Changes in Self-Representations Following Psychoanalytic Psychotherapy for Young Adults: A Comparative Typology.

PubMed

Werbart, Andrzej; Brusell, Lars; Iggedal, Rebecka; Lavfors, Kristin; Widholm, Alexander

2016-10-01

Changes in dynamic psychological structures are often a treatment goal in psychotherapy. The present study aimed at creating a typology of self-representations among young women and men in psychoanalytic psychotherapy, to study longitudinal changes in self-representations, and to compare self-representations in the clinical sample with those of a nonclinical group. Twenty-five women and sixteen men were interviewed according to Blatt's Object Relations Inventory pretreatment, at termination, and at a 1.5-year follow-up. In the comparison group, eleven women and nine men were interviewed at baseline, 1.5 years, and three years later. Typologies of the 123 self-descriptions in the clinical group and 60 in the nonclinical group were constructed by means of ideal-type analysis for men and women separately. Clusters of self-representations could be depicted on a two-dimensional matrix with the axes Relatedness-Self-definition and Integration-Nonintegration. In most cases, the self-descriptions changed over time in terms of belonging to different ideal-type clusters. In the clinical group, there was a movement toward increased integration in self-representations, but above all toward a better balance between relatedness and self-definition. The changes continued after termination, paralleled by reduced symptoms, improved functioning, and higher developmental levels of representations. No corresponding tendency could be observed in the nonclinical group.

A Compact Formula for Rotations as Spin Matrix Polynomials

DOE PAGES

Curtright, Thomas L.; Fairlie, David B.; Zachos, Cosmas K.

2014-08-12

Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. Here, the simple explicit result exhibits connections between group theory, combinatorics, and Fourier analysis, especially in the large spin limit. Salient intuitive features of the formula are illustrated and discussed.

BMS symmetry, soft particles and memory

NASA Astrophysics Data System (ADS)

Chatterjee, Atreya; Lowe, David A.

2018-05-01

In this work, we revisit unitary irreducible representations of the Bondi–Metzner–Sachs (BMS) group discovered by McCarthy. Representations are labelled by an infinite number of supermomenta in addition to 4-momentum. Tensor products of these irreducible representations lead to particle-like states dressed by soft gravitational modes. Conservation of 4-momentum and supermomentum in the scattering of such states leads to a memory effect encoded in the outgoing soft modes. We note there exist irreducible representations corresponding to soft states with strictly vanishing 4-momentum, which may nevertheless be produced by scattering of particle-like states. This fact has interesting implications for the S-matrix in gravitational theories.

Lanczos algorithm with matrix product states for dynamical correlation functions

NASA Astrophysics Data System (ADS)

Dargel, P. E.; Wöllert, A.; Honecker, A.; McCulloch, I. P.; Schollwöck, U.; Pruschke, T.

2012-05-01

The density-matrix renormalization group (DMRG) algorithm can be adapted to the calculation of dynamical correlation functions in various ways which all represent compromises between computational efficiency and physical accuracy. In this paper we reconsider the oldest approach based on a suitable Lanczos-generated approximate basis and implement it using matrix product states (MPS) for the representation of the basis states. The direct use of matrix product states combined with an ex post reorthogonalization method allows us to avoid several shortcomings of the original approach, namely the multitargeting and the approximate representation of the Hamiltonian inherent in earlier Lanczos-method implementations in the DMRG framework, and to deal with the ghost problem of Lanczos methods, leading to a much better convergence of the spectral weights and poles. We present results for the dynamic spin structure factor of the spin-1/2 antiferromagnetic Heisenberg chain. A comparison to Bethe ansatz results in the thermodynamic limit reveals that the MPS-based Lanczos approach is much more accurate than earlier approaches at minor additional numerical cost.

Sparse subspace clustering for data with missing entries and high-rank matrix completion.

PubMed

Fan, Jicong; Chow, Tommy W S

2017-09-01

Many methods have recently been proposed for subspace clustering, but they are often unable to handle incomplete data because of missing entries. Using matrix completion methods to recover missing entries is a common way to solve the problem. Conventional matrix completion methods require that the matrix should be of low-rank intrinsically, but most matrices are of high-rank or even full-rank in practice, especially when the number of subspaces is large. In this paper, a new method called Sparse Representation with Missing Entries and Matrix Completion is proposed to solve the problems of incomplete-data subspace clustering and high-rank matrix completion. The proposed algorithm alternately computes the matrix of sparse representation coefficients and recovers the missing entries of a data matrix. The proposed algorithm recovers missing entries through minimizing the representation coefficients, representation errors, and matrix rank. Thorough experimental study and comparative analysis based on synthetic data and natural images were conducted. The presented results demonstrate that the proposed algorithm is more effective in subspace clustering and matrix completion compared with other existing methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

The exponential parameterization of the neutrino mixing matrix as an SU(3) group element and an account for new experimental data

NASA Astrophysics Data System (ADS)

Zhukovsky, K. V.

2017-09-01

The exponential form of the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix for neutrinos is considered in the context of the fundamental representation of the SU(3) group. The logarithm of the mixing matrix is obtained. Based on the most recent experimental data on neutrino mixing, the exact values of the entries of the exponential matrix are calculated. The exact values for its real and imaginary parts are determined, respectively, in charge of the mixing without CP violation and of the pure CP violation effect. The hypothesis of complementarity for quarks and neutrinos is confirmed. The factorization of the exponential mixing matrix, which allows the separation of the mixing and of the CP violation itself in the form of the product of rotations around the real and imaginary axes, is demonstrated.

Entanglement classification in the noninteracting Fermi gas

NASA Astrophysics Data System (ADS)

Jafarizadeh, M. A.; Eghbalifam, F.; Nami, S.; Yahyavi, M.

In this paper, entanglement classification shared among the spins of localized fermions in the noninteracting Fermi gas is studied. It is proven that the Fermi gas density matrix is block diagonal on the basis of the projection operators to the irreducible representations of symmetric group Sn. Every block of density matrix is in the form of the direct product of a matrix and identity matrix. Then it is useful to study entanglement in every block of density matrix separately. The basis of corresponding Hilbert space are identified from the Schur-Weyl duality theorem. Also, it can be shown that the symmetric part of the density matrix is fully separable. Then it has been shown that the entanglement measure which is introduced in Eltschka et al. [New J. Phys. 10, 043104 (2008)] and Guhne et al. [New J. Phys. 7, 229 (2005)], is zero for the even n qubit Fermi gas density matrix. Then by focusing on three spin reduced density matrix, the entanglement classes have been investigated. In three qubit states there is an entanglement measure which is called 3-tangle. It can be shown that 3-tangle is zero for three qubit density matrix, but the density matrix is not biseparable for all possible values of its parameters and its eigenvectors are in the form of W-states. Then an entanglement witness for detecting non-separable state and an entanglement witness for detecting nonbiseparable states, have been introduced for three qubit density matrix by using convex optimization problem. Finally, the four spin reduced density matrix has been investigated by restricting the density matrix to the irreducible representations of Sn. The restricted density matrix to the subspaces of the irreducible representations: Ssym, S3,1 and S2,2 are denoted by ρsym, ρ3,1 and ρ2,2, respectively. It has been shown that some highly entangled classes (by using the results of Miyake [Phys. Rev. A 67, 012108 (2003)] for entanglement classification) do not exist in the blocks of density matrix ρ3,1 and ρ2,2, so these classes do not exist in the total Fermi gas density matrix.

On the representation matrices of the spin permutation group. [for atomic and molecular electronic structures

NASA Technical Reports Server (NTRS)

Wilson, S.

1977-01-01

A method is presented for the determination of the representation matrices of the spin permutation group (symmetric group), a detailed knowledge of these matrices being required in the study of the electronic structure of atoms and molecules. The method is characterized by the use of two different coupling schemes. Unlike the Yamanouchi spin algebraic scheme, the method is not recursive. The matrices for the fundamental transpositions can be written down directly in one of the two bases. The method results in a computationally significant reduction in the number of matrix elements that have to be stored when compared with, say, the standard Young tableaux group theoretical approach.

A path-oriented matrix-based knowledge representation system

NASA Technical Reports Server (NTRS)

Feyock, Stefan; Karamouzis, Stamos T.

1993-01-01

Experience has shown that designing a good representation is often the key to turning hard problems into simple ones. Most AI (Artificial Intelligence) search/representation techniques are oriented toward an infinite domain of objects and arbitrary relations among them. In reality much of what needs to be represented in AI can be expressed using a finite domain and unary or binary predicates. Well-known vector- and matrix-based representations can efficiently represent finite domains and unary/binary predicates, and allow effective extraction of path information by generalized transitive closure/path matrix computations. In order to avoid space limitations a set of abstract sparse matrix data types was developed along with a set of operations on them. This representation forms the basis of an intelligent information system for representing and manipulating relational data.

Coupling coefficients for tensor product representations of quantum SU(2)

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

Groenevelt, Wolter, E-mail: w.g.m.groenevelt@tudelft.nl

2014-10-15

We study tensor products of infinite dimensional irreducible {sup *}-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometricmore » orthogonal polynomials and q-Bessel-type functions.« less

An efficient approach to CI: General matrix element formulas for spin-coupled particle-hole excitations

NASA Astrophysics Data System (ADS)

Tavan, Paul; Schulten, Klaus

1980-03-01

A new, efficient algorithm for the evaluation of the matrix elements of the CI Hamiltonian in the basis of spin-coupled ν-fold excitations (over orthonormal orbitals) is developed for even electron systems. For this purpose we construct an orthonormal, spin-adapted CI basis in the framework of second quantization. As a prerequisite, spin and space parts of the fermion operators have to be separated; this makes it possible to introduce the representation theory of the permutation group. The ν-fold excitation operators are Serber spin-coupled products of particle-hole excitations. This construction is also designed for CI calculations from multireference (open-shell) states. The 2N-electron Hamiltonian is expanded in terms of spin-coupled particle-hole operators which map any ν-fold excitation on ν-, and ν±1-, and ν±2-fold excitations. For the calculation of the CI matrix this leaves one with only the evaluation of overlap matrix elements between spin-coupled excitations. This leads to a set of ten general matrix element formulas which contain Serber representation matrices of the permutation group Sν×Sν as parameters. Because of the Serber structure of the CI basis these group-theoretical parameters are kept to a minimum such that they can be stored readily in the central memory of a computer for ν?4 and even for higher excitations. As the computational effort required to obtain the CI matrix elements from the general formulas is very small, the algorithm presented appears to constitute for even electron systems a promising alternative to existing CI methods for multiply excited configurations, e.g., the unitary group approach. Our method makes possible the adaptation of spatial symmetries and the selection of any subset of configurations. The algorithm has been implemented in a computer program and tested extensively for ν?4 and singlet ground and excited states.

Spectral resolution of SU(3)-invariant solutions of the Yang-Baxter equation

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

Alishauskas, S.I.; Kulish, P.P.

1986-11-20

The spectral resolution of invariant R-matrices is computed on the basis of solution of the defining equation. Multiple representations in the Clebsch-Gordon series are considered by means of the classifying operator A: a linear combination of known operators of third and fourth degrees in the group generators. The matrix elements of A in a nonorthonormal basis are found. Explicit expressions are presented for the spectral resolutions for a number of representations.

Spectral resolution of SU(3)-invariant solutions of the Yang-Baxter equation

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

Alishavskas, S.I.; Kulish, P.P.

1986-11-01

The spectral resolution of invariant R-matrices is computed on the basis of solution of the defining equation. Multiple representations in the Clebsch-Gordon series are considered by means of the classifying operator A: a linear combination of known operators of third and fourth degrees in the group generators. The matrix elements of A in a nonorthonormal basis are found. Explicit expressions are presented for the spectral resolutions for a number of representations.

Assessing the effects of cocaine dependence and pathological gambling using group-wise sparse representation of natural stimulus FMRI data.

PubMed

Ren, Yudan; Fang, Jun; Lv, Jinglei; Hu, Xintao; Guo, Cong Christine; Guo, Lei; Xu, Jiansong; Potenza, Marc N; Liu, Tianming

2017-08-01

Assessing functional brain activation patterns in neuropsychiatric disorders such as cocaine dependence (CD) or pathological gambling (PG) under naturalistic stimuli has received rising interest in recent years. In this paper, we propose and apply a novel group-wise sparse representation framework to assess differences in neural responses to naturalistic stimuli across multiple groups of participants (healthy control, cocaine dependence, pathological gambling). Specifically, natural stimulus fMRI (N-fMRI) signals from all three groups of subjects are aggregated into a big data matrix, which is then decomposed into a common signal basis dictionary and associated weight coefficient matrices via an effective online dictionary learning and sparse coding method. The coefficient matrices associated with each common dictionary atom are statistically assessed for each group separately. With the inter-group comparisons based on the group-wise correspondence established by the common dictionary, our experimental results demonstrated that the group-wise sparse coding and representation strategy can effectively and specifically detect brain networks/regions affected by different pathological conditions of the brain under naturalistic stimuli.

Coherent states for quantum compact groups

NASA Astrophysics Data System (ADS)

Jurĉo, B.; Ŝťovíĉek, P.

1996-12-01

Coherent states are introduced and their properties are discussed for simple quantum compact groups A l, Bl, Cl and D l. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested.

Quantum groups, Yang-Baxter maps and quasi-determinants

NASA Astrophysics Data System (ADS)

Tsuboi, Zengo

2018-01-01

For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang-Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum Yang-Baxter map, which satisfies the set-theoretic Yang-Baxter equation. The map has a zero curvature representation among L-operators defined as images of the universal R-matrix. We find that the zero curvature representation can be solved by the Gauss decomposition of a product of L-operators. Thereby obtained a quasi-determinant expression of the quantum Yang-Baxter map associated with the quantum algebra Uq (gl (n)). Moreover, the map is identified with products of quasi-Plücker coordinates over a matrix composed of the L-operators. We also consider the quasi-classical limit, where the underlying quantum algebra reduces to a Poisson algebra. The quasi-determinant expression of the quantum Yang-Baxter map reduces to ratios of determinants, which give a new expression of a classical Yang-Baxter map.

Density matrix renormalization group for a highly degenerate quantum system: Sliding environment block approach

NASA Astrophysics Data System (ADS)

Schmitteckert, Peter

2018-04-01

We present an infinite lattice density matrix renormalization group sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct representation of commensurability issues and the treatment of degenerate systems. As an example we apply the method to a spin chain featuring a highly degenerate ground-state space where the new sweeping scheme provides an increase in performance as well as accuracy by many orders of magnitude compared to a recently published work.

Decoherence and Noise in Spin-based Solid State Quantum Computers. Approximation-Free Numerical Simulations

DTIC Science & Technology

2007-07-21

the spin coherent states P-representation", Conference on Quantum Computations and Many- Body Systems, February 2006, Key West, FL 9. B. N. Harmon...solid-state spin-based qubit systems was the focus of our project. Since decoherence is a complex many- body non-equilibrium process, and its...representation of the density matrix, see Sec. 3 below). This work prompted J. Taylor from the experimental group of C. Marcus and M. Lukin (funded by

Diagrammatic technique for calculating matrix elements of collective operators in superradiance. [eigenstates for N two-level atom systems

NASA Technical Reports Server (NTRS)

Lee, C. T.

1975-01-01

Adopting the so-called genealogical construction, one can express the eigenstates of collective operators corresponding to a specified mode for an N-atom system in terms of those for an (N-1) atom system. Using these Dicke states as bases and using the Wigner-Eckart theorem, a matrix element of a collective operator of an arbitrary mode can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME is obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups is then introduced. This gives a simple and systematic way of calculating the RME. This method is especially useful when the cooperation number r is close to N/2, where almost exact asymptotic expressions can be obtained easily. The result shows explicity the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes.

Representation learning via Dual-Autoencoder for recommendation.

PubMed

Zhuang, Fuzhen; Zhang, Zhiqiang; Qian, Mingda; Shi, Chuan; Xie, Xing; He, Qing

2017-06-01

Recommendation has provoked vast amount of attention and research in recent decades. Most previous works employ matrix factorization techniques to learn the latent factors of users and items. And many subsequent works consider external information, e.g., social relationships of users and items' attributions, to improve the recommendation performance under the matrix factorization framework. However, matrix factorization methods may not make full use of the limited information from rating or check-in matrices, and achieve unsatisfying results. Recently, deep learning has proven able to learn good representation in natural language processing, image classification, and so on. Along this line, we propose a new representation learning framework called Recommendation via Dual-Autoencoder (ReDa). In this framework, we simultaneously learn the new hidden representations of users and items using autoencoders, and minimize the deviations of training data by the learnt representations of users and items. Based on this framework, we develop a gradient descent method to learn hidden representations. Extensive experiments conducted on several real-world data sets demonstrate the effectiveness of our proposed method compared with state-of-the-art matrix factorization based methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Adinkras from ordered quartets of BC4 Coxeter group elements and regarding 1,358,954,496 matrix elements of the Gadget

NASA Astrophysics Data System (ADS)

Gates, S. James; Guyton, Forrest; Harmalkar, Siddhartha; Kessler, David S.; Korotkikh, Vadim; Meszaros, Victor A.

2017-06-01

We examine values of the Adinkra Holoraumy-induced Gadget representation space metric over all possible four-color, four-open node, and four-closed node adinkras. Of the 1,358,954,496 gadget matrix elements, only 226,492,416 are non-vanishing and take on one of three values: -1/3, 1/3, or 1 and thus a subspace isomorphic to a description of a body-centered tetrahedral molecule emerges.

Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F 2

NASA Astrophysics Data System (ADS)

Bentalha, Zine el abidine

2018-06-01

Exact analytical representation for the Coulomb matrix elements by means of Appell's double series F 2 is derived. The finite sum obtained for the Appell function F 2 allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.

Functional brain networks reconstruction using group sparsity-regularized learning.

PubMed

Zhao, Qinghua; Li, Will X Y; Jiang, Xi; Lv, Jinglei; Lu, Jianfeng; Liu, Tianming

2018-06-01

Investigating functional brain networks and patterns using sparse representation of fMRI data has received significant interests in the neuroimaging community. It has been reported that sparse representation is effective in reconstructing concurrent and interactive functional brain networks. To date, most of data-driven network reconstruction approaches rarely take consideration of anatomical structures, which are the substrate of brain function. Furthermore, it has been rarely explored whether structured sparse representation with anatomical guidance could facilitate functional networks reconstruction. To address this problem, in this paper, we propose to reconstruct brain networks utilizing the structure guided group sparse regression (S2GSR) in which 116 anatomical regions from the AAL template, as prior knowledge, are employed to guide the network reconstruction when performing sparse representation of whole-brain fMRI data. Specifically, we extract fMRI signals from standard space aligned with the AAL template. Then by learning a global over-complete dictionary, with the learned dictionary as a set of features (regressors), the group structured regression employs anatomical structures as group information to regress whole brain signals. Finally, the decomposition coefficients matrix is mapped back to the brain volume to represent functional brain networks and patterns. We use the publicly available Human Connectome Project (HCP) Q1 dataset as the test bed, and the experimental results indicate that the proposed anatomically guided structure sparse representation is effective in reconstructing concurrent functional brain networks.

Implementing the SU(2) Symmetry for the DMRG

NASA Astrophysics Data System (ADS)

Alvarez, Gonzalo

2010-03-01

In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992), Hamiltonian symmetries play an important role. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This talk will explain how the DMRG++ codefootnotetextarXiv:0902.3185 or Computer Physics Communications 180 (2009) 1572-1578. has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries will be discussed for typical tight-binding models of strongly correlated electronic systems. The computational bottleneck of the algorithm, and the use of shared memory parallelization will also be addressed. Finally, a roadmap for future work on DMRG++ will be presented.

Implementation of the SU(2) Hamiltonian Symmetry for the DMRG Algorithm

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

Alvarez, Gonzalo

2012-01-01

In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992, 1993) and Hamiltonian symmetries play an important role. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This paper explains how the the DMRG++ code (Alvarez, 2009) has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries are discussed for the one-orbital Hubbard model, and for a two-orbital Hubbard model for iron-based superconductors. The computational bottleneck of the algorithm and themore » use of shared memory parallelization are also addressed.« less

Highly Entangled, Non-random Subspaces of Tensor Products from Quantum Groups

NASA Astrophysics Data System (ADS)

Brannan, Michael; Collins, Benoît

2018-03-01

In this paper we describe a class of highly entangled subspaces of a tensor product of finite-dimensional Hilbert spaces arising from the representation theory of free orthogonal quantum groups. We determine their largest singular values and obtain lower bounds for the minimum output entropy of the corresponding quantum channels. An application to the construction of d-positive maps on matrix algebras is also presented.

Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations

NASA Astrophysics Data System (ADS)

Awata, Hidetoshi; Kanno, Hiroaki; Mironov, Andrei; Morozov, Alexei; Morozov, Andrey; Ohkubo, Yusuke; Zenkevich, Yegor

2016-10-01

R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. Calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the Yangian case by A. Smirnov but less general. We investigate the interplay between the R-matrix structure and the structure of DIM algebra intertwiners, i.e. of refined topological vertices and show that the R-matrix is diagonalized by the action of the spectral duality belonging to the SL(2, ℤ) group of DIM algebra automorphisms. We also construct the T-operators satisfying the RTT relations with the R-matrix from refined amplitudes on resolved conifold. We thus show that topological string theories on the toric Calabi-Yau threefolds can be naturally interpreted as lattice integrable models. Integrals of motion for these systems are related to q-deformation of the reflection matrices of the Liouville/Toda theories.

Neural representations and the cortical body matrix: implications for sports medicine and future directions.

PubMed

Wallwork, Sarah B; Bellan, Valeria; Catley, Mark J; Moseley, G Lorimer

2016-08-01

Neural representations, or neurotags, refer to the idea that networks of brain cells, distributed across multiple brain areas, work in synergy to produce outputs. The brain can be considered then, a complex array of neurotags, each influencing and being influenced by each other. The output of some neurotags act on other systems, for example, movement, or on consciousness, for example, pain. This concept of neurotags has sparked a new body of research into pain and rehabilitation. We draw on this research and the concept of a cortical body matrix-a network of representations that subserves the regulation and protection of the body and the space around it-to suggest important implications for rehabilitation of sports injury and for sports performance. Protective behaviours associated with pain have been reinterpreted in light of these conceptual models. With a particular focus on rehabilitation of the injured athlete, this review presents the theoretical underpinnings of the cortical body matrix and its application within the sporting context. Therapeutic approaches based on these ideas are discussed and the efficacy of the most tested approaches is addressed. By integrating current thought in pain and cognitive neuroscience related to sports rehabilitation, recommendations for clinical practice and future research are suggested. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

Superradiant effects on pulse propagation in resonant media. [atomic excitations/coherent radiation - operators (mathematics)/matrices (mathematics)

NASA Technical Reports Server (NTRS)

Lee, C.

1975-01-01

Adopting the so-called genealogical construction, the eigenstates of collective operators can be expressed corresponding to a specified mode for an N-atom system in terms of those for an (N-1)-atom system. Matrix element of a collective operator of an arbitrary mode is presented which can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME was obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups was then introduced. This gave a simple and systematic way of calculating the RME. Results show explicitly the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes and clears up the chief difficulty encounted in the problem of N two-level atoms, spread over large regions, interacting with a multimode radiation field.

Antisymmetric Wilson loops in N = 4 SYM beyond the planar limit

NASA Astrophysics Data System (ADS)

Gordon, James

2018-01-01

We study the 1/2 -BPS circular Wilson loop in the totally antisymmetric representation of the gauge group in N = 4 supersymmetric Yang-Mills. This observable is captured by a Gaussian matrix model with appropriate insertion. We compute the first 1 /N correction at leading order in 't Hooft coupling by means of the matrix model loop equations. Disagreement with the 1-loop effective action of the holographically dual D5-brane suggests the need to account for gravitational backreaction on the string theory side.

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

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

Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar

2016-06-15

We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators aremore » useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.« less

Face recognition using tridiagonal matrix enhanced multivariance products representation

NASA Astrophysics Data System (ADS)

Ã-zay, Evrim Korkmaz

2017-01-01

This study aims to retrieve face images from a database according to a target face image. For this purpose, Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) is taken into consideration. TMEMPR is a recursive algorithm based on Enhanced Multivariance Products Representation (EMPR). TMEMPR decomposes a matrix into three components which are a matrix of left support terms, a tridiagonal matrix of weight parameters for each recursion, and a matrix of right support terms, respectively. In this sense, there is an analogy between Singular Value Decomposition (SVD) and TMEMPR. However TMEMPR is a more flexible algorithm since its initial support terms (or vectors) can be chosen as desired. Low computational complexity is another advantage of TMEMPR because the algorithm has been constructed with recursions of certain arithmetic operations without requiring any iteration. The algorithm has been trained and tested with ORL face image database with 400 different grayscale images of 40 different people. TMEMPR's performance has been compared with SVD's performance as a result.

Theory and implementation of H-matrix based iterative and direct solvers for Helmholtz and elastodynamic oscillatory kernels

NASA Astrophysics Data System (ADS)

Chaillat, Stéphanie; Desiderio, Luca; Ciarlet, Patrick

2017-12-01

In this work, we study the accuracy and efficiency of hierarchical matrix (H-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known in the literature that standard H-matrix based methods, although very efficient tools for asymptotically smooth kernels, are not optimal for oscillatory kernels. H2-matrix and directional approaches have been proposed to overcome this problem. However the implementation of such methods is much more involved than the standard H-matrix representation. The central questions we address are twofold. (i) What is the frequency-range in which the H-matrix format is an efficient representation for 3D elastodynamic problems? (ii) What can be expected of such an approach to model problems in mechanical engineering? We show that even though the method is not optimal (in the sense that more involved representations can lead to faster algorithms) an efficient solver can be easily developed. The capabilities of the method are illustrated on numerical examples using the Boundary Element Method.

Kohn-Sham potentials from electron densities using a matrix representation within finite atomic orbital basis sets

NASA Astrophysics Data System (ADS)

Zhang, Xing; Carter, Emily A.

2018-01-01

We revisit the static response function-based Kohn-Sham (KS) inversion procedure for determining the KS effective potential that corresponds to a given target electron density within finite atomic orbital basis sets. Instead of expanding the potential in an auxiliary basis set, we directly update the potential in its matrix representation. Through numerical examples, we show that the reconstructed density rapidly converges to the target density. Preliminary results are presented to illustrate the possibility of obtaining a local potential in real space from the optimized potential in its matrix representation. We have further applied this matrix-based KS inversion approach to density functional embedding theory. A proof-of-concept study of a solvated proton transfer reaction demonstrates the method's promise.

Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)

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

Gould, Mark D.; Isaac, Phillip S.; Werry, Jason L.

Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary generators, on finite dimensional type 1 unitary irreducible representations. We compare our results with existing works that deal with only subsets of the class of type 1 unitary representations, all of which only present explicit matrix elements for elementary generators. Our work therefore provides an important extension to existing methods, and thus highlights the strength of our techniques which exploit the characteristic identities.

An efficient matrix product operator representation of the quantum chemical Hamiltonian

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

Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch; Dolfi, Michele, E-mail: dolfim@phys.ethz.ch

We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction schememore » presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries — abelian and non-abelian — and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.« less

Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems

NASA Astrophysics Data System (ADS)

Liu, Zhao; Bhatt, R. N.

2015-09-01

Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty, density-matrix-renormalization-group (DMRG) algorithms were developed for much larger system sizes. Very recently, it was realized that some model FQH states have exact matrix-product-state (MPS) representation. Motivated by this, here we report a MPS code, which is closely related to, but different from traditional DMRG language, for finite FQH systems on the cylinder geometry. By representing the many-body Hamiltonian as a matrix-product-operator (MPO) and using single-site update and density matrix correction, we show that our code can efficiently search the ground state of various FQH systems. We also compare the performance of our code with traditional DMRG. The possible generalization of our code to infinite FQH systems and other physical systems is also discussed.

Cross-label Suppression: a Discriminative and Fast Dictionary Learning with Group Regularization.

PubMed

Wang, Xiudong; Gu, Yuantao

2017-05-10

This paper addresses image classification through learning a compact and discriminative dictionary efficiently. Given a structured dictionary with each atom (columns in the dictionary matrix) related to some label, we propose crosslabel suppression constraint to enlarge the difference among representations for different classes. Meanwhile, we introduce group regularization to enforce representations to preserve label properties of original samples, meaning the representations for the same class are encouraged to be similar. Upon the cross-label suppression, we don't resort to frequently-used `0-norm or `1- norm for coding, and obtain computational efficiency without losing the discriminative power for categorization. Moreover, two simple classification schemes are also developed to take full advantage of the learnt dictionary. Extensive experiments on six data sets including face recognition, object categorization, scene classification, texture recognition and sport action categorization are conducted, and the results show that the proposed approach can outperform lots of recently presented dictionary algorithms on both recognition accuracy and computational efficiency.

An efficient classification method based on principal component and sparse representation.

PubMed

Zhai, Lin; Fu, Shujun; Zhang, Caiming; Liu, Yunxian; Wang, Lu; Liu, Guohua; Yang, Mingqiang

2016-01-01

As an important application in optical imaging, palmprint recognition is interfered by many unfavorable factors. An effective fusion of blockwise bi-directional two-dimensional principal component analysis and grouping sparse classification is presented. The dimension reduction and normalizing are implemented by the blockwise bi-directional two-dimensional principal component analysis for palmprint images to extract feature matrixes, which are assembled into an overcomplete dictionary in sparse classification. A subspace orthogonal matching pursuit algorithm is designed to solve the grouping sparse representation. Finally, the classification result is gained by comparing the residual between testing and reconstructed images. Experiments are carried out on a palmprint database, and the results show that this method has better robustness against position and illumination changes of palmprint images, and can get higher rate of palmprint recognition.

COMPADRE: an R and web resource for pathway activity analysis by component decompositions.

PubMed

Ramos-Rodriguez, Roberto-Rafael; Cuevas-Diaz-Duran, Raquel; Falciani, Francesco; Tamez-Peña, Jose-Gerardo; Trevino, Victor

2012-10-15

The analysis of biological networks has become essential to study functional genomic data. Compadre is a tool to estimate pathway/gene sets activity indexes using sub-matrix decompositions for biological networks analyses. The Compadre pipeline also includes one of the direct uses of activity indexes to detect altered gene sets. For this, the gene expression sub-matrix of a gene set is decomposed into components, which are used to test differences between groups of samples. This procedure is performed with and without differentially expressed genes to decrease false calls. During this process, Compadre also performs an over-representation test. Compadre already implements four decomposition methods [principal component analysis (PCA), Isomaps, independent component analysis (ICA) and non-negative matrix factorization (NMF)], six statistical tests (t- and f-test, SAM, Kruskal-Wallis, Welch and Brown-Forsythe), several gene sets (KEGG, BioCarta, Reactome, GO and MsigDB) and can be easily expanded. Our simulation results shown in Supplementary Information suggest that Compadre detects more pathways than over-representation tools like David, Babelomics and Webgestalt and less false positives than PLAGE. The output is composed of results from decomposition and over-representation analyses providing a more complete biological picture. Examples provided in Supplementary Information show the utility, versatility and simplicity of Compadre for analyses of biological networks. Compadre is freely available at http://bioinformatica.mty.itesm.mx:8080/compadre. The R package is also available at https://sourceforge.net/p/compadre.

Density matrix renormalization group simulations of SU(N ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz

NASA Astrophysics Data System (ADS)

Nataf, Pierre; Mila, Frédéric

2018-04-01

We develop an efficient method to perform density matrix renormalization group simulations of the SU(N ) Heisenberg chain with open boundary conditions taking full advantage of the SU(N ) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e., one particle per site in the fermionic formulation), we have benchmarked our results for the ground-state energy up to N =8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground-state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N =8 (six digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula and agree with the theoretical values expected from the SU (N) 1 Wess-Zumino-Witten conformal field theories.

SU(p,q) coherent states and a Gaussian de Finetti theorem

NASA Astrophysics Data System (ADS)

Leverrier, Anthony

2018-04-01

We prove a generalization of the quantum de Finetti theorem when the local space is an infinite-dimensional Fock space. In particular, instead of considering the action of the permutation group on n copies of that space, we consider the action of the unitary group U(n) on the creation operators of the n modes and define a natural generalization of the symmetric subspace as the space of states invariant under unitaries in U(n). Our first result is a complete characterization of this subspace, which turns out to be spanned by a family of generalized coherent states related to the special unitary group SU(p, q) of signature (p, q). More precisely, this construction yields a unitary representation of the noncompact simple real Lie group SU(p, q). We therefore find a dual unitary representation of the pair of groups U(n) and SU(p, q) on an n(p + q)-mode Fock space. The (Gaussian) SU(p, q) coherent states resolve the identity on the symmetric subspace, which implies a Gaussian de Finetti theorem stating that tracing over a few modes of a unitary-invariant state yields a state close to a mixture of Gaussian states. As an application of this de Finetti theorem, we show that the n × n upper-left submatrix of an n × n Haar-invariant unitary matrix is close in total variation distance to a matrix of independent normal variables if n3 = O(m).

Covariant n/sup 2/-plet mass formulas

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

Davidson, A.

Using a generalized internal symmetry group analogous to the Lorentz group, we have constructed a covariant n/sup 2/-plet mass operator. This operator is built as a scalar matrix in the (n;n*) representation, and its SU(n) breaking parameters are identified as intrinsic boost ones. Its basic properties are: covariance, Hermiticity, positivity, charge conjugation, quark contents, and a self-consistent n/sup 2/-1, 1 mixing. The GMO and the Okubo formulas are obtained by considering two different limits of the same generalized mass formula.

Graph-Theoretic Representations for Proximity Matrices through Strongly-Anti-Robinson or Circular Strongly-Anti-Robinson Matrices.

ERIC Educational Resources Information Center

Hubert, Lawrence; Arabie, Phipps; Meulman, Jacqueline

1998-01-01

Introduces a method for fitting order-constrained matrices that satisfy the strongly anti-Robinson restrictions (SAR). The method permits a representation of the fitted values in a (least-squares) SAR approximating matrix as lengths of paths in a graph. The approach is illustrated with a published proximity matrix. (SLD)

Introduction to quantized LIE groups and algebras

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

Tjin, T.

1992-10-10

In this paper, the authors give a self-contained introduction to the theory of quantum groups according to Drinfeld, highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups the authors study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then the authors explain in detail the concept of quantization for them. As an example the quantization of sl[sub 2] is explicitly carried out. Next, the authors show how quantum groups are related to the Yang-Baxtermore » equation and how they can be used to solve it. Using the quantum double construction, the authors explicitly construct the universal R matrix for the quantum sl[sub 2] algebra. In the last section, the authors deduce all finite-dimensional irreducible representations for q a root of unity. The authors also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory.« less

beachmat: A Bioconductor C++ API for accessing high-throughput biological data from a variety of R matrix types

PubMed Central

Pagès, Hervé

2018-01-01

Biological experiments involving genomics or other high-throughput assays typically yield a data matrix that can be explored and analyzed using the R programming language with packages from the Bioconductor project. Improvements in the throughput of these assays have resulted in an explosion of data even from routine experiments, which poses a challenge to the existing computational infrastructure for statistical data analysis. For example, single-cell RNA sequencing (scRNA-seq) experiments frequently generate large matrices containing expression values for each gene in each cell, requiring sparse or file-backed representations for memory-efficient manipulation in R. These alternative representations are not easily compatible with high-performance C++ code used for computationally intensive tasks in existing R/Bioconductor packages. Here, we describe a C++ interface named beachmat, which enables agnostic data access from various matrix representations. This allows package developers to write efficient C++ code that is interoperable with dense, sparse and file-backed matrices, amongst others. We evaluated the performance of beachmat for accessing data from each matrix representation using both simulated and real scRNA-seq data, and defined a clear memory/speed trade-off to motivate the choice of an appropriate representation. We also demonstrate how beachmat can be incorporated into the code of other packages to drive analyses of a very large scRNA-seq data set. PMID:29723188

beachmat: A Bioconductor C++ API for accessing high-throughput biological data from a variety of R matrix types.

PubMed

Lun, Aaron T L; Pagès, Hervé; Smith, Mike L

2018-05-01

Biological experiments involving genomics or other high-throughput assays typically yield a data matrix that can be explored and analyzed using the R programming language with packages from the Bioconductor project. Improvements in the throughput of these assays have resulted in an explosion of data even from routine experiments, which poses a challenge to the existing computational infrastructure for statistical data analysis. For example, single-cell RNA sequencing (scRNA-seq) experiments frequently generate large matrices containing expression values for each gene in each cell, requiring sparse or file-backed representations for memory-efficient manipulation in R. These alternative representations are not easily compatible with high-performance C++ code used for computationally intensive tasks in existing R/Bioconductor packages. Here, we describe a C++ interface named beachmat, which enables agnostic data access from various matrix representations. This allows package developers to write efficient C++ code that is interoperable with dense, sparse and file-backed matrices, amongst others. We evaluated the performance of beachmat for accessing data from each matrix representation using both simulated and real scRNA-seq data, and defined a clear memory/speed trade-off to motivate the choice of an appropriate representation. We also demonstrate how beachmat can be incorporated into the code of other packages to drive analyses of a very large scRNA-seq data set.

Method for making 2-electron response reduced density matrices approximately N-representable

NASA Astrophysics Data System (ADS)

Lanssens, Caitlin; Ayers, Paul W.; Van Neck, Dimitri; De Baerdemacker, Stijn; Gunst, Klaas; Bultinck, Patrick

2018-02-01

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not N-representable. That is, the response 2-RDM does not correspond to an actual physical N-electron wave function. We present a new algorithm for making these non-N-representable 2-RDMs approximately N-representable, i.e., it has the right symmetry and normalization and it fulfills the P-, Q-, and G-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, Q-matrix, and G-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-N-representable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.

Identifying group discriminative and age regressive sub-networks from DTI-based connectivity via a unified framework of non-negative matrix factorization and graph embedding

PubMed Central

Ghanbari, Yasser; Smith, Alex R.; Schultz, Robert T.; Verma, Ragini

2014-01-01

Diffusion tensor imaging (DTI) offers rich insights into the physical characteristics of white matter (WM) fiber tracts and their development in the brain, facilitating a network representation of brain’s traffic pathways. Such a network representation of brain connectivity has provided a novel means of investigating brain changes arising from pathology, development or aging. The high dimensionality of these connectivity networks necessitates the development of methods that identify the connectivity building blocks or sub-network components that characterize the underlying variation in the population. In addition, the projection of the subject networks into the basis set provides a low dimensional representation of it, that teases apart different sources of variation in the sample, facilitating variation-specific statistical analysis. We propose a unified framework of non-negative matrix factorization and graph embedding for learning sub-network patterns of connectivity by their projective non-negative decomposition into a reconstructive basis set, as well as, additional basis sets representing variational sources in the population like age and pathology. The proposed framework is applied to a study of diffusion-based connectivity in subjects with autism that shows localized sparse sub-networks which mostly capture the changes related to pathology and developmental variations. PMID:25037933

Tensor models, Kronecker coefficients and permutation centralizer algebras

NASA Astrophysics Data System (ADS)

Geloun, Joseph Ben; Ramgoolam, Sanjaye

2017-11-01

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

Characterizing the inverses of block tridiagonal, block Toeplitz matrices

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

Boffi, Nicholas M.; Hill, Judith C.; Reuter, Matthew G.

2014-12-04

We consider the inversion of block tridiagonal, block Toeplitz matrices and comment on the behaviour of these inverses as one moves away from the diagonal. Using matrix M bius transformations, we first present an O(1) representation (with respect to the number of block rows and block columns) for the inverse matrix and subsequently use this representation to characterize the inverse matrix. There are four symmetry-distinct cases where the blocks of the inverse matrix (i) decay to zero on both sides of the diagonal, (ii) oscillate on both sides, (iii) decay on one side and oscillate on the other and (iv)more » decay on one side and grow on the other. This characterization exposes the necessary conditions for the inverse matrix to be numerically banded and may also aid in the design of preconditioners and fast algorithms. Finally, we present numerical examples of these matrix types.« less

Lax representations for matrix short pulse equations

NASA Astrophysics Data System (ADS)

Popowicz, Z.

2017-10-01

The Lax representation for different matrix generalizations of Short Pulse Equations (SPEs) is considered. The four-dimensional Lax representations of four-component Matsuno, Feng, and Dimakis-Müller-Hoissen-Matsuno equations are obtained. The four-component Feng system is defined by generalization of the two-dimensional Lax representation to the four-component case. This system reduces to the original Feng equation, to the two-component Matsuno equation, or to the Yao-Zang equation. The three-component version of the Feng equation is presented. The four-component version of the Matsuno equation with its Lax representation is given. This equation reduces the new two-component Feng system. The two-component Dimakis-Müller-Hoissen-Matsuno equations are generalized to the four-parameter family of the four-component SPE. The bi-Hamiltonian structure of this generalization, for special values of parameters, is defined. This four-component SPE in special cases reduces to the new two-component SPE.

Cuntz-Krieger algebras representations from orbits of interval maps

NASA Astrophysics Data System (ADS)

Correia Ramos, C.; Martins, Nuno; Pinto, Paulo R.; Sousa Ramos, J.

2008-05-01

Let f be an expansive Markov interval map with finite transition matrix Af. Then for every point, we yield an irreducible representation of the Cuntz-Krieger algebra and show that two such representations are unitarily equivalent if and only if the points belong to the same generalized orbit. The restriction of each representation to the gauge part of is decomposed into irreducible representations, according to the decomposition of the orbit.

Dynamic graph system for a semantic database

DOEpatents

Mizell, David

2016-04-12

A method and system in a computer system for dynamically providing a graphical representation of a data store of entries via a matrix interface is disclosed. A dynamic graph system provides a matrix interface that exposes to an application program a graphical representation of data stored in a data store such as a semantic database storing triples. To the application program, the matrix interface represents the graph as a sparse adjacency matrix that is stored in compressed form. Each entry of the data store is considered to represent a link between nodes of the graph. Each entry has a first field and a second field identifying the nodes connected by the link and a third field with a value for the link that connects the identified nodes. The first, second, and third fields represent the rows, column, and elements of the adjacency matrix.

