linear equations with complex symmetric coefficient matrices. In many situations, these matrix problems need to be solved repeatedly for different right-hand sides, but with the same coefficient matrix. For instance, multiple right-hand sides arise in radiation problems due to multiple load cases, and also in scattering problems when multiple angles of incidence of an incoming plane wave need to be considered. In this talk, we discuss the iterative solution of multiple linear systems arising in radiation and scattering problems in structural acoustics by means of a complex symmetric variant of the BL-QMR method. First, we summarize the governing partial differential equations for time-harmonic structural acoustics, the finite-element discretization of these equations, and the resulting complex symmetric matrix problem. Next, we sketch the special version of BL-QMR method that exploits complex symmetry, and we describe the preconditioners we have used in conjunction with BL-QMR. Finally, we report some typical results of our extensive numerical tests to illustrate the typical convergence behavior of BL-QMR method for multiple radiation and scattering problems in structural acoustics, to identify appropriate preconditioners for these problems, and to demonstrate the importance of deflation in block Krylov-subspace methods. Our numerical results show that the multiple systems arising in structural acoustics can be solved very efficiently with the preconditioned BL-QMR method. In fact, for multiple systems with up to 40 and more different right-hand sides we get consistent and significant speed-ups over solving the systems individually.
DEFF Research Database (Denmark)
Montoya-Martinez, Jair; Artes-Rodriguez, Antonio; Pontil, Massimiliano
2014-01-01
We consider the estimation of the Brain Electrical Sources (BES) matrix from noisy electroencephalographic (EEG) measurements, commonly named as the EEG inverse problem. We propose a new method to induce neurophysiological meaningful solutions, which takes into account the smoothness, structured...... matrix and the squared Frobenius norm of the latent source matrix. We develop an alternating optimization algorithm to solve the resulting nonsmooth-nonconvex minimization problem. We analyze the convergence of the optimization procedure, and we compare, under different synthetic scenarios...
On the energy-momentum tensor in Moyal space
Energy Technology Data Exchange (ETDEWEB)
Balasin, Herbert; Schweda, Manfred [Vienna University of Technology, Institute for Theoretical Physics, Vienna (Austria); Blaschke, Daniel N. [Los Alamos National Laboratory, Theory Division, Los Alamos, NM (United States); Gieres, Francois [Universite de Lyon, Universite Claude Bernard Lyon 1 et CNRS/IN2P3, Institut de Physique Nucleaire de Lyon, Villeurbanne (France)
2015-06-15
We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)
Imanishi, K.; Uchide, T.
2016-12-01
There is a growing interest in source mechanisms of microearthquakes particularly for induced microseismic events in oil, gas, and geothermal fields. However, their reliable estimate is a difficult task due to low S/N ratio and poor knowledge of the underground structure. Dahm (1996) develop a relative moment tensor inversion (RMTI) method for earthquake source clusters, in which relative body-wave amplitudes for two earthquakes recorded at a common station are used to eliminate the effect of propagation paths. If the source mechanism of one of those earthquakes is known a priori, the other source mechanisms can be determined without a computation of Green's function. A difficulty in this method is that errors in the mechanism of reference events may lead to biased solutions for other events. In order to avoid this problem, we propose a method that iteratively applies the RMTI to source clusters improving each moment tensor. The procedure is as follows: (1) Sample co-located multiple earthquakes. At this time, their source mechanisms are not always accurately determined. (2) Apply the RMTI to estimate the source mechanism of each event relative to those of the other events. (3) Repeat the step 2 for the modified source mechanisms until the total residual becomes almost constant. We conducted numerical tests on synthetic data, where amplitudes were computed assuming double-couple sources, amplifying by factor between 0.3 and 5 as site effects, and adding 10% random noise. Initial solutions were given by adding 20-degree-wide random noises to strike, dip, and rake angles of input mechanisms. In a test with eight sources at 12 stations, the total residual rapidly drops during the first few iterations and settles down afterwards. After the three iterations, the solutions almost reach the input mechanisms. In contrast, both of the original RMTI (i.e., without iteration) and a general MTI (i.e., single-source, absolute MTI) could not reproduce the input mechanisms, where
Spin correlation tensor for measurement of quantum entanglement in electron-electron scattering
Tsurikov, D. E.; Samarin, S. N.; Williams, J. F.; Artamonov, O. M.
2017-04-01
We consider the problem of correct measurement of a quantum entanglement in the two-body electron-electron scattering. An expression is derived for a spin correlation tensor of a pure two-electron state. A geometric measure of a quantum entanglement as the distance between two forms of this tensor in entangled and separable cases is presented. Due to such definition, one does not need to look for the closest separable state to the analyzed state. We prove that introduced measure satisfies properties of a valid entanglement measure: nonnegativity, discriminance, normalization, non-growth under local operations and classical communication. This measure is calculated for a problem of electron-electron scattering. We prove that it does not depend on the azimuthal rotation angle of the second electron spin relative to the first electron spin before scattering. We specify how to find a spin correlation tensor and the related measure of a quantum entanglement in an experiment with electron-electron scattering. Finally, the introduced measure is extended to the mixed states.
The atomistic representation of first strain-gradient elastic tensors
Admal, Nikhil Chandra; Marian, Jaime; Po, Giacomo
2017-02-01
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical second-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy-Born rule. Using the derived expressions, we prove that the odd-order tensors vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic tensors for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices (fcc Al and Cu and bcc Fe and W) and multi-lattices (diamond-cubic Si). We observe that central potentials exhibit generalized Cauchy relations for the rank-six tensor of strain-gradient elastic moduli. In addition, this tensor is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic tensors to the choice of the cutoff radius.