Dynamic graph system for a semantic database

DOEpatents

Mizell, David

2015-01-27

A method and system in a computer system for dynamically providing a graphical representation of a data store of entries via a matrix interface is disclosed. A dynamic graph system provides a matrix interface that exposes to an application program a graphical representation of data stored in a data store such as a semantic database storing triples. To the application program, the matrix interface represents the graph as a sparse adjacency matrix that is stored in compressed form. Each entry of the data store is considered to represent a link between nodes of the graph. Each entry has a first field and a second field identifying the nodes connected by the link and a third field with a value for the link that connects the identified nodes. The first, second, and third fields represent the rows, column, and elements of the adjacency matrix.

Matrix representations of SOn + 2 in an SOn × SO2 basis and some isoscalar factors for SOn + 2 ⊃ SOn × SO2

NASA Astrophysics Data System (ADS)

Pan, Feng; Cao, Yu-Fang

1992-02-01

Vector coherent state (VCS) theory is applied to the group chain SOn+2⊇SOn×SO2. Matrix elements of SOn+2 generators in the SOn+2⊇SOn×SO2 basis are derived. A new formula for the evaluation of some isoscalar factors for SOn+2⊇SOn×SO2 with branching multiplicity is derived in the VCS framework. As a simple example, a new expression of some isoscalar factors for SO5⊇SO3×SO2, which involves only 6j coefficients and K-normalization factors, are obtained by using this formula.

Generalized Pauli constraints in reduced density matrix functional theory.

PubMed

Theophilou, Iris; Lathiotakis, Nektarios N; Marques, Miguel A L; Helbig, Nicole

2015-04-21

Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman's ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.

Similarity preserving low-rank representation for enhanced data representation and effective subspace learning.

PubMed

Zhang, Zhao; Yan, Shuicheng; Zhao, Mingbo

2014-05-01

Latent Low-Rank Representation (LatLRR) delivers robust and promising results for subspace recovery and feature extraction through mining the so-called hidden effects, but the locality of both similar principal and salient features cannot be preserved in the optimizations. To solve this issue for achieving enhanced performance, a boosted version of LatLRR, referred to as Regularized Low-Rank Representation (rLRR), is proposed through explicitly including an appropriate Laplacian regularization that can maximally preserve the similarity among local features. Resembling LatLRR, rLRR decomposes given data matrix from two directions by seeking a pair of low-rank matrices. But the similarities of principal and salient features can be effectively preserved by rLRR. As a result, the correlated features are well grouped and the robustness of representations is also enhanced. Based on the outputted bi-directional low-rank codes by rLRR, an unsupervised subspace learning framework termed Low-rank Similarity Preserving Projections (LSPP) is also derived for feature learning. The supervised extension of LSPP is also discussed for discriminant subspace learning. The validity of rLRR is examined by robust representation and decomposition of real images. Results demonstrated the superiority of our rLRR and LSPP in comparison to other related state-of-the-art algorithms. Copyright © 2014 Elsevier Ltd. All rights reserved.

On the asymptotic states and the quantum S matrix of the η-deformed AdS 5 × S 5 superstring

DOE PAGES

Engelund, Oluf Tang; Roiban, Radu

2015-03-31

We investigate the worldsheet S matrix of string theory in η-deformed AdS 5 × S 5. By computing the six-point tree-level S matrix we explicitly show that there is no particle production at this level, as required by the classical integrability of the theory. At one and two loops we show that integrability requires that the classical two-particle states be redefined in a non-local and η-dependent way. This is a significant departure from the undeformed theory which is probably related to the quantum group symmetry of the worldsheet theory. We use generalized unitarity to carry out the loop calculations andmore » identify a set of integrals that allow us to give a two-loop Feynman integral representation of the logarithmic terms of the two-loop S matrix. We finally also discuss aspects of the calculation of the two-loop rational terms.« less

Detecting double compressed MPEG videos with the same quantization matrix and synchronized group of pictures structure

NASA Astrophysics Data System (ADS)

Aghamaleki, Javad Abbasi; Behrad, Alireza

2018-01-01

Double compression detection is a crucial stage in digital image and video forensics. However, the detection of double compressed videos is challenging when the video forger uses the same quantization matrix and synchronized group of pictures (GOP) structure during the recompression history to conceal tampering effects. A passive approach is proposed for detecting double compressed MPEG videos with the same quantization matrix and synchronized GOP structure. To devise the proposed algorithm, the effects of recompression on P frames are mathematically studied. Then, based on the obtained guidelines, a feature vector is proposed to detect double compressed frames on the GOP level. Subsequently, sparse representations of the feature vectors are used for dimensionality reduction and enrich the traces of recompression. Finally, a support vector machine classifier is employed to detect and localize double compression in temporal domain. The experimental results show that the proposed algorithm achieves the accuracy of more than 95%. In addition, the comparisons of the results of the proposed method with those of other methods reveal the efficiency of the proposed algorithm.

BPS States, Crystals, and Matrices

DOE PAGES

Sułkowski, Piotr

2011-01-01

We review free fermion, melting crystal, and matrix model representations of wall-crossing phenomena on local, toric Calabi-Yau manifolds. We consider both unrefined and refined BPS counting of closed BPS states involving D2- and D0-branes bound to a D6-brane, as well as open BPS states involving open D2-branes ending on an additional D4-brane. Appropriate limit of these constructions provides, among the others, matrix model representation of refined and unrefined topological string amplitudes.

Birman—Wenzl—Murakami Algebra and Topological Basis

NASA Astrophysics Data System (ADS)

Zhou, Cheng-Cheng; Xue, Kang; Wang, Gang-Cheng; Sun, Chun-Fang; Du, Gui-Jiao

2012-02-01

In this paper, we use entangled states to construct 9 × 9-matrix representations of Temperley—Lieb algebra (TLA), then a family of 9 × 9-matrix representations of Birman—Wenzl—Murakami algebra (BWMA) have been presented. Based on which, three topological basis states have been found. And we apply topological basis states to recast nine-dimensional BWMA into its three-dimensional counterpart. Finally, we find the topological basis states are spin singlet states in special case.

Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2018-01-01

A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.

Factorization of differential expansion for non-rectangular representations

NASA Astrophysics Data System (ADS)

Morozov, A.

2018-04-01

Factorization of the differential expansion (DE) coefficients for colored HOMFLY-PT polynomials of antiparallel double braids, originally discovered for rectangular representations R, in the case of rectangular representations R, is extended to the first non-rectangular representations R = [2, 1] and R = [3, 1]. This increases chances that such factorization will take place for generic R, thus fixing the shape of the DE. We illustrate the power of the method by conjecturing the DE-induced expression for double-braid polynomials for all R = [r, 1]. In variance with the rectangular case, the knowledge for double braids is not fully sufficient to deduce the exclusive Racah matrix S¯ — the entries in the sectors with nontrivial multiplicities sum up and remain unseparated. Still, a considerable piece of the matrix is extracted directly and its other elements can be found by solving the unitarity constraints.

Matrix approaches to assess terrestrial nitrogen scheme in CLM4.5

NASA Astrophysics Data System (ADS)

Du, Z.

2017-12-01

Terrestrial carbon (C) and nitrogen (N) cycles have been commonly represented by a series of balance equations to track their influxes into and effluxes out of individual pools in earth system models (ESMs). This representation matches our understanding of C and N cycle processes well but makes it difficult to track model behaviors. To overcome these challenges, we developed a matrix approach, which reorganizes the series of terrestrial C and N balance equations in the CLM4.5 into two matrix equations based on original representation of C and N cycle processes and mechanisms. The matrix approach would consequently help improve the comparability of models and data, evaluate impacts of additional model components, facilitate benchmark analyses, model intercomparisons, and data-model fusion, and improve model predictive power.

The neuroscience of body memory: From the self through the space to the others.

PubMed

Riva, Giuseppe

2017-07-25

Our experience of the body is not direct; rather, it is mediated by perceptual information, influenced by internal information, and recalibrated through stored implicit and explicit body representation (body memory). This paper presents an overview of the current investigations related to body memory by bringing together recent studies from neuropsychology, neuroscience, and evolutionary and cognitive psychology. To do so, in the paper, I explore the origin of representations of human body to elucidate their developmental process and, in particular, their relationship with more explicit concepts of self. First, it is suggested that our bodily experience is constructed from early development through the continuous integration of sensory and cultural data from six different representations of the body, i.e., the Sentient Body (Minimal Selfhood), the Spatial Body (Self Location), the Active Body (Agency), the Personal Body (Whole Body Ownership - Me); the Objectified Body (Objectified Self - Mine), and the Social Body (Body Satisfaction - Ideal Me). Then, it is suggested that these six representations can be combined in a coherent supramodal representation, i.e. the "body matrix", through a predictive, multisensory processing activated by central, top-down, attentional processes. From an evolutionary perspective, the main goal of the body matrix is to allow the self to protect and extend its boundaries at both the homeostatic and psychological levels. From one perspective, the self extends its boundaries (peripersonal space) through the enactment and recognition of motor schemas. From another perspective, the body matrix, by defining the boundaries of the body, also defines where the self is present, i.e., in the body that is processed by the body matrix as the most likely to be its one, and in the space surrounding it. In the paper I also introduce and discuss the concept of "embodied medicine": the use of advanced technology for altering the body matrix with the goal of improving our health and well-being. Copyright © 2017 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Visualization-based analysis of multiple response survey data

NASA Astrophysics Data System (ADS)

Timofeeva, Anastasiia

2017-11-01

During the survey, the respondents are often allowed to tick more than one answer option for a question. Analysis and visualization of such data have difficulties because of the need for processing multiple response variables. With standard representation such as pie and bar charts, information about the association between different answer options is lost. The author proposes a visualization approach for multiple response variables based on Venn diagrams. For a more informative representation with a large number of overlapping groups it is suggested to use similarity and association matrices. Some aggregate indicators of dissimilarity (similarity) are proposed based on the determinant of the similarity matrix and the maximum eigenvalue of association matrix. The application of the proposed approaches is well illustrated by the example of the analysis of advertising sources. Intersection of sets indicates that the same consumer audience is covered by several advertising sources. This information is very important for the allocation of the advertising budget. The differences between target groups in advertising sources are of interest. To identify such differences the hypothesis of homogeneity and independence are tested. Recent approach to the problem are briefly reviewed and compared. An alternative procedure is suggested. It is based on partition of a consumer audience into pairwise disjoint subsets and includes hypothesis testing of the difference between the population proportions. It turned out to be more suitable for the real problem being solved.

Exponentially more precise quantum simulation of fermions in the configuration interaction representation

NASA Astrophysics Data System (ADS)

Babbush, Ryan; Berry, Dominic W.; Sanders, Yuval R.; Kivlichan, Ian D.; Scherer, Artur; Wei, Annie Y.; Love, Peter J.; Aspuru-Guzik, Alán

2018-01-01

We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in Babbush et al (2016 New Journal of Physics 18, 033032), we employ a recently developed technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The algorithm of this paper involves simulation under an oracle for the sparse, first-quantized representation of the molecular Hamiltonian known as the configuration interaction (CI) matrix. We construct and query the CI matrix oracle to allow for on-the-fly computation of molecular integrals in a way that is exponentially more efficient than classical numerical methods. Whereas second-quantized representations of the wavefunction require \\widetilde{{ O }}(N) qubits, where N is the number of single-particle spin-orbitals, the CI matrix representation requires \\widetilde{{ O }}(η ) qubits, where η \\ll N is the number of electrons in the molecule of interest. We show that the gate count of our algorithm scales at most as \\widetilde{{ O }}({η }2{N}3t).

Matrix elements of hyperfine structure operators in the SL and jj representations for the s, p{sup N}, and d{sup N} configurations and the SL-jj transformation

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

Childs, W.J.

1997-09-01

Matrix elements of the hyperfine operators corresponding to the magnetic-dipole (A) and electric-quadrupole (B) hyperfine structures constants are given as linear combinations of the appropriate radial integrals for all states of the s, p{sup N}, and d{sub N} configurations in both the SL and pure jj representations. The associated SL-jj transformations are also given. 13 refs., 10 tabs.

Almost analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2017-11-01

We present an almost analytical new approach to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of solving this matrix eigenvalue problem purely numerically, which may suffer from the computational inaccuracy for big data, first, we consider a pair of integral and differential equations, which are related to the so-called prolate spheroidal wave functions (PSWF). For the PSWF differential equation, the pair of the eigenvectors (PSWF) and eigenvalues can be obtained from a relatively small number of analytical Legendre functions. Then, the eigenvalues in the PSWF integral equation are expressed in terms of functional values of the PSWF and the eigenvalues of the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data; ordinary irregular waves and rogue waves. We found that the present almost analytical method is better than the conventional data-independent Fourier representation and, also, the conventional direct numerical K-L representation in terms of both accuracy and computational cost. This work was supported by the National Research Foundation of Korea (NRF). (NRF-2017R1D1A1B03028299).

Video based object representation and classification using multiple covariance matrices.

PubMed

Zhang, Yurong; Liu, Quan

2017-01-01

Video based object recognition and classification has been widely studied in computer vision and image processing area. One main issue of this task is to develop an effective representation for video. This problem can generally be formulated as image set representation. In this paper, we present a new method called Multiple Covariance Discriminative Learning (MCDL) for image set representation and classification problem. The core idea of MCDL is to represent an image set using multiple covariance matrices with each covariance matrix representing one cluster of images. Firstly, we use the Nonnegative Matrix Factorization (NMF) method to do image clustering within each image set, and then adopt Covariance Discriminative Learning on each cluster (subset) of images. At last, we adopt KLDA and nearest neighborhood classification method for image set classification. Promising experimental results on several datasets show the effectiveness of our MCDL method.

Classical simulation of quantum many-body systems

NASA Astrophysics Data System (ADS)

Huang, Yichen

Classical simulation of quantum many-body systems is in general a challenging problem for the simple reason that the dimension of the Hilbert space grows exponentially with the system size. In particular, merely encoding a generic quantum many-body state requires an exponential number of bits. However, condensed matter physicists are mostly interested in local Hamiltonians and especially their ground states, which are highly non-generic. Thus, we might hope that at least some physical systems allow efficient classical simulation. Starting with one-dimensional (1D) quantum systems (i.e., the simplest nontrivial case), the first basic question is: Which classes of states have efficient classical representations? It turns out that this question is quantitatively related to the amount of entanglement in the state, for states with "little entanglement'' are well approximated by matrix product states (a data structure that can be manipulated efficiently on a classical computer). At a technical level, the mathematical notion for "little entanglement'' is area law, which has been proved for unique ground states in 1D gapped systems. We establish an area law for constant-fold degenerate ground states in 1D gapped systems and thus explain the effectiveness of matrix-product-state methods in (e.g.) symmetry breaking phases. This result might not be intuitively trivial as degenerate ground states in gapped systems can be long-range correlated. Suppose an efficient classical representation exists. How can one find it efficiently? The density matrix renormalization group is the leading numerical method for computing ground states in 1D quantum systems. However, it is a heuristic algorithm and the possibility that it may fail in some cases cannot be completely ruled out. Recently, a provably efficient variant of the density matrix renormalization group has been developed for frustration-free 1D gapped systems. We generalize this algorithm to all (i.e., possibly frustrated) 1D gapped systems. Note that the ground-state energy of 1D gapless Hamiltonians is computationally intractable even in the presence of translational invariance. It is tempting to extend methods and tools in 1D to two and higher dimensions (2+D), e.g., matrix product states are generalized to tensor network states. Since an area law for entanglement (if formulated properly) implies efficient matrix product state representations in 1D, an interesting question is whether a similar implication holds in 2+D. Roughly speaking, we show that an area law for entanglement (in any reasonable formulation) does not always imply efficient tensor network representations of the ground states of 2+D local Hamiltonians even in the presence of translational invariance. It should be emphasized that this result does not contradict with the common sense that in practice quantum states with more entanglement usually require more space to be stored classically; rather, it demonstrates that the relationship between entanglement and efficient classical representations is still far from being well understood. Excited eigenstates participate in the dynamics of quantum systems and are particularly relevant to the phenomenon of many-body localization (absence of transport at finite temperature in strongly correlated systems). We study the entanglement of excited eigenstates in random spin chains and expect that its singularities coincide with dynamical quantum phase transitions. This expectation is confirmed in the disordered quantum Ising chain using both analytical and numerical methods. Finally, we study the problem of generating ground states (possibly with topological order) in 1D gapped systems using quantum circuits. This is an interesting problem both in theory and in practice. It not only characterizes the essential difference between the entanglement patterns that give rise to trivial and nontrivial topological order, but also quantifies the difficulty of preparing quantum states with a quantum computer (in experiments).

Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra by quantum separation of variables

NASA Astrophysics Data System (ADS)

Pezelier, Baptiste

2018-02-01

In this proceeding, we recall the notion of quantum integrable systems on a lattice and then introduce the Sklyanin’s Separation of Variables method. We sum up the main results for the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazanov-Stroganov Lax operator. These results apply as well to the spectral analysis of the lattice sine-Gordon model with open boundary conditions. The transfer matrix spectrum (both eigenvalues and eigenstates) is completely characterized in terms of the set of solutions to a discrete system of polynomial equations. We state an equivalent characterization as the set of solutions to a Baxter’s like T-Q functional equation, allowing us to rewrite the transfer matrix eigenstates in an algebraic Bethe ansatz form.

Split Octonion Reformulation for Electromagnetic Chiral Media of Massive Dyons

NASA Astrophysics Data System (ADS)

Chanyal, B. C.

2017-12-01

In an explicit, unified, and covariant formulation of an octonion algebra, we study and generalize the electromagnetic chiral fields equations of massive dyons with the split octonionic representation. Starting with 2×2 Zorn’s vector matrix realization of split-octonion and its dual Euclidean spaces, we represent the unified structure of split octonionic electric and magnetic induction vectors for chiral media. As such, in present paper, we describe the chiral parameter and pairing constants in terms of split octonionic matrix representation of Drude-Born-Fedorov constitutive relations. We have expressed a split octonionic electromagnetic field vector for chiral media, which exhibits the unified field structure of electric and magnetic chiral fields of dyons. The beauty of split octonionic representation of Zorn vector matrix realization is that, the every scalar and vector components have its own meaning in the generalized chiral electromagnetism of dyons. Correspondingly, we obtained the alternative form of generalized Proca-Maxwell’s equations of massive dyons in chiral media. Furthermore, the continuity equations, Poynting theorem and wave propagation for generalized electromagnetic fields of chiral media of massive dyons are established by split octonionic form of Zorn vector matrix algebra.

An efficient basis set representation for calculating electrons in molecules

DOE PAGES

Jones, Jeremiah R.; Rouet, Francois -Henry; Lawler, Keith V.; ...

2016-04-27

The method of McCurdy, Baertschy, and Rescigno, is generalised to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. Themore » calculation of contracted two-electron matrix elements among orbitals requires only O( Nlog (N)) multiplication operations, not O( N 4), where N is the number of basis functions; N = n 3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionisation potentials are reported for 1- (He +, H + 2), 2- (H 2, He), 10- (CH 4), and 56-electron (C 8H 8) systems.« less

Super-resolution Doppler beam sharpening method using fast iterative adaptive approach-based spectral estimation

NASA Astrophysics Data System (ADS)

Mao, Deqing; Zhang, Yin; Zhang, Yongchao; Huang, Yulin; Yang, Jianyu

2018-01-01

Doppler beam sharpening (DBS) is a critical technology for airborne radar ground mapping in forward-squint region. In conventional DBS technology, the narrow-band Doppler filter groups formed by fast Fourier transform (FFT) method suffer from low spectral resolution and high side lobe levels. The iterative adaptive approach (IAA), based on the weighted least squares (WLS), is applied to the DBS imaging applications, forming narrower Doppler filter groups than the FFT with lower side lobe levels. Regrettably, the IAA is iterative, and requires matrix multiplication and inverse operation when forming the covariance matrix, its inverse and traversing the WLS estimate for each sampling point, resulting in a notably high computational complexity for cubic time. We propose a fast IAA (FIAA)-based super-resolution DBS imaging method, taking advantage of the rich matrix structures of the classical narrow-band filtering. First, we formulate the covariance matrix via the FFT instead of the conventional matrix multiplication operation, based on the typical Fourier structure of the steering matrix. Then, by exploiting the Gohberg-Semencul representation, the inverse of the Toeplitz covariance matrix is computed by the celebrated Levinson-Durbin (LD) and Toeplitz-vector algorithm. Finally, the FFT and fast Toeplitz-vector algorithm are further used to traverse the WLS estimates based on the data-dependent trigonometric polynomials. The method uses the Hermitian feature of the echo autocorrelation matrix R to achieve its fast solution and uses the Toeplitz structure of R to realize its fast inversion. The proposed method enjoys a lower computational complexity without performance loss compared with the conventional IAA-based super-resolution DBS imaging method. The results based on simulations and measured data verify the imaging performance and the operational efficiency.

Attitude Estimation or Quaternion Estimation?

NASA Technical Reports Server (NTRS)

Markley, F. Landis

2003-01-01

The attitude of spacecraft is represented by a 3x3 orthogonal matrix with unity determinant, which belongs to the three-dimensional special orthogonal group SO(3). The fact that all three-parameter representations of SO(3) are singular or discontinuous for certain attitudes has led to the use of higher-dimensional nonsingular parameterizations, especially the four-component quaternion. In attitude estimation, we are faced with the alternatives of using an attitude representation that is either singular or redundant. Estimation procedures fall into three broad classes. The first estimates a three-dimensional representation of attitude deviations from a reference attitude parameterized by a higher-dimensional nonsingular parameterization. The deviations from the reference are assumed to be small enough to avoid any singularity or discontinuity of the three-dimensional parameterization. The second class, which estimates a higher-dimensional representation subject to enough constraints to leave only three degrees of freedom, is difficult to formulate and apply consistently. The third class estimates a representation of SO(3) with more than three dimensions, treating the parameters as independent. We refer to the most common member of this class as quaternion estimation, to contrast it with attitude estimation. We analyze the first and third of these approaches in the context of an extended Kalman filter with simplified kinematics and measurement models.

Representation of the five- and six-dimensional harmonic oscillators in a u(5) ⊃ so(5) ⊃ so(3) basis

NASA Astrophysics Data System (ADS)

Rowe, D. J.

1994-06-01

The duality that exists between the two subgroups SU(1,1) and O(5) of Sp(5,R) to construct basis states for the five-dimensional harmonic oscillator which simultaneously reduce the Sp(5,R)⊇U(5)⊇O(5)⊇SO(3) and Sp(5,R)⊇ SU(1,1)⊇U(1) subgroup chains is used. It is shown that the vector-coherent-state wave functions of the fundamental five-dimensional SO(5) irrep [1,0] realize the traceless bosons introduced by Lohe and Hurst to classify the irreps of the orthogonal groups and employed in Chacon, Moshinsky, and Sharp's construction of a basis for the five-dimensional harmonic oscillator. Moreover, it is shown that VCS theory provides a simple mechanism for constructing matrix elements of the traceless boson operators. These matrix elements are used to extend the VCS representations of SO(5) in an SO(3) basis, given in a previous paper, to irreps of U(5) in an SO(5)⊇ SO(3) basis. The extension to U(6)⊇U(5)⊇SO(5)⊇SO(3) is also given.

Another elementary proof of the Jordan form of a matrix

NASA Astrophysics Data System (ADS)

Budhi, Wono Setya

2012-05-01

In this paper we establish the Jordan Form for a matrix using the elementary concepts of vector differentiation and partial fractions. The idea comes from the resolvent of the operator. For the matrix, the Laurent series is finite and easy to compute through rational representation. We also give a proof of some famous theorems in matrix analysis as consequences from the result.

Visual Tracking Based on Extreme Learning Machine and Sparse Representation

PubMed Central

Wang, Baoxian; Tang, Linbo; Yang, Jinglin; Zhao, Baojun; Wang, Shuigen

2015-01-01

The existing sparse representation-based visual trackers mostly suffer from both being time consuming and having poor robustness problems. To address these issues, a novel tracking method is presented via combining sparse representation and an emerging learning technique, namely extreme learning machine (ELM). Specifically, visual tracking can be divided into two consecutive processes. Firstly, ELM is utilized to find the optimal separate hyperplane between the target observations and background ones. Thus, the trained ELM classification function is able to remove most of the candidate samples related to background contents efficiently, thereby reducing the total computational cost of the following sparse representation. Secondly, to further combine ELM and sparse representation, the resultant confidence values (i.e., probabilities to be a target) of samples on the ELM classification function are used to construct a new manifold learning constraint term of the sparse representation framework, which tends to achieve robuster results. Moreover, the accelerated proximal gradient method is used for deriving the optimal solution (in matrix form) of the constrained sparse tracking model. Additionally, the matrix form solution allows the candidate samples to be calculated in parallel, thereby leading to a higher efficiency. Experiments demonstrate the effectiveness of the proposed tracker. PMID:26506359

Three Interpretations of the Matrix Equation Ax = b

ERIC Educational Resources Information Center

Larson, Christine; Zandieh, Michelle

2013-01-01

Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…

Assessment of Matrix Multiplication Learning with a Rule-Based Analytical Model--"A Bayesian Network Representation"

ERIC Educational Resources Information Center

Zhang, Zhidong

2016-01-01

This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model,…

Introduction to Matrix Algebra, Student's Text, Unit 23.

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

Unit 23 in the SMSG secondary school mathematics series is a student text covering the following topics in matrix algebra: matrix operations, the algebra of 2 X 2 matrices, matrices and linear systems, representation of column matrices as geometric vectors, and transformations of the plane. Listed in the appendix are four research exercises in…

A simple procedure for construction of the orthonormal basis vectors of irreducible representations of O(5) in the OT (3) ⊗ON (2) basis

NASA Astrophysics Data System (ADS)

Pan, Feng; Ding, Xiaoxue; Launey, Kristina D.; Draayer, J. P.

2018-06-01

A simple and effective algebraic isospin projection procedure for constructing orthonormal basis vectors of irreducible representations of O (5) ⊃OT (3) ⊗ON (2) from those in the canonical O (5) ⊃ SUΛ (2) ⊗ SUI (2) basis is outlined. The expansion coefficients are components of null space vectors of the projection matrix with four nonzero elements in each row in general. Explicit formulae for evaluating OT (3)-reduced matrix elements of O (5) generators are derived.

Some applications of the Kronecker product in Hubbard representation

NASA Astrophysics Data System (ADS)

Enríquez, Marco; Rosas-Ortiz, Oscar

2014-10-01

The properties of the Kronecker product are revisited in terms of Hubbard operators. The simplest representation of a Hubbard operator Xi,jn is a square matrix of size n with an entry equal to 1 and zero elsewhere. This framework simplifies the calculation of the Kronecker product of arbitrary matrices no matter the size or the number of the involved factors. Some applications are presented, these include the algebra of permutation matrices, the Hadamard matrix, the XXX Heisenberg model and the interaction of an atom with radiation fields.

Micromechanical Modeling of Woven Metal Matrix Composites

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Pindera, Marek-Jerzy

1997-01-01

This report presents the results of an extensive micromechanical modeling effort for woven metal matrix composites. The model is employed to predict the mechanical response of 8-harness (8H) satin weave carbon/copper (C/Cu) composites. Experimental mechanical results for this novel high thermal conductivity material were recently reported by Bednarcyk et al. along with preliminary model results. The micromechanics model developed herein is based on an embedded approach. A micromechanics model for the local (micro-scale) behavior of the woven composite, the original method of cells (Aboudi), is embedded in a global (macro-scale) micromechanics model (the three-dimensional generalized method of cells (GMC-3D) (Aboudi). This approach allows representation of true repeating unit cells for woven metal matrix composites via GMC-3D, and representation of local effects, such as matrix plasticity, yarn porosity, and imperfect fiber-matrix bonding. In addition, the equations of GMC-3D were reformulated to significantly reduce the number of unknown quantities that characterize the deformation fields at the microlevel in order to make possible the analysis of actual microstructures of woven composites. The resulting micromechanical model (WCGMC) provides an intermediate level of geometric representation, versatility, and computational efficiency with respect to previous analytical and numerical models for woven composites, but surpasses all previous modeling work by allowing the mechanical response of a woven metal matrix composite, with an elastoplastic matrix, to be examined for the first time. WCGMC is employed to examine the effects of composite microstructure, porosity, residual stresses, and imperfect fiber-matrix bonding on the predicted mechanical response of 8H satin C/Cu. The previously reported experimental results are summarized, and the model predictions are compared to monotonic and cyclic tensile and shear test data. By considering appropriate levels of porosity, residual stresses, and imperfect fiber-matrix debonding, reasonably good qualitative and quantitative correlation is achieved between model and experiment.

N=2 Minimal Conformal Field Theories and Matrix Bifactorisations of x d

NASA Astrophysics Data System (ADS)

Davydov, Alexei; Camacho, Ana Ros; Runkel, Ingo

2018-01-01

We establish an action of the representations of N = 2-superconformal symmetry on the category of matrix factorisations of the potentials x d and x d - y d , for d odd. More precisely we prove a tensor equivalence between (a) the category of Neveu-Schwarz-type representations of the N = 2 minimal super vertex operator algebra at central charge 3-6/d, and (b) a full subcategory of graded matrix factorisations of the potential x d - y d . The subcategory in (b) is given by permutation-type matrix factorisations with consecutive index sets. The physical motivation for this result is the Landau-Ginzburg/conformal field theory correspondence, where it amounts to the equivalence of a subset of defects on both sides of the correspondence. Our work builds on results by Brunner and Roggenkamp [BR], where an isomorphism of fusion rules was established.

Subspace Clustering via Learning an Adaptive Low-Rank Graph.

PubMed

Yin, Ming; Xie, Shengli; Wu, Zongze; Zhang, Yun; Gao, Junbin

2018-08-01

By using a sparse representation or low-rank representation of data, the graph-based subspace clustering has recently attracted considerable attention in computer vision, given its capability and efficiency in clustering data. However, the graph weights built using the representation coefficients are not the exact ones as the traditional definition is in a deterministic way. The two steps of representation and clustering are conducted in an independent manner, thus an overall optimal result cannot be guaranteed. Furthermore, it is unclear how the clustering performance will be affected by using this graph. For example, the graph parameters, i.e., the weights on edges, have to be artificially pre-specified while it is very difficult to choose the optimum. To this end, in this paper, a novel subspace clustering via learning an adaptive low-rank graph affinity matrix is proposed, where the affinity matrix and the representation coefficients are learned in a unified framework. As such, the pre-computed graph regularizer is effectively obviated and better performance can be achieved. Experimental results on several famous databases demonstrate that the proposed method performs better against the state-of-the-art approaches, in clustering.

The Atom in a Molecule: Implications for Molecular Structure and Properties

DTIC Science & Technology

2016-05-23

unlimited. PA Clearance #16075.” Atomic- Product Representations of Molecules Employ “van der Waals” products of atomic states to represent molecules...representation the electrons “stay home” with each nucleus. Atomic fragment operators are well-defined over product representations. Expectation values of...release; distribution unlimited. PA Clearance #16075.” Hamiltonian Matrix in the Atomic- Product Basis Technical Questions Addressed: J. Chem. Phys

Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases

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

Conrady, Florian; Hnybida, Jeff; Department of Physics, University of Waterloo, Waterloo, Ontario

2011-01-15

We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete basis diagonalized by J{sup 3} and a continuous basis diagonalized by K{sup 1}, and for both the discrete and continuous series of SU(1,1). For completeness, we also treat the more conventional SU(2) decomposition as a fifth case. The derivation proceeds in a functional/differential framework and exploits the fact that state functions and differential operators have a similar structure in all five cases. The states aremore » defined explicitly and related to SU(1,1) and SU(2) matrix elements.« less

An Efficient Local Correlation Matrix Decomposition Approach for the Localization Implementation of Ensemble-Based Assimilation Methods

NASA Astrophysics Data System (ADS)

Zhang, Hongqin; Tian, Xiangjun

2018-04-01

Ensemble-based data assimilation methods often use the so-called localization scheme to improve the representation of the ensemble background error covariance (Be). Extensive research has been undertaken to reduce the computational cost of these methods by using the localized ensemble samples to localize Be by means of a direct decomposition of the local correlation matrix C. However, the computational costs of the direct decomposition of the local correlation matrix C are still extremely high due to its high dimension. In this paper, we propose an efficient local correlation matrix decomposition approach based on the concept of alternating directions. This approach is intended to avoid direct decomposition of the correlation matrix. Instead, we first decompose the correlation matrix into 1-D correlation matrices in the three coordinate directions, then construct their empirical orthogonal function decomposition at low resolution. This procedure is followed by the 1-D spline interpolation process to transform the above decompositions to the high-resolution grid. Finally, an efficient correlation matrix decomposition is achieved by computing the very similar Kronecker product. We conducted a series of comparison experiments to illustrate the validity and accuracy of the proposed local correlation matrix decomposition approach. The effectiveness of the proposed correlation matrix decomposition approach and its efficient localization implementation of the nonlinear least-squares four-dimensional variational assimilation are further demonstrated by several groups of numerical experiments based on the Advanced Research Weather Research and Forecasting model.

Screening of matrix metalloproteinases available from the protein data bank: insights into biological functions, domain organization, and zinc binding groups.

PubMed

Nicolotti, Orazio; Miscioscia, Teresa Fabiola; Leonetti, Francesco; Muncipinto, Giovanni; Carotti, Angelo

2007-01-01

A total of 142 matrix metalloproteinase (MMP) X-ray crystallographic structures were retrieved from the Protein Data Bank (PDB) and analyzed by an automated and efficient routine, developed in-house, with a series of bioinformatic tools. Highly informative heat maps and hierarchical clusterograms provided a reliable and comprehensive representation of the relationships existing among MMPs, enlarging and complementing the current knowledge in the field. Multiple sequence and structural alignments permitted better location and display of key MMP motifs and quantification of the residue consensus at each amino acid position in the most critical binding subsites of MMPs. The MMP active site consensus sequences, the C-alpha root-mean-square deviation (RMSd) analysis of diverse enzymatic subsites, and the examination of the chemical nature, binding topologies, and zinc binding groups (ZBGs) of ligands extracted from crystallographic complexes provided useful insights on the structural arrangements of the most potent MMP inhibitors.

Table-sized matrix model in fractional learning

NASA Astrophysics Data System (ADS)

Soebagyo, J.; Wahyudin; Mulyaning, E. C.

2018-05-01

This article provides an explanation of the fractional learning model i.e. a Table-Sized Matrix model in which fractional representation and its operations are symbolized by the matrix. The Table-Sized Matrix are employed to develop problem solving capabilities as well as the area model. The Table-Sized Matrix model referred to in this article is used to develop an understanding of the fractional concept to elementary school students which can then be generalized into procedural fluency (algorithm) in solving the fractional problem and its operation.

Left caloric vestibular stimulation as a tool to reveal implicit and explicit parameters of body representation.

PubMed

Sedda, A; Tonin, D; Salvato, G; Gandola, M; Bottini, G

2016-04-01

Homeostatic parameters, such as temperature, are related to body representation. In this study, we measured whether caloric vestibular stimulation (CVS) alters body temperature and tactile processing, and if in the direction predicted by a holistic body matrix representation. Skin temperature and tactile two-point discrimination (TPD) acuity were measured for both arms before, immediately after and with a delay from CVS. Participants were also administered a personality questionnaire and an anxiety inventory to rule out confounding factors. Two control experiments were planned to exclude casual variations. Our results show that temperature drops significantly in both arms after CVS. CVS also induces a bilateral improvement in tactile acuity (even though not immediately after but in the delayed condition). Finally, these effects are not due to learning, as demonstrated by the control experiment. In summary, our results suggest that vestibular stimulation updates body representation, supporting the evidence in favor of a body matrix. Copyright © 2016 Elsevier Inc. All rights reserved.

Low-dimensional Representation of Error Covariance

NASA Technical Reports Server (NTRS)

Tippett, Michael K.; Cohn, Stephen E.; Todling, Ricardo; Marchesin, Dan

2000-01-01

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

GC[Formula: see text]NMF: A Novel Matrix Factorization Framework for Gene-Phenotype Association Prediction.

PubMed

Zhang, Yaogong; Liu, Jiahui; Liu, Xiaohu; Hong, Yuxiang; Fan, Xin; Huang, Yalou; Wang, Yuan; Xie, Maoqiang

2018-04-24

Gene-phenotype association prediction can be applied to reveal the inherited basis of human diseases and facilitate drug development. Gene-phenotype associations are related to complex biological processes and influenced by various factors, such as relationship between phenotypes and that among genes. While due to sparseness of curated gene-phenotype associations and lack of integrated analysis of the joint effect of multiple factors, existing applications are limited to prediction accuracy and potential gene-phenotype association detection. In this paper, we propose a novel method by exploiting weighted graph constraint learned from hierarchical structures of phenotype data and group prior information among genes by inheriting advantages of Non-negative Matrix Factorization (NMF), called Weighted Graph Constraint and Group Centric Non-negative Matrix Factorization (GC[Formula: see text]NMF). Specifically, first we introduce the depth of parent-child relationships between two adjacent phenotypes in hierarchical phenotypic data as weighted graph constraint for a better phenotype understanding. Second, we utilize intra-group correlation among genes in a gene group as group constraint for gene understanding. Such information provides us with the intuition that genes in a group probably result in similar phenotypes. The model not only allows us to achieve a high-grade prediction performance, but also helps us to learn interpretable representation of genes and phenotypes simultaneously to facilitate future biological analysis. Experimental results on biological gene-phenotype association datasets of mouse and human demonstrate that GC[Formula: see text]NMF can obtain superior prediction accuracy and good understandability for biological explanation over other state-of-the-arts methods.

Characterizing and differentiating task-based and resting state fMRI signals via two-stage sparse representations.

PubMed

Zhang, Shu; Li, Xiang; Lv, Jinglei; Jiang, Xi; Guo, Lei; Liu, Tianming

2016-03-01

A relatively underexplored question in fMRI is whether there are intrinsic differences in terms of signal composition patterns that can effectively characterize and differentiate task-based or resting state fMRI (tfMRI or rsfMRI) signals. In this paper, we propose a novel two-stage sparse representation framework to examine the fundamental difference between tfMRI and rsfMRI signals. Specifically, in the first stage, the whole-brain tfMRI or rsfMRI signals of each subject were composed into a big data matrix, which was then factorized into a subject-specific dictionary matrix and a weight coefficient matrix for sparse representation. In the second stage, all of the dictionary matrices from both tfMRI/rsfMRI data across multiple subjects were composed into another big data-matrix, which was further sparsely represented by a cross-subjects common dictionary and a weight matrix. This framework has been applied on the recently publicly released Human Connectome Project (HCP) fMRI data and experimental results revealed that there are distinctive and descriptive atoms in the cross-subjects common dictionary that can effectively characterize and differentiate tfMRI and rsfMRI signals, achieving 100% classification accuracy. Moreover, our methods and results can be meaningfully interpreted, e.g., the well-known default mode network (DMN) activities can be recovered from the very noisy and heterogeneous aggregated big-data of tfMRI and rsfMRI signals across all subjects in HCP Q1 release.

Molecular symmetry with quaternions.

PubMed

Fritzer, H P

2001-09-01

A new and relatively simple version of the quaternion calculus is offered which is especially suitable for applications in molecular symmetry and structure. After introducing the real quaternion algebra and its classical matrix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism properties of the algebra are discussed. The correlation of the unit quaternions with both the Cayley-Klein and the Euler parameters through the group SU(2) is presented. Besides rotations the extension of quaternions to other important symmetry operations, reflections and the spatial inversion, is given. Finally, the power of the quaternion calculus for molecular symmetry problems is revealed by treating some examples applied to icosahedral symmetry.

Atomic spectral-product representations of molecular electronic structure: metric matrices and atomic-product composition of molecular eigenfunctions.

PubMed

Ben-Nun, M; Mills, J D; Hinde, R J; Winstead, C L; Boatz, J A; Gallup, G A; Langhoff, P W

2009-07-02

Recent progress is reported in development of ab initio computational methods for the electronic structures of molecules employing the many-electron eigenstates of constituent atoms in spectral-product forms. The approach provides a universal atomic-product description of the electronic structure of matter as an alternative to more commonly employed valence-bond- or molecular-orbital-based representations. The Hamiltonian matrix in this representation is seen to comprise a sum over atomic energies and a pairwise sum over Coulombic interaction terms that depend only on the separations of the individual atomic pairs. Overall electron antisymmetry can be enforced by unitary transformation when appropriate, rather than as a possibly encumbering or unnecessary global constraint. The matrix representative of the antisymmetrizer in the spectral-product basis, which is equivalent to the metric matrix of the corresponding explicitly antisymmetric basis, provides the required transformation to antisymmetric or linearly independent states after Hamiltonian evaluation. Particular attention is focused in the present report on properties of the metric matrix and on the atomic-product compositions of molecular eigenstates as described in the spectral-product representations. Illustrative calculations are reported for simple but prototypically important diatomic (H(2), CH) and triatomic (H(3), CH(2)) molecules employing algorithms and computer codes devised recently for this purpose. This particular implementation of the approach combines Slater-orbital-based one- and two-electron integral evaluations, valence-bond constructions of standard tableau functions and matrices, and transformations to atomic eigenstate-product representations. The calculated metric matrices and corresponding potential energy surfaces obtained in this way elucidate a number of aspects of the spectral-product development, including the nature of closure in the representation, the general redundancy or linear dependence of its explicitly antisymmetrized form, the convergence of the apparently disparate atomic-product and explicitly antisymmetrized atomic-product forms to a common invariant subspace, and the nature of a chemical bonding descriptor provided by the atomic-product compositions of molecular eigenstates. Concluding remarks indicate additional studies in progress and the prognosis for performing atomic spectral-product calculations more generally and efficiently.

On some 3-point functions in the W 4 CFT and related braiding matrix

NASA Astrophysics Data System (ADS)

Furlan, P.; Petkova, V. B.

2015-12-01

We construct a class of 3-point constants in the sl(4) Toda conformal theory W 4, extending the examples in Fateev and Litvinov [1]. Their knowledge allows to determine the braiding/fusing matrix transforming 4-point conformal blocks of one fundamental, labelled by the 6-dimensional sl(4) representation, and three partially degenerate vertex operators. It is a 3 × 3 submatrix of the generic 6 × 6 fusing matrix consistent with the fusion rules for the particular class of representations. We check a braiding relation which has wider applications to conformal models with sl(4) symmetry. The 3-point constants in dual regions of central charge are compared in preparation for a BPS like relation in the widehat{sl}(4) WZW model.

Construction of general colored R matrices for the Yang-Baxter equation and q-boson realization of quantum algebra SL[sub q](2) when q is a root of unity

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

Ge, M.L.; Sun, C.P.; Xue, K.

1992-10-20

In this paper, through a general q-boson realization of quantum algebra sl[sub q](2) and its universal R matrix an operator R matrix with many parameters is obtained in terms of q-boson operators. Building finite-dimensional representations of q-boson algebra, the authors construct various colored R matrices associated with nongeneric representations of sl[sub q](2) with dimension-independent parameters. The nonstandard R matrices obtained by Lee-Couture and Murakami are their special examples.

Exact representation of the asymptotic drift speed and diffusion matrix for a class of velocity-jump processes

NASA Astrophysics Data System (ADS)

Mascia, Corrado

2016-01-01

This paper examines a class of linear hyperbolic systems which generalizes the Goldstein-Kac model to an arbitrary finite number of speeds vi with transition rates μij. Under the basic assumptions that the transition matrix is symmetric and irreducible, and the differences vi -vj generate all the space, the system exhibits a large-time behavior described by a parabolic advection-diffusion equation. The main contribution is to determine explicit formulas for the asymptotic drift speed and diffusion matrix in term of the kinetic parameters vi and μij, establishing a complete connection between microscopic and macroscopic coefficients. It is shown that the drift speed is the arithmetic mean of the velocities vi. The diffusion matrix has a more complicate representation, based on the graph with vertices the velocities vi and arcs weighted by the transition rates μij. The approach is based on an exhaustive analysis of the dispersion relation and on the application of a variant of the Kirchoff's matrix tree Theorem from graph theory.

Semiclassical propagation: Hilbert space vs. Wigner representation

NASA Astrophysics Data System (ADS)

Gottwald, Fabian; Ivanov, Sergei D.

2018-03-01

A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. Based on this viewpoint, the Wigner Herman-Kluk propagator is conceptually the most general one. Nonetheless, the respective semiclassical expressions for expectation values in terms of the density matrix and the Wigner function are mathematically proven here to coincide. The only remaining difference is a mere technical flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states beyond minimal uncertainty. This flexibility is investigated numerically on prototypical potentials and it turns out to provide neither qualitative nor quantitative improvements. Given the aforementioned generality, utilizing the Wigner representation for semiclassical propagation thus leads to the same performance as employing the respective most-developed (Hilbert-space) methods for the density matrix.

Determinant representations of spin-operator matrix elements in the XX spin chain and their applications

NASA Astrophysics Data System (ADS)

Wu, Ning

2018-01-01

For the one-dimensional spin-1/2 XX model with either periodic or open boundary conditions, it is shown by using a fermionic approach that the matrix element of the spin operator Sj- (Sj-Sj'+ ) between two eigenstates with numbers of excitations n and n +1 (n and n ) can be expressed as the determinant of an appropriate (n +1 )×(n +1 ) matrix whose entries involve the coefficients of the canonical transformations diagonalizing the model. In the special case of a homogeneous periodic XX chain, the matrix element of Sj- reduces to a variant of the Cauchy determinant that can be evaluated analytically to yield a factorized expression. The obtained compact representations of these matrix elements are then applied to two physical scenarios: (i) Nonlinear optical response of molecular aggregates, for which the determinant representation of the transition dipole matrix elements between eigenstates provides a convenient way to calculate the third-order nonlinear responses for aggregates from small to large sizes compared with the optical wavelength; and (ii) real-time dynamics of an interacting Dicke model consisting of a single bosonic mode coupled to a one-dimensional XX spin bath. In this setup, full quantum calculation up to N ≤16 spins for vanishing intrabath coupling shows that the decay of the reduced bosonic occupation number approaches a finite plateau value (in the long-time limit) that depends on the ratio between the number of excitations and the total number of spins. Our results can find useful applications in various "system-bath" systems, with the system part inhomogeneously coupled to an interacting XX chain.

Sparse representation of whole-brain fMRI signals for identification of functional networks.

PubMed

Lv, Jinglei; Jiang, Xi; Li, Xiang; Zhu, Dajiang; Chen, Hanbo; Zhang, Tuo; Zhang, Shu; Hu, Xintao; Han, Junwei; Huang, Heng; Zhang, Jing; Guo, Lei; Liu, Tianming

2015-02-01

There have been several recent studies that used sparse representation for fMRI signal analysis and activation detection based on the assumption that each voxel's fMRI signal is linearly composed of sparse components. Previous studies have employed sparse coding to model functional networks in various modalities and scales. These prior contributions inspired the exploration of whether/how sparse representation can be used to identify functional networks in a voxel-wise way and on the whole brain scale. This paper presents a novel, alternative methodology of identifying multiple functional networks via sparse representation of whole-brain task-based fMRI signals. Our basic idea is that all fMRI signals within the whole brain of one subject are aggregated into a big data matrix, which is then factorized into an over-complete dictionary basis matrix and a reference weight matrix via an effective online dictionary learning algorithm. Our extensive experimental results have shown that this novel methodology can uncover multiple functional networks that can be well characterized and interpreted in spatial, temporal and frequency domains based on current brain science knowledge. Importantly, these well-characterized functional network components are quite reproducible in different brains. In general, our methods offer a novel, effective and unified solution to multiple fMRI data analysis tasks including activation detection, de-activation detection, and functional network identification. Copyright © 2014 Elsevier B.V. All rights reserved.

Quantifying matrix product state

NASA Astrophysics Data System (ADS)

Bhatia, Amandeep Singh; Kumar, Ajay

2018-03-01

Motivated by the concept of quantum finite-state machines, we have investigated their relation with matrix product state of quantum spin systems. Matrix product states play a crucial role in the context of quantum information processing and are considered as a valuable asset for quantum information and communication purpose. It is an effective way to represent states of entangled systems. In this paper, we have designed quantum finite-state machines of one-dimensional matrix product state representations for quantum spin systems.

Vector-valued Jack polynomials and wavefunctions on the torus

NASA Astrophysics Data System (ADS)

Dunkl, Charles F.

2017-06-01

The Hamiltonian of the quantum Calogero-Sutherland model of N identical particles on the circle with 1/r 2 interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials taking values in modules of the symmetric group and the matrix solution of a system of linear differential equations one constructs novel eigenfunctions of the Hamiltonian. Like the usual wavefunctions each eigenfunction determines a symmetric probability density on the N-torus. The construction applies to any irreducible representation of the symmetric group. The methods depend on the theory of generalized Jack polynomials due to Griffeth, and the Yang-Baxter graph approach of Luque and the author.

Nonlinear Semi-Supervised Metric Learning Via Multiple Kernels and Local Topology.

PubMed

Li, Xin; Bai, Yanqin; Peng, Yaxin; Du, Shaoyi; Ying, Shihui

2018-03-01

Changing the metric on the data may change the data distribution, hence a good distance metric can promote the performance of learning algorithm. In this paper, we address the semi-supervised distance metric learning (ML) problem to obtain the best nonlinear metric for the data. First, we describe the nonlinear metric by the multiple kernel representation. By this approach, we project the data into a high dimensional space, where the data can be well represented by linear ML. Then, we reformulate the linear ML by a minimization problem on the positive definite matrix group. Finally, we develop a two-step algorithm for solving this model and design an intrinsic steepest descent algorithm to learn the positive definite metric matrix. Experimental results validate that our proposed method is effective and outperforms several state-of-the-art ML methods.

Adjoints and Low-rank Covariance Representation

NASA Technical Reports Server (NTRS)

Tippett, Michael K.; Cohn, Stephen E.

2000-01-01

Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

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

Theophilou, Iris; Helbig, Nicole; Lathiotakis, Nektarios N.

Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violatesmore » the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.« less

Noniterative MAP reconstruction using sparse matrix representations.

PubMed

Cao, Guangzhi; Bouman, Charles A; Webb, Kevin J

2009-09-01

We present a method for noniterative maximum a posteriori (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large and fully populated (i.e., not sparse). In order to overcome this problem, we introduce two new ideas. The first idea is a novel theory for the lossy source coding of matrix transformations which we refer to as matrix source coding. This theory is based on a distortion metric that reflects the distortions produced in the final matrix-vector product, rather than the distortions in the coded matrix itself. The resulting algorithms are shown to require orthonormal transformations of both the measurement data and the matrix rows and columns before quantization and coding. The second idea is a method for efficiently storing and computing the required orthonormal transformations, which we call a sparse-matrix transform (SMT). The SMT is a generalization of the classical FFT in that it uses butterflies to compute an orthonormal transform; but unlike an FFT, the SMT uses the butterflies in an irregular pattern, and is numerically designed to best approximate the desired transforms. We demonstrate the potential of the noniterative MAP reconstruction with examples from optical tomography. The method requires offline computation to encode the inverse transform. However, once these offline computations are completed, the noniterative MAP algorithm is shown to reduce both storage and computation by well over two orders of magnitude, as compared to a linear iterative reconstruction methods.

A matrix solution for the simulation of magnetic fields with ideal current loops

NASA Technical Reports Server (NTRS)

Stankiewicz, N.

1979-01-01

A matrix formulation is presented for describing axisymmetric magnetic field data with ideal current loops. A computer program written in APL is used to invert the matrix and hence to solve for the coil strengths which are used to represent the field data. Examples are given of the coil representation for (1) measured magnetic data, (2) refocusing fields, and (3) PPM focusing fields.

Discriminative Dictionary Learning With Two-Level Low Rank and Group Sparse Decomposition for Image Classification.

PubMed

Wen, Zaidao; Hou, Zaidao; Jiao, Licheng

2017-11-01

Discriminative dictionary learning (DDL) framework has been widely used in image classification which aims to learn some class-specific feature vectors as well as a representative dictionary according to a set of labeled training samples. However, interclass similarities and intraclass variances among input samples and learned features will generally weaken the representability of dictionary and the discrimination of feature vectors so as to degrade the classification performance. Therefore, how to explicitly represent them becomes an important issue. In this paper, we present a novel DDL framework with two-level low rank and group sparse decomposition model. In the first level, we learn a class-shared and several class-specific dictionaries, where a low rank and a group sparse regularization are, respectively, imposed on the corresponding feature matrices. In the second level, the class-specific feature matrix will be further decomposed into a low rank and a sparse matrix so that intraclass variances can be separated to concentrate the corresponding feature vectors. Extensive experimental results demonstrate the effectiveness of our model. Compared with the other state-of-the-arts on several popular image databases, our model can achieve a competitive or better performance in terms of the classification accuracy.

Attitude Representations for Kalman Filtering

NASA Technical Reports Server (NTRS)

Markley, F. Landis; Bauer, Frank H. (Technical Monitor)

2001-01-01

The four-component quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation, it represents the attitude matrix as a homogeneous quadratic function, and its dynamic propagation equation is bilinear in the quaternion and the angular velocity. The quaternion is required to obey a unit norm constraint, though, so Kalman filters often employ a quaternion for the global attitude estimate and a three-component representation for small errors about the estimate. We consider these mixed attitude representations for both a first-order Extended Kalman filter and a second-order filter, as well for quaternion-norm-preserving attitude propagation.

Analytic tools for investigating the structure of network reliability measures with regard to observation correlations

NASA Astrophysics Data System (ADS)

Prószyński, W.; Kwaśniak, M.

2018-03-01

A global measure of observation correlations in a network is proposed, together with the auxiliary indices related to non-diagonal elements of the correlation matrix. Based on the above global measure, a specific representation of the correlation matrix is presented, being the result of rigorously proven theorem formulated within the present research. According to the theorem, each positive definite correlation matrix can be expressed by a scale factor and a so-called internal weight matrix. Such a representation made it possible to investigate the structure of the basic reliability measures with regard to observation correlations. Numerical examples carried out for two test networks illustrate the structure of those measures that proved to be dependent on global correlation index. Also, the levels of global correlation are proposed. It is shown that one can readily find an approximate value of the global correlation index, and hence the correlation level, for the expected values of auxiliary indices being the only knowledge about a correlation matrix of interest. The paper is an extended continuation of the previous study of authors that was confined to the elementary case termed uniform correlation. The extension covers arbitrary correlation matrices and a structure of correlation effect.

Finding Imaging Patterns of Structural Covariance via Non-Negative Matrix Factorization

PubMed Central

Sotiras, Aristeidis; Resnick, Susan M.; Davatzikos, Christos

2015-01-01

In this paper, we investigate the use of Non-Negative Matrix Factorization (NNMF) for the analysis of structural neuroimaging data. The goal is to identify the brain regions that co-vary across individuals in a consistent way, hence potentially being part of underlying brain networks or otherwise influenced by underlying common mechanisms such as genetics and pathologies. NNMF offers a directly data-driven way of extracting relatively localized co-varying structural regions, thereby transcending limitations of Principal Component Analysis (PCA), Independent Component Analysis (ICA) and other related methods that tend to produce dispersed components of positive and negative loadings. In particular, leveraging upon the well known ability of NNMF to produce parts-based representations of image data, we derive decompositions that partition the brain into regions that vary in consistent ways across individuals. Importantly, these decompositions achieve dimensionality reduction via highly interpretable ways and generalize well to new data as shown via split-sample experiments. We empirically validate NNMF in two data sets: i) a Diffusion Tensor (DT) mouse brain development study, and ii) a structural Magnetic Resonance (sMR) study of human brain aging. We demonstrate the ability of NNMF to produce sparse parts-based representations of the data at various resolutions. These representations seem to follow what we know about the underlying functional organization of the brain and also capture some pathological processes. Moreover, we show that these low dimensional representations favorably compare to descriptions obtained with more commonly used matrix factorization methods like PCA and ICA. PMID:25497684

Weighted Discriminative Dictionary Learning based on Low-rank Representation

NASA Astrophysics Data System (ADS)

Chang, Heyou; Zheng, Hao

2017-01-01

Low-rank representation has been widely used in the field of pattern classification, especially when both training and testing images are corrupted with large noise. Dictionary plays an important role in low-rank representation. With respect to the semantic dictionary, the optimal representation matrix should be block-diagonal. However, traditional low-rank representation based dictionary learning methods cannot effectively exploit the discriminative information between data and dictionary. To address this problem, this paper proposed weighted discriminative dictionary learning based on low-rank representation, where a weighted representation regularization term is constructed. The regularization associates label information of both training samples and dictionary atoms, and encourages to generate a discriminative representation with class-wise block-diagonal structure, which can further improve the classification performance where both training and testing images are corrupted with large noise. Experimental results demonstrate advantages of the proposed method over the state-of-the-art methods.

Application of Fuzzy Logic to Matrix FMECA

NASA Astrophysics Data System (ADS)

Shankar, N. Ravi; Prabhu, B. S.

2001-04-01

A methodology combining the benefits of Fuzzy Logic and Matrix FMEA is presented in this paper. The presented methodology extends the risk prioritization beyond the conventional Risk Priority Number (RPN) method. Fuzzy logic is used to calculate the criticality rank. Also the matrix approach is improved further to develop a pictorial representation retaining all relevant qualitative and quantitative information of several FMEA elements relationships. The methodology presented is demonstrated by application to an illustrative example.

Hyperspherical Symmetry of Hydrogenic Orbitals and Recoupling Coefficients among Alternative Bases

NASA Astrophysics Data System (ADS)

Aquilanti, Vincenzo; Cavalli, Simonetta; Coletti, Cecilia

1998-04-01

Fock's representation of momentum space hydrogenic orbitals in terms of harmonics on the hypersphere S3 of a four-dimensional space is extended to classify alternative bases. These orbitals are of interest for Sturmian expansions of use in atomic and molecular structure calculations and for the description of atoms in fields. Because of the correspondence between the S3 manifold and the SU\\(2\\) group, new sum rules are established which are of relevance for the connection, not only among hydrogen atom orbitals in different bases, but also among the usual vector coupling coefficients and rotation matrix elements.

Description of quantum states using in free space optic communication

NASA Astrophysics Data System (ADS)

Kučera, Petr

2017-11-01

In the article we concentrate our attention on the quantum description of states which are prepared by light sources. The main goal of the article is the determination of density matrix of background radiation source. It is shown that these matrix elements satisfy Geometric distribution in the number state representation.

Matrix models and stochastic growth in Donaldson-Thomas theory

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

Szabo, Richard J.; Tierz, Miguel; Departamento de Analisis Matematico, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used tomore » show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.« less

Implementation of a digital optical matrix-vector multiplier using a holographic look-up table and residue arithmetic

NASA Technical Reports Server (NTRS)

Habiby, Sarry F.

1987-01-01

The design and implementation of a digital (numerical) optical matrix-vector multiplier are presented. The objective is to demonstrate the operation of an optical processor designed to minimize computation time in performing a practical computing application. This is done by using the large array of processing elements in a Hughes liquid crystal light valve, and relying on the residue arithmetic representation, a holographic optical memory, and position coded optical look-up tables. In the design, all operations are performed in effectively one light valve response time regardless of matrix size. The features of the design allowing fast computation include the residue arithmetic representation, the mapping approach to computation, and the holographic memory. In addition, other features of the work include a practical light valve configuration for efficient polarization control, a model for recording multiple exposures in silver halides with equal reconstruction efficiency, and using light from an optical fiber for a reference beam source in constructing the hologram. The design can be extended to implement larger matrix arrays without increasing computation time.

Matrix product representation of the stationary state of the open zero range process

NASA Astrophysics Data System (ADS)

Bertin, Eric; Vanicat, Matthieu

2018-06-01

Many one-dimensional lattice particle models with open boundaries, like the paradigmatic asymmetric simple exclusion process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not explicitly depend on the lattice site. In contrast, the stationary state of the open 1D zero-range process (ZRP) takes an inhomogeneous factorized form, with site-dependent probability weights. We show that in spite of the absence of correlations, the stationary state of the open ZRP can also be represented in a matrix product form, where the matrices are site-independent, non-commuting and determined from algebraic relations resulting from the master equation. We recover the known distribution of the open ZRP in two different ways: first, using an explicit representation of the matrices and boundary vectors; second, from the sole knowledge of the algebraic relations satisfied by these matrices and vectors. Finally, an interpretation of the relation between the matrix product form and the inhomogeneous factorized form is proposed within the framework of hidden Markov chains.

SAR Polarimetry

NASA Technical Reports Server (NTRS)

vanZyl, Jakob J.

2012-01-01

Radar Scattering includes: Surface Characteristics, Geometric Properties, Dielectric Properties, Rough Surface Scattering, Geometrical Optics and Small Perturbation Method Solutions, Integral Equation Method, Magellan Image of Pancake Domes on Venus, Dickinson Impact Crater on Venus (Magellan), Lakes on Titan (Cassini Radar, Longitudinal Dunes on Titan (Cassini Radar), Rough Surface Scattering: Effect of Dielectric Constant, Vegetation Scattering, Effect of Soil Moisture. Polarimetric Radar includes: Principles of Polarimetry: Field Descriptions, Wave Polarizations: Geometrical Representations, Definition of Ellipse Orientation Angles, Scatter as Polarization Transformer, Scattering Matrix, Coordinate Systems, Scattering Matrix, Covariance Matrix, Pauli Basis and Coherency Matrix, Polarization Synthesis, Polarimeter Implementation.

Singularity-free extraction of a quaternion from a direction-cosine matrix. [for spacecraft control and guidance

NASA Technical Reports Server (NTRS)

Klumpp, A. R.

1976-01-01

A computer algorithm for extracting a quaternion from a direction-cosine matrix (DCM) is described. The quaternion provides a four-parameter representation of rotation, as against the nine-parameter representation afforded by a DCM. Commanded attitude in space shuttle steering is conveniently computed by DCM, while actual attitude is computed most compactly as a quaternion, as is attitude error. The unit length of the rotation quaternion, and interchangeable of a quaternion and its negative, are used to advantage in the extraction algorithm. Protection of the algorithm against square root failure and division overflow are considered. Necessary and sufficient conditions for handling the rotation vector element of largest magnitude are discussed

System identification of analytical models of damped structures

NASA Technical Reports Server (NTRS)

Fuh, J.-S.; Chen, S.-Y.; Berman, A.

1984-01-01

A procedure is presented for identifying linear nonproportionally damped system. The system damping is assumed to be representable by a real symmetric matrix. Analytical mass, stiffness and damping matrices which constitute an approximate representation of the system are assumed to be available. Given also are an incomplete set of measured natural frequencies, damping ratios and complex mode shapes of the structure, normally obtained from test data. A method is developed to find the smallest changes in the analytical model so that the improved model can exactly predict the measured modal parameters. The present method uses the orthogonality relationship to improve mass and damping matrices and the dynamic equation to find the improved stiffness matrix.

Percent recoveries of anthropogenic organic compounds with and without the addition of ascorbic acid to preserve finished-water samples containing free chlorine, 2004-10

USGS Publications Warehouse

Valder, Joshua F.; Delzer, Gregory C.; Bender, David A.; Price, Curtis V.

2011-01-01

This report presents finished-water matrix-spike recoveries of 270 anthropogenic organic compounds with and without the addition of ascorbic acid to preserve water samples containing free chlorine. Percent recoveries were calculated using analytical results from a study conducted during 2004-10 for the National Water-Quality Assessment (NAWQA) Program of the U.S. Geological Survey (USGS). The study was intended to characterize the effect of quenching on finished-water matrix-spike recoveries and to better understand the potential oxidation and transformation of 270 anthropogenic organic compounds. The anthropogenic organic compounds studied include those on analytical schedules 1433, 2003, 2033, 2060, 2020, and 4024 of the USGS National Water Quality Laboratory. Three types of samples were collected from 34 NAWQA locations across the Nation: (1) quenched finished-water samples (not spiked), (2) quenched finished-water matrix-spike samples, and (3) nonquenched finished-water matrix-spike samples. Percent recoveries of anthropogenic organic compounds in quenched and nonquenched finished-water matrix-spike samples are presented. Comparisons of percent recoveries between quenched and nonquenched spiked samples can be used to show how quenching affects finished-water samples. A maximum of 18 surface-water and 34 groundwater quenched finished-water matrix-spike samples paired with nonquenched finished-water matrix-spike samples were analyzed. Percent recoveries for the study are presented in two ways: (1) finished-water matrix-spike samples supplied by surface-water or groundwater, and (2) by use (or source) group category for surface-water and groundwater supplies. Graphical representations of percent recoveries for the quenched and nonquenched finished-water matrix-spike samples also are presented.

Effective representation of amide III, II, I, and A modes on local vibrational modes: Analysis of ab initio quantum calculation results.

PubMed

Hahn, Seungsoo

2016-10-28

The Hamiltonian matrix for the first excited vibrational states of a protein can be effectively represented by local vibrational modes constituting amide III, II, I, and A modes to simulate various vibrational spectra. Methods for obtaining the Hamiltonian matrix from ab initio quantum calculation results are discussed, where the methods consist of three steps: selection of local vibrational mode coordinates, calculation of a reduced Hessian matrix, and extraction of the Hamiltonian matrix from the Hessian matrix. We introduce several methods for each step. The methods were assessed based on the density functional theory calculation results of 24 oligopeptides with four different peptide lengths and six different secondary structures. The completeness of a Hamiltonian matrix represented in the reduced local mode space is improved by adopting a specific atom group for each amide mode and reducing the effect of ignored local modes. The calculation results are also compared to previous models using C=O stretching vibration and transition dipole couplings. We found that local electric transition dipole moments of the amide modes are mainly bound on the local peptide planes. Their direction and magnitude are well conserved except amide A modes, which show large variation. Contrary to amide I modes, the vibrational coupling constants of amide III, II, and A modes obtained by analysis of a dipeptide are not transferable to oligopeptides with the same secondary conformation because coupling constants are affected by the surrounding atomic environment.

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

PubMed

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

2017-08-02

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

Robust Image Regression Based on the Extended Matrix Variate Power Exponential Distribution of Dependent Noise.

PubMed

Luo, Lei; Yang, Jian; Qian, Jianjun; Tai, Ying; Lu, Gui-Fu

2017-09-01

Dealing with partial occlusion or illumination is one of the most challenging problems in image representation and classification. In this problem, the characterization of the representation error plays a crucial role. In most current approaches, the error matrix needs to be stretched into a vector and each element is assumed to be independently corrupted. This ignores the dependence between the elements of error. In this paper, it is assumed that the error image caused by partial occlusion or illumination changes is a random matrix variate and follows the extended matrix variate power exponential distribution. This has the heavy tailed regions and can be used to describe a matrix pattern of l×m dimensional observations that are not independent. This paper reveals the essence of the proposed distribution: it actually alleviates the correlations between pixels in an error matrix E and makes E approximately Gaussian. On the basis of this distribution, we derive a Schatten p -norm-based matrix regression model with L q regularization. Alternating direction method of multipliers is applied to solve this model. To get a closed-form solution in each step of the algorithm, two singular value function thresholding operators are introduced. In addition, the extended Schatten p -norm is utilized to characterize the distance between the test samples and classes in the design of the classifier. Extensive experimental results for image reconstruction and classification with structural noise demonstrate that the proposed algorithm works much more robustly than some existing regression-based methods.

Automatic face naming by learning discriminative affinity matrices from weakly labeled images.

PubMed

Xiao, Shijie; Xu, Dong; Wu, Jianxin

2015-10-01

Given a collection of images, where each image contains several faces and is associated with a few names in the corresponding caption, the goal of face naming is to infer the correct name for each face. In this paper, we propose two new methods to effectively solve this problem by learning two discriminative affinity matrices from these weakly labeled images. We first propose a new method called regularized low-rank representation by effectively utilizing weakly supervised information to learn a low-rank reconstruction coefficient matrix while exploring multiple subspace structures of the data. Specifically, by introducing a specially designed regularizer to the low-rank representation method, we penalize the corresponding reconstruction coefficients related to the situations where a face is reconstructed by using face images from other subjects or by using itself. With the inferred reconstruction coefficient matrix, a discriminative affinity matrix can be obtained. Moreover, we also develop a new distance metric learning method called ambiguously supervised structural metric learning by using weakly supervised information to seek a discriminative distance metric. Hence, another discriminative affinity matrix can be obtained using the similarity matrix (i.e., the kernel matrix) based on the Mahalanobis distances of the data. Observing that these two affinity matrices contain complementary information, we further combine them to obtain a fused affinity matrix, based on which we develop a new iterative scheme to infer the name of each face. Comprehensive experiments demonstrate the effectiveness of our approach.

EvolQG - An R package for evolutionary quantitative genetics

PubMed Central

Melo, Diogo; Garcia, Guilherme; Hubbe, Alex; Assis, Ana Paula; Marroig, Gabriel

2016-01-01

We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable and there is evidence the phenotypic matrix is sufficiently similar to the genetic matrix. Given this mathematical representation of available variation, the \\textbf{EvolQG} package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification. PMID:27785352

Finding imaging patterns of structural covariance via Non-Negative Matrix Factorization.

PubMed

Sotiras, Aristeidis; Resnick, Susan M; Davatzikos, Christos

2015-03-01

In this paper, we investigate the use of Non-Negative Matrix Factorization (NNMF) for the analysis of structural neuroimaging data. The goal is to identify the brain regions that co-vary across individuals in a consistent way, hence potentially being part of underlying brain networks or otherwise influenced by underlying common mechanisms such as genetics and pathologies. NNMF offers a directly data-driven way of extracting relatively localized co-varying structural regions, thereby transcending limitations of Principal Component Analysis (PCA), Independent Component Analysis (ICA) and other related methods that tend to produce dispersed components of positive and negative loadings. In particular, leveraging upon the well known ability of NNMF to produce parts-based representations of image data, we derive decompositions that partition the brain into regions that vary in consistent ways across individuals. Importantly, these decompositions achieve dimensionality reduction via highly interpretable ways and generalize well to new data as shown via split-sample experiments. We empirically validate NNMF in two data sets: i) a Diffusion Tensor (DT) mouse brain development study, and ii) a structural Magnetic Resonance (sMR) study of human brain aging. We demonstrate the ability of NNMF to produce sparse parts-based representations of the data at various resolutions. These representations seem to follow what we know about the underlying functional organization of the brain and also capture some pathological processes. Moreover, we show that these low dimensional representations favorably compare to descriptions obtained with more commonly used matrix factorization methods like PCA and ICA. Copyright © 2014 Elsevier Inc. All rights reserved.

RPBS: Rotational Projected Binary Structure for point cloud representation

NASA Astrophysics Data System (ADS)

Fang, Bin; Zhou, Zhiwei; Ma, Tao; Hu, Fangyu; Quan, Siwen; Ma, Jie

2018-03-01

In this paper, we proposed a novel three-dimension local surface descriptor named RPBS for point cloud representation. First, points cropped form the query point within a predefined radius is regard as a local surface patch. Then pose normalization is done to the local surface to equip our descriptor with the invariance to rotation transformation. To obtain more information about the cropped surface, multi-view representation is formed by successively rotating it along the coordinate axis. Further, orthogonal projections to the three coordinate plane are adopted to construct two-dimension distribution matrixes, and binarization is applied to each matrix by following the rule that whether the grid is occupied, if yes, set the grid one, otherwise zero. We calculate the binary maps from all the viewpoints and concatenate them together as the final descriptor. Comparative experiments for evaluating our proposed descriptor is conducted on the standard dataset named Bologna with several state-of-the-art 3D descriptors, and results show that our descriptor achieves the best performance on feature matching experiments.

A path-oriented knowledge representation system: Defusing the combinatorial system

NASA Technical Reports Server (NTRS)

Karamouzis, Stamos T.; Barry, John S.; Smith, Steven L.; Feyock, Stefan

1995-01-01

LIMAP is a programming system oriented toward efficient information manipulation over fixed finite domains, and quantification over paths and predicates. A generalization of Warshall's Algorithm to precompute paths in a sparse matrix representation of semantic nets is employed to allow questions involving paths between components to be posed and answered easily. LIMAP's ability to cache all paths between two components in a matrix cell proved to be a computational obstacle, however, when the semantic net grew to realistic size. The present paper describes a means of mitigating this combinatorial explosion to an extent that makes the use of the LIMAP representation feasible for problems of significant size. The technique we describe radically reduces the size of the search space in which LIMAP must operate; semantic nets of more than 500 nodes have been attacked successfully. Furthermore, it appears that the procedure described is applicable not only to LIMAP, but to a number of other combinatorially explosive search space problems found in AI as well.

Studying effects of non-equilibrium radiative transfer via HPC

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

Holladay, Daniel

This report presents slides on Ph.D. Research Goals; Local Thermodynamic Equilibrium (LTE) Implications; Calculating an Opacity; Opacity: Pictographic Representation; Opacity: Pictographic Representation; Opacity: Pictographic Representation; Collisional Radiative Modeling; Radiative and Collisional Excitation; Photo and Electron Impact Ionization; Autoionization; The Rate Matrix; Example: Total Photoionization rate; The Rate Coefficients; inlinlte version 1.1; inlinlte: Verification; New capabilities: Rate Matrix – Flexibility; Memory Option Comparison; Improvements over previous DCA solver; Inter- and intra-node load balancing; Load Balance – Full Picture; Load Balance – Full Picture; Load Balance – Internode; Load Balance – Scaling; Description; Performance; xRAGE Simulation; Post-process @ 2hr; Post-process @ 4hr;more » Post-process @ 8hr; Takeaways; Performance for 1 realization; Motivation for QOI; Multigroup Er; Transport and NLTE large effects (1mm, 1keV); Transport large effect, NLTE lesser (1mm, 750eV); Blastwave Diagnostici – Description & Performance; Temperature Comparison; NLTE has effect on dynamics at wall; NLTE has lesser effect in the foam; Global Takeaways; The end.« less

Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime

NASA Astrophysics Data System (ADS)

Dugave, Maxime; Göhmann, Frank; Kozlowski, Karol K.; Suzuki, Junji

2016-09-01

We use the form factors of the quantum transfer matrix in the zero-temperature limit in order to study the two-point ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime. We obtain novel form factor series representations of the correlation functions which differ from those derived either from the q-vertex-operator approach or from the algebraic Bethe Ansatz approach to the usual transfer matrix. We advocate that our novel representations are numerically more efficient and allow for a straightforward calculation of the large-distance asymptotic behaviour of the two-point functions. Keeping control over the temperature corrections to the two-point functions we see that these are of order {T}∞ in the whole antiferromagnetic massive regime. The isotropic limit of our result yields a novel form factor series representation for the two-point correlation functions of the XXX chain at zero magnetic field. Dedicated to the memory of Petr Petrovich Kulish.

Classical space-times from the S-matrix

NASA Astrophysics Data System (ADS)

Neill, Duff; Rothstein, Ira Z.

2013-12-01

We show that classical space-times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space-time as a series in GN. At no point of the derivation is any use made of the Einstein-Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniques. The notion of a space-time metric is only introduced at the end of the calculation where it is extracted by matching the potential determined by the S-matrix to the geodesic motion of a test particle. Other static space-times such as Kerr follow in a similar manner. Furthermore, given that the procedure is action independent and depends only upon the choice of the representation of the little group, solutions to Yang-Mills (YM) theory can be generated in the same fashion. Moreover, the squaring relation between the YM and gravity three point functions shows that the seeds that generate solutions in the two theories are algebraically related. From a technical standpoint our methodology can also be utilized to calculate quantities relevant for the binary inspiral problem more efficiently then the more traditional Feynman diagram approach.

An automated graphics tool for comparative genomics: the Coulson plot generator

PubMed Central

2013-01-01

Background Comparative analysis is an essential component to biology. When applied to genomics for example, analysis may require comparisons between the predicted presence and absence of genes in a group of genomes under consideration. Frequently, genes can be grouped into small categories based on functional criteria, for example membership of a multimeric complex, participation in a metabolic or signaling pathway or shared sequence features and/or paralogy. These patterns of retention and loss are highly informative for the prediction of function, and hence possible biological context, and can provide great insights into the evolutionary history of cellular functions. However, representation of such information in a standard spreadsheet is a poor visual means from which to extract patterns within a dataset. Results We devised the Coulson Plot, a new graphical representation that exploits a matrix of pie charts to display comparative genomics data. Each pie is used to describe a complex or process from a separate taxon, and is divided into sectors corresponding to the number of proteins (subunits) in a complex/process. The predicted presence or absence of proteins in each complex are delineated by occupancy of a given sector; this format is visually highly accessible and makes pattern recognition rapid and reliable. A key to the identity of each subunit, plus hierarchical naming of taxa and coloring are included. A java-based application, the Coulson plot generator (CPG) automates graphic production, with a tab or comma-delineated text file as input and generating an editable portable document format or svg file. Conclusions CPG software may be used to rapidly convert spreadsheet data to a graphical matrix pie chart format. The representation essentially retains all of the information from the spreadsheet but presents a graphically rich format making comparisons and identification of patterns significantly clearer. While the Coulson plot format is highly useful in comparative genomics, its original purpose, the software can be used to visualize any dataset where entity occupancy is compared between different classes. Availability CPG software is available at sourceforge http://sourceforge.net/projects/coulson and http://dl.dropbox.com/u/6701906/Web/Sites/Labsite/CPG.html PMID:23621955

A unified data representation theory for network visualization, ordering and coarse-graining

PubMed Central

Kovács, István A.; Mizsei, Réka; Csermely, Péter

2015-01-01

Representation of large data sets became a key question of many scientific disciplines in the last decade. Several approaches for network visualization, data ordering and coarse-graining accomplished this goal. However, there was no underlying theoretical framework linking these problems. Here we show an elegant, information theoretic data representation approach as a unified solution of network visualization, data ordering and coarse-graining. The optimal representation is the hardest to distinguish from the original data matrix, measured by the relative entropy. The representation of network nodes as probability distributions provides an efficient visualization method and, in one dimension, an ordering of network nodes and edges. Coarse-grained representations of the input network enable both efficient data compression and hierarchical visualization to achieve high quality representations of larger data sets. Our unified data representation theory will help the analysis of extensive data sets, by revealing the large-scale structure of complex networks in a comprehensible form. PMID:26348923

System for information discovery

DOEpatents

Pennock, Kelly A [Richland, WA; Miller, Nancy E [Kennewick, WA

2002-11-19

A sequence of word filters are used to eliminate terms in the database which do not discriminate document content, resulting in a filtered word set and a topic word set whose members are highly predictive of content. These two word sets are then formed into a two dimensional matrix with matrix entries calculated as the conditional probability that a document will contain a word in a row given that it contains the word in a column. The matrix representation allows the resultant vectors to be utilized to interpret document contents.

Local-global analysis of crack growth in continuously reinfoced ceramic matrix composites

NASA Technical Reports Server (NTRS)

Ballarini, Roberto; Ahmed, Shamim

1989-01-01

This paper describes the development of a mathematical model for predicting the strength and micromechanical failure characteristics of continuously reinforced ceramic matrix composites. The local-global analysis models the vicinity of a propagating crack tip as a local heterogeneous region (LHR) consisting of spring-like representation of the matrix, fibers and interfaces. Parametric studies are conducted to investigate the effects of LHR size, component properties, and interface conditions on the strength and sequence of the failure processes in the unidirectional composite system.

Second level semi-degenerate fields in W_3 Toda theory: matrix element and differential equation

NASA Astrophysics Data System (ADS)

Belavin, Vladimir; Cao, Xiangyu; Estienne, Benoit; Santachiara, Raoul

2017-03-01

In a recent study we considered W_3 Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl_3 . We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.

Higher Rank ABJM Wilson Loops from Matrix Models

NASA Astrophysics Data System (ADS)

Cookmeyer, Jonathan; Liu, James; Zayas, Leopoldo

2017-01-01

We compute the expectation values of 1/6 supersymmetric Wilson Loops in ABJM theory in higher rank representations. Using standard matrix model techniques, we calculate the expectation value in the rank m fully symmetric and fully antisymmetric representation where m is scaled with N. To leading order, we find agreement with the classical action of D6 and D2 branes in AdS4 ×CP3 respectively. Further, we compute the first subleading order term, which, on the AdS side, makes a prediction for the one-loop effective action of the corresponding D6 and D2 branes. Supported by the National Science Foundation under Grant No. PHY 1559988 and the US Department of Energy under Grant No. DE-SC0007859.

Current algebras, measures quasi-invariant under diffeomorphism groups, and infinite quantum systems with accumulation points

NASA Astrophysics Data System (ADS)

Sakuraba, Takao

The approach to quantum physics via current algebra and unitary representations of the diffeomorphism group is established. This thesis studies possible infinite Bose gas systems using this approach. Systems of locally finite configurations and systems of configurations with accumulation points are considered, with the main emphasis on the latter. In Chapter 2, canonical quantization, quantization via current algebra and unitary representations of the diffeomorphism group are reviewed. In Chapter 3, a new definition of the space of configurations is proposed and an axiom for general configuration spaces is abstracted. Various subsets of the configuration space, including those specifying the number of points in a Borel set and those specifying the number of accumulation points in a Borel set are proved to be measurable using this axiom. In Chapter 4, known results on the space of locally finite configurations and Poisson measure are reviewed in the light of the approach developed in Chapter 3, including the approach to current algebra in the Poisson space by Albeverio, Kondratiev, and Rockner. Goldin and Moschella considered unitary representations of the group of diffeomorphisms of the line based on self-similar random processes, which may describe infinite quantum gas systems with clusters. In Chapter 5, the Goldin-Moschella theory is developed further. Their construction of measures quasi-invariant under diffeomorphisms is reviewed, and a rigorous proof of their conjectures is given. It is proved that their measures with distinct correlation parameters are mutually singular. A quasi-invariant measure constructed by Ismagilov on the space of configurations with accumulation points on the circle is proved to be singular with respect to the Goldin-Moschella measures. Finally a generalization of the Goldin-Moschella measures to the higher-dimensional case is studied, where the notion of covariance matrix and the notion of condition number play important roles. A rigorous construction of measures quasi-invariant under the group of diffeomorphisms of d-dimensional space stabilizing a point is given.

Representations for the Generalized Drazin Inverse of the Sum in a Banach Algebra and Its Application for Some Operator Matrices

PubMed Central

Liu, Xiaoji; Qin, Xiaolan

2015-01-01

We investigate additive properties of the generalized Drazin inverse in a Banach algebra A. We find explicit expressions for the generalized Drazin inverse of the sum a + b, under new conditions on a, b ∈ A. As an application we give some new representations for the generalized Drazin inverse of an operator matrix. PMID:25729767

Representations for the generalized Drazin inverse of the sum in a Banach algebra and its application for some operator matrices.

PubMed

Liu, Xiaoji; Qin, Xiaolan

2015-01-01

We investigate additive properties of the generalized Drazin inverse in a Banach algebra A. We find explicit expressions for the generalized Drazin inverse of the sum a + b, under new conditions on a, b ∈ A. As an application we give some new representations for the generalized Drazin inverse of an operator matrix.

Invariant operators, orthogonal bases and correlators in general tensor models

NASA Astrophysics Data System (ADS)

Diaz, Pablo; Rey, Soo-Jong

2018-07-01

We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry Gd = U (N1) ⊗ ⋯ ⊗ U (Nd). As a continuation and completion of our earlier work, we present two natural ways of counting invariants, one for arbitrary Gd and another valid for large rank of Gd. We construct bases of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of Gd diagonalizes the two-point function of the free theory. It is analogous to the restricted Schur basis used in matrix models. We show that the constructions get almost identical as we swap the Littlewood-Richardson numbers in multi-matrix models with Kronecker coefficients in general tensor models. We explore the parallelism between matrix model and tensor model in depth from the perspective of representation theory and comment on several ideas for future investigation.

Robust infrared targets tracking with covariance matrix representation

NASA Astrophysics Data System (ADS)

Cheng, Jian

2009-07-01

Robust infrared target tracking is an important and challenging research topic in many military and security applications, such as infrared imaging guidance, infrared reconnaissance, scene surveillance, etc. To effectively tackle the nonlinear and non-Gaussian state estimation problems, particle filtering is introduced to construct the theory framework of infrared target tracking. Under this framework, the observation probabilistic model is one of main factors for infrared targets tracking performance. In order to improve the tracking performance, covariance matrices are introduced to represent infrared targets with the multi-features. The observation probabilistic model can be constructed by computing the distance between the reference target's and the target samples' covariance matrix. Because the covariance matrix provides a natural tool for integrating multiple features, and is scale and illumination independent, target representation with covariance matrices can hold strong discriminating ability and robustness. Two experimental results demonstrate the proposed method is effective and robust for different infrared target tracking, such as the sensor ego-motion scene, and the sea-clutter scene.

Frequency domain system identification methods - Matrix fraction description approach

NASA Technical Reports Server (NTRS)

Horta, Luca G.; Juang, Jer-Nan

1993-01-01

This paper presents the use of matrix fraction descriptions for least-squares curve fitting of the frequency spectra to compute two matrix polynomials. The matrix polynomials are intermediate step to obtain a linearized representation of the experimental transfer function. Two approaches are presented: first, the matrix polynomials are identified using an estimated transfer function; second, the matrix polynomials are identified directly from the cross/auto spectra of the input and output signals. A set of Markov parameters are computed from the polynomials and subsequently realization theory is used to recover a minimum order state space model. Unevenly spaced frequency response functions may be used. Results from a simple numerical example and an experiment are discussed to highlight some of the important aspect of the algorithm.

MATRIX-VBS Condensing Organic Aerosols in an Aerosol Microphysics Model

NASA Technical Reports Server (NTRS)

Gao, Chloe Y.; Tsigaridis, Konstas; Bauer, Susanne E.

2015-01-01

The condensation of organic aerosols is represented in a newly developed box-model scheme, where its effect on the growth and composition of particles are examined. We implemented the volatility-basis set (VBS) framework into the aerosol mixing state resolving microphysical scheme Multiconfiguration Aerosol TRacker of mIXing state (MATRIX). This new scheme is unique and advances the representation of organic aerosols in models in that, contrary to the traditional treatment of organic aerosols as non-volatile in most climate models and in the original version of MATRIX, this new scheme treats them as semi-volatile. Such treatment is important because low-volatility organics contribute significantly to the growth of particles. The new scheme includes several classes of semi-volatile organic compounds from the VBS framework that can partition among aerosol populations in MATRIX, thus representing the growth of particles via condensation of low volatility organic vapors. Results from test cases representing Mexico City and a Finish forrest condistions show good representation of the time evolutions of concentration for VBS species in the gas phase and in the condensed particulate phase. Emitted semi-volatile primary organic aerosols evaporate almost completely in the high volatile range, and they condense more efficiently in the low volatility range.

Protein Sub-Nuclear Localization Based on Effective Fusion Representations and Dimension Reduction Algorithm LDA.

PubMed

Wang, Shunfang; Liu, Shuhui

2015-12-19

An effective representation of a protein sequence plays a crucial role in protein sub-nuclear localization. The existing representations, such as dipeptide composition (DipC), pseudo-amino acid composition (PseAAC) and position specific scoring matrix (PSSM), are insufficient to represent protein sequence due to their single perspectives. Thus, this paper proposes two fusion feature representations of DipPSSM and PseAAPSSM to integrate PSSM with DipC and PseAAC, respectively. When constructing each fusion representation, we introduce the balance factors to value the importance of its components. The optimal values of the balance factors are sought by genetic algorithm. Due to the high dimensionality of the proposed representations, linear discriminant analysis (LDA) is used to find its important low dimensional structure, which is essential for classification and location prediction. The numerical experiments on two public datasets with KNN classifier and cross-validation tests showed that in terms of the common indexes of sensitivity, specificity, accuracy and MCC, the proposed fusing representations outperform the traditional representations in protein sub-nuclear localization, and the representation treated by LDA outperforms the untreated one.

Protein Sub-Nuclear Localization Based on Effective Fusion Representations and Dimension Reduction Algorithm LDA

PubMed Central

Wang, Shunfang; Liu, Shuhui

2015-01-01

An effective representation of a protein sequence plays a crucial role in protein sub-nuclear localization. The existing representations, such as dipeptide composition (DipC), pseudo-amino acid composition (PseAAC) and position specific scoring matrix (PSSM), are insufficient to represent protein sequence due to their single perspectives. Thus, this paper proposes two fusion feature representations of DipPSSM and PseAAPSSM to integrate PSSM with DipC and PseAAC, respectively. When constructing each fusion representation, we introduce the balance factors to value the importance of its components. The optimal values of the balance factors are sought by genetic algorithm. Due to the high dimensionality of the proposed representations, linear discriminant analysis (LDA) is used to find its important low dimensional structure, which is essential for classification and location prediction. The numerical experiments on two public datasets with KNN classifier and cross-validation tests showed that in terms of the common indexes of sensitivity, specificity, accuracy and MCC, the proposed fusing representations outperform the traditional representations in protein sub-nuclear localization, and the representation treated by LDA outperforms the untreated one. PMID:26703574

Representing k-graphs as Matrix Algebras

NASA Astrophysics Data System (ADS)

Rosjanuardi, R.

2018-05-01

For any commutative unital ring R and finitely aligned k-graph Λ with |Λ| < ∞ without cycles, we can realise Kumjian-Pask algebra KP R (Λ) as a direct sum of of matrix algebra over some vertices v with properties ν = νΛ, i.e: ⊕ νΛ=ν M |Λv|(R). When there is only a single vertex ν ∈ Λ° such that ν = νΛ, we can realise the Kumjian-Pask algebra as the matrix algebra M |ΛV|(R). Hence the matrix algebra M |vΛ|(R) can be regarded as a representation of the k-graph Λ. In this talk we will figure out the relation between finitely aligned k-graph and matrix algebra.

Les résonances d'un trou noir de Schwarzschild.

NASA Astrophysics Data System (ADS)

Bachelot, A.; Motet-Bachelot, A.

1993-09-01

This paper is devoted to the theoretical and computational investigations of the scattering frequencies of scalar, electromagnetic, gravitational waves around a spherical black hole. The authors adopt a time dependent approach: construction of wave operators for the hyperbolic Regge-Wheeler equation; asymptotic completeness; outgoing and incoming spectral representations; meromorphic continuation of the Heisenberg matrix; approximation by dumping and cut-off of the potentials and interpretation of the semi group Z(t) in the framework of the membrane paradigma. They develop a new procedure for the computation of the resonances by the spectral analysis of the transient scattered wave, based on Prony's algorithm.

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

PubMed

Kopský, Vojtech

2006-03-01

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

Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group

NASA Astrophysics Data System (ADS)

You, Yi-Zhuang; Qi, Xiao-Liang; Xu, Cenke

We introduce the spectrum bifurcation renormalization group (SBRG) as a generalization of the real-space renormalization group for the many-body localized (MBL) system without truncating the Hilbert space. Starting from a disordered many-body Hamiltonian in the full MBL phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local conserved quantities and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the MBL phase. In particular, we focus on the 1 d interacting Majorana chain with strong disorder, and map out its phase diagram using the entanglement entropy. The SBRG flow also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space decorated with small blackholes.

NoGOA: predicting noisy GO annotations using evidences and sparse representation.

PubMed

Yu, Guoxian; Lu, Chang; Wang, Jun

2017-07-21

Gene Ontology (GO) is a community effort to represent functional features of gene products. GO annotations (GOA) provide functional associations between GO terms and gene products. Due to resources limitation, only a small portion of annotations are manually checked by curators, and the others are electronically inferred. Although quality control techniques have been applied to ensure the quality of annotations, the community consistently report that there are still considerable noisy (or incorrect) annotations. Given the wide application of annotations, however, how to identify noisy annotations is an important but yet seldom studied open problem. We introduce a novel approach called NoGOA to predict noisy annotations. NoGOA applies sparse representation on the gene-term association matrix to reduce the impact of noisy annotations, and takes advantage of sparse representation coefficients to measure the semantic similarity between genes. Secondly, it preliminarily predicts noisy annotations of a gene based on aggregated votes from semantic neighborhood genes of that gene. Next, NoGOA estimates the ratio of noisy annotations for each evidence code based on direct annotations in GOA files archived on different periods, and then weights entries of the association matrix via estimated ratios and propagates weights to ancestors of direct annotations using GO hierarchy. Finally, it integrates evidence-weighted association matrix and aggregated votes to predict noisy annotations. Experiments on archived GOA files of six model species (H. sapiens, A. thaliana, S. cerevisiae, G. gallus, B. Taurus and M. musculus) demonstrate that NoGOA achieves significantly better results than other related methods and removing noisy annotations improves the performance of gene function prediction. The comparative study justifies the effectiveness of integrating evidence codes with sparse representation for predicting noisy GO annotations. Codes and datasets are available at http://mlda.swu.edu.cn/codes.php?name=NoGOA .

Non-Markovianity of Gaussian Channels.

PubMed

Torre, G; Roga, W; Illuminati, F

2015-08-14

We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.

Reconstructing householder vectors from Tall-Skinny QR

DOE PAGES

Ballard, Grey Malone; Demmel, James; Grigori, Laura; ...

2015-08-05

The Tall-Skinny QR (TSQR) algorithm is more communication efficient than the standard Householder algorithm for QR decomposition of matrices with many more rows than columns. However, TSQR produces a different representation of the orthogonal factor and therefore requires more software development to support the new representation. Further, implicitly applying the orthogonal factor to the trailing matrix in the context of factoring a square matrix is more complicated and costly than with the Householder representation. We show how to perform TSQR and then reconstruct the Householder vector representation with the same asymptotic communication efficiency and little extra computational cost. We demonstratemore » the high performance and numerical stability of this algorithm both theoretically and empirically. The new Householder reconstruction algorithm allows us to design more efficient parallel QR algorithms, with significantly lower latency cost compared to Householder QR and lower bandwidth and latency costs compared with Communication-Avoiding QR (CAQR) algorithm. Experiments on supercomputers demonstrate the benefits of the communication cost improvements: in particular, our experiments show substantial improvements over tuned library implementations for tall-and-skinny matrices. Furthermore, we also provide algorithmic improvements to the Householder QR and CAQR algorithms, and we investigate several alternatives to the Householder reconstruction algorithm that sacrifice guarantees on numerical stability in some cases in order to obtain higher performance.« less

Modified signed-digit arithmetic based on redundant bit representation.

PubMed

Huang, H; Itoh, M; Yatagai, T

1994-09-10

Fully parallel modified signed-digit arithmetic operations are realized based on redundant bit representation of the digits proposed. A new truth-table minimizing technique is presented based on redundant-bitrepresentation coding. It is shown that only 34 minterms are enough for implementing one-step modified signed-digit addition and subtraction with this new representation. Two optical implementation schemes, correlation and matrix multiplication, are described. Experimental demonstrations of the correlation architecture are presented. Both architectures use fixed minterm masks for arbitrary-length operands, taking full advantage of the parallelism of the modified signed-digit number system and optics.

Theory and experimental results of transfer-NOE experiments. 1. The influence of the off rate versus cross-relaxation rates

NASA Astrophysics Data System (ADS)

Lippens, R. M.; Cerf, C.; Hallenga, K.

The theory of the transferred nuclear Overhauser effect is presented in the framework of an extended relaxation matrix representation. This matrix representation allows a coherent description of all one- and two-dimensional experiments. We present analytical solutions for the buildup of magnetization in the 2D transfer-NOE experiment, for all ratios of the off rate k to the cross-relaxation rates R involved. We show that systematic deviations in distance determination occur when the off rate becomes comparable to or smaller than the relaxation rates. Experimental results on the peptide/protein system oxytocin/neurophysin confirming this analysis are presented. The importance of residual mobility in the bound ligand, as demonstrated by the experimental data, is also discussed.

Local representation of the electronic dielectric response function

DOE PAGES

Lu, Deyu; Ge, Xiaochuan

2015-12-11

We present a local representation of the electronic dielectric response function, based on a spatial partition of the dielectric response into contributions from each occupied Wannier orbital using a generalized density functional perturbation theory. This procedure is fully ab initio, and therefore allows us to rigorously define local metrics, such as “bond polarizability,” on Wannier centers. We show that the locality of the bare response function is determined by the locality of three quantities: Wannier functions of the occupied manifold, the density matrix, and the Hamiltonian matrix. Furthermore, in systems with a gap, the bare dielectric response is exponentially localized,more » which supports the physical picture of the dielectric response function as a collection of interacting local responses that can be captured by a tight-binding model.« less

The controversial nuclear matrix: a balanced point of view.

PubMed

Martelli, A M; Falcieri, E; Zweyer, M; Bortul, R; Tabellini, G; Cappellini, A; Cocco, L; Manzoli, L

2002-10-01

The nuclear matrix is defined as the residual framework after the removal of the nuclear envelope, chromatin, and soluble components by sequential extractions. According to several investigators the nuclear matrix provides the structural basis for intranuclear order. However, the existence itself and the nature of this structure is still uncertain. Although the techniques used for the visualization of the nuclear matrix have improved over the years, it is still unclear to what extent the isolated nuclear matrix corresponds to an in vivo existing structure. Therefore, considerable skepticism continues to surround the nuclear matrix fraction as an accurate representation of the situation in living cells. Here, we summarize the experimental evidence in favor of, or against, the presence of a diffuse nucleoskeleton as a facilitating organizational nonchromatin structure of the nucleus.

Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics

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

Jiang, Tongsong, E-mail: jiangtongsong@sina.com; Department of Mathematics, Heze University, Heze, Shandong 274015; Jiang, Ziwu

In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics.

A supertree of early tetrapods.

PubMed Central

Ruta, Marcello; Jeffery, Jonathan E; Coates, Michael I

2003-01-01

A genus-level supertree for early tetrapods is built using a matrix representation of 50 source trees. The analysis of all combined trees delivers a long-stemmed topology in which most taxonomic groups are assigned to the tetrapod stem. A second analysis, which excludes source trees superseded by more comprehensive studies, supports a deep phylogenetic split between lissamphibian and amniote total groups. Instances of spurious groups are rare in both analyses. The results of the pruned second analysis are mostly comparable with those of a recent, character-based and large-scale phylogeny of Palaeozoic tetrapods. Outstanding areas of disagreement include the branching sequence of lepospondyls and the content of the amniote crown group, in particular the placement of diadectomorphs as stem diapsids. Supertrees are unsurpassed in their ability to summarize relationship patterns from multiple independent topologies. Therefore, they might be used as a simple test of the degree of corroboration of nodes in the contributory analyses. However, we urge caution in using them as a replacement for character-based cladograms and for inferring macroevolutionary patterns. PMID:14667343

Direct Iterative Nonlinear Inversion by Multi-frequency T-matrix Completion

NASA Astrophysics Data System (ADS)

Jakobsen, M.; Wu, R. S.

2016-12-01

Researchers in the mathematical physics community have recently proposed a conceptually new method for solving nonlinear inverse scattering problems (like FWI) which is inspired by the theory of nonlocality of physical interactions. The conceptually new method, which may be referred to as the T-matrix completion method, is very interesting since it is not based on linearization at any stage. Also, there are no gradient vectors or (inverse) Hessian matrices to calculate. However, the convergence radius of this promising T-matrix completion method is seriously restricted by it's use of single-frequency scattering data only. In this study, we have developed a modified version of the T-matrix completion method which we believe is more suitable for applications to nonlinear inverse scattering problems in (exploration) seismology, because it makes use of multi-frequency data. Essentially, we have simplified the single-frequency T-matrix completion method of Levinson and Markel and combined it with the standard sequential frequency inversion (multi-scale regularization) method. For each frequency, we first estimate the experimental T-matrix by using the Moore-Penrose pseudo inverse concept. Then this experimental T-matrix is used to initiate an iterative procedure for successive estimation of the scattering potential and the T-matrix using the Lippmann-Schwinger for the nonlinear relation between these two quantities. The main physical requirements in the basic iterative cycle is that the T-matrix should be data-compatible and the scattering potential operator should be dominantly local; although a non-local scattering potential operator is allowed in the intermediate iterations. In our simplified T-matrix completion strategy, we ensure that the T-matrix updates are always data compatible simply by adding a suitable correction term in the real space coordinate representation. The use of singular-value decomposition representations are not required in our formulation since we have developed an efficient domain decomposition method. The results of several numerical experiments for the SEG/EAGE salt model illustrate the importance of using multi-frequency data when performing frequency domain full waveform inversion in strongly scattering media via the new concept of T-matrix completion.

A canonical state-space representation for SISO systems using multipoint Jordan CFE. [Continued-Fraction Expansion

NASA Technical Reports Server (NTRS)

Hwang, Chyi; Guo, Tong-Yi; Shieh, Leang-San

1991-01-01

A canonical state-space realization based on the multipoint Jordan continued-fraction expansion (CFE) is presented for single-input-single-output (SISO) systems. The similarity transformation matrix which relates the new canonical form to the phase-variable canonical form is also derived. The presented canonical state-space representation is particularly attractive for the application of SISO system theory in which a reduced-dimensional time-domain model is necessary.

MRL and SuperFine+MRL: new supertree methods

PubMed Central

2012-01-01

Background Supertree methods combine trees on subsets of the full taxon set together to produce a tree on the entire set of taxa. Of the many supertree methods, the most popular is MRP (Matrix Representation with Parsimony), a method that operates by first encoding the input set of source trees by a large matrix (the "MRP matrix") over {0,1, ?}, and then running maximum parsimony heuristics on the MRP matrix. Experimental studies evaluating MRP in comparison to other supertree methods have established that for large datasets, MRP generally produces trees of equal or greater accuracy than other methods, and can run on larger datasets. A recent development in supertree methods is SuperFine+MRP, a method that combines MRP with a divide-and-conquer approach, and produces more accurate trees in less time than MRP. In this paper we consider a new approach for supertree estimation, called MRL (Matrix Representation with Likelihood). MRL begins with the same MRP matrix, but then analyzes the MRP matrix using heuristics (such as RAxML) for 2-state Maximum Likelihood. Results We compared MRP and SuperFine+MRP with MRL and SuperFine+MRL on simulated and biological datasets. We examined the MRP and MRL scores of each method on a wide range of datasets, as well as the resulting topological accuracy of the trees. Our experimental results show that MRL, coupled with a very good ML heuristic such as RAxML, produced more accurate trees than MRP, and MRL scores were more strongly correlated with topological accuracy than MRP scores. Conclusions SuperFine+MRP, when based upon a good MP heuristic, such as TNT, produces among the best scores for both MRP and MRL, and is generally faster and more topologically accurate than other supertree methods we tested. PMID:22280525

Derivatives in discrete mathematics: a novel graph-theoretical invariant for generating new 2/3D molecular descriptors. I. Theory and QSPR application

NASA Astrophysics Data System (ADS)

Marrero-Ponce, Yovani; Santiago, Oscar Martínez; López, Yoan Martínez; Barigye, Stephen J.; Torrens, Francisco

2012-11-01

In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ( partial ) of a molecular graph (MG) with respect to a given event ( E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub- graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns ( n) and rows ( m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ i , can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ i for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating among different atoms, an atomic weighting scheme (atom-type labels) is used in the formation of the matrix Q or in LOVIs state. The obtained indices were utilized to describe the partition coefficient (Log P) and the reactivity index (Log K) of the 34 derivatives of 2-furylethylenes. In all the cases, our MDs showed better statistical results than those previously obtained using some of the most used families of MDs in chemometric practice. Therefore, it has been demonstrated to that the proposed MDs are useful in molecular design and permit obtaining easier and robust mathematical models than the majority of those reported in the literature. All this range of mentioned possibilities open "the doors" to the creation of a new family of MDs, using the graph derivative, and avail a new tool for QSAR/QSPR and molecular diversity/similarity studies.

Derivatives in discrete mathematics: a novel graph-theoretical invariant for generating new 2/3D molecular descriptors. I. Theory and QSPR application.

PubMed

Marrero-Ponce, Yovani; Santiago, Oscar Martínez; López, Yoan Martínez; Barigye, Stephen J; Torrens, Francisco

2012-11-01

In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ([Formula: see text]) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ(i), can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ(i) for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating among different atoms, an atomic weighting scheme (atom-type labels) is used in the formation of the matrix Q or in LOVIs state. The obtained indices were utilized to describe the partition coefficient (Log P) and the reactivity index (Log K) of the 34 derivatives of 2-furylethylenes. In all the cases, our MDs showed better statistical results than those previously obtained using some of the most used families of MDs in chemometric practice. Therefore, it has been demonstrated to that the proposed MDs are useful in molecular design and permit obtaining easier and robust mathematical models than the majority of those reported in the literature. All this range of mentioned possibilities open "the doors" to the creation of a new family of MDs, using the graph derivative, and avail a new tool for QSAR/QSPR and molecular diversity/similarity studies.

Implementation of a fast digital optical matrix-vector multiplier using a holographic look-up table and residue arithmetic

NASA Technical Reports Server (NTRS)

Habiby, Sarry F.; Collins, Stuart A., Jr.

1987-01-01

The design and implementation of a digital (numerical) optical matrix-vector multiplier are presented. A Hughes liquid crystal light valve, the residue arithmetic representation, and a holographic optical memory are used to construct position coded optical look-up tables. All operations are performed in effectively one light valve response time with a potential for a high information density.

Implementation of a fast digital optical matrix-vector multiplier using a holographic look-up table and residue arithmetic.

PubMed

Habiby, S F; Collins, S A

1987-11-01

The design and implementation of a digital (numerical) optical matrix-vector multiplier are presented. A Hughes liquid crystal light valve, the residue arithmetic representation, and a holographic optical memory are used to construct position coded optical look-up tables. All operations are performed in effectively one light valve response time with a potential for a high information density.

DYMAFLEX: DYnamic Manipulation FLight EXperiment

DTIC Science & Technology

2013-09-03

thrust per nozzle and minimize propellant mass and tank mass. This study compared carbon dioxide, nitrous oxide, and R134-A. These results were...equations of mo- tion of a space manipulator, showing their top- level, matrix- vector representation to be of iden- tical form to those of a fixed-base...the system inertia matrix, q is the po- sition state vector (consisting of the manipulator joint angles θ, spacecraft attitude quaternion, and

The role of national identity representation in the relation between in-group identification and out-group derogation: ethnic versus civic representation.

PubMed

Meeus, Joke; Duriez, Bart; Vanbeselaere, Norbert; Boen, Filip

2010-06-01

Two studies investigated whether the content of in-group identity affects the relation between in-group identification and ethnic prejudice. The first study among university students, tested whether national identity representations (i.e., ethnic vs. civic) moderate or mediate the relation between Flemish in-group identification and ethnic prejudice. A moderation hypothesis is supported when those higher in identification who subscribe to a more ethnic representation display higher ethnic prejudice levels than those higher in identification who subscribe to a more civic representation. A mediation hypothesis is supported when those higher in identification tend towards one specific representation, which in turn, should predict ethnic prejudice. Results supported a mediation hypothesis and showed that the more respondents identified with the Flemish in-group, the more ethnic their identity representation, and the more they were inclined to display ethnic prejudice. The second study tested this mediation from a longitudinal perspective in a two-wave study among high school students. In-group identification at Time 1 predicted over-time changes in identity representation, which in turn, predicted changes in ethnic prejudice. In addition to this, changes in identity representation were predicted by initial ethnic prejudice levels. The implications of these findings are discussed.

Kalman Filter Estimation of Spinning Spacecraft Attitude using Markley Variables

NASA Technical Reports Server (NTRS)

Sedlak, Joseph E.; Harman, Richard

2004-01-01

There are several different ways to represent spacecraft attitude and its time rate of change. For spinning or momentum-biased spacecraft, one particular representation has been put forward as a superior parameterization for numerical integration. Markley has demonstrated that these new variables have fewer rapidly varying elements for spinning spacecraft than other commonly used representations and provide advantages when integrating the equations of motion. The current work demonstrates how a Kalman filter can be devised to estimate the attitude using these new variables. The seven Markley variables are subject to one constraint condition, making the error covariance matrix singular. The filter design presented here explicitly accounts for this constraint by using a six-component error state in the filter update step. The reduced dimension error state is unconstrained and its covariance matrix is nonsingular.

Magnetic Photon Splitting: The S-Matrix Formulation in the Landau Representation

NASA Technical Reports Server (NTRS)

Baring, Matthew G.

1999-01-01

Calculations of reaction rates for the third-order QED process of photon splitting gamma yields gamma.gamma in strong magnetic fields traditionally have employed either the effective Lagrangian method or variants of Schwinger's proper-time technique. Recently, Mentzel, Berg and Wunner [1] presented an alternative derivation via an S-matrix formulation in the Landau representation. Advantages of such a formulation include the ability to compute rates near pair resonances above pair threshold. This paper presents new developments of the Landau representation formalism as applied to photon splitting, providing significant, advances beyond the work of [1] by summing over the spin quantum numbers of the electron propagators, and analytically integrating over the component of momentum of the intermediate states that is parallel to field. The ensuing tractable expressions for the scattering amplitudes are satisfyingly compact, and of an appearance familiar to S-matrix theory applications. Such developments can facilitate numerical computations of splitting considerably both below and above pair threshold. Specializations to two regimes of interest are obtained, namely the limit of highly supercritical fields and the domain where photon energies are far inferior to that for the threshold of single-photon pair creation. In particular, for the first time the low-frequency amplitudes are simply expressed in terms of the Gamma function, its integral and its derivatives. In addition, the equivalence of the asymptotic forms in these two domains to extant results from effective Lagrangian/proper- time formulations is demonstrated.

Quantum Stochastic Trajectories: The Fokker-Planck-Bohm Equation Driven by the Reduced Density Matrix.

PubMed

Avanzini, Francesco; Moro, Giorgio J

2018-03-15

The quantum molecular trajectory is the deterministic trajectory, arising from the Bohm theory, that describes the instantaneous positions of the nuclei of molecules by assuring the agreement with the predictions of quantum mechanics. Therefore, it provides the suitable framework for representing the geometry and the motions of molecules without neglecting their quantum nature. However, the quantum molecular trajectory is extremely demanding from the computational point of view, and this strongly limits its applications. To overcome such a drawback, we derive a stochastic representation of the quantum molecular trajectory, through projection operator techniques, for the degrees of freedom of an open quantum system. The resulting Fokker-Planck operator is parametrically dependent upon the reduced density matrix of the open system. Because of the pilot role played by the reduced density matrix, this stochastic approach is able to represent accurately the main features of the open system motions both at equilibrium and out of equilibrium with the environment. To verify this procedure, the predictions of the stochastic and deterministic representation are compared for a model system of six interacting harmonic oscillators, where one oscillator is taken as the open quantum system of interest. The undeniable advantage of the stochastic approach is that of providing a simplified and self-contained representation of the dynamics of the open system coordinates. Furthermore, it can be employed to study the out of equilibrium dynamics and the relaxation of quantum molecular motions during photoinduced processes, like photoinduced conformational changes and proton transfers.

Yangians and Yang-Baxter R-operators for ortho-symplectic superalgebras

NASA Astrophysics Data System (ADS)

Fuksa, J.; Isaev, A. P.; Karakhanyan, D.; Kirschner, R.

2017-04-01

Yang-Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start with the formulation of graded algebras and the linear superspace carrying the vector (fundamental) representation of the ortho-symplectic supergroup. On this basis we study the analogy of the Yang-Baxter operators considered earlier for the cases of orthogonal and symplectic symmetries: the vector (fundamental) R-matrix, the L-operator defining the Yangian algebra and its first and second order evaluations. We investigate the condition for L (u) in the case of the truncated expansion in inverse powers of u and give examples of Lie algebra representations obeying these conditions. We construct the R-operator intertwining two superspinor representations and study the fusion of L-operators involving the tensor product of such representations.

Stereo-tomography in triangulated models

NASA Astrophysics Data System (ADS)

Yang, Kai; Shao, Wei-Dong; Xing, Feng-yuan; Xiong, Kai

2018-04-01

Stereo-tomography is a distinctive tomographic method. It is capable of estimating the scatterer position, the local dip of scatterer and the background velocity simultaneously. Building a geologically consistent velocity model is always appealing for applied and earthquake seismologists. Differing from the previous work to incorporate various regularization techniques into the cost function of stereo-tomography, we think extending stereo-tomography to the triangulated model will be the most straightforward way to achieve this goal. In this paper, we provided all the Fréchet derivatives of stereo-tomographic data components with respect to model components for slowness-squared triangulated model (or sloth model) in 2D Cartesian coordinate based on the ray perturbation theory for interfaces. A sloth model representation means a sparser model representation when compared with conventional B-spline model representation. A sparser model representation leads to a smaller scale of stereo-tomographic (Fréchet) matrix, a higher-accuracy solution when solving linear equations, a faster convergence rate and a lower requirement for quantity of data space. Moreover, a quantitative representation of interface strengthens the relationships among different model components, which makes the cross regularizations among these model components, such as node coordinates, scatterer coordinates and scattering angles, etc., more straightforward and easier to be implemented. The sensitivity analysis, the model resolution matrix analysis and a series of synthetic data examples demonstrate the correctness of the Fréchet derivatives, the applicability of the regularization terms and the robustness of the stereo-tomography in triangulated model. It provides a solid theoretical foundation for the real applications in the future.

Unitary cocycle representations of the Galilean line group: Quantum mechanical principle of equivalence

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

MacGregor, B.R.; McCoy, A.E.; Wickramasekara, S., E-mail: wickrama@grinnell.edu

2012-09-15

We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these representations determine the structure of quantum mechanics in non-inertialmore » reference frames. Our representations of the Galilean line group contain the usual unitary projective representations of the Galilei group, but have a more intricate cocycle structure. The transformation formula for the Hamiltonian under the Galilean line group shows that in a non-inertial reference frame it acquires a fictitious potential energy term that is proportional to the inertial mass, suggesting the equivalence of inertial mass and gravitational mass in quantum mechanics. - Highlights: Black-Right-Pointing-Pointer A formulation of Galilean quantum mechanics in non-inertial reference frames is given. Black-Right-Pointing-Pointer The key concept is the Galilean line group, an infinite dimensional group. Black-Right-Pointing-Pointer Unitary, cocycle representations of the Galilean line group are constructed. Black-Right-Pointing-Pointer A non-central extension of the group underlies these representations. Black-Right-Pointing-Pointer Quantum equivalence principle and gravity emerge from these representations.« less

A laid-back trip through the Hennigian Forests

PubMed Central

2017-01-01

Background This paper is a comment on the idea of matrix-free Cladistics. Demonstration of this idea’s efficiency is a major goal of the study. Within the proposed framework, the ordinary (phenetic) matrix is necessary only as “source” of Hennigian trees, not as a primary subject of the analysis. Switching from the matrix-based thinking to the matrix-free Cladistic approach clearly reveals that optimizations of the character-state changes are related not to the real processes, but to the form of the data representation. Methods We focused our study on the binary data. We wrote the simple ruby-based script FORESTER version 1.0 that helps represent a binary matrix as an array of the rooted trees (as a “Hennigian forest”). The binary representations of the genomic (DNA) data have been made by script 1001. The Average Consensus method as well as the standard Maximum Parsimony (MP) approach has been used to analyze the data. Principle findings The binary matrix may be easily re-written as a set of rooted trees (maximal relationships). The latter might be analyzed by the Average Consensus method. Paradoxically, this method, if applied to the Hennigian forests, in principle can help to identify clades despite the absence of the direct evidence from the primary data. Our approach may handle the clock- or non clock-like matrices, as well as the hypothetical, molecular or morphological data. Discussion Our proposal clearly differs from the numerous phenetic alignment-free techniques of the construction of the phylogenetic trees. Dealing with the relations, not with the actual “data” also distinguishes our approach from all optimization-based methods, if the optimization is defined as a way to reconstruct the sequences of the character-state changes on a tree, either the standard alignment-based techniques or the “direct” alignment-free procedure. We are not viewing our recent framework as an alternative to the three-taxon statement analysis (3TA), but there are two major differences between our recent proposal and the 3TA, as originally designed and implemented: (1) the 3TA deals with the three-taxon statements or minimal relationships. According to the logic of 3TA, the set of the minimal trees must be established as a binary matrix and used as an input for the parsimony program. In this paper, we operate directly with maximal relationships written just as trees, not as binary matrices, while also using the Average Consensus method instead of the MP analysis. The solely ‘reversal’-based groups can always be found by our method without the separate scoring of the putative reversals before analyses. PMID:28740753

Identities of almost Stable Group Representations

NASA Astrophysics Data System (ADS)

Vovsi, S. M.; Khung Shon, Nguen

1988-02-01

It is proved that almost stable group representations over a field have a finite basis of identities. Moreover, a variety generated by an arbitrary almost stable representation is Specht and all of its subvarieties have a finite uniformly bounded basis rank. In particular, the identities of an arbitrary representation of a finite group are finitely based.Bibliography: 17 titles.

Matrix Transfer Function Design for Flexible Structures: An Application

NASA Technical Reports Server (NTRS)

Brennan, T. J.; Compito, A. V.; Doran, A. L.; Gustafson, C. L.; Wong, C. L.

1985-01-01

The application of matrix transfer function design techniques to the problem of disturbance rejection on a flexible space structure is demonstrated. The design approach is based on parameterizing a class of stabilizing compensators for the plant and formulating the design specifications as a constrained minimization problem in terms of these parameters. The solution yields a matrix transfer function representation of the compensator. A state space realization of the compensator is constructed to investigate performance and stability on the nominal and perturbed models. The application is made to the ACOSSA (Active Control of Space Structures) optical structure.

Comments on higher rank Wilson loops in N = 2∗

NASA Astrophysics Data System (ADS)

Liu, James T.; Zayas, Leopoldo A. Pando; Zhou, Shan

2018-01-01

For N = 2∗ theory with U( N ) gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with n rows and k columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigen-value distributions in various regimes of parameters ( N, λ , n, k) where λ is the 't Hooft coupling. In the large N limit we present analytic results for the leading and sub-leading contributions. In the particular cases of only one row or one column we reproduce previously known results for the totally symmetry and totally antisymmetric representations. We also extensively discusss the N = 4 limit of the N = 2∗ theory. While establishing these connections we clarify aspects of various orders of limits and how to relax them; we also find it useful to explicitly address details of the genus expansion. As a result, for the totally symmetric Wilson loop we find new contributions that improve the comparison with the dual holographic computation at one loop order in the appropriate regime.

45 CFR 1611.6 - Representation of groups.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 45 Public Welfare 4 2012-10-01 2012-10-01 false Representation of groups. 1611.6 Section 1611.6... ELIGIBILITY § 1611.6 Representation of groups. (a) A recipient may provide legal assistance to a group... practical means of obtaining, funds to retain private counsel and either: (1) The group, or for a non...

45 CFR 1611.6 - Representation of groups.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 45 Public Welfare 4 2014-10-01 2014-10-01 false Representation of groups. 1611.6 Section 1611.6... ELIGIBILITY § 1611.6 Representation of groups. (a) A recipient may provide legal assistance to a group... practical means of obtaining, funds to retain private counsel and either: (1) The group, or for a non...

45 CFR 1611.6 - Representation of groups.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 45 Public Welfare 4 2013-10-01 2013-10-01 false Representation of groups. 1611.6 Section 1611.6... ELIGIBILITY § 1611.6 Representation of groups. (a) A recipient may provide legal assistance to a group... practical means of obtaining, funds to retain private counsel and either: (1) The group, or for a non...

45 CFR 1611.6 - Representation of groups.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 45 Public Welfare 4 2010-10-01 2010-10-01 false Representation of groups. 1611.6 Section 1611.6... ELIGIBILITY § 1611.6 Representation of groups. (a) A recipient may provide legal assistance to a group... practical means of obtaining, funds to retain private counsel and either: (1) The group, or for a non...

Jones's matrix representation of optical instruments. II - Fourier interferometers /spectrometers and spectropolarimeters/.

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1971-01-01

Our method of matrix synthesis of optical components and instruments is applied to the derivation of Jones's matrices appropriate for Fourier interferometers (spectrometers and spectropolarimeters). These matrices are obtained for both the source beam and the detector beam. In the course of synthesis, Jones's matrices of the various reflectors (plane mirrors; retroreflectors: roofed mirror, trihedral and prism cube corner, cat's eye) used by these interferometers are also obtained.

Quantum mechanics in non-inertial reference frames: Time-dependent rotations and loop prolongations

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

Klink, W.H., E-mail: william-klink@uiowa.edu; Wickramasekara, S., E-mail: wickrama@grinnell.edu; Department of Physics, Grinnell College, Grinnell, IA 50112

2013-09-15

This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group to include transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. In previous work, we have shown that there exist representations of the Galilean line group that uphold the non-relativistic equivalence principle asmore » well as representations that violate the equivalence principle. In these previous studies, the focus was on linear accelerations. In this paper, we undertake an extension of the formulation to include rotational accelerations. We show that the incorporation of rotational accelerations requires a class of loop prolongations of the Galilean line group and their unitary cocycle representations. We recover the centrifugal and Coriolis force effects from these loop representations. Loops are more general than groups in that their multiplication law need not be associative. Hence, our broad theoretical claim is that a Galilean quantum theory that holds in arbitrary non-inertial reference frames requires going beyond groups and group representations, the well-established framework for implementing symmetry transformations in quantum mechanics. -- Highlights: •A formulation of Galilean quantum mechanics in non-inertial reference frames is presented. •The Galilei group is generalized to infinite dimensional Galilean line group. •Loop prolongations of Galilean line group contain central extensions of Galilei group. •Unitary representations of the loops are constructed. •These representations lead to terms in the Hamiltonian corresponding to fictitious forces, including centrifugal and Coriolis forces.« less

Decentralized modal identification using sparse blind source separation

NASA Astrophysics Data System (ADS)

Sadhu, A.; Hazra, B.; Narasimhan, S.; Pandey, M. D.

2011-12-01

Popular ambient vibration-based system identification methods process information collected from a dense array of sensors centrally to yield the modal properties. In such methods, the need for a centralized processing unit capable of satisfying large memory and processing demands is unavoidable. With the advent of wireless smart sensor networks, it is now possible to process information locally at the sensor level, instead. The information at the individual sensor level can then be concatenated to obtain the global structure characteristics. A novel decentralized algorithm based on wavelet transforms to infer global structure mode information using measurements obtained using a small group of sensors at a time is proposed in this paper. The focus of the paper is on algorithmic development, while the actual hardware and software implementation is not pursued here. The problem of identification is cast within the framework of under-determined blind source separation invoking transformations of measurements to the time-frequency domain resulting in a sparse representation. The partial mode shape coefficients so identified are then combined to yield complete modal information. The transformations are undertaken using stationary wavelet packet transform (SWPT), yielding a sparse representation in the wavelet domain. Principal component analysis (PCA) is then performed on the resulting wavelet coefficients, yielding the partial mixing matrix coefficients from a few measurement channels at a time. This process is repeated using measurements obtained from multiple sensor groups, and the results so obtained from each group are concatenated to obtain the global modal characteristics of the structure.

Reflection Positive Stochastic Processes Indexed by Lie Groups

NASA Astrophysics Data System (ADS)

Jorgensen, Palle E. T.; Neeb, Karl-Hermann; Ólafsson, Gestur

2016-06-01

Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in representation theory, it is related to the Cartan duality of symmetric Lie groups (Lie groups with an involution) and results in a transformation of a unitary representation of a symmetric Lie group to a unitary representation of its Cartan dual. In this article we continue our investigation of representation theoretic aspects of reflection positivity by discussing reflection positive Markov processes indexed by Lie groups, measures on path spaces, and invariant gaussian measures in spaces of distribution vectors. This provides new constructions of reflection positive unitary representations.

N-representability-driven reconstruction of the two-electron reduced-density matrix for a real-time time-dependent electronic structure method

NASA Astrophysics Data System (ADS)

Jeffcoat, David B.; DePrince, A. Eugene

2014-12-01

Propagating the equations of motion (EOM) for the one-electron reduced-density matrix (1-RDM) requires knowledge of the corresponding two-electron RDM (2-RDM). We show that the indeterminacy of this expression can be removed through a constrained optimization that resembles the variational optimization of the ground-state 2-RDM subject to a set of known N-representability conditions. Electronic excitation energies can then be obtained by propagating the EOM for the 1-RDM and following the dipole moment after the system interacts with an oscillating external electric field. For simple systems with well-separated excited states whose symmetry differs from that of the ground state, excitation energies obtained from this method are comparable to those obtained from full configuration interaction computations. Although the optimized 2-RDM satisfies necessary N-representability conditions, the procedure cannot guarantee a unique mapping from the 1-RDM to the 2-RDM. This deficiency is evident in the mean-field-quality description of transitions to states of the same symmetry as the ground state, as well as in the inability of the method to describe Rabi oscillations.

On determinant representations of scalar products and form factors in the SoV approach: the XXX case

NASA Astrophysics Data System (ADS)

Kitanine, N.; Maillet, J. M.; Niccoli, G.; Terras, V.

2016-03-01

In the present article we study the form factors of quantum integrable lattice models solvable by the separation of variables (SoVs) method. It was recently shown that these models admit universal determinant representations for the scalar products of the so-called separate states (a class which includes in particular all the eigenstates of the transfer matrix). These results permit to obtain simple expressions for the matrix elements of local operators (form factors). However, these representations have been obtained up to now only for the completely inhomogeneous versions of the lattice models considered. In this article we give a simple algebraic procedure to rewrite the scalar products (and hence the form factors) for the SoV related models as Izergin or Slavnov type determinants. This new form leads to simple expressions for the form factors in the homogeneous and thermodynamic limits. To make the presentation of our method clear, we have chosen to explain it first for the simple case of the XXX Heisenberg chain with anti-periodic boundary conditions. We would nevertheless like to stress that the approach presented in this article applies as well to a wide range of models solved in the SoV framework.

Application of Semi-Definite Programming for Many-Fermion Systems

NASA Astrophysics Data System (ADS)

Zhao, Zhengji; Braams, Bastiaan; Fukuda, Mituhiro; Overton, Michael

2003-03-01

The ground state energy and other important observables of a many-fermion system with one- and two-body interactions only can all be obtained from the first order and second order Reduced Density Matrices (RDM's) of the system. Using these density matrices and a family of associated representability conditions one may obtain an approximation method for electronic structure theory that is in the mathematical form of Semi-Definite Programming (SDP): minimize a linear matrix functional over a space of positive semidefinite matrices subject to linear constraints. The representability conditions are some known necessary conditions, starting with the well-known P, Q, and G conditions [Claude Garrod and Jerome K. Percus, Reducation of the N-Particle Variational Problem, J. Math. Phys. 5 (1964) 1756-1776]. The RDM method with SDP has great potential advantages over the wave function method when the particle number N is large. The dimension of the full configuration space increases exponentially with N, but in RDM method with SDP the dimension of the objective matrix (which includes RDM's) increases only polynomially with N. We will report on the effect of adding the generalized three-index conditions proposed in [R. M. Erdahl, Representability, Int. J. Quantum Chem. 13 (1978) 697-718].

Identifying seasonal mobility profiles from anonymized and aggregated mobile phone data. Application in food security.

PubMed

Zufiria, Pedro J; Pastor-Escuredo, David; Úbeda-Medina, Luis; Hernandez-Medina, Miguel A; Barriales-Valbuena, Iker; Morales, Alfredo J; Jacques, Damien C; Nkwambi, Wilfred; Diop, M Bamba; Quinn, John; Hidalgo-Sanchís, Paula; Luengo-Oroz, Miguel

2018-01-01

We propose a framework for the systematic analysis of mobile phone data to identify relevant mobility profiles in a population. The proposed framework allows finding distinct human mobility profiles based on the digital trace of mobile phone users characterized by a Matrix of Individual Trajectories (IT-Matrix). This matrix gathers a consistent and regularized description of individual trajectories that enables multi-scale representations along time and space, which can be used to extract aggregated indicators such as a dynamic multi-scale population count. Unsupervised clustering of individual trajectories generates mobility profiles (clusters of similar individual trajectories) which characterize relevant group behaviors preserving optimal aggregation levels for detailed and privacy-secured mobility characterization. The application of the proposed framework is illustrated by analyzing fully anonymized data on human mobility from mobile phones in Senegal at the arrondissement level over a calendar year. The analysis of monthly mobility patterns at the livelihood zone resolution resulted in the discovery and characterization of seasonal mobility profiles related with economic activities, agricultural calendars and rainfalls. The use of these mobility profiles could support the timely identification of mobility changes in vulnerable populations in response to external shocks (such as natural disasters, civil conflicts or sudden increases of food prices) to monitor food security.

Kraus operator solutions to a fermionic master equation describing a thermal bath and their matrix representation

NASA Astrophysics Data System (ADS)

Xiang-Guo, Meng; Ji-Suo, Wang; Hong-Yi, Fan; Cheng-Wei, Xia

2016-04-01

We solve the fermionic master equation for a thermal bath to obtain its explicit Kraus operator solutions via the fermionic state approach. The normalization condition of the Kraus operators is proved. The matrix representation for these solutions is obtained, which is incongruous with the result in the book completed by Nielsen and Chuang [Quantum Computation and Quantum Information, Cambridge University Press, 2000]. As especial cases, we also present the Kraus operator solutions to master equations for describing the amplitude-decay model and the diffusion process at finite temperature. Project supported by the National Natural Science Foundation of China (Grant No. 11347026), the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2013AM012 and ZR2012AM004), and the Research Fund for the Doctoral Program and Scientific Research Project of Liaocheng University, Shandong Province, China.

The finite scaling for S = 1 XXZ chains with uniaxial single-ion-type anisotropy

NASA Astrophysics Data System (ADS)

Wang, Honglei; Xiong, Xingliang

2014-03-01

The scaling behavior of criticality for spin-1 XXZ chains with uniaxial single-ion-type anisotropy is investigated by employing the infinite matrix product state representation with the infinite time evolving block decimation method. At criticality, the accuracy of the ground state of a system is limited by the truncation dimension χ of the local Hilbert space. We present four evidences for the scaling of the entanglement entropy, the largest eigenvalue of the Schmidt decomposition, the correlation length, and the connection between the actual correlation length ξ and the energy. The result shows that the finite scalings are governed by the central charge of the critical system. Also, it demonstrates that the infinite time evolving block decimation algorithm by the infinite matrix product state representation can be a quite accurate method to simulate the critical properties at criticality.

Quasi-periodic Solutions of the Kaup-Kupershmidt Hierarchy

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Wu, Lihua; He, Guoliang

2013-08-01

Based on solving the Lenard recursion equations and the zero-curvature equation, we derive the Kaup-Kupershmidt hierarchy associated with a 3×3 matrix spectral problem. Resorting to the characteristic polynomial of the Lax matrix for the Kaup-Kupershmidt hierarchy, we introduce a trigonal curve {K}_{m-1} and present the corresponding Baker-Akhiezer function and meromorphic function on it. The Abel map is introduced to straighten out the Kaup-Kupershmidt flows. With the aid of the properties of the Baker-Akhiezer function and the meromorphic function and their asymptotic expansions, we arrive at their explicit Riemann theta function representations. The Riemann-Jacobi inversion problem is achieved by comparing the asymptotic expansion of the Baker-Akhiezer function and its Riemann theta function representation, from which quasi-periodic solutions of the entire Kaup-Kupershmidt hierarchy are obtained in terms of the Riemann theta functions.

Limited Rank Matrix Learning, discriminative dimension reduction and visualization.

PubMed

Bunte, Kerstin; Schneider, Petra; Hammer, Barbara; Schleif, Frank-Michael; Villmann, Thomas; Biehl, Michael

2012-02-01

We present an extension of the recently introduced Generalized Matrix Learning Vector Quantization algorithm. In the original scheme, adaptive square matrices of relevance factors parameterize a discriminative distance measure. We extend the scheme to matrices of limited rank corresponding to low-dimensional representations of the data. This allows to incorporate prior knowledge of the intrinsic dimension and to reduce the number of adaptive parameters efficiently. In particular, for very large dimensional data, the limitation of the rank can reduce computation time and memory requirements significantly. Furthermore, two- or three-dimensional representations constitute an efficient visualization method for labeled data sets. The identification of a suitable projection is not treated as a pre-processing step but as an integral part of the supervised training. Several real world data sets serve as an illustration and demonstrate the usefulness of the suggested method. Copyright © 2011 Elsevier Ltd. All rights reserved.

[Medication advertisements in the illustrated press and the image of Brazilian nurses (1920-1925)].

PubMed

Porto, Fernando; Santos, Tânia Cristina Franco

2010-09-01

This is a historical and social study about the symbolic effect of medication advertisements presented by women using object representations used by nurses, featured on Fon-Fon Magazine, which describes the medication advertisements featured on Fon-Fon Magazine; analyzes the object representations of the nurse image present in the referred advertisements and discusses on the symbolic effect of those representations on the consumption of medication by the Brazilian society. The document sources were in print, iconographic and literature referring to the History of Brazil, the Press, Advertising and of Nursing. The medication advertisements, analyzed using an analysis matrix based on concepts of semiotics, were obtained from the Fon-Fon Magazine. The study showed that the analyzed advertisements invested in object representations used by nurses to gain reliability regarding the medication being announced.

A d-dimensional stress tensor for Minkd+2 gravity

NASA Astrophysics Data System (ADS)

Kapec, Daniel; Mitra, Prahar

2018-05-01

We consider the tree-level scattering of massless particles in ( d+2)-dimensional asymptotically flat spacetimes. The S -matrix elements are recast as correlation functions of local operators living on a space-like cut ℳ d of the null momentum cone. The Lorentz group SO( d + 1 , 1) is nonlinearly realized as the Euclidean conformal group on ℳ d . Operators of non-trivial spin arise from massless particles transforming in non-trivial representations of the little group SO( d), and distinguished operators arise from the soft-insertions of gauge bosons and gravitons. The leading soft-photon operator is the shadow transform of a conserved spin-one primary operator J a , and the subleading soft-graviton operator is the shadow transform of a conserved spin-two symmetric traceless primary operator T ab . The universal form of the soft-limits ensures that J a and T ab obey the Ward identities expected of a conserved current and energy momentum tensor in a Euclidean CFT d , respectively.

Individual differences in ensemble perception reveal multiple, independent levels of ensemble representation.

PubMed

Haberman, Jason; Brady, Timothy F; Alvarez, George A

2015-04-01

Ensemble perception, including the ability to "see the average" from a group of items, operates in numerous feature domains (size, orientation, speed, facial expression, etc.). Although the ubiquity of ensemble representations is well established, the large-scale cognitive architecture of this process remains poorly defined. We address this using an individual differences approach. In a series of experiments, observers saw groups of objects and reported either a single item from the group or the average of the entire group. High-level ensemble representations (e.g., average facial expression) showed complete independence from low-level ensemble representations (e.g., average orientation). In contrast, low-level ensemble representations (e.g., orientation and color) were correlated with each other, but not with high-level ensemble representations (e.g., facial expression and person identity). These results suggest that there is not a single domain-general ensemble mechanism, and that the relationship among various ensemble representations depends on how proximal they are in representational space. (c) 2015 APA, all rights reserved).

Reflection K-matrices for a nineteen vertex model with Uq [ osp (2 | 2) (2) ] symmetry

NASA Astrophysics Data System (ADS)

Vieira, R. S.; Lima Santos, A.

2017-09-01

We derive the solutions of the boundary Yang-Baxter equation associated with a supersymmetric nineteen vertex model constructed from the three-dimensional representation of the twisted quantum affine Lie superalgebra Uq [ osp (2 | 2) (2) ]. We found three classes of solutions. The type I solution is characterized by three boundary free-parameters and all elements of the corresponding reflection K-matrix are different from zero. In the type II solution, the reflection K-matrix is even (every element of the K-matrix with an odd parity is null) and it has only one boundary free-parameter. Finally, the type III solution corresponds to a diagonal reflection K-matrix with two boundary free-parameters.

MODELS FOR THE COMPLEX REPRESENTATIONS OF THE GROUPS \\mathrm{GL}(n,\\,q)

NASA Astrophysics Data System (ADS)

Klyachko, Alexander A.

1984-02-01

The main result of the paper consists in the construction of a model of the full linear group over a finite field, i.e. its representations such that each irreducible representation occurs as a component precisely once. The series of representations thus constructed has the well-known Gel'fand-Graev representation as first term.Bibliography: 12 titles.

Social representations of climate change in Swedish lay focus groups: local or distant, gradual or catastrophic?

PubMed

Wibeck, Victoria

2014-02-01

This paper explores social representations of climate change, investigating how climate change is discussed by Swedish laypeople interacting in focus group interviews. The analysis focuses on prototypical examples and metaphors, which were key devices for objectifying climate change representations. The paper analyzes how the interaction of focus group participants with other speakers, ideas, arguments, and broader social representations shaped their representations of climate change. Climate change was understood as a global but distant issue with severe consequences. There was a dynamic tension between representations of climate change as a gradual vs. unpredictable process. Implications for climate change communication are discussed.

Spectral Approaches to Learning Predictive Representations

DTIC Science & Technology

2012-09-01

conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed...to the mean to form an initial prediction of x̂(ht). Similarly, Equation 2.3b can be interpreted as using the dynamics matrix A and error covarianceQ...in the sense of Lyapunov if its dynamics matrix A is. Thus, the Lyapunov criterion can be interpreted as holding for an LDS if, for a given covariance

Computational neural networks in chemistry: Model free mapping devices for predicting chemical reactivity from molecular structure

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

Elrod, D.W.

1992-01-01

Computational neural networks (CNNs) are a computational paradigm inspired by the brain's massively parallel network of highly interconnected neurons. The power of computational neural networks derives not so much from their ability to model the brain as from their ability to learn by example and to map highly complex, nonlinear functions, without the need to explicitly specify the functional relationship. Two central questions about CNNs were investigated in the context of predicting chemical reactions: (1) the mapping properties of neural networks and (2) the representation of chemical information for use in CNNs. Chemical reactivity is here considered an example ofmore » a complex, nonlinear function of molecular structure. CNN's were trained using modifications of the back propagation learning rule to map a three dimensional response surface similar to those typically observed in quantitative structure-activity and structure-property relationships. The computational neural network's mapping of the response surface was found to be robust to the effects of training sample size, noisy data and intercorrelated input variables. The investigation of chemical structure representation led to the development of a molecular structure-based connection-table representation suitable for neural network training. An extension of this work led to a BE-matrix structure representation that was found to be general for several classes of reactions. The CNN prediction of chemical reactivity and regiochemistry was investigated for electrophilic aromatic substitution reactions, Markovnikov addition to alkenes, Saytzeff elimination from haloalkanes, Diels-Alder cycloaddition, and retro Diels-Alder ring opening reactions using these connectivity-matrix derived representations. The reaction predictions made by the CNNs were more accurate than those of an expert system and were comparable to predictions made by chemists.« less

Is Hidden Crossings Theory a New MOCC Method?

NASA Astrophysics Data System (ADS)

Krstić, Predrag; Schultz, David

1998-05-01

We find un unitary transformation of the scaled adiabatic Hamiltonian of a two-center, one-electron collision system which yields a new representation for the matrix elements of nonadiabatic radial coupling, valid for low-to-intermediate collision velocities. These are given in analytic form once the topology of the branch points of the adiabatic Hamiltonian in the plane of complex internuclear distance R is known. The matrix elements do not depend on origin of electronic coordinates and properly vanish at large internuclear distances. The role of the rotational couplings in the new representation is also discussed. The aproach is appropriately extended and compared with the PSS treatment in the fully quantal description of the collision. We apply new radial and rotational matrix elements in the standard Molecular Orbital Close Coupling (MOCC) approach to describe excitation and ionization in collisions of antiprotons with He^+ and of alpha-particles with hydrogen(P.S. Krstić et al, J. Phys. B. 31, in press (1998).). The results are compared with those obtained from the standard MOCC method and from the direct solutions of the Schrödinger equation on lattice (LTDSE)(D.R. Schultz et al, Phys. Rev. A 56, 3710 (1997)).

Bodily illusions in health and disease: physiological and clinical perspectives and the concept of a cortical 'body matrix'.

PubMed

Moseley, G Lorimer; Gallace, Alberto; Spence, Charles

2012-01-01

Illusions that induce a feeling of ownership over an artificial body or body-part have been used to explore the complex relationships that exist between the brain's representation of the body and the integrity of the body itself. Here we discuss recent findings in both healthy volunteers and clinical populations that highlight the robust relationship that exists between a person's sense of ownership over a body part, cortical processing of tactile input from that body part, and its physiological regulation. We propose that a network of multisensory and homeostatic brain areas may be responsible for maintaining a 'body-matrix'. That is, a dynamic neural representation that not only extends beyond the body surface to integrate both somatotopic and peripersonal sensory data, but also integrates body-centred spatial sensory data. The existence of such a 'body-matrix' allows our brain to adapt to even profound anatomical and configurational changes to our body. It also plays an important role in maintaining homeostatic control over the body. Its alteration can be seen to have both deleterious and beneficial effects in various clinical populations. Copyright © 2011 Elsevier Ltd. All rights reserved.

The principles of the Brazilian Unified Health System, studied based on similitude analysis

PubMed Central

de Pontes, Ana Paula Munhen; de Oliveira, Denize Cristina; Gomes, Antonio Marcos Tosoli

2014-01-01

Objectives to analyze and compare the incorporation of the ethical-doctrinal and organizational principles into the social representations of the Unified Health System (SUS) among health professionals. Method a study grounded in Social Representations Theory, undertaken with 125 subjects, in eight health institutions in Rio de Janeiro. The free word association technique was applied to the induction term "SUS", the words evoked being analyzed using the techniques of the Vergès matrix and similitude analysis. Results it was identified that the professionals' social representations vary depending on their level of education, and that those with higher education represent a subgroup responsible for the process of representational change identified. This result was confirmed through similitude analysis. Conclusion a process of representational change is ongoing, in which it was ascertained that the professionals incorporated the principles of the SUS into their symbolic constructions. The similitude analysis was shown to be a fruitful technique for research in nursing. PMID:24553704

Integrable generalizations of non-linear multiple three-wave interaction models

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1989-07-01

Integrable generalizations of multiple three-wave interaction models in terms of r-matrix formulation are investigated. The Lax representations, complete sets of first integrals in involution are constructed, the quantization leading to Gaudin's models is discussed.

The Effects of Multiple Linked Representations on Students' Learning of Linear Relationships

ERIC Educational Resources Information Center

Ozgun-Koca, S. Asli

2004-01-01

The focus of this study was on comparing three groups of Algebra I 9th-year students: one group using linked representation software, the second group using similar software but with semi-linked representations, and the control group in order to examine the effects on students' understanding of linear relationships. Data collection methods…

Non-Abelian statistics of vortices with non-Abelian Dirac fermions.

PubMed

Yasui, Shigehiro; Hirono, Yuji; Itakura, Kazunori; Nitta, Muneto

2013-05-01

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined nonlocally by Majorana fermions located at two spatially separated vortices.

Irreducible representations of finitely generated nilpotent groups

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

Beloshapka, I V; Gorchinskiy, S O

2016-01-31

We prove that irreducible complex representations of finitely generated nilpotent groups are monomial if and only if they have finite weight, which was conjectured by Parshin. Note that we consider (possibly infinite-dimensional) representations without any topological structure. In addition, we prove that for certain induced representations, irreducibility is implied by Schur irreducibility. Both results are obtained in a more general form for representations over an arbitrary field. Bibliography: 21 titles.

Density-matrix-based algorithm for solving eigenvalue problems

NASA Astrophysics Data System (ADS)

Polizzi, Eric

2009-03-01

A fast and stable numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques and takes its inspiration from the contour integration and density-matrix representation in quantum mechanics. It will be shown that this algorithm—named FEAST—exhibits high efficiency, robustness, accuracy, and scalability on parallel architectures. Examples from electronic structure calculations of carbon nanotubes are presented, and numerical performances and capabilities are discussed.

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

Niccoli, G.

The antiperiodic transfer matrices associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra are analyzed by generalizing the approach introduced recently in the framework of Sklyanin's quantum separation of variables (SOV) for cyclic representations, spin-1/2 highest weight representations, and also for spin-1/2 representations of the 6-vertex reflection algebra. Such SOV approach allow us to derive exactly results which represent complicate tasks for more traditional methods based on Bethe ansatz and Baxter Q-operator. In particular, we both prove the completeness of the SOV characterization of the transfer matrix spectrum and its simplicity. Then, the derived characterization of local operatorsmore » by Sklyanin's quantum separate variables and the expression of the scalar products of separate states by determinant formulae allow us to compute the form factors of the local spin operators by one determinant formulae similar to those of the scalar products.« less

Color Sparse Representations for Image Processing: Review, Models, and Prospects.

PubMed

Barthélemy, Quentin; Larue, Anthony; Mars, Jérôme I

2015-11-01

Sparse representations have been extended to deal with color images composed of three channels. A review of dictionary-learning-based sparse representations for color images is made here, detailing the differences between the models, and comparing their results on the real and simulated data. These models are considered in a unifying framework that is based on the degrees of freedom of the linear filtering/transformation of the color channels. Moreover, this allows it to be shown that the scalar quaternionic linear model is equivalent to constrained matrix-based color filtering, which highlights the filtering implicitly applied through this model. Based on this reformulation, the new color filtering model is introduced, using unconstrained filters. In this model, spatial morphologies of color images are encoded by atoms, and colors are encoded by color filters. Color variability is no longer captured in increasing the dictionary size, but with color filters, this gives an efficient color representation.

Genetic Algorithm for Traveling Salesman Problem with Modified Cycle Crossover Operator

PubMed Central

Mohamd Shoukry, Alaa; Gani, Showkat

2017-01-01

Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions; however, they give good approximation usually in time. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. The genetic algorithm depends on selection criteria, crossover, and mutation operators. To tackle the traveling salesman problem using genetic algorithms, there are various representations such as binary, path, adjacency, ordinal, and matrix representations. In this article, we propose a new crossover operator for traveling salesman problem to minimize the total distance. This approach has been linked with path representation, which is the most natural way to represent a legal tour. Computational results are also reported with some traditional path representation methods like partially mapped and order crossovers along with new cycle crossover operator for some benchmark TSPLIB instances and found improvements. PMID:29209364

Genetic Algorithm for Traveling Salesman Problem with Modified Cycle Crossover Operator.

PubMed

Hussain, Abid; Muhammad, Yousaf Shad; Nauman Sajid, M; Hussain, Ijaz; Mohamd Shoukry, Alaa; Gani, Showkat

2017-01-01

Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions; however, they give good approximation usually in time. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. The genetic algorithm depends on selection criteria, crossover, and mutation operators. To tackle the traveling salesman problem using genetic algorithms, there are various representations such as binary, path, adjacency, ordinal, and matrix representations. In this article, we propose a new crossover operator for traveling salesman problem to minimize the total distance. This approach has been linked with path representation, which is the most natural way to represent a legal tour. Computational results are also reported with some traditional path representation methods like partially mapped and order crossovers along with new cycle crossover operator for some benchmark TSPLIB instances and found improvements.

Boundary Quantum Knizhnik-Zamolodchikov Equations and Bethe Vectors

NASA Astrophysics Data System (ADS)

Reshetikhin, Nicolai; Stokman, Jasper; Vlaar, Bart

2015-06-01

Solutions to boundary quantum Knizhnik-Zamolodchikov equations are constructed as bilateral sums involving "off-shell" Bethe vectors in case the reflection matrix is diagonal and only the 2-dimensional representation of is involved. We also consider their rational and classical degenerations.

Unique semantic space in the brain of each beholder predicts perceived similarity

PubMed Central

Charest, Ian; Kievit, Rogier A.; Schmitz, Taylor W.; Deca, Diana; Kriegeskorte, Nikolaus

2014-01-01

The unique way in which each of us perceives the world must arise from our brain representations. If brain imaging could reveal an individual’s unique mental representation, it could help us understand the biological substrate of our individual experiential worlds in mental health and disease. However, imaging studies of object vision have focused on commonalities between individuals rather than individual differences and on category averages rather than representations of particular objects. Here we investigate the individually unique component of brain representations of particular objects with functional MRI (fMRI). Subjects were presented with unfamiliar and personally meaningful object images while we measured their brain activity on two separate days. We characterized the representational geometry by the dissimilarity matrix of activity patterns elicited by particular object images. The representational geometry remained stable across scanning days and was unique in each individual in early visual cortex and human inferior temporal cortex (hIT). The hIT representation predicted perceived similarity as reflected in dissimilarity judgments. Importantly, hIT predicted the individually unique component of the judgments when the objects were personally meaningful. Our results suggest that hIT brain representational idiosyncrasies accessible to fMRI are expressed in an individual's perceptual judgments. The unique way each of us perceives the world thus might reflect the individually unique representation in high-level visual areas. PMID:25246586

Dioptric power: its nature and its representation in three- and four-dimensional space.

PubMed

Harris, W F

1997-06-01

Dioptric power expressed in the familiar three-component form of sphere, cylinder, and axis is unsuited to mathematical and statistical treatments; there is a particular class of power that cannot be represented in the familiar form; and it is possible that sphere, cylinder, and axis will prove inadequate in future clinical and research applications in optometry and ophthalmology. Dioptric power expressed as the four-component dioptric power matrix, however, overcomes these shortcomings. The intention in this paper is to provide a definitive statement on the nature, function, and mathematical representation of dioptric power in terms of the matrix and within the limitations of paraxial or linear optics. The approach is universal in the sense that its point of departure is not power of the familiar form (that is, of thin systems) but of systems in general (thick or thin). Familiar types of power are then seen within the context of power in general. Dioptric power is defined, for systems that may be thick and astigmatic, in terms of the ray transfer matrix. A functional definition is presented for dioptric power and its components: it defines the additive contribution of incident position to emergent direction of a ray passing through the system. For systems that are thin (or thin-equivalent) it becomes possible to describe an alternative and more familiar function; for such systems dioptric power can be regarded as the increase in reduced surface curvature of a wavefront brought about by the system as the wavefront passes through it. The curvital and torsional components of the power are explored in some detail. Dioptric power, at its most general, defines a four-dimensional inner product space called dioptric power space. The familiar types of power define a three-dimensional subspace called symmetric dioptric power space. For completeness a one-dimensional antisymmetric power space is also defined: it is orthogonal in four dimensions to symmetric dioptric power space. Various bases are defined for the spaces as are coordinate vectors with respect to them. Vectorial representations of power in the literature apply only to thin systems and are not obviously generalizable to systems in general. They are shown to be merely different coordinate representations of the same subspace, the space of symmetric powers. Some of the uses and disadvantages of the different representations are described. None of the coordinate vectors fully represent, by themselves, the essential character of dioptric power. Their use is limited to applications, such as finding a mean, where addition and scalar multiplication are involved. The full character of power is represented by the dioptric power matrix; it is in this form that power is appropriate for all mathematical relationships.

Knowledge of damage identification about tensegrities via flexibility disassembly

NASA Astrophysics Data System (ADS)

Jiang, Ge; Feng, Xiaodong; Du, Shigui

2017-12-01

Tensegrity structures composing of continuous cables and discrete struts are under tension and compression, respectively. In order to determine the damage extents of tensegrity structures, a new method for tensegrity structural damage identification is presented based on flexibility disassembly. To decompose a tensegrity structural flexibility matrix into the matrix represention of the connectivity between degress-of-freedoms and the diagonal matrix comprising of magnitude informations. Step 1: Calculate perturbation flexibility; Step 2: Compute the flexibility connectivity matrix and perturbation flexibility parameters; Step 3: Calculate the perturbation stiffness parameters. The efficiency of the proposed method is demonstrated by a numeical example comprising of 12 cables and 4 struts with pretensioned. Accurate identification of local damage depends on the availability of good measured data, an accurate and reasonable algorithm.

Sparse nonnegative matrix factorization with ℓ0-constraints

PubMed Central

Peharz, Robert; Pernkopf, Franz

2012-01-01

Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the ℓ1-norm of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the ℓ0-pseudo-norm. In this paper, we propose a framework for approximate NMF which constrains the ℓ0-norm of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches. PMID:22505792

Stochastic determination of matrix determinants

NASA Astrophysics Data System (ADS)

Dorn, Sebastian; Enßlin, Torsten A.

2015-07-01

Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations—matrices—acting on the data are often not accessible directly but are only represented indirectly in form of a computer routine. Such a routine implements the transformation a data vector undergoes under matrix multiplication. While efficient probing routines to estimate a matrix's diagonal or trace, based solely on such computationally affordable matrix-vector multiplications, are well known and frequently used in signal inference, there is no stochastic estimate for its determinant. We introduce a probing method for the logarithm of a determinant of a linear operator. Our method rests upon a reformulation of the log-determinant by an integral representation and the transformation of the involved terms into stochastic expressions. This stochastic determinant determination enables large-size applications in Bayesian inference, in particular evidence calculations, model comparison, and posterior determination.

Critique of Macro Flow/Damage Surface Representations for Metal Matrix Composites Using Micromechanics

NASA Technical Reports Server (NTRS)

Lissenden, Cliff J.; Arnold, Steven M.

1996-01-01

Guidance for the formulation of robust, multiaxial, constitutive models for advanced materials is provided by addressing theoretical and experimental issues using micromechanics. The multiaxial response of metal matrix composites, depicted in terms of macro flow/damage surfaces, is predicted at room and elevated temperatures using an analytical micromechanical model that includes viscoplastic matrix response as well as fiber-matrix debonding. Macro flow/damage surfaces (i.e., debonding envelopes, matrix threshold surfaces, macro 'yield' surfaces, surfaces of constant inelastic strain rate, and surfaces of constant dissipation rate) are determined for silicon carbide/titanium in three stress spaces. Residual stresses are shown to offset the centers of the flow/damage surfaces from the origin and their shape is significantly altered by debonding. The results indicate which type of flow/damage surfaces should be characterized and what loadings applied to provide the most meaningful experimental data for guiding theoretical model development and verification.

Stochastic determination of matrix determinants.

PubMed

Dorn, Sebastian; Ensslin, Torsten A

2015-07-01

Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations-matrices-acting on the data are often not accessible directly but are only represented indirectly in form of a computer routine. Such a routine implements the transformation a data vector undergoes under matrix multiplication. While efficient probing routines to estimate a matrix's diagonal or trace, based solely on such computationally affordable matrix-vector multiplications, are well known and frequently used in signal inference, there is no stochastic estimate for its determinant. We introduce a probing method for the logarithm of a determinant of a linear operator. Our method rests upon a reformulation of the log-determinant by an integral representation and the transformation of the involved terms into stochastic expressions. This stochastic determinant determination enables large-size applications in Bayesian inference, in particular evidence calculations, model comparison, and posterior determination.

Scalar products of Bethe vectors in models with {\\mathfrak{gl}}(2| 1) symmetry 1. Super-analog of Reshetikhin formula

NASA Astrophysics Data System (ADS)

Hutsalyuk, A.; Liashyk, A.; Pakuliak, S. Z.; Ragoucy, E.; Slavnov, N. A.

2016-11-01

We study the scalar products of Bethe vectors in integrable models solvable by the nested algebraic Bethe ansatz and possessing {gl}(2| 1) symmetry. Using explicit formulas of the monodromy matrix entries’ multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with {gl}(1| 1) symmetry. Dedicated to the memory of Petr Petrovich Kulish.

Elementary Treatment of Some Difficulties in the Construction of Irreducible Representations of the Rotation Group in Terms of Products of the Spin-1/2 Representation.

ERIC Educational Resources Information Center

Daniels, J. M.

1979-01-01

Explains why failure to distinguish clearly between three concepts: a vector, its components, and its representatives, renders understanding of how the representations of the rotation group are constructed from products of the spin-half representation, difficult to comprehend. (Author/GA)

Analytical representation of dynamical quantities in G W from a matrix resolvent

NASA Astrophysics Data System (ADS)

Gesenhues, J.; Nabok, D.; Rohlfing, M.; Draxl, C.

2017-12-01

The power of the G W formalism is, to a large extent, based on the explicit treatment of dynamical correlations in the self-energy. This dynamics is taken into account by calculating the energy dependence of the screened Coulomb interaction W , followed by a convolution with the Green's function G . In order to obtain the energy dependence of W the prevalent methods are plasmon-pole models and numerical integration techniques. In this paper, we discuss an alternative approach, in which the energy-dependent screening is calculated by determining the resolvent, which is set up from a matrix representation of the dielectric function. On the one hand, this refrains from a numerical energy convolution and allows one to actually write down the energy dependence of W explicitly (like in the plasmon-pole models). On the other hand, the method is at least as accurate as the numerical approaches due to its multipole nature. We discuss the theoretical setup in some detail, give insight into the computational aspects, and present results for Si, C, GaAs, and LiF. Finally, we argue that the analytic representability is not only useful for educational purposes but may also be of avail for the development of theory that goes beyond G W .

Quantum mechanics in noninertial reference frames: Violations of the nonrelativistic equivalence principle

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

Klink, W.H.; Wickramasekara, S., E-mail: wickrama@grinnell.edu; Department of Physics, Grinnell College, Grinnell, IA 50112

2014-01-15

In previous work we have developed a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group that includes transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as is the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. A special feature of these previously constructed representations is that they all respect the non-relativistic equivalence principle, wherein the fictitious forces associated with linear acceleration canmore » equivalently be described by gravitational forces. In this paper we exhibit a large class of cocycle representations of the Galilean line group that violate the equivalence principle. Nevertheless the classical mechanics analogue of these cocycle representations all respect the equivalence principle. -- Highlights: •A formulation of Galilean quantum mechanics in non-inertial reference frames is given. •The key concept is the Galilean line group, an infinite dimensional group. •A large class of general cocycle representations of the Galilean line group is constructed. •These representations show violations of the equivalence principle at the quantum level. •At the classical limit, no violations of the equivalence principle are detected.« less

Automatic detection of sweep-meshable volumes

DOEpatents

Tautges,; Timothy J. , White; David, R [Pittsburgh, PA

2006-05-23

A method of and software for automatically determining whether a mesh can be generated by sweeping for a representation of a geometric solid comprising: classifying surface mesh schemes for surfaces of the representation locally using surface vertex types; grouping mappable and submappable surfaces of the representation into chains; computing volume edge types for the representation; recursively traversing surfaces of the representation and grouping the surfaces into source, target, and linking surface lists; and checking traversal direction when traversing onto linking surfaces.

Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function.

PubMed

Poelmans, Ward; Van Raemdonck, Mario; Verstichel, Brecht; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Alcoba, Diego R; Bultinck, Patrick; Van Neck, Dimitri

2015-09-08

We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.

Low-dimensional representations of the three component loop braid group

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

Bruillard, Paul; Chang, Liang; Hong, Seung-Moon

2015-11-01

Motivated by physical and topological applications, we study representations of the group LB3 o motions of 3 unlinked oriented circles in R3. Our point of view is to regard the three strand braid group B3 as a subgroup of LB3 and study the problem of extending B3 representations. We introduce the notion of a standard extension and characterize B3 represenations admiting such an extension. In particular we show, using a classification result of Tuba and Wenzl, that every irreducible B3 representation of dimension at most 5 has a (standard) extension. We show that this result is sharp by exhibiting anmore » irreducible 6-dimensional B3 representation that has no extension (standard or otherwise). We obtain complete classifications of (1) irreducible 2-dimensional LB3 representations (2) extensions of irreducible B3 representations and (3) irreducible LB3 representations whose restriction to B3 has abelian image.« less

Braid group representation on quantum computation

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

Aziz, Ryan Kasyfil, E-mail: kasyfilryan@gmail.com; Muchtadi-Alamsyah, Intan, E-mail: ntan@math.itb.ac.id

2015-09-30

There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.

Graphics Flutter Analysis Methods, an interactive computing system at Lockheed-California Company

NASA Technical Reports Server (NTRS)

Radovcich, N. A.

1975-01-01

An interactive computer graphics system, Graphics Flutter Analysis Methods (GFAM), was developed to complement FAMAS, a matrix-oriented batch computing system, and other computer programs in performing complex numerical calculations using a fully integrated data management system. GFAM has many of the matrix operation capabilities found in FAMAS, but on a smaller scale, and is utilized when the analysis requires a high degree of interaction between the engineer and computer, and schedule constraints exclude the use of batch entry programs. Applications of GFAM to a variety of preliminary design, development design, and project modification programs suggest that interactive flutter analysis using matrix representations is a feasible and cost effective computing tool.

A penny-shaped crack in a filament reinforced matrix. 1: The filament model

NASA Technical Reports Server (NTRS)

Erdogan, F.; Pacella, A. H.

1973-01-01

The electrostatic problem of a penny-shaped crack in an elastic matrix which reinforced by filaments or fibers perpendicular to the plane of the crack was studied. The elastic filament model was developed for application to evaluation studies of the stress intensity factor along the periphery of the crack, the stresses in the filaments or fibers, and the interface shear between the matrix and the filaments or fibers. The requirements expected of the model are a sufficiently accurate representation of the filament and applicability to the interaction problems involving a cracked elastic continuum with multi-filament reinforcements. The technique for developing the model and numerical examples of it are shown.

Comments on higher rank Wilson loops in N$$ \\mathcal{N} $$ = 2∗

DOE PAGES

Liu, James T.; Zayas, Leopoldo A. Pando; Zhou, Shan

2018-01-01

For N = 2∗ theory with U(N) gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with n rows and k columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigenvalue distributions in various regimes of parameters (N, λ, n, k) where λ is the ’t Hooft coupling. In the large N limit we present analytic results for the leading and sub-leading contributions. In the particular cases of only one row or one column we reproduce previouslymore » known results for the totally symmetry and totally antisymmetric representations. We also extensively discusss the N = 4 limit of the N = 2∗ theory. While establishing these connections we clarify aspects of various orders of limits and how to relax them; we also find it useful to explicitly address details of the genus expansion. As a result, for the totally symmetric Wilson loop we find new contributions that improve the comparison with the dual holographic computation at one loop order in the appropriate regime.« less

Primary Teachers' Representational Practices: From Competency to Fluency

ERIC Educational Resources Information Center

Nichols, Kim; Stevenson, Michael; Hedberg, John; Gillies, Robyn Margaret

2016-01-01

Eighteen primary teachers across three conditions (Representational Fluency, Representational Agency, Comparison) received two days of training around an inquiry unit on plate tectonics replete with representations. The Representational Agency group also received training around the semiotic and material affordances of representations while the…

Inequivalent coherent state representations in group field theory

NASA Astrophysics Data System (ADS)

Kegeles, Alexander; Oriti, Daniele; Tomlin, Casey

2018-06-01

In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with an infinite number of degrees of freedom on compact manifolds. We also show that these representations break translation symmetry. Since such representations can be regarded as quantum gravitational systems with an infinite number of fundamental pre-geometric building blocks, they may be more suitable for the description of effective geometrical phases of the theory.

Groupwise registration of MR brain images with tumors.

PubMed

Tang, Zhenyu; Wu, Yihong; Fan, Yong

2017-08-04

A novel groupwise image registration framework is developed for registering MR brain images with tumors. Our method iteratively estimates a normal-appearance counterpart for each tumor image to be registered and constructs a directed graph (digraph) of normal-appearance images to guide the groupwise image registration. Particularly, our method maps each tumor image to its normal appearance counterpart by identifying and inpainting brain tumor regions with intensity information estimated using a low-rank plus sparse matrix decomposition based image representation technique. The estimated normal-appearance images are groupwisely registered to a group center image guided by a digraph of images so that the total length of 'image registration paths' to be the minimum, and then the original tumor images are warped to the group center image using the resulting deformation fields. We have evaluated our method based on both simulated and real MR brain tumor images. The registration results were evaluated with overlap measures of corresponding brain regions and average entropy of image intensity information, and Wilcoxon signed rank tests were adopted to compare different methods with respect to their regional overlap measures. Compared with a groupwise image registration method that is applied to normal-appearance images estimated using the traditional low-rank plus sparse matrix decomposition based image inpainting, our method achieved higher image registration accuracy with statistical significance (p  =  7.02  ×  10 -9 ).

Positive Feeling, Negative Meaning: Visualizing the Mental Representations of In-Group and Out-Group Smiles

PubMed Central

Dotsch, Ron; Wentura, Dirk

2016-01-01

Even though smiles are seen as universal facial expressions, research shows that there exist various kinds of smiles (i.e., affiliative smiles, dominant smiles). Accordingly, we suggest that there also exist various mental representations of smiles. Which representation is employed in cognition may depend on social factors, such as the smiling person’s group membership: Since in-group members are typically seen as more benevolent than out-group members, in-group smiles should be associated with more benevolent social meaning than those conveyed by out-group members. We visualized in-group and out-group smiles with reverse correlation image classification. These visualizations indicated that mental representations of in-group smiles indeed express more benevolent social meaning than those of out-group smiles. The affective meaning of these visualized smiles was not influenced by group membership. Importantly, the effect occurred even though participants were not instructed to attend to the nature of the smile, pointing to an automatic association between group membership and intention. PMID:26963621

New subspace methods for ATR

NASA Astrophysics Data System (ADS)

Zhang, Peng; Peng, Jing; Sims, S. Richard F.

2005-05-01

In ATR applications, each feature is a convolution of an image with a filter. It is important to use most discriminant features to produce compact representations. We propose two novel subspace methods for dimension reduction to address limitations associated with Fukunaga-Koontz Transform (FKT). The first method, Scatter-FKT, assumes that target is more homogeneous, while clutter can be anything other than target and anywhere. Thus, instead of estimating a clutter covariance matrix, Scatter-FKT computes a clutter scatter matrix that measures the spread of clutter from the target mean. We choose dimensions along which the difference in variation between target and clutter is most pronounced. When the target follows a Gaussian distribution, Scatter-FKT can be viewed as a generalization of FKT. The second method, Optimal Bayesian Subspace, is derived from the optimal Bayesian classifier. It selects dimensions such that the minimum Bayes error rate can be achieved. When both target and clutter follow Gaussian distributions, OBS computes optimal subspace representations. We compare our methods against FKT using character image as well as IR data.

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

NASA Technical Reports Server (NTRS)

Coutsias, Evangelos A.; Torres, David; Hagstrom, Thomas

1994-01-01

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Extraction of food consumption systems by nonnegative matrix factorization (NMF) for the assessment of food choices.

PubMed

Zetlaoui, Mélanie; Feinberg, Max; Verger, Philippe; Clémençon, Stephan

2011-12-01

In Western countries where food supply is satisfactory, consumers organize their diets around a large combination of foods. It is the purpose of this article to examine how recent nonnegative matrix factorization (NMF) techniques can be applied to food consumption data to understand these combinations. Such data are nonnegative by nature and of high dimension. The NMF model provides a representation of consumption data through latent vectors with nonnegative coefficients, that we call consumption systems (CS), in a small number. As the NMF approach may encourage sparsity of the data representation produced, the resulting CS are easily interpretable. Beyond the illustration of its properties we provide through a simple simulation result, the NMF method is applied to data issued from a French consumption survey. The numerical results thus obtained are displayed and thoroughly discussed. A clustering based on the k-means method is also achieved in the resulting latent consumption space, to recover food consumption patterns easily usable for nutritionists. © 2011, The International Biometric Society.

Nonnegative matrix factorization and sparse representation for the automated detection of periodic limb movements in sleep.

PubMed

Shokrollahi, Mehrnaz; Krishnan, Sridhar; Dopsa, Dustin D; Muir, Ryan T; Black, Sandra E; Swartz, Richard H; Murray, Brian J; Boulos, Mark I

2016-11-01

Stroke is a leading cause of death and disability in adults, and incurs a significant economic burden to society. Periodic limb movements (PLMs) in sleep are repetitive movements involving the great toe, ankle, and hip. Evolving evidence suggests that PLMs may be associated with high blood pressure and stroke, but this relationship remains underexplored. Several issues limit the study of PLMs including the need to manually score them, which is time-consuming and costly. For this reason, we developed a novel automated method for nocturnal PLM detection, which was shown to be correlated with (a) the manually scored PLM index on polysomnography, and (b) white matter hyperintensities on brain imaging, which have been demonstrated to be associated with PLMs. Our proposed algorithm consists of three main stages: (1) representing the signal in the time-frequency plane using time-frequency matrices (TFM), (2) applying K-nonnegative matrix factorization technique to decompose the TFM matrix into its significant components, and (3) applying kernel sparse representation for classification (KSRC) to the decomposed signal. Our approach was applied to a dataset that consisted of 65 subjects who underwent polysomnography. An overall classification of 97 % was achieved for discrimination of the aforementioned signals, demonstrating the potential of the presented method.

Exact solution of corner-modified banded block-Toeplitz eigensystems

NASA Astrophysics Data System (ADS)

Cobanera, Emilio; Alase, Abhijeet; Ortiz, Gerardo; Viola, Lorenza

2017-05-01

Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded block quasi-Toeplitz matrices that we call corner-modified. Corner modifications of otherwise arbitrary banded block-Toeplitz matrices capture the effect of boundary conditions and the associated breakdown of translational invariance. Our algorithm leverages the interplay between a non-standard, projector-based method of kernel determination (physically, a bulk-boundary separation) and families of linear representations of the algebra of matrix Laurent polynomials. Thanks to the fact that these representations act on infinite-dimensional carrier spaces in which translation symmetry is restored, it becomes possible to determine the eigensystem of an auxiliary projected block-Laurent matrix. This results in an analytic eigenvector Ansatz, independent of the system size, which we prove is guaranteed to contain the full solution of the original finite-dimensional problem. The actual solution is then obtained by imposing compatibility with a boundary matrix, whose shape is also independent of system size. As an application, we show analytically that eigenvectors of short-ranged fermionic tight-binding models may display power-law corrections to exponential behavior, and demonstrate the phenomenon for the paradigmatic Majorana chain of Kitaev.

Quantum mechanics in noninertial reference frames: Relativistic accelerations and fictitious forces

NASA Astrophysics Data System (ADS)

Klink, W. H.; Wickramasekara, S.

2016-06-01

One-particle systems in relativistically accelerating reference frames can be associated with a class of unitary representations of the group of arbitrary coordinate transformations, an extension of the Wigner-Bargmann definition of particles as the physical realization of unitary irreducible representations of the Poincaré group. Representations of the group of arbitrary coordinate transformations become necessary to define unitary operators implementing relativistic acceleration transformations in quantum theory because, unlike in the Galilean case, the relativistic acceleration transformations do not themselves form a group. The momentum operators that follow from these representations show how the fictitious forces in noninertial reference frames are generated in quantum theory.

Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to theoretical spectra.

PubMed

Desbiens, Raphaël; Tremblay, Pierre; Genest, Jérôme; Bouchard, Jean-Pierre

2006-01-20

The instrument line shape (ILS) of a Fourier-transform spectrometer is expressed in a matrix form. For all line shape effects that scale with wavenumber, the ILS matrix is shown to be transposed in the spectral and interferogram domains. The novel representation of the ILS matrix in the interferogram domain yields an insightful physical interpretation of the underlying process producing self-apodization. Working in the interferogram domain circumvents the problem of taking into account the effects of finite optical path difference and permits a proper discretization of the equations. A fast algorithm in O(N log2 N), based on the fractional Fourier transform, is introduced that permits the application of a constant resolving power line shape to theoretical spectra or forward models. The ILS integration formalism is validated with experimental data.

Diffeomorphism Group Representations in Relativistic Quantum Field Theory

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

Goldin, Gerald A.; Sharp, David H.

We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.

The topological particle and Morse theory

NASA Astrophysics Data System (ADS)

Rogers, Alice

2000-09-01

Canonical BRST quantization of the topological particle defined by a Morse function h is described. Stochastic calculus, using Brownian paths which implement the WKB method in a new way providing rigorous tunnelling results even in curved space, is used to give an explicit and simple expression for the matrix elements of the evolution operator for the BRST Hamiltonian. These matrix elements lead to a representation of the manifold cohomology in terms of critical points of h along lines developed by Witten (Witten E 1982 J. Diff. Geom. 17 661-92).

Construction of the Fock Matrix on a Grid-Based Molecular Orbital Basis Using GPGPUs.

PubMed

Losilla, Sergio A; Watson, Mark A; Aspuru-Guzik, Alán; Sundholm, Dage

2015-05-12

We present a GPGPU implementation of the construction of the Fock matrix in the molecular orbital basis using the fully numerical, grid-based bubbles representation. For a test set of molecules containing up to 90 electrons, the total Hartree-Fock energies obtained from reference GTO-based calculations are reproduced within 10(-4) Eh to 10(-8) Eh for most of the molecules studied. Despite the very large number of arithmetic operations involved, the high performance obtained made the calculations possible on a single Nvidia Tesla K40 GPGPU card.

Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})

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

Roche, Ph., E-mail: philippe.roche@univ-montp2.fr

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

Integrable hierarchies of Heisenberg ferromagnet equation

NASA Astrophysics Data System (ADS)

Nugmanova, G.; Azimkhanova, A.

2016-08-01

In this paper we consider the coupled Kadomtsev-Petviashvili system. From compatibility conditions we obtain the form of matrix operators. After using a gauge transformation, obtained a new type of Lax representation for the hierarchy of Heisenberg ferromagnet equation, which is equivalent to the gauge coupled Kadomtsev-Petviashvili system.

Modified Stereographic Projections of Point Groups and Diagrams of Their Irreducible Representations

NASA Astrophysics Data System (ADS)

Kettle, Sidney F. A.

1999-05-01

Modified versions of the stereographic projections of the point groups of classical crystallography are presented. They show the consequences of symmetry operations rather than emphasizing the existence of symmetry elements. These projections may be used to give pictures of the irreducible representations of point groups and several examples are given. Such pictures add physical reality to the irreducible representations and facilitate simple lecture demonstration of many important aspects and applications of group theory in chemistry.

Beyond one-size-fits-all: Tailoring diversity approaches to the representation of social groups.

PubMed

Apfelbaum, Evan P; Stephens, Nicole M; Reagans, Ray E

2016-10-01

When and why do organizational diversity approaches that highlight the importance of social group differences (vs. equality) help stigmatized groups succeed? We theorize that social group members' numerical representation in an organization, compared with the majority group, influences concerns about their distinctiveness, and consequently, whether diversity approaches are effective. We combine laboratory and field methods to evaluate this theory in a professional setting, in which White women are moderately represented and Black individuals are represented in very small numbers. We expect that focusing on differences (vs. equality) will lead to greater performance and persistence among White women, yet less among Black individuals. First, we demonstrate that Black individuals report greater representation-based concerns than White women (Study 1). Next, we observe that tailoring diversity approaches to these concerns yields greater performance and persistence (Studies 2 and 3). We then manipulate social groups' perceived representation and find that highlighting differences (vs. equality) is more effective when groups' representation is moderate, but less effective when groups' representation is very low (Study 4). Finally, we content-code the diversity statements of 151 major U.S. law firms and find that firms that emphasize differences have lower attrition rates among White women, whereas firms that emphasize equality have lower attrition rates among racial minorities (Study 5). (PsycINFO Database Record (c) 2016 APA, all rights reserved).

On inducing finite dimensional physical field representations for massless particles in even dimensions

NASA Technical Reports Server (NTRS)

Bhansali, Vineer

1993-01-01

Assuming trivial action of Euclidean translations, the method of induced representations is used to derive a correspondence between massless field representations transforming under the full generalized even dimensional Lorentz group, and highest weight states of the relevant little group. This gives a connection between 'helicity' and 'chirality' in all dimensions. Restrictions on 'gauge independent' representations for physical particles that this induction imposes are also stated.

Mexican High School Students' Social Representations of Mathematics, Its Teaching and Learning

ERIC Educational Resources Information Center

Martínez-Sierra, Gustavo; Miranda-Tirado, Marisa

2015-01-01

This paper reports a qualitative research that identifies Mexican high school students' social representations of mathematics. For this purpose, the social representations of "mathematics", "learning mathematics" and "teaching mathematics" were identified in a group of 50 students. Focus group interviews were carried…

Flat bases of invariant polynomials and P-matrices of E{sub 7} and E{sub 8}

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

Talamini, Vittorino

2010-02-15

Let G be a compact group of linear transformations of a Euclidean space V. The G-invariant C{sup {infinity}} functions can be expressed as C{sup {infinity}} functions of a finite basic set of G-invariant homogeneous polynomials, sometimes called an integrity basis. The mathematical description of the orbit space V/G depends on the integrity basis too: it is realized through polynomial equations and inequalities expressing rank and positive semidefiniteness conditions of the P-matrix, a real symmetric matrix determined by the integrity basis. The choice of the basic set of G-invariant homogeneous polynomials forming an integrity basis is not unique, so it ismore » not unique the mathematical description of the orbit space too. If G is an irreducible finite reflection group, Saito et al. [Commun. Algebra 8, 373 (1980)] characterized some special basic sets of G-invariant homogeneous polynomials that they called flat. They also found explicitly the flat basic sets of invariant homogeneous polynomials of all the irreducible finite reflection groups except of the two largest groups E{sub 7} and E{sub 8}. In this paper the flat basic sets of invariant homogeneous polynomials of E{sub 7} and E{sub 8} and the corresponding P-matrices are determined explicitly. Using the results here reported one is able to determine easily the P-matrices corresponding to any other integrity basis of E{sub 7} or E{sub 8}. From the P-matrices one may then write down the equations and inequalities defining the orbit spaces of E{sub 7} and E{sub 8} relatively to a flat basis or to any other integrity basis. The results here obtained may be employed concretely to study analytically the symmetry breaking in all theories where the symmetry group is one of the finite reflection groups E{sub 7} and E{sub 8} or one of the Lie groups E{sub 7} and E{sub 8} in their adjoint representations.« less

Group sparse multiview patch alignment framework with view consistency for image classification.

PubMed

Gui, Jie; Tao, Dacheng; Sun, Zhenan; Luo, Yong; You, Xinge; Tang, Yuan Yan

2014-07-01

No single feature can satisfactorily characterize the semantic concepts of an image. Multiview learning aims to unify different kinds of features to produce a consensual and efficient representation. This paper redefines part optimization in the patch alignment framework (PAF) and develops a group sparse multiview patch alignment framework (GSM-PAF). The new part optimization considers not only the complementary properties of different views, but also view consistency. In particular, view consistency models the correlations between all possible combinations of any two kinds of view. In contrast to conventional dimensionality reduction algorithms that perform feature extraction and feature selection independently, GSM-PAF enjoys joint feature extraction and feature selection by exploiting l(2,1)-norm on the projection matrix to achieve row sparsity, which leads to the simultaneous selection of relevant features and learning transformation, and thus makes the algorithm more discriminative. Experiments on two real-world image data sets demonstrate the effectiveness of GSM-PAF for image classification.

Speeded Probed Recall Is Affected by Grouping.

PubMed

Morra, Sergio; Epidendio, Valentina

2015-01-01

Most of the evidence from previous studies on speeded probed recall supported primacy-gradient models of serial order representation. Two experiments investigated the effect of grouping on speeded probed recall. Six-word lists, followed by a number between 1 and 6, were presented for speeded recall of the word in the position indicated by the number. Grouping was manipulated through interstimulus intervals. In both experiments, a significant Position × Grouping interaction was found in RT. It is concluded that the results are not consistent with models of order representation only based on a primacy gradient. Possible alternative representations of serial order are also discussed; a case is made for a holistic order representation.

Quantum mechanics in noninertial reference frames: Relativistic accelerations and fictitious forces

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

Klink, W.H., E-mail: william-klink@uiowa.edu; Wickramasekara, S., E-mail: wickrama@grinnell.edu

2016-06-15

One-particle systems in relativistically accelerating reference frames can be associated with a class of unitary representations of the group of arbitrary coordinate transformations, an extension of the Wigner–Bargmann definition of particles as the physical realization of unitary irreducible representations of the Poincaré group. Representations of the group of arbitrary coordinate transformations become necessary to define unitary operators implementing relativistic acceleration transformations in quantum theory because, unlike in the Galilean case, the relativistic acceleration transformations do not themselves form a group. The momentum operators that follow from these representations show how the fictitious forces in noninertial reference frames are generated inmore » quantum theory.« less

Tensor and Spin Representations of SO(4) and Discrete Quantum Gravity

NASA Astrophysics Data System (ADS)

Lorente, M.; Kramer, P.

Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the corresponding algebra, the unitary representations of the group in terms of the generalized Euler angles are constructed. These mathematical results help us to a more complete description of the Barret-Crane model in Quantum Gravity. In particular a complete realization of the weight function for the partition function is given and a new geometrical interpretation of the asymptotic limit for the Regge action is presented.

Team Action Imagery and Team Cognition: Imagery of Game Situations and Required Team Actions Promotes a Functional Structure in Players' Representations of Team-Level Tactics.

PubMed

Frank, Cornelia; Linstromberg, Gian-Luca; Hennig, Linda; Heinen, Thomas; Schack, Thomas

2018-02-01

A team's cognitions of interpersonally coordinated actions are a crucial component for successful team performance. Here, we present an approach to practice team action by way of imagery and examine its impact on team cognitions in long-term memory. We investigated the impact of a 4-week team action imagery intervention on futsal players' mental representations of team-level tactics. Skilled futsal players were assigned to either an imagery training group or a no imagery training control group. Participants in the imagery training group practiced four team-level tactics by imagining team actions in specific game situations for three times a week. Results revealed that the imagery training group's representations were more similar to that of an expert representation after the intervention compared with the control group. This study indicates that team action imagery training can have a significant impact on players' tactical skill representations and thus order formation in long-term memory.

Precision pointing of scientific instruments on space station: The LFGGREC perspective

NASA Technical Reports Server (NTRS)

Blackwell, C. C.; Sirlin, S. W.; Laskin, R. A.

1988-01-01

An application of Lyapunov function-gradient-generated robustness-enhancing control (LFGGREC) is explored. The attention is directed to a reduced-complexity representation of the pointing problem presented by the system composed of the Space Infrared Telescope Facility gimbaled to a space station configuration. Uncertainties include disturbance forces applied in the crew compartment area and control moments applied to adjacent scientific payloads (modeled as disturbance moments). Also included are uncertainties in gimbal friction and in the structural component of the system, as reflected in the inertia matrix, the damping matrix, and the stiffness matrix, and the effect of the ignored vibrational dynamics of the structure. The emphasis is on the adaptation of LFGGREC to this particular configuration and on the robustness analysis.

Quantity processing in deaf and hard of hearing children: evidence from symbolic and nonsymbolic comparison tasks.

PubMed

Rodríguez-Santos, José Miguel; Calleja, Marina; García-Orza, Javier; Iza, Mauricio; Damas, Jesús

2014-01-01

Deaf children usually achieve lower scores on numerical tasks than normally hearing peers. Explanations for mathematical disabilities in hearing children are based on quantity representation deficits (Geary, 1994) or on deficits in accessing these representations (Rousselle & Noël, 2008). The present study aimed to verify, by means of symbolic (Arabic digits) and nonsymbolic (dot constellations and hands) magnitude comparison tasks, whether deaf children show deficits in representations or in accessing numerical representations. The study participants were 10 prelocutive deaf children and 10 normally hearing children. Numerical distance and magnitude were manipulated. Response time (RT) analysis showed similar magnitude and distance effects in both groups on the 3 tasks. However, slower RTs were observed among the deaf participants on the symbolic task alone. These results suggest that although both groups' quantity representations were similar, the deaf group experienced a delay in accessing representations from symbolic codes.

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

Representation: a call to action for allied health professionals.

PubMed

Rourke, K M; Kuck, L; Rosenbloom, J; Wilson, S L

2000-01-01

The Coalition of Allied Health Leadership (CAHL) Representation Project committee examined the representation of allied health professionals in political and other policy-making groups and found it both fragmented and lacking. The benefits to individuals participating in such groups, as well as to the allied health profession as a whole and to the groups themselves, are described. Individuals are urged to participate, and the means to do so are presented.

Finding a Hadamard matrix by simulated annealing of spin vectors

NASA Astrophysics Data System (ADS)

Bayu Suksmono, Andriyan

2017-05-01

Reformulation of a combinatorial problem into optimization of a statistical-mechanics system enables finding a better solution using heuristics derived from a physical process, such as by the simulated annealing (SA). In this paper, we present a Hadamard matrix (H-matrix) searching method based on the SA on an Ising model. By equivalence, an H-matrix can be converted into a seminormalized Hadamard (SH) matrix, whose first column is unit vector and the rest ones are vectors with equal number of -1 and +1 called SH-vectors. We define SH spin vectors as representation of the SH vectors, which play a similar role as the spins on Ising model. The topology of the lattice is generalized into a graph, whose edges represent orthogonality relationship among the SH spin vectors. Starting from a randomly generated quasi H-matrix Q, which is a matrix similar to the SH-matrix without imposing orthogonality, we perform the SA. The transitions of Q are conducted by random exchange of {+, -} spin-pair within the SH-spin vectors that follow the Metropolis update rule. Upon transition toward zeroth energy, the Q-matrix is evolved following a Markov chain toward an orthogonal matrix, at which the H-matrix is said to be found. We demonstrate the capability of the proposed method to find some low-order H-matrices, including the ones that cannot trivially be constructed by the Sylvester method.

Cups and Downs

ERIC Educational Resources Information Center

Stewart, Ian

2012-01-01

Martin Gardner wrote about a coin-flipping trick, performed by a blindfolded magician. The paper analyses this trick, and compares it with a similar trick using three cups flipped in pairs. Several different methods of analysis are discussed, including a graphical analysis of the state space and a representation in terms of a matrix. These methods…

The Circumplex Pattern of the Life Styles Inventory: A Reanalysis.

ERIC Educational Resources Information Center

Levin, Joseph

1991-01-01

A reanalysis of the intercorrelation matrix from a principal components analysis of the Life Styles Inventory was conducted using a Canadian sample. Using nonmetric multidimensional scaling, analyses show an almost perfect circumplex pattern. Results illustrate the inadequacy of factor analytic procedures for the analysis and representation of a…

A Vector Representation for Thermodynamic Relationships

ERIC Educational Resources Information Center

Pogliani, Lionello

2006-01-01

The existing vector formalism method for thermodynamic relationship maintains tractability and uses accessible mathematics, which can be seen as a diverting and entertaining step into the mathematical formalism of thermodynamics and as an elementary application of matrix algebra. The method is based on ideas and operations apt to improve the…

Yang-Baxter maps, discrete integrable equations and quantum groups

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Sergeev, Sergey M.

2018-01-01

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang-Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper we present detailed considerations of the above scheme on the example of the algebra Uq (sl (2)) leading to discrete Liouville equations, however the approach is rather general and can be applied to any quantized Lie algebra.

Cluster structure of EU-15 countries derived from the correlation matrix analysis of macroeconomic index fluctuations

NASA Astrophysics Data System (ADS)

Gligor, M.; Ausloos, M.

2007-05-01

The statistical distances between countries, calculated for various moving average time windows, are mapped into the ultrametric subdominant space as in classical Minimal Spanning Tree methods. The Moving Average Minimal Length Path (MAMLP) algorithm allows a decoupling of fluctuations with respect to the mass center of the system from the movement of the mass center itself. A Hamiltonian representation given by a factor graph is used and plays the role of cost function. The present analysis pertains to 11 macroeconomic (ME) indicators, namely the GDP (x1), Final Consumption Expenditure (x2), Gross Capital Formation (x3), Net Exports (x4), Consumer Price Index (y1), Rates of Interest of the Central Banks (y2), Labour Force (z1), Unemployment (z2), GDP/hour worked (z3), GDP/capita (w1) and Gini coefficient (w2). The target group of countries is composed of 15 EU countries, data taken between 1995 and 2004. By two different methods (the Bipartite Factor Graph Analysis and the Correlation Matrix Eigensystem Analysis) it is found that the strongly correlated countries with respect to the macroeconomic indicators fluctuations can be partitioned into stable clusters.

Multiview alignment hashing for efficient image search.

PubMed

Liu, Li; Yu, Mengyang; Shao, Ling

2015-03-01

Hashing is a popular and efficient method for nearest neighbor search in large-scale data spaces by embedding high-dimensional feature descriptors into a similarity preserving Hamming space with a low dimension. For most hashing methods, the performance of retrieval heavily depends on the choice of the high-dimensional feature descriptor. Furthermore, a single type of feature cannot be descriptive enough for different images when it is used for hashing. Thus, how to combine multiple representations for learning effective hashing functions is an imminent task. In this paper, we present a novel unsupervised multiview alignment hashing approach based on regularized kernel nonnegative matrix factorization, which can find a compact representation uncovering the hidden semantics and simultaneously respecting the joint probability distribution of data. In particular, we aim to seek a matrix factorization to effectively fuse the multiple information sources meanwhile discarding the feature redundancy. Since the raised problem is regarded as nonconvex and discrete, our objective function is then optimized via an alternate way with relaxation and converges to a locally optimal solution. After finding the low-dimensional representation, the hashing functions are finally obtained through multivariable logistic regression. The proposed method is systematically evaluated on three data sets: 1) Caltech-256; 2) CIFAR-10; and 3) CIFAR-20, and the results show that our method significantly outperforms the state-of-the-art multiview hashing techniques.

A General Exponential Framework for Dimensionality Reduction.

PubMed

Wang, Su-Jing; Yan, Shuicheng; Yang, Jian; Zhou, Chun-Guang; Fu, Xiaolan

2014-02-01

As a general framework, Laplacian embedding, based on a pairwise similarity matrix, infers low dimensional representations from high dimensional data. However, it generally suffers from three issues: 1) algorithmic performance is sensitive to the size of neighbors; 2) the algorithm encounters the well known small sample size (SSS) problem; and 3) the algorithm de-emphasizes small distance pairs. To address these issues, here we propose exponential embedding using matrix exponential and provide a general framework for dimensionality reduction. In the framework, the matrix exponential can be roughly interpreted by the random walk over the feature similarity matrix, and thus is more robust. The positive definite property of matrix exponential deals with the SSS problem. The behavior of the decay function of exponential embedding is more significant in emphasizing small distance pairs. Under this framework, we apply matrix exponential to extend many popular Laplacian embedding algorithms, e.g., locality preserving projections, unsupervised discriminant projections, and marginal fisher analysis. Experiments conducted on the synthesized data, UCI, and the Georgia Tech face database show that the proposed new framework can well address the issues mentioned above.

Matrix basis for plane and modal waves in a Timoshenko beam.

PubMed

Claeyssen, Julio Cesar Ruiz; Tolfo, Daniela de Rosso; Tonetto, Leticia

2016-11-01

Plane waves and modal waves of the Timoshenko beam model are characterized in closed form by introducing robust matrix basis that behave according to the nature of frequency and wave or modal numbers. These new characterizations are given in terms of a finite number of coupling matrices and closed form generating scalar functions. Through Liouville's technique, these latter are well behaved at critical or static situations. Eigenanalysis is formulated for exponential and modal waves. Modal waves are superposition of four plane waves, but there are plane waves that cannot be modal waves. Reflected and transmitted waves at an interface point are formulated in matrix terms, regardless of having a conservative or a dissipative situation. The matrix representation of modal waves is used in a crack problem for determining the reflected and transmitted matrices. Their euclidean norms are seen to be dominated by certain components at low and high frequencies. The matrix basis technique is also used with a non-local Timoshenko model and with the wave interaction with a boundary. The matrix basis allows to characterize reflected and transmitted waves in spectral and non-spectral form.

Audio Motor Training at the Foot Level Improves Space Representation.

PubMed

Aggius-Vella, Elena; Campus, Claudio; Finocchietti, Sara; Gori, Monica

2017-01-01

Spatial representation is developed thanks to the integration of visual signals with the other senses. It has been shown that the lack of vision compromises the development of some spatial representations. In this study we tested the effect of a new rehabilitation device called ABBI (Audio Bracelet for Blind Interaction) to improve space representation. ABBI produces an audio feedback linked to body movement. Previous studies from our group showed that this device improves the spatial representation of space in early blind adults around the upper part of the body. Here we evaluate whether the audio motor feedback produced by ABBI can also improve audio spatial representation of sighted individuals in the space around the legs. Forty five blindfolded sighted subjects participated in the study, subdivided into three experimental groups. An audio space localization (front-back discrimination) task was performed twice by all groups of subjects before and after different kind of training conditions. A group (experimental) performed an audio-motor training with the ABBI device placed on their foot. Another group (control) performed a free motor activity without audio feedback associated with body movement. The other group (control) passively listened to the ABBI sound moved at foot level by the experimenter without producing any body movement. Results showed that only the experimental group, which performed the training with the audio-motor feedback, showed an improvement in accuracy for sound discrimination. No improvement was observed for the two control groups. These findings suggest that the audio-motor training with ABBI improves audio space perception also in the space around the legs in sighted individuals. This result provides important inputs for the rehabilitation of the space representations in the lower part of the body.

Audio Motor Training at the Foot Level Improves Space Representation

PubMed Central

Aggius-Vella, Elena; Campus, Claudio; Finocchietti, Sara; Gori, Monica

2017-01-01

Spatial representation is developed thanks to the integration of visual signals with the other senses. It has been shown that the lack of vision compromises the development of some spatial representations. In this study we tested the effect of a new rehabilitation device called ABBI (Audio Bracelet for Blind Interaction) to improve space representation. ABBI produces an audio feedback linked to body movement. Previous studies from our group showed that this device improves the spatial representation of space in early blind adults around the upper part of the body. Here we evaluate whether the audio motor feedback produced by ABBI can also improve audio spatial representation of sighted individuals in the space around the legs. Forty five blindfolded sighted subjects participated in the study, subdivided into three experimental groups. An audio space localization (front-back discrimination) task was performed twice by all groups of subjects before and after different kind of training conditions. A group (experimental) performed an audio-motor training with the ABBI device placed on their foot. Another group (control) performed a free motor activity without audio feedback associated with body movement. The other group (control) passively listened to the ABBI sound moved at foot level by the experimenter without producing any body movement. Results showed that only the experimental group, which performed the training with the audio-motor feedback, showed an improvement in accuracy for sound discrimination. No improvement was observed for the two control groups. These findings suggest that the audio-motor training with ABBI improves audio space perception also in the space around the legs in sighted individuals. This result provides important inputs for the rehabilitation of the space representations in the lower part of the body. PMID:29326564

Local matrix learning in clustering and applications for manifold visualization.

PubMed

Arnonkijpanich, Banchar; Hasenfuss, Alexander; Hammer, Barbara

2010-05-01

Electronic data sets are increasing rapidly with respect to both, size of the data sets and data resolution, i.e. dimensionality, such that adequate data inspection and data visualization have become central issues of data mining. In this article, we present an extension of classical clustering schemes by local matrix adaptation, which allows a better representation of data by means of clusters with an arbitrary spherical shape. Unlike previous proposals, the method is derived from a global cost function. The focus of this article is to demonstrate the applicability of this matrix clustering scheme to low-dimensional data embedding for data inspection. The proposed method is based on matrix learning for neural gas and manifold charting. This provides an explicit mapping of a given high-dimensional data space to low dimensionality. We demonstrate the usefulness of this method for data inspection and manifold visualization. 2009 Elsevier Ltd. All rights reserved.

Representational neglect for words as revealed by bisection tasks.

PubMed

Arduino, Lisa S; Marinelli, Chiara Valeria; Pasotti, Fabrizio; Ferrè, Elisa Raffaella; Bottini, Gabriella

2012-03-01

In the present study, we showed that a representational disorder for words can dissociate from both representational neglect for objects and neglect dyslexia. This study involved 14 brain-damaged patients with left unilateral spatial neglect and a group of normal subjects. Patients were divided into four groups based on presence of left neglect dyslexia and representational neglect for non-verbal material, as evaluated by the Clock Drawing test. The patients were presented with bisection tasks for words and lines. The word bisection tasks (with words of five and seven letters) comprised the following: (1) representational bisection: the experimenter pronounced a word and then asked the patient to name the letter in the middle position; (2) visual bisection: same as (1) with stimuli presented visually; and (3) motor bisection: the patient was asked to cross out the letter in the middle position. The standard line bisection task was presented using lines of different length. Consistent with the literature, long lines were bisected to the right and short lines, rendered comparable in length to the words of the word bisection test, deviated to the left (crossover effect). Both patients and controls showed the same leftward bias on words in the visual and motor bisection conditions. A significant difference emerged between the groups only in the case of the representational bisection task, whereas the group exhibiting neglect dyslexia associated with representational neglect for objects showed a significant rightward bias, while the other three patient groups and the controls showed a leftward bisection bias. Neither the presence of neglect alone nor the presence of visual neglect dyslexia was sufficient to produce a specific disorder in mental imagery. These results demonstrate a specific representational neglect for words independent of both representational neglect and neglect dyslexia. ©2011 The British Psychological Society.

Group-sparse representation with dictionary learning for medical image denoising and fusion.

PubMed

Li, Shutao; Yin, Haitao; Fang, Leyuan

2012-12-01

Recently, sparse representation has attracted a lot of interest in various areas. However, the standard sparse representation does not consider the intrinsic structure, i.e., the nonzero elements occur in clusters, called group sparsity. Furthermore, there is no dictionary learning method for group sparse representation considering the geometrical structure of space spanned by atoms. In this paper, we propose a novel dictionary learning method, called Dictionary Learning with Group Sparsity and Graph Regularization (DL-GSGR). First, the geometrical structure of atoms is modeled as the graph regularization. Then, combining group sparsity and graph regularization, the DL-GSGR is presented, which is solved by alternating the group sparse coding and dictionary updating. In this way, the group coherence of learned dictionary can be enforced small enough such that any signal can be group sparse coded effectively. Finally, group sparse representation with DL-GSGR is applied to 3-D medical image denoising and image fusion. Specifically, in 3-D medical image denoising, a 3-D processing mechanism (using the similarity among nearby slices) and temporal regularization (to perverse the correlations across nearby slices) are exploited. The experimental results on 3-D image denoising and image fusion demonstrate the superiority of our proposed denoising and fusion approaches.

Beyond Low-Rank Representations: Orthogonal clustering basis reconstruction with optimized graph structure for multi-view spectral clustering.

PubMed

Wang, Yang; Wu, Lin

2018-07-01

Low-Rank Representation (LRR) is arguably one of the most powerful paradigms for Multi-view spectral clustering, which elegantly encodes the multi-view local graph/manifold structures into an intrinsic low-rank self-expressive data similarity embedded in high-dimensional space, to yield a better graph partition than their single-view counterparts. In this paper we revisit it with a fundamentally different perspective by discovering LRR as essentially a latent clustered orthogonal projection based representation winged with an optimized local graph structure for spectral clustering; each column of the representation is fundamentally a cluster basis orthogonal to others to indicate its members, which intuitively projects the view-specific feature representation to be the one spanned by all orthogonal basis to characterize the cluster structures. Upon this finding, we propose our technique with the following: (1) We decompose LRR into latent clustered orthogonal representation via low-rank matrix factorization, to encode the more flexible cluster structures than LRR over primal data objects; (2) We convert the problem of LRR into that of simultaneously learning orthogonal clustered representation and optimized local graph structure for each view; (3) The learned orthogonal clustered representations and local graph structures enjoy the same magnitude for multi-view, so that the ideal multi-view consensus can be readily achieved. The experiments over multi-view datasets validate its superiority, especially over recent state-of-the-art LRR models. Copyright © 2018 Elsevier Ltd. All rights reserved.

Random Versus Blocked Practice to Enhance Mental Representation in Golf Putting.

PubMed

Fazeli, Davoud; Taheri, HamidReza; Saberi Kakhki, Alireza

2017-06-01

The purpose of this study was to investigate changes in mental representation from either random or blocked practice when engaged in golf putting. Thirty participants were randomly assigned to random practice, blocked practice, and no-practice groups. First, we measured novice golfers' initial mental representation levels and required them to perform 18 putting trials as a pre-test. We then asked random and blocked groups to practice in accordance with their group assignment for six consecutive days (10 blocks each day, 18 trials each). A week after the last practice session, we re-measured all participants' final mental representation levels and required them to perform 18 putting trials to evaluate learning retention through practice. While those engaged in the random practice method putted more poorly during acquisition (i.e., practice) than those in blocked practice, the random practice group experienced more accurate retention during the final putting trials, and they showed a more structured mental representation than those in blocked practice, one that was more similar to that of skilled golfers. These results support the acquisition of a rich mental representation through random versus blocked practice.

Joint and collaborative representation with local Volterra kernels convolution feature for face recognition

NASA Astrophysics Data System (ADS)

Feng, Guang; Li, Hengjian; Dong, Jiwen; Chen, Xi; Yang, Huiru

2018-04-01

In this paper, we proposed a joint and collaborative representation with Volterra kernel convolution feature (JCRVK) for face recognition. Firstly, the candidate face images are divided into sub-blocks in the equal size. The blocks are extracted feature using the two-dimensional Voltera kernels discriminant analysis, which can better capture the discrimination information from the different faces. Next, the proposed joint and collaborative representation is employed to optimize and classify the local Volterra kernels features (JCR-VK) individually. JCR-VK is very efficiently for its implementation only depending on matrix multiplication. Finally, recognition is completed by using the majority voting principle. Extensive experiments on the Extended Yale B and AR face databases are conducted, and the results show that the proposed approach can outperform other recently presented similar dictionary algorithms on recognition accuracy.

Context of the beginning of tobacco use in different social groups

PubMed Central

Panaino, Edina Ferreira; Soares, Cássia Baldini; Campos, Célia Maria Sivalli

2014-01-01

Objective analyze contextual aspects of the beginning of tobacco use in different social groups, from everyday representations about the act of smoking. Methods five focus groups were conducted to promote discussion about the context of beginning of tobacco use, with groups of people who represented different patterns of social reproduction. The data analysis was based on the theory of social representations, which contextualizes how each group presents the tobacco consumption. Results the contexts of the beginning of tobacco use were diverse, according to patterns of social reproduction; there were common representations to all groups, but there were also unique representations of each social group. Tobacco is represented as indispensable for groups in unstable social reproduction situations, and as an instrument of pleasure and stress relief for those who can access other material assets. Conclusions the study contributed to exposing the concepts on tobacco consumption that are socially disseminated, which can serve as an instrument to planning programs and health actions. PMID:25029047

The enhancement of students’ mathematical representation in junior high school using cognitive apprenticeship instruction (CAI)

NASA Astrophysics Data System (ADS)

Yusepa, B. G. P.; Kusumah, Y. S.; Kartasasmita, B. G.

2018-03-01

This study aims to get an in-depth understanding of the enhancement of students’ mathematical representation. This study is experimental research with pretest-posttest control group design. The subject of this study is the students’ of the eighth grade from junior high schools in Bandung: high-level and middle-level. In each school, two parallel groups were chosen as a control group and an experimental group. The experimental group was given cognitive apprenticeship instruction (CAI) treatment while the control group was given conventional learning. The results show that the enhancement of students’ mathematical representation who obtained CAI treatment was better than the conventional one, viewed which can be observed from the overall, mathematical prior knowledge (MPK), and school level. It can be concluded that CAI can be used as a good alternative learning model to enhance students’ mathematical representation.

Volta-Based Cells Materials Chemical Multiple Representation to Improve Ability of Student Representation

NASA Astrophysics Data System (ADS)

Helsy, I.; Maryamah; Farida, I.; Ramdhani, M. A.

2017-09-01

This study aimed to describe the application of teaching materials, analyze the increase in the ability of students to connect the three levels of representation and student responses after application of multiple representations based teaching materials chemistry. The method used quasi one-group pretest-posttest design to 71 students. The results showed the application of teaching materials carried 88% with very good category. A significant increase ability to connect the three levels of representation of students after the application of multiple representations based teaching materials chemistry with t-value > t-crit (11.402 > 1.991). Recapitulation N-gain pretest and posttest showed relatively similar for all groups is 0.6 criterion being achievement. Students gave a positive response to the application of multiple representations based teaching materials chemistry. Students agree teaching materials used in teaching chemistry (88%), and agrees teaching materials to provide convenience in connecting the three levels of representation (95%).

The Effect of Sexual Experience on the Social Representation of Sex in Portuguese Young Adults.

PubMed

Gomes, Alexandra; Nunes, Cristina

2014-04-26

This study aimed to observe the effect of sexual experience on the social representation of sex in Portuguese young adults. According to social representation theory, the central core of the social representation should be the same in all individuals that share a common social ground, however differences should be found in the peripheral system. It was used a free evocation task to assess the social representation of sex in Portuguese individuals aging between 18 and 25 years old. Nine hundred and sixty individuals were grouped by their sexual experience and condom use habits. A prototypical analysis was conducted to assess the structure of the social representation and statistical differences were analyzed using the qui-square independency test to search for an association between the structure and the group evoking it. The results supported the hypothesis of a common central core for all groups that shows a romanticized vision of sex. The differences found in the peripheral system suggest that sexual experience affects the representation of sex in a way that seems clearer to these individuals the necessity of protection when it comes to sex.

Differentiation of Streptococcus pneumoniae Conjunctivitis Outbreak Isolates by Matrix-Assisted Laser Desorption Ionization-Time of Flight Mass Spectrometry▿

PubMed Central

Williamson, Yulanda M.; Moura, Hercules; Woolfitt, Adrian R.; Pirkle, James L.; Barr, John R.; Carvalho, Maria Da Gloria; Ades, Edwin P.; Carlone, George M.; Sampson, Jacquelyn S.

2008-01-01

Streptococcus pneumoniae (pneumococcus [Pnc]) is a causative agent of many infectious diseases, including pneumonia, septicemia, otitis media, and conjunctivitis. There have been documented conjunctivitis outbreaks in which nontypeable (NT), nonencapsulated Pnc has been identified as the etiological agent. The use of mass spectrometry to comparatively and differentially analyze protein and peptide profiles of whole-cell microorganisms remains somewhat uncharted. In this report, we discuss a comparative proteomic analysis between NT S. pneumoniae conjunctivitis outbreak strains (cPnc) and other known typeable or NT pneumococcal and streptococcal isolates (including Pnc TIGR4 and R6, Streptococcus oralis, Streptococcus mitis, Streptococcus pseudopneumoniae, and Streptococcus pyogenes) and nonstreptococcal isolates (including Escherichia coli, Enterococcus faecalis, and Staphylococcus aureus) as controls. cPnc cells and controls were grown to mid-log phase, harvested, and subsequently treated with a 10% trifluoroacetic acid-sinapinic acid matrix mixture. Protein and peptide fragments of the whole-cell bacterial isolate-matrix combinations ranging in size from 2 to 14 kDa were evaluated by matrix-assisted laser desorption ionization-time of flight mass spectrometry. Additionally Random Forest analytical tools and dendrogramic representations (Genesis) suggested similarities and clustered the isolates into distinct clonal groups, respectively. Also, a peak list of protein and peptide masses was obtained and compared to a known Pnc protein mass library, in which a peptide common and unique to cPnc isolates was tentatively identified. Information gained from this study will lead to the identification and validation of proteins that are commonly and exclusively expressed in cPnc strains which could potentially be used as a biomarker in the rapid diagnosis of pneumococcal conjunctivitis. PMID:18708515

State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Read, Julie L.; Younes, Ahmad Bani; Macomber, Brent; Turner, James; Junkins, John L.

2015-06-01

The Modified Chebyshev Picard Iteration (MCPI) method has recently proven to be highly efficient for a given accuracy compared to several commonly adopted numerical integration methods, as a means to solve for perturbed orbital motion. This method utilizes Picard iteration, which generates a sequence of path approximations, and Chebyshev Polynomials, which are orthogonal and also enable both efficient and accurate function approximation. The nodes consistent with discrete Chebyshev orthogonality are generated using cosine sampling; this strategy also reduces the Runge effect and as a consequence of orthogonality, there is no matrix inversion required to find the basis function coefficients. The MCPI algorithms considered herein are parallel-structured so that they are immediately well-suited for massively parallel implementation with additional speedup. MCPI has a wide range of applications beyond ephemeris propagation, including the propagation of the State Transition Matrix (STM) for perturbed two-body motion. A solution is achieved for a spherical harmonic series representation of earth gravity (EGM2008), although the methodology is suitable for application to any gravity model. Included in this representation the normalized, Associated Legendre Functions are given and verified numerically. Modifications of the classical algorithm techniques, such as rewriting the STM equations in a second-order cascade formulation, gives rise to additional speedup. Timing results for the baseline formulation and this second-order formulation are given.

Dynamic Textures Modeling via Joint Video Dictionary Learning.

PubMed

Wei, Xian; Li, Yuanxiang; Shen, Hao; Chen, Fang; Kleinsteuber, Martin; Wang, Zhongfeng

2017-04-06

Video representation is an important and challenging task in the computer vision community. In this paper, we consider the problem of modeling and classifying video sequences of dynamic scenes which could be modeled in a dynamic textures (DT) framework. At first, we assume that image frames of a moving scene can be modeled as a Markov random process. We propose a sparse coding framework, named joint video dictionary learning (JVDL), to model a video adaptively. By treating the sparse coefficients of image frames over a learned dictionary as the underlying "states", we learn an efficient and robust linear transition matrix between two adjacent frames of sparse events in time series. Hence, a dynamic scene sequence is represented by an appropriate transition matrix associated with a dictionary. In order to ensure the stability of JVDL, we impose several constraints on such transition matrix and dictionary. The developed framework is able to capture the dynamics of a moving scene by exploring both sparse properties and the temporal correlations of consecutive video frames. Moreover, such learned JVDL parameters can be used for various DT applications, such as DT synthesis and recognition. Experimental results demonstrate the strong competitiveness of the proposed JVDL approach in comparison with state-of-the-art video representation methods. Especially, it performs significantly better in dealing with DT synthesis and recognition on heavily corrupted data.

Using an iterative eigensolver to compute vibrational energies with phase-spaced localized basis functions.

PubMed

Brown, James; Carrington, Tucker

2015-07-28

Although phase-space localized Gaussians are themselves poor basis functions, they can be used to effectively contract a discrete variable representation basis [A. Shimshovitz and D. J. Tannor, Phys. Rev. Lett. 109, 070402 (2012)]. This works despite the fact that elements of the Hamiltonian and overlap matrices labelled by discarded Gaussians are not small. By formulating the matrix problem as a regular (i.e., not a generalized) matrix eigenvalue problem, we show that it is possible to use an iterative eigensolver to compute vibrational energy levels in the Gaussian basis.

The application of trigonal curve to the Mikhailov-Shabat-Sokolov flows

NASA Astrophysics Data System (ADS)

He, Guoliang; Geng, Xianguo; Wu, Lihua

2016-08-01

Resorting to the characteristic polynomial of Lax matrix for the Mikhailov-Shabat-Sokolov hierarchy associated with a {3 × 3} matrix spectral problem, we introduce a trigonal curve, from which we deduce the associated Baker-Akhiezer function, meromorphic functions and Dubrovin-type equations. The straightening out of the Mikhailov-Shabat-Sokolov flows is exactly given through the Abel map. On the basis of these results and the theory of trigonal curve, we obtain the explicit theta function representations of the Baker-Akhiezer function, the meromorphic functions, and in particular, that of solutions for the entire Mikhailov-Shabat-Sokolov hierarchy.

Dermis, acellular dermal matrix, and fibroblasts from different layers of pig skin exhibit different profibrotic characteristics: evidence from in vivo study

PubMed Central

Zuo, Yanhai; Lu, Shuliang

2017-01-01

To explore the profibrotic characteristics of the autografted dermis, acellular dermal matrix, and dermal fibroblasts from superficial/deep layers of pig skin, 93 wounds were established on the dorsa of 7 pigs. 72 wounds autografted with the superficial/deep dermis and acellular dermal matrix served as the superficial/deep dermis and acellular dermal matrix group, respectively, and were sampled at 2, 4, and 8 weeks post-wounding. 21 wounds autografted with/without superficial/deep dermal fibroblasts served as the superficial/deep dermal fibroblast group and the control group, respectively, and were sampled at 2 weeks post-wounding. The hematoxylin and eosin staining showed that the wounded skin thicknesses in the deep dermis group (superficial acellular dermal matrix group) were significantly greater than those in the superficial dermis group (deep acellular dermal matrix group) at each time point, the thickness of the cutting plane in the deep dermal fibroblast group was significantly greater than that in the superficial dermal fibroblast group and the control group. The western blots showed that the α-smooth muscle actin expression in the deep dermis group (superficial acellular dermal matrix group) was significantly greater than that in the superficial dermis group (deep acellular dermal matrix group) at each time point. In summary, the deep dermis and dermal fibroblasts exhibited more profibrotic characteristics than the superficial ones, on the contrary, the deep acellular dermal matrix exhibited less profibrotic characteristics than the superficial one. PMID:28423561

Making It in America: Differences between Eminent Blacks and White Ethnic Groups.

ERIC Educational Resources Information Center

Lieberson, Stanley; Carter, Donna K.

1979-01-01

This study compares the representation in "Who's Who in America" of six groups: Blacks, Slavs, Jews, the English, and Scandinavians. Changes in the representation level of each group during the period 1924-1974 are examined. (Author/MC)

Orbit-product representation and correction of Gaussian belief propagation

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

Johnson, Jason K; Chertkov, Michael; Chernyak, Vladimir

We present a new interpretation of Gaussian belief propagation (GaBP) based on the 'zeta function' representation of the determinant as a product over orbits of a graph. We show that GaBP captures back-tracking orbits of the graph and consider how to correct this estimate by accounting for non-backtracking orbits. We show that the product over non-backtracking orbits may be interpreted as the determinant of the non-backtracking adjacency matrix of the graph with edge weights based on the solution of GaBP. An efficient method is proposed to compute a truncated correction factor including all non-backtracking orbits up to a specified length.

[x, p] = i{h_bar} ?

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

Tang, Jau

1996-03-01

Heisenberg`s commutation relation for position x and momentum p, and its validity for relativistic harmonic oscillators are examined, using the techniques of Lie algebra and dual-bosonic representation of x, p and the Hamiltonian H. A modification with [x, p] =i{h_bar}({minus_plus} 1 + H/m{sub 0}c{sup 2}) is proposed for a particle and an antiparticle in a harmonic potential. For a 2 {times} 2 matrix representation for x, p and H operators, the quantized eigenenergy E is given by (E - m{sub 0}c{sup 2})/{h_bar}{omega} = 3/2, 5/2, 7/2, ..., where 1/2 is not allowed.

The Effects of Measurement Error on Statistical Models for Analyzing Change. Final Report.

ERIC Educational Resources Information Center

Dunivant, Noel

The results of six major projects are discussed including a comprehensive mathematical and statistical analysis of the problems caused by errors of measurement in linear models for assessing change. In a general matrix representation of the problem, several new analytic results are proved concerning the parameters which affect bias in…

Phase dilemma in natural orbital functional theory from the N-representability perspective

NASA Astrophysics Data System (ADS)

Mitxelena, Ion; Rodriguez-Mayorga, Mauricio; Piris, Mario

2018-06-01

Any rigorous approach to first-order reduced density matrix ( Γ) functional theory faces the phase dilemma, that is, having to deal with a large number of possible combinations of signs in terms of the electron-electron interaction energy. This problem was discovered by reducing a ground-state energy generated from an approximate N-particle wavefunction into a functional of Γ, known as the top-down method. Here, we show that the phase dilemma also appears in the bottom-up method, in which the functional E[ Γ] is generated by progressive inclusion of N-representability conditions on the reconstructed two-particle reduced density matrix. It is shown that an adequate choice of signs is essential to accurately describe model systems with strong non-dynamic (static) electron correlation, specifically, the one-dimensional Hubbard model with periodic boundary conditions and hydrogen rings. For the latter, the Piris natural orbital functional 7 (PNOF7), with phases equal to -1 for the inter-pair energy terms containing the exchange-time-inversion integrals, agrees with exact diagonalization results.

Matrix product state description of Halperin states

NASA Astrophysics Data System (ADS)

Crépel, V.; Estienne, B.; Bernevig, B. A.; Lecheminant, P.; Regnault, N.

2018-04-01

Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact matrix product state (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wave functions, the Halperin states. These can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wave-function symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation lengths, which are compared to plasma analogy arguments.

A network of discrete events for the representation and analysis of diffusion dynamics.

PubMed

Pintus, Alberto M; Pazzona, Federico G; Demontis, Pierfranco; Suffritti, Giuseppe B

2015-11-14

We developed a coarse-grained description of the phenomenology of diffusive processes, in terms of a space of discrete events and its representation as a network. Once a proper classification of the discrete events underlying the diffusive process is carried out, their transition matrix is calculated on the basis of molecular dynamics data. This matrix can be represented as a directed, weighted network where nodes represent discrete events, and the weight of edges is given by the probability that one follows the other. The structure of this network reflects dynamical properties of the process of interest in such features as its modularity and the entropy rate of nodes. As an example of the applicability of this conceptual framework, we discuss here the physics of diffusion of small non-polar molecules in a microporous material, in terms of the structure of the corresponding network of events, and explain on this basis the diffusivity trends observed. A quantitative account of these trends is obtained by considering the contribution of the various events to the displacement autocorrelation function.

Genomicus update 2015: KaryoView and MatrixView provide a genome-wide perspective to multispecies comparative genomics

PubMed Central

Louis, Alexandra; Nguyen, Nga Thi Thuy; Muffato, Matthieu; Roest Crollius, Hugues

2015-01-01

The Genomicus web server (http://www.genomicus.biologie.ens.fr/genomicus) is a visualization tool allowing comparative genomics in four different phyla (Vertebrate, Fungi, Metazoan and Plants). It provides access to genomic information from extant species, as well as ancestral gene content and gene order for vertebrates and flowering plants. Here we present the new features available for vertebrate genome with a focus on new graphical tools. The interface to enter the database has been improved, two pairwise genome comparison tools are now available (KaryoView and MatrixView) and the multiple genome comparison tools (PhyloView and AlignView) propose three new kinds of representation and a more intuitive menu. These new developments have been implemented for Genomicus portal dedicated to vertebrates. This allows the analysis of 68 extant animal genomes, as well as 58 ancestral reconstructed genomes. The Genomicus server also provides access to ancestral gene orders, to facilitate evolutionary and comparative genomics studies, as well as computationally predicted regulatory interactions, thanks to the representation of conserved non-coding elements with their putative gene targets. PMID:25378326

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

Kolda, Tamara Gibson

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

Role of working memory in transformation of visual and motor representations for use in mental simulation.

PubMed

Gabbard, Carl; Lee, Jihye; Caçola, Priscila

2013-01-01

This study examined the role of visual working memory when transforming visual representations to motor representations in the context of motor imagery. Participants viewed randomized number sequences of three, four, and five digits, and then reproduced the sequence by finger tapping using motor imagery or actually executing the movements; movement duration was recorded. One group viewed the stimulus for three seconds and responded immediately, while the second group had a three-second view followed by a three-second blank screen delay before responding. As expected, delay group times were longer with each condition and digit load. Whereas correlations between imagined and executed actions (temporal congruency) were significant in a positive direction for both groups, interestingly, the delay group's values were significantly stronger. That outcome prompts speculation that delay influenced the congruency between motor representation and actual execution.

That's what friends are for: how intergroup friendships promote historically disadvantaged groups' substantive political representation.

PubMed

Kokkonen, Andrej; Karlsson, David

2017-12-01

The interests of historically disadvantaged groups risk being overlooked if they are not present in the decision-making process. However, a mere presence in politics does not guarantee political success. Often groups need allies to promote their interests successfully. We argue that one way to identify such allies is to judge politicians by whether they have friends in historically disadvantaged groups, as intergroup friendships have been shown to make people understand and feel empathy for outgroups. In other words, intergroup friendships may function as an important complement to descriptive representation. We test our argument with a unique survey that asks all elected political representatives in Sweden's 290 municipalities (response rate 79 per cent) about their friendship ties to, and their representation of, five historically disadvantaged groups: women, immigrants, youths, pensioners and blue-collar workers. We find a strong correlation between representatives' friendship ties to these groups and their commitment to represent them. The correlation is especially strong for youths and blue-collar workers, which likely can be explained by the fact that these groups usually lack crucial political resources (such as experience and education). We conclude that friendship ties function as an important complement to descriptive representation for achieving substantive representation. © London School of Economics and Political Science 2017.

Heading-vector navigation based on head-direction cells and path integration.

PubMed

Kubie, John L; Fenton, André A

2009-05-01

Insect navigation is guided by heading vectors that are computed by path integration. Mammalian navigation models, on the other hand, are typically based on map-like place representations provided by hippocampal place cells. Such models compute optimal routes as a continuous series of locations that connect the current location to a goal. We propose a "heading-vector" model in which head-direction cells or their derivatives serve both as key elements in constructing the optimal route and as the straight-line guidance during route execution. The model is based on a memory structure termed the "shortcut matrix," which is constructed during the initial exploration of an environment when a set of shortcut vectors between sequential pairs of visited waypoint locations is stored. A mechanism is proposed for calculating and storing these vectors that relies on a hypothesized cell type termed an "accumulating head-direction cell." Following exploration, shortcut vectors connecting all pairs of waypoint locations are computed by vector arithmetic and stored in the shortcut matrix. On re-entry, when local view or place representations query the shortcut matrix with a current waypoint and goal, a shortcut trajectory is retrieved. Since the trajectory direction is in head-direction compass coordinates, navigation is accomplished by tracking the firing of head-direction cells that are tuned to the heading angle. Section 1 of the manuscript describes the properties of accumulating head-direction cells. It then shows how accumulating head-direction cells can store local vectors and perform vector arithmetic to perform path-integration-based homing. Section 2 describes the construction and use of the shortcut matrix for computing direct paths between any pair of locations that have been registered in the shortcut matrix. In the discussion, we analyze the advantages of heading-based navigation over map-based navigation. Finally, we survey behavioral evidence that nonhippocampal, heading-based navigation is used in small mammals and humans. Copyright 2008 Wiley-Liss, Inc.

Artificial intelligence systems based on texture descriptors for vaccine development.

PubMed

Nanni, Loris; Brahnam, Sheryl; Lumini, Alessandra

2011-02-01

The aim of this work is to analyze and compare several feature extraction methods for peptide classification that are based on the calculation of texture descriptors starting from a matrix representation of the peptide. This texture-based representation of the peptide is then used to train a support vector machine classifier. In our experiments, the best results are obtained using local binary patterns variants and the discrete cosine transform with selected coefficients. These results are better than those previously reported that employed texture descriptors for peptide representation. In addition, we perform experiments that combine standard approaches based on amino acid sequence. The experimental section reports several tests performed on a vaccine dataset for the prediction of peptides that bind human leukocyte antigens and on a human immunodeficiency virus (HIV-1). Experimental results confirm the usefulness of our novel descriptors. The matlab implementation of our approaches is available at http://bias.csr.unibo.it/nanni/TexturePeptide.zip.

Effects of dynamically variable saturation and matrix-conduit coupling of flow in karst aquifers

USGS Publications Warehouse

Reimann, T.; Geyer, T.; Shoemaker, W.B.; Liedl, R.; Sauter, M.

2011-01-01

Well-developed karst aquifers consist of highly conductive conduits and a relatively low permeability fractured and/or porous rock matrix and therefore behave as a dual-hydraulic system. Groundwater flow within highly permeable strata is rapid and transient and depends on local flow conditions, i.e., pressurized or nonpressurized flow. The characterization of karst aquifers is a necessary and challenging task because information about hydraulic and spatial conduit properties is poorly defined or unknown. To investigate karst aquifers, hydraulic stresses such as large recharge events can be simulated with hybrid (coupled discrete continuum) models. Since existing hybrid models are simplifications of the system dynamics, a new karst model (ModBraC) is presented that accounts for unsteady and nonuniform discrete flow in variably saturated conduits employing the Saint-Venant equations. Model performance tests indicate that ModBraC is able to simulate (1) unsteady and nonuniform flow in variably filled conduits, (2) draining and refilling of conduits with stable transition between free-surface and pressurized flow and correct storage representation, (3) water exchange between matrix and variably filled conduits, and (4) discharge routing through branched and intermeshed conduit networks. Subsequently, ModBraC is applied to an idealized catchment to investigate the significance of free-surface flow representation. A parameter study is conducted with two different initial conditions: (1) pressurized flow and (2) free-surface flow. If free-surface flow prevails, the systems is characterized by (1) a time lag for signal transmission, (2) a typical spring discharge pattern representing the transition from pressurized to free-surface flow, and (3) a reduced conduit-matrix interaction during free-surface flow. Copyright 2011 by the American Geophysical Union.

Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation

NASA Astrophysics Data System (ADS)

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

A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer.

PubMed

Sharma, Sandeep

2015-01-14

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10(12) many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a(3)Πu, b(3)Σg (-), A(1)Πu, c(3)Σu (+), B(1)Δg, B(') (1)Σg (+), d(3)Πg, and C(1)Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations (1)Σg (+), (1)Σu (+), (1)Σg (-), and (1)Σu (-), to an estimated accuracy of 0.1 mEh of the exact result in this basis.

A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer

NASA Astrophysics Data System (ADS)

Sharma, Sandeep

2015-01-01

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 1012 many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a3Πu, b 3 Σg - , A1Πu, c 3 Σu + , B1Δg, B ' 1 Σg + , d3Πg, and C1Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations 1 Σg + , 1 Σu + , 1 Σg - , and 1 Σu - , to an estimated accuracy of 0.1 mEh of the exact result in this basis.

A novel physical eco-hydrological model concept for preferential flow based on experimental applications.

NASA Astrophysics Data System (ADS)

Jackisch, Conrad; van Schaik, Loes; Graeff, Thomas; Zehe, Erwin

2014-05-01

Preferential flow through macropores often determines hydrological characteristics - especially regarding runoff generation and fast transport of solutes. Macropore settings may yet be very different in nature and dynamics, depending on their origin. While biogenic structures follow activity cycles (e.g. earth worms) and population conditions (e.g. roots), pedogenic and geogenic structures may depend on water stress (e.g. cracks) or large events (e.g. flushed voids between skeleton and soil pipes) or simply persist (e.g. bedrock interface). On the one hand, such dynamic site characteristics can be observed in seasonal changes in its reaction to precipitation. On the other hand, sprinkling experiments accompanied by tracers or time-lapse 3D Ground-Penetrating-Radar are suitable tools to determine infiltration patterns and macropore configuration. However, model representation of the macropore-matrix system is still problematic, because models either rely on effective parameters (assuming well-mixed state) or on explicit advection strongly simplifying or neglecting interaction with the diffusive flow domain. Motivated by the dynamic nature of macropores, we present a novel model approach for interacting diffusive and advective water, solutes and energy transport in structured soils. It solely relies on scale- and process-aware observables. A representative set of macropores (data from sprinkling experiments) determines the process model scale through 1D advective domains. These are connected to a 2D matrix domain which is defined by pedo-physical retention properties. Water is represented as particles. Diffusive flow is governed by a 2D random walk of these particles while advection may take place in the macropore domain. Macropore-matrix interaction is computed as dissipation of the advective momentum of a particle by its experienced drag from the matrix domain. Through a representation of matrix and macropores as connected diffusive and advective domains for water transport we open up double domain concepts linking porescale physics to preferential macroscale fingerprints without effective parameterisation or mixing assumptions. Moreover, solute transport, energy balance aspects and lateral heterogeneity in soil moisture distribution are intrinsically captured. In addition, macropore and matrix domain settings may change over time based on physical and stochastic observations. The representativity concept allows scaleability from plotscale to the lower mesoscale.

Thermodynamic characterization of networks using graph polynomials

NASA Astrophysics Data System (ADS)

Ye, Cheng; Comin, César H.; Peron, Thomas K. DM.; Silva, Filipi N.; Rodrigues, Francisco A.; Costa, Luciano da F.; Torsello, Andrea; Hancock, Edwin R.

2015-09-01

In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the polynomial is linked to the Boltzmann partition function of a network. This allows us to compute a number of thermodynamic quantities for the network, including the average energy and entropy. Assuming that the system does not change volume, we can also compute the temperature, defined as the rate of change of entropy with energy. All three thermodynamic variables can be approximated using low-order Taylor series that can be computed using the traces of powers of the Laplacian matrix, avoiding explicit computation of the normalized Laplacian spectrum. These polynomial approximations allow a smoothed representation of the evolution of networks to be constructed in the thermodynamic space spanned by entropy, energy, and temperature. We show how these thermodynamic variables can be computed in terms of simple network characteristics, e.g., the total number of nodes and node degree statistics for nodes connected by edges. We apply the resulting thermodynamic characterization to real-world time-varying networks representing complex systems in the financial and biological domains. The study demonstrates that the method provides an efficient tool for detecting abrupt changes and characterizing different stages in network evolution.

Manifold regularized discriminative nonnegative matrix factorization with fast gradient descent.

PubMed

Guan, Naiyang; Tao, Dacheng; Luo, Zhigang; Yuan, Bo

2011-07-01

Nonnegative matrix factorization (NMF) has become a popular data-representation method and has been widely used in image processing and pattern-recognition problems. This is because the learned bases can be interpreted as a natural parts-based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole. For practical classification tasks, however, NMF ignores both the local geometry of data and the discriminative information of different classes. In addition, existing research results show that the learned basis is unnecessarily parts-based because there is neither explicit nor implicit constraint to ensure the representation parts-based. In this paper, we introduce the manifold regularization and the margin maximization to NMF and obtain the manifold regularized discriminative NMF (MD-NMF) to overcome the aforementioned problems. The multiplicative update rule (MUR) can be applied to optimizing MD-NMF, but it converges slowly. In this paper, we propose a fast gradient descent (FGD) to optimize MD-NMF. FGD contains a Newton method that searches the optimal step length, and thus, FGD converges much faster than MUR. In addition, FGD includes MUR as a special case and can be applied to optimizing NMF and its variants. For a problem with 165 samples in R(1600), FGD converges in 28 s, while MUR requires 282 s. We also apply FGD in a variant of MD-NMF and experimental results confirm its efficiency. Experimental results on several face image datasets suggest the effectiveness of MD-NMF.

Narrative, memory and social representations: a conversation between history and social psychology.

PubMed

Jovchelovitch, Sandra

2012-12-01

This paper explores relations between narrative, memory and social representations by examining how social representations express the ways in which communities deal with the historical past. Drawing on a case study of social representations of the Brazilian public sphere, it shows how a specific narrative of origins re-invents history as a useful mythological resource for defending identity, building inter-group solidarity and maintaining social cohesion. Produced by a time-travelling dialogue between multiple sources, this historical narrative is functional both to transform, to stabilise and give resilience to specific social representations of public life. The Brazilian case shows that historical narratives, which tend to be considered as part of the stable core of representational fields, are neither homogenous nor consensual but open polyphasic platforms for the construction of alternative, often contradictory, representations. These representations do not go away because they are ever changing and situated, recruit multiple ways of thinking and fulfil functions of identity, inter-group solidarity and social cohesion. In the disjunction between historiography and the past as social representation are the challenges and opportunities for the dialogue between historians and social psychologists.

A Coordinated Approach to Curricular Review and Development in Undergraduate Geoscience Programs: Using a Matrix to Identify and Track Skills and Skill Development

NASA Astrophysics Data System (ADS)

MacDonald, R.; Savina, M. E.

2003-12-01

One approach to curriculum review and development is to construct a matrix of the desired skills versus courses in the departmental curriculum. The matrix approach requires faculty to articulate their goals, identify specific skills, and assess where in the curriculum students will learn and practice these skills and where there are major skills gaps. Faculty members in the Geology Department at Carleton College developed a matrix of skills covered in geology courses with the following objectives: 1) Geology majors should begin their "senior integrative exercise" having practiced multiple times all of the formal steps in the research process (recognizing problems, writing proposals, carrying out a project, reporting a project in several ways); 2) Geology majors should learn and practice a variety of professional and life skills life (e.g. computer skills, field skills, lab skills, and interpretive skills).The matrix was used to identify where in the curriculum various research methods and skills were addressed and to map potential student experiences to the objectives. In Carleton's non-hierarchical curriculum, the matrix was used to verify that students have many opportunities to practice research and life skills regardless of the path they take to completion of the major. In William and Mary's more structured curriculum, the matrix was used to ensure that skills build upon each other from course to course. Faculty members in the Geology Department at the College of William and Mary first used this approach to focus on teaching quantitative skills across the geology curriculum, and later used it in terms of teaching research, communication, and information literacy skills. After articulating goals and skills, faculty members in both departments developed more specific skill lists within each category of skills, then described the current assignments and activities in each course relative to the specific components of the matrix and discussed whether to add assignment or activities. We have found that much conversation among faculty and change within courses happens simply as a result of compiling the matrix. One effect of the use of the matrix is that faculty in the department know fairly specifically what skills students are learning and practicing in their other geology courses. Moreover, some faculty members are better suited by background or inclination to teach certain sets of skills. This coordinated approach avoids unnecessary duplication and allows faculty to build on skills and topics developed in previous courses. The matrix can also be used as a planning tool to identify gaps in the curriculum. In our experience, the skills matrix is a powerful organizational and communication tool. The skills matrix is a representation of what the department believes actually happens in the curriculum. Thus, development of a skills matrix provides a basis for departmental discussions of student learning goals and objectives as well as for describing the existing curriculum. The matrix is also a graphic representation, to college administrators and outside evaluators, of the "intentionality" of an entire curriculum, going beyond single courses and their syllabi. It can be used effectively to engage administration in discussions of departmental planning and needs analysis.

Matrix basis for plane and modal waves in a Timoshenko beam

PubMed Central

Tolfo, Daniela de Rosso; Tonetto, Leticia

2016-01-01

Plane waves and modal waves of the Timoshenko beam model are characterized in closed form by introducing robust matrix basis that behave according to the nature of frequency and wave or modal numbers. These new characterizations are given in terms of a finite number of coupling matrices and closed form generating scalar functions. Through Liouville’s technique, these latter are well behaved at critical or static situations. Eigenanalysis is formulated for exponential and modal waves. Modal waves are superposition of four plane waves, but there are plane waves that cannot be modal waves. Reflected and transmitted waves at an interface point are formulated in matrix terms, regardless of having a conservative or a dissipative situation. The matrix representation of modal waves is used in a crack problem for determining the reflected and transmitted matrices. Their euclidean norms are seen to be dominated by certain components at low and high frequencies. The matrix basis technique is also used with a non-local Timoshenko model and with the wave interaction with a boundary. The matrix basis allows to characterize reflected and transmitted waves in spectral and non-spectral form. PMID:28018668

Distance learning in discriminative vector quantization.

PubMed

Schneider, Petra; Biehl, Michael; Hammer, Barbara

2009-10-01

Discriminative vector quantization schemes such as learning vector quantization (LVQ) and extensions thereof offer efficient and intuitive classifiers based on the representation of classes by prototypes. The original methods, however, rely on the Euclidean distance corresponding to the assumption that the data can be represented by isotropic clusters. For this reason, extensions of the methods to more general metric structures have been proposed, such as relevance adaptation in generalized LVQ (GLVQ) and matrix learning in GLVQ. In these approaches, metric parameters are learned based on the given classification task such that a data-driven distance measure is found. In this letter, we consider full matrix adaptation in advanced LVQ schemes. In particular, we introduce matrix learning to a recent statistical formalization of LVQ, robust soft LVQ, and we compare the results on several artificial and real-life data sets to matrix learning in GLVQ, a derivation of LVQ-like learning based on a (heuristic) cost function. In all cases, matrix adaptation allows a significant improvement of the classification accuracy. Interestingly, however, the principled behavior of the models with respect to prototype locations and extracted matrix dimensions shows several characteristic differences depending on the data sets.

3D tensor-based blind multispectral image decomposition for tumor demarcation

NASA Astrophysics Data System (ADS)

Kopriva, Ivica; Peršin, Antun

2010-03-01

Blind decomposition of multi-spectral fluorescent image for tumor demarcation is formulated exploiting tensorial structure of the image. First contribution of the paper is identification of the matrix of spectral responses and 3D tensor of spatial distributions of the materials present in the image from Tucker3 or PARAFAC models of 3D image tensor. Second contribution of the paper is clustering based estimation of the number of the materials present in the image as well as matrix of their spectral profiles. 3D tensor of the spatial distributions of the materials is recovered through 3-mode multiplication of the multi-spectral image tensor and inverse of the matrix of spectral profiles. Tensor representation of the multi-spectral image preserves its local spatial structure that is lost, due to vectorization process, when matrix factorization-based decomposition methods (such as non-negative matrix factorization and independent component analysis) are used. Superior performance of the tensor-based image decomposition over matrix factorization-based decompositions is demonstrated on experimental red-green-blue (RGB) image with known ground truth as well as on RGB fluorescent images of the skin tumor (basal cell carcinoma).

Control Synthesis of Discrete-Time T-S Fuzzy Systems: Reducing the Conservatism Whilst Alleviating the Computational Burden.

PubMed

Xie, Xiangpeng; Yue, Dong; Zhang, Huaguang; Peng, Chen

2017-09-01

The augmented multi-indexed matrix approach acts as a powerful tool in reducing the conservatism of control synthesis of discrete-time Takagi-Sugeno fuzzy systems. However, its computational burden is sometimes too heavy as a tradeoff. Nowadays, reducing the conservatism whilst alleviating the computational burden becomes an ideal but very challenging problem. This paper is toward finding an efficient way to achieve one of satisfactory answers. Different from the augmented multi-indexed matrix approach in the literature, we aim to design a more efficient slack variable approach under a general framework of homogenous matrix polynomials. Thanks to the introduction of a new extended representation for homogeneous matrix polynomials, related matrices with the same coefficient are collected together into one sole set and thus those redundant terms of the augmented multi-indexed matrix approach can be removed, i.e., the computational burden can be alleviated in this paper. More importantly, due to the fact that more useful information is involved into control design, the conservatism of the proposed approach as well is less than the counterpart of the augmented multi-indexed matrix approach. Finally, numerical experiments are given to show the effectiveness of the proposed approach.

Performance and consistency of indicator groups in two biodiversity hotspots.

PubMed

Trindade-Filho, Joaquim; Loyola, Rafael Dias

2011-01-01

In a world limited by data availability and limited funds for conservation, scientists and practitioners must use indicator groups to define spatial conservation priorities. Several studies have evaluated the effectiveness of indicator groups, but still little is known about the consistency in performance of these groups in different regions, which would allow their a priori selection. We systematically examined the effectiveness and the consistency of nine indicator groups in representing mammal species in two top-ranked Biodiversity Hotspots (BH): the Brazilian Cerrado and the Atlantic Forest. To test for group effectiveness we first found the best sets of sites able to maximize the representation of each indicator group in the BH and then calculated the average representation of different target species by the indicator groups in the BH. We considered consistent indicator groups whose representation of target species was not statistically different between BH. We called effective those groups that outperformed the target-species representation achieved by random sets of species. Effective indicator groups required the selection of less than 2% of the BH area for representing target species. Restricted-range species were the most effective indicators for the representation of all mammal diversity as well as target species. It was also the only group with high consistency. We show that several indicator groups could be applied as shortcuts for representing mammal species in the Cerrado and the Atlantic Forest to develop conservation plans, however, only restricted-range species consistently held as the most effective indicator group for such a task. This group is of particular importance in conservation planning as it captures high diversity of endemic and endangered species.

Performance and Consistency of Indicator Groups in Two Biodiversity Hotspots

PubMed Central

Trindade-Filho, Joaquim; Loyola, Rafael Dias

2011-01-01

Background In a world limited by data availability and limited funds for conservation, scientists and practitioners must use indicator groups to define spatial conservation priorities. Several studies have evaluated the effectiveness of indicator groups, but still little is known about the consistency in performance of these groups in different regions, which would allow their a priori selection. Methodology/Principal Findings We systematically examined the effectiveness and the consistency of nine indicator groups in representing mammal species in two top-ranked Biodiversity Hotspots (BH): the Brazilian Cerrado and the Atlantic Forest. To test for group effectiveness we first found the best sets of sites able to maximize the representation of each indicator group in the BH and then calculated the average representation of different target species by the indicator groups in the BH. We considered consistent indicator groups whose representation of target species was not statistically different between BH. We called effective those groups that outperformed the target-species representation achieved by random sets of species. Effective indicator groups required the selection of less than 2% of the BH area for representing target species. Restricted-range species were the most effective indicators for the representation of all mammal diversity as well as target species. It was also the only group with high consistency. Conclusions/Significance We show that several indicator groups could be applied as shortcuts for representing mammal species in the Cerrado and the Atlantic Forest to develop conservation plans, however, only restricted-range species consistently held as the most effective indicator group for such a task. This group is of particular importance in conservation planning as it captures high diversity of endemic and endangered species. PMID:21637330

Adaptive multi-view clustering based on nonnegative matrix factorization and pairwise co-regularization

NASA Astrophysics Data System (ADS)

Zhang, Tianzhen; Wang, Xiumei; Gao, Xinbo

2018-04-01

Nowadays, several datasets are demonstrated by multi-view, which usually include shared and complementary information. Multi-view clustering methods integrate the information of multi-view to obtain better clustering results. Nonnegative matrix factorization has become an essential and popular tool in clustering methods because of its interpretation. However, existing nonnegative matrix factorization based multi-view clustering algorithms do not consider the disagreement between views and neglects the fact that different views will have different contributions to the data distribution. In this paper, we propose a new multi-view clustering method, named adaptive multi-view clustering based on nonnegative matrix factorization and pairwise co-regularization. The proposed algorithm can obtain the parts-based representation of multi-view data by nonnegative matrix factorization. Then, pairwise co-regularization is used to measure the disagreement between views. There is only one parameter to auto learning the weight values according to the contribution of each view to data distribution. Experimental results show that the proposed algorithm outperforms several state-of-the-arts algorithms for multi-view clustering.

The fourfold way of the genetic code.

PubMed

Jiménez-Montaño, Miguel Angel

2009-11-01

We describe a compact representation of the genetic code that factorizes the table in quartets. It represents a "least grammar" for the genetic language. It is justified by the Klein-4 group structure of RNA bases and codon doublets. The matrix of the outer product between the column-vector of bases and the corresponding row-vector V(T)=(C G U A), considered as signal vectors, has a block structure consisting of the four cosets of the KxK group of base transformations acting on doublet AA. This matrix, translated into weak/strong (W/S) and purine/pyrimidine (R/Y) nucleotide classes, leads to a code table with mixed and unmixed families in separate regions. A basic difference between them is the non-commuting (R/Y) doublets: AC/CA, GU/UG. We describe the degeneracy in the canonical code and the systematic changes in deviant codes in terms of the divisors of 24, employing modulo multiplication groups. We illustrate binary sub-codes characterizing mutations in the quartets. We introduce a decision-tree to predict the mode of tRNA recognition corresponding to each codon, and compare our result with related findings by Jestin and Soulé [Jestin, J.-L., Soulé, C., 2007. Symmetries by base substitutions in the genetic code predict 2' or 3' aminoacylation of tRNAs. J. Theor. Biol. 247, 391-394], and the rearrangements of the table by Delarue [Delarue, M., 2007. An asymmetric underlying rule in the assignment of codons: possible clue to a quick early evolution of the genetic code via successive binary choices. RNA 13, 161-169] and Rodin and Rodin [Rodin, S.N., Rodin, A.S., 2008. On the origin of the genetic code: signatures of its primordial complementarity in tRNAs and aminoacyl-tRNA synthetases. Heredity 100, 341-355], respectively.

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

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

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE PAGES

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter; ...

2016-06-30

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

Fuzzy associative memories

NASA Technical Reports Server (NTRS)

Kosko, Bart

1991-01-01

Mappings between fuzzy cubes are discussed. This level of abstraction provides a surprising and fruitful alternative to the propositional and predicate-calculas reasoning techniques used in expert systems. It allows one to reason with sets instead of propositions. Discussed here are fuzzy and neural function estimators, neural vs. fuzzy representation of structured knowledge, fuzzy vector-matrix multiplication, and fuzzy associative memory (FAM) system architecture.

The Matrix: A Pedagogical Tool for Teaching Employment Discrimination Law

ERIC Educational Resources Information Center

Johns, Roger J.

2008-01-01

The teaching of law in collegiate schools of business has a long history and a set of purposes that includes training students to know and understand their basic legal rights and obligations in the business arena, to recognize and avoid the liability-laden situations that would necessitate legal representation, to know when to engage legal…

Vectors, Change of Basis and Matrix Representation: Onto-Semiotic Approach in the Analysis of Creating Meaning

ERIC Educational Resources Information Center

Montiel, Mariana; Wilhelmi, Miguel R.; Vidakovic, Draga; Elstak, Iwan

2012-01-01

In a previous study, the onto-semiotic approach was employed to analyse the mathematical notion of different coordinate systems, as well as some situations and university students' actions related to these coordinate systems in the context of multivariate calculus. This study approaches different coordinate systems through the process of change of…

Speckle noise reduction for optical coherence tomography based on adaptive 2D dictionary

NASA Astrophysics Data System (ADS)

Lv, Hongli; Fu, Shujun; Zhang, Caiming; Zhai, Lin

2018-05-01

As a high-resolution biomedical imaging modality, optical coherence tomography (OCT) is widely used in medical sciences. However, OCT images often suffer from speckle noise, which can mask some important image information, and thus reduce the accuracy of clinical diagnosis. Taking full advantage of nonlocal self-similarity and adaptive 2D-dictionary-based sparse representation, in this work, a speckle noise reduction algorithm is proposed for despeckling OCT images. To reduce speckle noise while preserving local image features, similar nonlocal patches are first extracted from the noisy image and put into groups using a gamma- distribution-based block matching method. An adaptive 2D dictionary is then learned for each patch group. Unlike traditional vector-based sparse coding, we express each image patch by the linear combination of a few matrices. This image-to-matrix method can exploit the local correlation between pixels. Since each image patch might belong to several groups, the despeckled OCT image is finally obtained by aggregating all filtered image patches. The experimental results demonstrate the superior performance of the proposed method over other state-of-the-art despeckling methods, in terms of objective metrics and visual inspection.

Group Analysis in FieldTrip of Time-Frequency Responses: A Pipeline for Reproducibility at Every Step of Processing, Going From Individual Sensor Space Representations to an Across-Group Source Space Representation.

PubMed

Andersen, Lau M

2018-01-01

An important aim of an analysis pipeline for magnetoencephalographic (MEG) data is that it allows for the researcher spending maximal effort on making the statistical comparisons that will answer his or her questions. The example question being answered here is whether the so-called beta rebound differs between novel and repeated stimulations. Two analyses are presented: going from individual sensor space representations to, respectively, an across-group sensor space representation and an across-group source space representation. The data analyzed are neural responses to tactile stimulations of the right index finger in a group of 20 healthy participants acquired from an Elekta Neuromag System. The processing steps covered for the first analysis are MaxFiltering the raw data, defining, preprocessing and epoching the data, cleaning the data, finding and removing independent components related to eye blinks, eye movements and heart beats, calculating participants' individual evoked responses by averaging over epoched data and subsequently removing the average response from single epochs, calculating a time-frequency representation and baselining it with non-stimulation trials and finally calculating a grand average, an across-group sensor space representation. The second analysis starts from the grand average sensor space representation and after identification of the beta rebound the neural origin is imaged using beamformer source reconstruction. This analysis covers reading in co-registered magnetic resonance images, segmenting the data, creating a volume conductor, creating a forward model, cutting out MEG data of interest in the time and frequency domains, getting Fourier transforms and estimating source activity with a beamformer model where power is expressed relative to MEG data measured during periods of non-stimulation. Finally, morphing the source estimates onto a common template and performing group-level statistics on the data are covered. Functions for saving relevant figures in an automated and structured manner are also included. The protocol presented here can be applied to any research protocol where the emphasis is on source reconstruction of induced responses where the underlying sources are not coherent.

Confinement in F4 Exceptional Gauge Group Using Domain Structures

NASA Astrophysics Data System (ADS)

Rafibakhsh, Shahnoosh; Shahlaei, Amir

2017-03-01

We calculate the potential between static quarks in the fundamental representation of the F4 exceptional gauge group using domain structures of the thick center vortex model. As non-trivial center elements are absent, the asymptotic string tension is lost while an intermediate linear potential is observed. SU(2) is a subgroup of F4. Investigating the decomposition of the 26 dimensional representation of F4 to the SU(2) representations, might explain what accounts for the intermediate linear potential, in the exceptional groups with no center element.

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

Guedes, Carlos; Oriti, Daniele; Raasakka, Matti

The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-productmore » carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.« less

Coupled-cluster based R-matrix codes (CCRM): Recent developments

NASA Astrophysics Data System (ADS)

Sur, Chiranjib; Pradhan, Anil K.

2008-05-01

We report the ongoing development of the new coupled-cluster R-matrix codes (CCRM) for treating electron-ion scattering and radiative processes within the framework of the relativistic coupled-cluster method (RCC), interfaced with the standard R-matrix methodology. The RCC method is size consistent and in principle equivalent to an all-order many-body perturbation theory. The RCC method is one of the most accurate many-body theories, and has been applied for several systems. This project should enable the study of electron-interactions with heavy atoms/ions, utilizing not only high speed computing platforms but also improved theoretical description of the relativistic and correlation effects for the target atoms/ions as treated extensively within the RCC method. Here we present a comprehensive outline of the newly developed theoretical method and a schematic representation of the new suite of CCRM codes. We begin with the flowchart and description of various stages involved in this development. We retain the notations and nomenclature of different stages as analogous to the standard R-matrix codes.

Mueller coherency matrix method for contrast image in tissue polarimetry

NASA Astrophysics Data System (ADS)

Arce-Diego, J. L.; Fanjul-Vélez, F.; Samperio-García, D.; Pereda-Cubián, D.

2007-07-01

In this work, we propose the use of the Mueller Coherency matrix of biological tissues in order to increase the information from tissue images and so their contrast. This method involves different Mueller Coherency matrix based parameters, like the eigenvalues analysis, the entropy factor calculation, polarization components crosstalks, linear and circular polarization degrees, hermiticity or the Quaternions analysis in case depolarisation properties of tissue are sufficiently low. All these parameters make information appear clearer and so increase image contrast, so pathologies like cancer could be detected in a sooner stage of development. The election will depend on the concrete pathological process under study. This Mueller Coherency matrix method can be applied to a single tissue point, or it can be combined with a tomographic technique, so as to obtain a 3D representation of polarization contrast parameters in pathological tissues. The application of this analysis to concrete diseases can lead to tissue burn depth estimation or cancer early detection.

A parallel computer implementation of fast low-rank QR approximation of the Biot-Savart law

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

White, D A; Fasenfest, B J; Stowell, M L

2005-11-07

In this paper we present a low-rank QR method for evaluating the discrete Biot-Savart law on parallel computers. It is assumed that the known current density and the unknown magnetic field are both expressed in a finite element expansion, and we wish to compute the degrees-of-freedom (DOF) in the basis function expansion of the magnetic field. The matrix that maps the current DOF to the field DOF is full, but if the spatial domain is properly partitioned the matrix can be written as a block matrix, with blocks representing distant interactions being low rank and having a compressed QR representation.more » The matrix partitioning is determined by the number of processors, the rank of each block (i.e. the compression) is determined by the specific geometry and is computed dynamically. In this paper we provide the algorithmic details and present computational results for large-scale computations.« less

Thermal form-factor approach to dynamical correlation functions of integrable lattice models

NASA Astrophysics Data System (ADS)

Göhmann, Frank; Karbach, Michael; Klümper, Andreas; Kozlowski, Karol K.; Suzuki, Junji

2017-11-01

We propose a method for calculating dynamical correlation functions at finite temperature in integrable lattice models of Yang-Baxter type. The method is based on an expansion of the correlation functions as a series over matrix elements of a time-dependent quantum transfer matrix rather than the Hamiltonian. In the infinite Trotter-number limit the matrix elements become time independent and turn into the thermal form factors studied previously in the context of static correlation functions. We make this explicit with the example of the XXZ model. We show how the form factors can be summed utilizing certain auxiliary functions solving finite sets of nonlinear integral equations. The case of the XX model is worked out in more detail leading to a novel form-factor series representation of the dynamical transverse two-point function.

Simplified microstrip discontinuity modeling using the transmission line matrix method interfaced to microwave CAD

NASA Astrophysics Data System (ADS)

Thompson, James H.; Apel, Thomas R.

1990-07-01

A technique for modeling microstrip discontinuities is presented which is derived from the transmission line matrix method of solving three-dimensional electromagnetic problems. In this technique the microstrip patch under investigation is divided into an integer number of square and half-square (triangle) subsections. An equivalent lumped-element model is calculated for each subsection. These individual models are then interconnected as dictated by the geometry of the patch. The matrix of lumped elements is then solved using either of two microwave CAD software interfaces with each port properly defined. Closed-form expressions for the lumped-element representation of the individual subsections is presented and experimentally verified through the X-band frequency range. A model demonstrating the use of symmetry and block construction of a circuit element is discussed, along with computer program development and CAD software interface.

A spatial operator algebra for manipulator modeling and control

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Kreutz, K.; Milman, M.

1988-01-01

A powerful new spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed along with its implementation in the Ada programming language. Applications of this algebra to robotics include an operator representation of the manipulator Jacobian matrix; the robot dynamical equations formulated in terms of the spatial algebra, showing the complete equivalence between the recursive Newton-Euler formulations to robot dynamics; the operator factorization and inversion of the manipulator mass matrix which immediately results in O(N) recursive forward dynamics algorithms; the joint accelerations of a manipulator due to a tip contact force; the recursive computation of the equivalent mass matrix as seen at the tip of a manipulator; and recursive forward dynamics of a closed chain system. Finally, additional applications and current research involving the use of the spatial operator algebra are discussed in general terms.

Entanglement classification with matrix product states

NASA Astrophysics Data System (ADS)

Sanz, M.; Egusquiza, I. L.; di Candia, R.; Saberi, H.; Lamata, L.; Solano, E.

2016-07-01

We propose an entanglement classification for symmetric quantum states based on their diagonal matrix-product-state (MPS) representation. The proposed classification, which preserves the stochastic local operation assisted with classical communication (SLOCC) criterion, relates entanglement families to the interaction length of Hamiltonians. In this manner, we establish a connection between entanglement classification and condensed matter models from a quantum information perspective. Moreover, we introduce a scalable nesting property for the proposed entanglement classification, in which the families for N parties carry over to the N + 1 case. Finally, using techniques from algebraic geometry, we prove that the minimal nontrivial interaction length n for any symmetric state is bounded by .

An efficient method for computation of the manipulator inertia matrix

NASA Technical Reports Server (NTRS)

Fijany, Amir; Bejczy, Antal K.

1989-01-01

An efficient method of computation of the manipulator inertia matrix is presented. Using spatial notations, the method leads to the definition of the composite rigid-body spatial inertia, which is a spatial representation of the notion of augmented body. The previously proposed methods, the physical interpretations leading to their derivation, and their redundancies are analyzed. The proposed method achieves a greater efficiency by eliminating the redundancy in the intrinsic equations as well as by a better choice of coordinate frame for their projection. In this case, removing the redundancy leads to greater efficiency of the computation in both serial and parallel senses.

Machine learning reveals orbital interaction in materials

NASA Astrophysics Data System (ADS)

Lam Pham, Tien; Kino, Hiori; Terakura, Kiyoyuki; Miyake, Takashi; Tsuda, Koji; Takigawa, Ichigaku; Chi Dam, Hieu

2017-12-01

We propose a novel representation of materials named an 'orbital-field matrix (OFM)', which is based on the distribution of valence shell electrons. We demonstrate that this new representation can be highly useful in mining material data. Experimental investigation shows that the formation energies of crystalline materials, atomization energies of molecular materials, and local magnetic moments of the constituent atoms in bimetal alloys of lanthanide metal and transition-metal can be predicted with high accuracy using the OFM. Knowledge regarding the role of the coordination numbers of the transition-metal and lanthanide elements in determining the local magnetic moments of the transition-metal sites can be acquired directly from decision tree regression analyses using the OFM.

Computer-Based Learning: Graphical Integration of Whole and Sectional Neuroanatomy Improves Long-Term Retention

PubMed Central

Naaz, Farah; Chariker, Julia H.; Pani, John R.

2013-01-01

A study was conducted to test the hypothesis that instruction with graphically integrated representations of whole and sectional neuroanatomy is especially effective for learning to recognize neural structures in sectional imagery (such as MRI images). Neuroanatomy was taught to two groups of participants using computer graphical models of the human brain. Both groups learned whole anatomy first with a three-dimensional model of the brain. One group then learned sectional anatomy using two-dimensional sectional representations, with the expectation that there would be transfer of learning from whole to sectional anatomy. The second group learned sectional anatomy by moving a virtual cutting plane through the three-dimensional model. In tests of long-term retention of sectional neuroanatomy, the group with graphically integrated representation recognized more neural structures that were known to be challenging to learn. This study demonstrates the use of graphical representation to facilitate a more elaborated (deeper) understanding of complex spatial relations. PMID:24563579

Characterization of high order spatial discretizations and lumping techniques for discontinuous finite element SN transport

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

Maginot, P. G.; Ragusa, J. C.; Morel, J. E.

2013-07-01

We examine several possible methods of mass matrix lumping for discontinuous finite element discrete ordinates transport using a Lagrange interpolatory polynomial trial space. Though positive outflow angular flux is guaranteed with traditional mass matrix lumping in a purely absorbing 1-D slab cell for the linear discontinuous approximation, we show that when used with higher degree interpolatory polynomial trial spaces, traditional lumping does yield strictly positive outflows and does not increase in accuracy with an increase in trial space polynomial degree. As an alternative, we examine methods which are 'self-lumping'. Self-lumping methods yield diagonal mass matrices by using numerical quadrature restrictedmore » to the Lagrange interpolatory points. Using equally-spaced interpolatory points, self-lumping is achieved through the use of closed Newton-Cotes formulas, resulting in strictly positive outflows in pure absorbers for odd power polynomials in 1-D slab geometry. By changing interpolatory points from the traditional equally-spaced points to the quadrature points of the Gauss-Legendre or Lobatto-Gauss-Legendre quadratures, it is possible to generate solution representations with a diagonal mass matrix and a strictly positive outflow for any degree polynomial solution representation in a pure absorber medium in 1-D slab geometry. Further, there is no inherent limit to local truncation error order of accuracy when using interpolatory points that correspond to the quadrature points of high order accuracy numerical quadrature schemes. (authors)« less

Modeling reactive transport processes in fractured rock using the time domain random walk approach within a dual-porosity framework

NASA Astrophysics Data System (ADS)

Roubinet, D.; Russian, A.; Dentz, M.; Gouze, P.

2017-12-01

Characterizing and modeling hydrodynamic reactive transport in fractured rock are critical challenges for various research fields and applications including environmental remediation, geological storage, and energy production. To this end, we consider a recently developed time domain random walk (TDRW) approach, which is adapted to reproduce anomalous transport behaviors and capture heterogeneous structural and physical properties. This method is also very well suited to optimize numerical simulations by memory-shared massive parallelization and provide numerical results at various scales. So far, the TDRW approach has been applied for modeling advective-diffusive transport with mass transfer between mobile and immobile regions and simple (theoretical) reactions in heterogeneous porous media represented as single continuum domains. We extend this approach to dual-continuum representations considering a highly permeable fracture network embedded into a poorly permeable rock matrix with heterogeneous geochemical reactions occurring in both geological structures. The resulting numerical model enables us to extend the range of the modeled heterogeneity scales with an accurate representation of solute transport processes and no assumption on the Fickianity of these processes. The proposed model is compared to existing particle-based methods that are usually used to model reactive transport in fractured rocks assuming a homogeneous surrounding matrix, and is used to evaluate the impact of the matrix heterogeneity on the apparent reaction rates for different 2D and 3D simple-to-complex fracture network configurations.

BCD Beam Search: considering suboptimal partial solutions in Bad Clade Deletion supertrees.

PubMed

Fleischauer, Markus; Böcker, Sebastian

2018-01-01

Supertree methods enable the reconstruction of large phylogenies. The supertree problem can be formalized in different ways in order to cope with contradictory information in the input. Some supertree methods are based on encoding the input trees in a matrix; other methods try to find minimum cuts in some graph. Recently, we introduced Bad Clade Deletion (BCD) supertrees which combines the graph-based computation of minimum cuts with optimizing a global objective function on the matrix representation of the input trees. The BCD supertree method has guaranteed polynomial running time and is very swift in practice. The quality of reconstructed supertrees was superior to matrix representation with parsimony (MRP) and usually on par with SuperFine for simulated data; but particularly for biological data, quality of BCD supertrees could not keep up with SuperFine supertrees. Here, we present a beam search extension for the BCD algorithm that keeps alive a constant number of partial solutions in each top-down iteration phase. The guaranteed worst-case running time of the new algorithm is still polynomial in the size of the input. We present an exact and a randomized subroutine to generate suboptimal partial solutions. Both beam search approaches consistently improve supertree quality on all evaluated datasets when keeping 25 suboptimal solutions alive. Supertree quality of the BCD Beam Search algorithm is on par with MRP and SuperFine even for biological data. This is the best performance of a polynomial-time supertree algorithm reported so far.

The q-dependent detrended cross-correlation analysis of stock market

NASA Astrophysics Data System (ADS)

Zhao, Longfeng; Li, Wei; Fenu, Andrea; Podobnik, Boris; Wang, Yougui; Stanley, H. Eugene

2018-02-01

Properties of the q-dependent cross-correlation matrices of the stock market have been analyzed by using random matrix theory and complex networks. The correlation structures of the fluctuations at different magnitudes have unique properties. The cross-correlations among small fluctuations are much stronger than those among large fluctuations. The large and small fluctuations are dominated by different groups of stocks. We use complex network representation to study these q-dependent matrices and discover some new identities. By utilizing those q-dependent correlation-based networks, we are able to construct some portfolios of those more independent stocks which consistently perform better. The optimal multifractal order for portfolio optimization is around q  =  2 under the mean-variance portfolio framework, and q\\in[2, 6] under the expected shortfall criterion. These results have deepened our understanding regarding the collective behavior of the complex financial system.

Selective processing of threatening information: effects of attachment representation and anxiety disorder on attention and memory.

PubMed

Zeijlmans van Emmichoven, Ingeborg A; van IJzendoorn, Marinus H; de Ruiter, Corine; Brosschot, Jos F

2003-01-01

To investigate the effect of the mental representation of attachment on information processing, 28 anxiety disorder outpatients, as diagnosed by the Anxiety Disorders Interview Schedule-Revised, were administered the Adult Attachment Interview and the State-Trait Anxiety Inventory. They also completed an emotional Stroop task with subliminal and supraliminal exposure conditions, a free recall memory task, and a recognition test. All tasks contained threatening, neutral, and positively valenced stimuli. A nonclinical comparison group of 56 participants completed the same measures. Results on the Stroop task showed color-naming interference for threatening words in the supraliminal condition only. Nonclinical participants with insecure attachment representations showed a global response inhibition to the Stroop task. Clinical participants with secure attachment representations showed the largest Stroop interference of the threatening words compared to the other groups. Results on the free recall task showed superior recall of all types of stimuli by participants with secure attachment representations. In the outpatient group, participants with secure attachment representations showed superior recall of threatening words on the free recall task, compared to insecure participants. Results on the recognition task showed no differences between attachment groups. We conclude that secure attachment representations are characterized by open communication about and processing of threatening information, leading to less defensive exclusion of negative material during the attentional stage of information processing and to better recall of threatening information in a later stage. Attachment insecurity, but not the type of insecurity, seems a decisive factor in attention and memory processes.

Supervised graph hashing for histopathology image retrieval and classification.

PubMed

Shi, Xiaoshuang; Xing, Fuyong; Xu, KaiDi; Xie, Yuanpu; Su, Hai; Yang, Lin

2017-12-01

In pathology image analysis, morphological characteristics of cells are critical to grade many diseases. With the development of cell detection and segmentation techniques, it is possible to extract cell-level information for further analysis in pathology images. However, it is challenging to conduct efficient analysis of cell-level information on a large-scale image dataset because each image usually contains hundreds or thousands of cells. In this paper, we propose a novel image retrieval based framework for large-scale pathology image analysis. For each image, we encode each cell into binary codes to generate image representation using a novel graph based hashing model and then conduct image retrieval by applying a group-to-group matching method to similarity measurement. In order to improve both computational efficiency and memory requirement, we further introduce matrix factorization into the hashing model for scalable image retrieval. The proposed framework is extensively validated with thousands of lung cancer images, and it achieves 97.98% classification accuracy and 97.50% retrieval precision with all cells of each query image used. Copyright © 2017 Elsevier B.V. All rights reserved.

Young Children's Representations of Groups of Objects: The Relationship between Abstraction and Representation.

ERIC Educational Resources Information Center

Kato, Yasuhiko; Kamii, Constance; Ozaki, Kyoko; Nagahiro, Mariko

2002-01-01

Interviews 60 Japanese children between the ages of 3 and 7 years to investigate the relationship between levels of abstraction and representation. Indicates that abstraction and representation are closely related. Implies that educators need to focus more on the mental relationships children make because the meaning children can give to…

How Pictorial Knowledge Representations Mediate Collaborative Knowledge Construction in Groups

ERIC Educational Resources Information Center

Naykki, Piia; Jarvela, Sanna

2008-01-01

This study investigates the process of collaborative knowledge construction when technology and pictorial knowledge representations are used for visualizing individual and groups' shared ideas. The focus of the study is on how teacher-students contribute to the group's collaborative knowledge construction and use each other's ideas and tools as an…

Tactile mental body parts representation in obesity.

PubMed

Scarpina, Federica; Castelnuovo, Gianluca; Molinari, Enrico

2014-12-30

Obese people׳s distortions in visually-based mental body-parts representations have been reported in previous studies, but other sensory modalities have largely been neglected. In the present study, we investigated possible differences in tactilely-based body-parts representation between an obese and a healthy-weight group; additionally we explore the possible relationship between the tactile- and the visually-based body representation. Participants were asked to estimate the distance between two tactile stimuli that were simultaneously administered on the arm or on the abdomen, in the absence of visual input. The visually-based body-parts representation was investigated by a visual imagery method in which subjects were instructed to compare the horizontal extension of body part pairs. According to the results, the obese participants overestimated the size of the tactilely-perceived distances more than the healthy-weight group when the arm, and not the abdomen, was stimulated. Moreover, they reported a lower level of accuracy than did the healthy-weight group when estimating horizontal distances relative to their bodies, confirming an inappropriate visually-based mental body representation. Our results imply that body representation disturbance in obese people is not limited to the visual mental domain, but it spreads to the tactilely perceived distances. The inaccuracy was not a generalized tendency but was body-part related. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Social workers' and nurses' illness representations about Alzheimer disease: an exploratory study.

PubMed

Shinan-Altman, Shiri; Werner, Perla; Cohen, Miri

2014-01-01

Professionals' perceptions of patients' diseases (illness representations) are a major factor influencing the quality of treatment they provide. The aim of the study was to examine and compare Alzheimer disease (AD) illness representations among 2 main professional groups involved in the care of Alzheimer patients. A total of 327 nurses and social workers in Israel were asked to report their cognitive representations (dimensions of identity, cause, timeline, consequences, control, coherence, timeline cycle) and emotional representations. Knowledge about AD, demographic, and occupational characteristics were also obtained. Participants perceived AD as a chronic disease associated with severe consequences. Statistically significant differences were found between the groups, as nurses attributed psychological reasons to AD more than the social workers. Nevertheless, social workers perceived AD as more chronic with severe consequences compared with the nurses. Despite some resemblance, there were differences between the social workers and nurses regarding AD illness representations. Therefore, continuing to distribute materials to professionals regarding AD is recommended, with attention to the unique characteristics of each professional group. Furthermore, the findings encourage the development of training and support programs that will not only deal with the organizational and instrumental levels of treating AD patients but also with the assessment and consequences of professionals' illness representations.

Cortical Reorganization in Dual Innervation by Single Peripheral Nerve.

PubMed

Zheng, Mou-Xiong; Shen, Yun-Dong; Hua, Xu-Yun; Hou, Ao-Lin; Zhu, Yi; Xu, Wen-Dong

2017-09-21

Functional recovery after peripheral nerve injury and repair is related with cortical reorganization. However, the mechanism of innervating dual targets by 1 donor nerve is largely unknown. To investigate the cortical reorganization when the phrenic nerve simultaneously innervates the diaphragm and biceps. Total brachial plexus (C5-T1) injury rats were repaired by phrenic nerve-musculocutaneous nerve transfer with end-to-side (n = 15) or end-to-end (n = 15) neurorrhaphy. Brachial plexus avulsion (n = 5) and sham surgery (n = 5) rats were included for control. Behavioral observation, electromyography, and histologic studies were used for confirming peripheral nerve reinnervation. Cortical representations of the diaphragm and reinnervated biceps were studied by intracortical microstimulation techniques before and at months 0.5, 3, 5, 7, and 10 after surgery. At month 0.5 after complete brachial plexus injury, the motor representation of the injured forelimb disappeared. The diaphragm representation was preserved in the "end-to-side" group but absent in the "end-to-end" group. Rhythmic contraction of biceps appeared in "end-to-end" and "end-to-side" groups, and the biceps representation reappeared in the original biceps and diaphragm areas at months 3 and 5. At month 10, it was completely located in the original biceps area in the "end-to-end" group. Part of the biceps representation remained in the original diaphragm area in the "end-to-side" group. Destroying the contralateral motor cortex did not eliminate respiration-related contraction of biceps. The brain tends to resume biceps representation from the original diaphragm area to the original biceps area following phrenic nerve transfer. The original diaphragm area partly preserves reinnervated biceps representation after end-to-side transfer. Copyright © 2017 by the Congress of Neurological Surgeons

Come Together, Right Now: Dynamic Overwriting of an Object’s History through Common Fate

PubMed Central

Luria, Roy; Vogel, Edward K.

2015-01-01

The objects around us constantly move and interact, and the perceptual system needs to monitor on-line these interactions and to update the object’s status accordingly. Gestalt grouping principles, such as proximity and common fate, play a fundamental role in how we perceive and group these objects. Here, we investigated situations in which the initial object representation as a separate item was updated by a subsequent Gestalt grouping cue (i.e., proximity or common fate). We used a version of the color change detection paradigm, in which the objects started to move separately, then met and stayed stationary, or moved separately, met, and then continued to move together. We monitored the object representations on-line using the contralateral delay activity (CDA; an ERP component indicative of the number of maintained objects), during their movement, and after the objects disappeared and became working memory representations. The results demonstrated that the objects’ representations (as indicated by the CDA amplitude) persisted as being separate, even after a Gestalt proximity cue (when the objects “met” and remained stationary on the same position). Only a strong common fate Gestalt cue (when the objects not just met but also moved together) was able to override the objects’ initial separate status, creating an integrated representation. These results challenge the view that Gestalt principles cause reflexive grouping. Instead, the object initial representation plays an important role that can override even powerful grouping cues. PMID:24564468

Come together, right now: dynamic overwriting of an object's history through common fate.

PubMed

Luria, Roy; Vogel, Edward K

2014-08-01

The objects around us constantly move and interact, and the perceptual system needs to monitor on-line these interactions and to update the object's status accordingly. Gestalt grouping principles, such as proximity and common fate, play a fundamental role in how we perceive and group these objects. Here, we investigated situations in which the initial object representation as a separate item was updated by a subsequent Gestalt grouping cue (i.e., proximity or common fate). We used a version of the color change detection paradigm, in which the objects started to move separately, then met and stayed stationary, or moved separately, met, and then continued to move together. We monitored the object representations on-line using the contralateral delay activity (CDA; an ERP component indicative of the number of maintained objects), during their movement, and after the objects disappeared and became working memory representations. The results demonstrated that the objects' representations (as indicated by the CDA amplitude) persisted as being separate, even after a Gestalt proximity cue (when the objects "met" and remained stationary on the same position). Only a strong common fate Gestalt cue (when the objects not just met but also moved together) was able to override the objects' initial separate status, creating an integrated representation. These results challenge the view that Gestalt principles cause reflexive grouping. Instead, the object initial representation plays an important role that can override even powerful grouping cues.

Do Public Involvement Activities in Biomedical Research and Innovation Recruit Representatively? A Systematic Qualitative Review.

PubMed

Lander, Jonas; Hainz, Tobias; Hirschberg, Irene; Bossert, Sabine; Strech, Daniel

2016-01-01

Public involvement activities (PIAs) may contribute to the governance of ethically challenging biomedical research and innovation by informing, consulting with and engaging the public in developments and decision-making processes. For PIAs to capture a population's preferences (e.g. on issues in whole genome sequencing, biobanks or genome editing), a central methodological requirement is to involve a sufficiently representative subgroup of the general public. While the existing literature focusses on theoretical and normative aspects of 'representation', this study assesses empirically how such considerations are implemented in practice. It evaluates how PIA reports describe representation objectives, the recruitment process and levels of representation achieved. PIA reports were included from a systematic literature search if they directly reported a PIA conducted in a relevant discipline such as genomics, biobanks, biotechnology or others. PIA reports were analyzed with thematic text analysis. The text analysis was guided by an assessment matrix based on PIA-specific guidelines and frameworks. We included 46 relevant reports, most focusing on issues in genomics. 27 reports (59%) explicitly described representation objectives, though mostly without adjusting eligibility criteria and recruiting methods to the specific objective. 11 reports (24%) explicitly reported to have achieved the intended representation; the rest either reported failure or were silent on this issue. Representation of study samples in PIAs in biomedical research and innovation is currently not reported systematically. Improved reporting on representation would not only improve the validity and value of PIAs, but could also contribute to PIA results being used more often in relevant policy and decision-making processes. © 2016 S. Karger AG, Basel.

Dimensional analysis using toric ideals: primitive invariants.

PubMed

Atherton, Mark A; Bates, Ronald A; Wynn, Henry P

2014-01-01

Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units [Formula: see text] etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer [Formula: see text] matrix from the initial integer [Formula: see text] matrix holding the exponents for the derived quantities. The [Formula: see text] matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups) is obtained directly from the toric ideal defined by [Formula: see text]. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of [Formula: see text], is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.

With age comes representational wisdom in social signals.

PubMed

van Rijsbergen, Nicola; Jaworska, Katarzyna; Rousselet, Guillaume A; Schyns, Philippe G

2014-12-01

In an increasingly aging society, age has become a foundational dimension of social grouping broadly targeted by advertising and governmental policies. However, perception of old age induces mainly strong negative social biases. To characterize their cognitive and perceptual foundations, we modeled the mental representations of faces associated with three age groups (young age, middle age, and old age), in younger and older participants. We then validated the accuracy of each mental representation of age with independent validators. Using statistical image processing, we identified the features of mental representations that predict perceived age. Here, we show that whereas younger people mentally dichotomize aging into two groups, themselves (younger) and others (older), older participants faithfully represent the features of young age, middle age, and old age, with richer representations of all considered ages. Our results demonstrate that, contrary to popular public belief, older minds depict socially relevant information more accurately than their younger counterparts. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Evaluation of a Computer-Based Training Program for Enhancing Arithmetic Skills and Spatial Number Representation in Primary School Children.

PubMed

Rauscher, Larissa; Kohn, Juliane; Käser, Tanja; Mayer, Verena; Kucian, Karin; McCaskey, Ursina; Esser, Günter; von Aster, Michael

2016-01-01

Calcularis is a computer-based training program which focuses on basic numerical skills, spatial representation of numbers and arithmetic operations. The program includes a user model allowing flexible adaptation to the child's individual knowledge and learning profile. The study design to evaluate the training comprises three conditions (Calcularis group, waiting control group, spelling training group). One hundred and thirty-eight children from second to fifth grade participated in the study. Training duration comprised a minimum of 24 training sessions of 20 min within a time period of 6-8 weeks. Compared to the group without training (waiting control group) and the group with an alternative training (spelling training group), the children of the Calcularis group demonstrated a higher benefit in subtraction and number line estimation with medium to large effect sizes. Therefore, Calcularis can be used effectively to support children in arithmetic performance and spatial number representation.

Squeezed states: A geometric framework

NASA Technical Reports Server (NTRS)

Ali, S. T.; Brooke, J. A.; Gazeau, J.-P.

1992-01-01

A general definition of squeezed states is proposed and its main features are illustrated through a discussion of the standard optical coherent states represented by 'Gaussian pure states'. The set-up involves representations of groups on Hilbert spaces over homogeneous spaces of the group, and relies on the construction of a square integrable (coherent state) group representation modulo a subgroup. This construction depends upon a choice of a Borel section which has a certain permissible arbitrariness in its selection; this freedom is attributable to a squeezing of the defining coherent states of the representation, and corresponds in this way to a sort of gauging.

From Spatial Intelligence to Spatial Competences: The Results of Applied Geo-Research in Italian Schools

ERIC Educational Resources Information Center

Sarno, Emilia

2012-01-01

This contribution explains the connection between spatial intelligence and spatial competences and by indicating how the first is the cognitive matrix of abilities necessary to move in space as well as to represent it. Indeed, two are principal factors involved in the spatial intelligence: orientation and representation. Both are based on a close…

Sparse Matrix Motivated Reconstruction of Far-Field Radiation Patterns

DTIC Science & Technology

2015-03-01

method for base - station antenna radiation patterns. IEEE Antennas Propagation Magazine. 2001;43(2):132. 4. Vasiliadis TG, Dimitriou D, Sergiadis JD...algorithm based on sparse representations of radiation patterns using the inverse Discrete Fourier Transform (DFT) and the inverse Discrete Cosine...patterns using a Model- Based Parameter Estimation (MBPE) technique that reduces the computational time required to model radiation patterns. Another

Birefringence of Cellotape: Jones Representation and Experimental Analysis

ERIC Educational Resources Information Center

Belendez, Augusto; Fernandez, Elena; Frances, Jorge; Neipp, Cristian

2010-01-01

In this paper, we analyse a simple experiment to study the effects of polarized light. A simple optical system composed of a polarizer, a retarder (cellotape) and an analyser is used to study the effect on the polarization state of the light which impinges on the setup. The optical system is characterized by means of a Jones matrix, and a simple…

Computer Aided Multi-Data Fusion Dismount Modeling

DTIC Science & Technology

2012-03-22

The ability of geometric morphometric methods to estimate a known covariance matrix., volume 49. Systematic Biology, 2000. [39] Wang C., Yuen M...the use of human shape descriptors like landmarks, body composition, body segmentation, skeletonisation, body representation using geometrical shapes...Springer. [10] Bookstein, F. L. “ Morphometric Tools for Landmark Data: Geometry and Biology.” Cambridge University Press, 1991. [11] Borengasser, M

The Effective Potential Energy Surfaces of the Nonadiabatic Collision

DTIC Science & Technology

2009-03-01

effective PESs data was extracted for the equilibrium H2 bond length and used to calculate inelastic scattering matrix elements using the time ...very grateful not only for the time he devoted each week to discussing the status of the work, but also his infectious love of learning that is...33 Structure of the Asymptotic Representation ................................................................. 43 The Time -Dependent

Position Error Covariance Matrix Validation and Correction

NASA Technical Reports Server (NTRS)

Frisbee, Joe, Jr.

2016-01-01

In order to calculate operationally accurate collision probabilities, the position error covariance matrices predicted at times of closest approach must be sufficiently accurate representations of the position uncertainties. This presentation will discuss why the Gaussian distribution is a reasonable expectation for the position uncertainty and how this assumed distribution type is used in the validation and correction of position error covariance matrices.

ORNL Resolved Resonance Covariance Generation for ENDF/B-VII.1

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

Leal, Luiz C.; Guber, Klaus H.; Wiarda, Dorothea

2012-12-01

Resonance-parameter covariance matrix (RPCM) evaluations in the resolved resonance regionwere done at the Oak Ridge National Laboratory (ORNL) for the chromium isotopes, titanium isotopes, 19F, 58Ni, 60Ni, 35Cl, 37Cl, 39K, 41K, 55Mn, 233U, 235U, 238U, and 239Pu using the computer code SAMMY. The retroactive approach of the code SAMMY was used to generate the RPCMs for 233U. For 235U, the approach used for covariance generation was similar to the retroactive approach with the distinction that real experimental data were used as opposed to data generated from the resonance parameters. RPCMs for 238U and 239Pu were generated together with the resonancemore » parameter evaluations. The RPCMs were then converted in the ENDF format using the FILE32 representation. Alternatively, for computer storage reasons, the FILE32 was converted in the FILE33 cross section covariance matrix (CSCM). Both representations were processed using the computer code PUFF-IV. This paper describes the procedures used to generate the RPCM and CSCM in the resonance region for ENDF/B-VII.1. The impact of data uncertainty in nuclear reactor benchmark calculations is also presented.« less

Genomicus update 2015: KaryoView and MatrixView provide a genome-wide perspective to multispecies comparative genomics.

PubMed

Louis, Alexandra; Nguyen, Nga Thi Thuy; Muffato, Matthieu; Roest Crollius, Hugues

2015-01-01

The Genomicus web server (http://www.genomicus.biologie.ens.fr/genomicus) is a visualization tool allowing comparative genomics in four different phyla (Vertebrate, Fungi, Metazoan and Plants). It provides access to genomic information from extant species, as well as ancestral gene content and gene order for vertebrates and flowering plants. Here we present the new features available for vertebrate genome with a focus on new graphical tools. The interface to enter the database has been improved, two pairwise genome comparison tools are now available (KaryoView and MatrixView) and the multiple genome comparison tools (PhyloView and AlignView) propose three new kinds of representation and a more intuitive menu. These new developments have been implemented for Genomicus portal dedicated to vertebrates. This allows the analysis of 68 extant animal genomes, as well as 58 ancestral reconstructed genomes. The Genomicus server also provides access to ancestral gene orders, to facilitate evolutionary and comparative genomics studies, as well as computationally predicted regulatory interactions, thanks to the representation of conserved non-coding elements with their putative gene targets. © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.

The association in a two-way contingency table through log odds ratio analysis: the case of Sarno river pollution.

PubMed

Camminatiello, Ida; D'Ambra, Antonello; Sarnacchiaro, Pasquale

2014-01-01

In this paper we are proposing a general framework for the analysis of the complete set of log Odds Ratios (ORs) generated by a two-way contingency table. Starting from the RC (M) association model and hypothesizing a Poisson distribution for the counts of the two-way contingency table we are obtaining the weighted Log Ratio Analysis that we are extending to the study of log ORs. Particularly we are obtaining an indirect representation of the log ORs and some synthesis measures. Then for studying the matrix of log ORs we are performing a generalized Singular Value Decomposition that allows us to obtain a direct representation of log ORs. We also expect to get summary measures of association too. We have considered the matrix of complete set of ORs, because, it is linked to the two-way contingency table in terms of variance and it allows us to represent all the ORs on a factorial plan. Finally, a two-way contingency table, which crosses pollution of the Sarno river and sampling points, is to be analyzed to illustrate the proposed framework.

Spatial Pyramid Covariance based Compact Video Code for Robust Face Retrieval in TV-series.

PubMed

Li, Yan; Wang, Ruiping; Cui, Zhen; Shan, Shiguang; Chen, Xilin

2016-10-10

We address the problem of face video retrieval in TV-series which searches video clips based on the presence of specific character, given one face track of his/her. This is tremendously challenging because on one hand, faces in TV-series are captured in largely uncontrolled conditions with complex appearance variations, and on the other hand retrieval task typically needs efficient representation with low time and space complexity. To handle this problem, we propose a compact and discriminative representation for the huge body of video data, named Compact Video Code (CVC). Our method first models the face track by its sample (i.e., frame) covariance matrix to capture the video data variations in a statistical manner. To incorporate discriminative information and obtain more compact video signature suitable for retrieval, the high-dimensional covariance representation is further encoded as a much lower-dimensional binary vector, which finally yields the proposed CVC. Specifically, each bit of the code, i.e., each dimension of the binary vector, is produced via supervised learning in a max margin framework, which aims to make a balance between the discriminability and stability of the code. Besides, we further extend the descriptive granularity of covariance matrix from traditional pixel-level to more general patchlevel, and proceed to propose a novel hierarchical video representation named Spatial Pyramid Covariance (SPC) along with a fast calculation method. Face retrieval experiments on two challenging TV-series video databases, i.e., the Big Bang Theory and Prison Break, demonstrate the competitiveness of the proposed CVC over state-of-the-art retrieval methods. In addition, as a general video matching algorithm, CVC is also evaluated in traditional video face recognition task on a standard Internet database, i.e., YouTube Celebrities, showing its quite promising performance by using an extremely compact code with only 128 bits.

Classification and Realizations of Type III Factor Representations of Cuntz-Krieger Algebras Associated with Quasi-Free States

NASA Astrophysics Data System (ADS)

Kawamura, Katsunori

2009-03-01

We completely classify type III factor representations of Cuntz-Krieger algebras associated with quasi-free states up to unitary equivalence. Furthermore, we realize these representations on concrete Hilbert spaces without using GNS construction. Free groups and their type II1 factor representations are used in these realizations.

Modulators of the extracellular matrix and risk of anterior cruciate ligament ruptures.

PubMed

Rahim, Masouda; Mannion, Sasha; Klug, Blake; Hobbs, Hayden; van der Merwe, Willem; Posthumus, Michael; Collins, Malcolm; September, Alison V

2017-02-01

The extracellular matrix (ECM) of ligaments continuously undergoes remodelling in order to maintain tissue homeostasis. Several key mediators of ECM remodelling were chosen for investigation in the present study. It is thought that polymorphisms within genes encoding signalling molecules may contribute to inter-individual variation in the responses to mechanical loading, potentially altering risk of injury. A genetic association study was conducted on 232 asymptomatic controls (CON) and 234 participants with surgically diagnosed anterior cruciate ligament (ACL) ruptures; of which 135 participants reported a non-contact mechanism of injury (NON subgroup). All participants were genotyped for ten variants in eight genes encoding ECM remodelling proteins. Haplotypes and allele combinations were also inferred. The CASP8 rs3834129 ins allele was significantly over-represented in the male CON group compared to the male NON subgroup (p=0.047, OR: 1.46, 95% CI: 1.01-2.12). In female participants, the IL1B rs16944 TT genotype was significantly under-represented in the CON group compared to the NON subgroup (p=0.039, OR: 3.06, 95% CI: 1.09-8.64). Haplotype analysis revealed an under-representation of the CASP8 rs3834129-rs1045485 del-G haplotype in the CON group compared to both the ACL group (p=0.042; haplo.score:2.03) and the NON subgroup (p=0.037; haplo.score:2.09). Furthermore, following a pathway-based approach, genetic variants involved in the cell signalling cascade were associated with ACL injury risk. The novel independent associations and allele combinations observed implicate the apoptosis and cell signalling cascades as potential contributors to ACL injury susceptibility. Furthermore, these genetic variants may potentially modulate ECM remodelling in response to loading and ultimately contribute to ligament capacity. Copyright © 2016 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.

La structure de Jordan des matrices de transfert des modeles de boucles et la relation avec les hamiltoniens XXZ

NASA Astrophysics Data System (ADS)

Morin-Duchesne, Alexi

Lattice models such as percolation, the Ising model and the Potts model are useful for the description of phase transitions in two dimensions. Finding analytical solutions is done by calculating the partition function, which in turn requires finding eigenvalues of transfer matrices. At the critical point, the two dimensional statistical models are invariant under conformal transformations and the construction of rational conformal field theories, as the continuum limit of these lattice models, allows one to compute the partition function at the critical point. Many researchers think however that the paradigm of rational conformal conformal field theories can be extended to include models with non diagonalizable transfer matrices. These models would then be described, in the scaling limit, by logarithmic conformal field theories and the representations of the Virasoro algebra coming into play would be indecomposable. We recall the construction of the double-row transfer matrix DN (λ, u) of the Fortuin-Kasteleyn model, seen as an element of the Temperley-Lieb algebra. This transfer matrix comes into play in physical theories through its representation in link modules (or standard modules). The vector space on which this representation acts decomposes into sectors labelled by a physical parameter d, the number of defects, which remains constant or decreases in the link representations. This thesis is devoted to the identification of the Jordan structure of DN(λ, u) in the link representations. The parameter β = 2 cos λ = -(q + q-1) fixes the theory : for instance β = 1 for percolation and 2 for the Ising model. On the geometry of the strip with open boundary conditions, we show that DN(λ, u) has the same Jordan blocks as its highest Fourier coefficient, FN. We study the non-diagonalizability of FN through the divergences of some of the eigenstates of ρ(F N) that appear at the critical values of λ. The Jordan cells we find in ρ(DN(λ, u)) have rank 2 and couple sectors d and d' when specific constraints on λ, d, d' and N are satisfied. For the model of critical dense polymers (β = 0) on the strip, the eigenvalues of ρ(DN(λ, u)) were known, but their degeneracies only conjectured. By constructing an isomorphism between the link modules on the strip and a subspace of spin modules of the XXZ model at q = i, we prove this conjecture. We also show that the restriction of the Hamiltonian to any sector d is diagonalizable, and that the XX Hamiltonian has rank 2 Jordan cells when N is even. Finally, we study the Jordan structure of the transfer matrix T N(λ, ν) for periodic boundary conditions. When λ = πa/b and a, b ∈ Z× , the matrix TN(λ, ν) has Jordan blocks between sectors, but also within sectors. The approach using FN admits a generalization to the present case and allows us to probe the Jordan cells that tie different sectors. The rank of these cells exceeds 2 in some cases and can grow indefinitely with N. For the Jordan blocks within a sector, we show that the link modules on the cylinder and the XXZ spin modules are isomorphic except for specific curves in the (q, ν) plane. By using the behavior of the transformation ĩd N in a neighborhood of the critical values (qc, ν c), we explicitly build Jordan partners of rank 2 and discuss the existence of Jordan cells with higher rank. Keywords : phase transitions, Ising model, Potts model, Fortuin-Kasteleyn model, transfer matrix method, XXZ Hamiltonian, logarithmic conformal field theory, Jordan structure.

Matter in transition

DOE PAGES

Anderson, Lara B.; Gray, James; Raghuram, Nikhil; ...

2016-04-13

In this study, we explore a novel type of transition in certain 6D and 4D quantum field theories, in which the matter content of the theory changes while the gauge group and other parts of the spectrum remain invariant. Such transitions can occur, for example, for SU(6) and SU(7) gauge groups, where matter fields in a three-index antisymmetric representation and the fundamental representation are exchanged in the transition for matter in the two-index antisymmetric representation. These matter transitions are realized by passing through superconformal theories at the transition point. We explore these transitions in dual F-theory and heterotic descriptions, wheremore » a number of novel features arise. For example, in the heterotic description the relevant 6D SU(7) theories are described by bundles on K3 surfaces where the geometry of the K3 is constrained in addition to the bundle structure. On the F-theory side, non-standard representations such as the three-index antisymmetric representation of SU(N) require Weierstrass models that cannot be realized from the standard SU(N) Tate form. We also briefly describe some other situations, with groups such as Sp(3), SO(12), and SU(3), where analogous matter transitions can occur between different representations. For SU(3), in particular, we find a matter transition between adjoint matter and matter in the symmetric representation, giving an explicit Weierstrass model for the F-theory description of the symmetric representation that complements another recent analogous construction.« less

Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver.

PubMed

Nakata, Maho; Braams, Bastiaan J; Fujisawa, Katsuki; Fukuda, Mituhiro; Percus, Jerome K; Yamashita, Makoto; Zhao, Zhengji

2008-04-28

The reduced density matrix (RDM) method, which is a variational calculation based on the second-order reduced density matrix, is applied to the ground state energies and the dipole moments for 57 different states of atoms, molecules, and to the ground state energies and the elements of 2-RDM for the Hubbard model. We explore the well-known N-representability conditions (P, Q, and G) together with the more recent and much stronger T1 and T2(') conditions. T2(') condition was recently rederived and it implies T2 condition. Using these N-representability conditions, we can usually calculate correlation energies in percentage ranging from 100% to 101%, whose accuracy is similar to CCSD(T) and even better for high spin states or anion systems where CCSD(T) fails. Highly accurate calculations are carried out by handling equality constraints and/or developing multiple precision arithmetic in the semidefinite programming (SDP) solver. Results show that handling equality constraints correctly improves the accuracy from 0.1 to 0.6 mhartree. Additionally, improvements by replacing T2 condition with T2(') condition are typically of 0.1-0.5 mhartree. The newly developed multiple precision arithmetic version of SDP solver calculates extraordinary accurate energies for the one dimensional Hubbard model and Be atom. It gives at least 16 significant digits for energies, where double precision calculations gives only two to eight digits. It also provides physically meaningful results for the Hubbard model in the high correlation limit.

A tight and explicit representation of Q in sparse QR factorization

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

Ng, E.G.; Peyton, B.W.

1992-05-01

In QR factorization of a sparse m{times}n matrix A (m {ge} n) the orthogonal factor Q is often stored implicitly as a lower trapezoidal matrix H known as the Householder matrix. This paper presents a simple characterization of the row structure of Q, which could be used as the basis for a sparse data structure that can store Q explicitly. The new characterization is a simple extension of a well known row-oriented characterization of the structure of H. Hare, Johnson, Olesky, and van den Driessche have recently provided a complete sparsity analysis of the QR factorization. Let U be themore » matrix consisting of the first n columns of Q. Using results from, we show that the data structures for H and U resulting from our characterizations are tight when A is a strong Hall matrix. We also show that H and the lower trapezoidal part of U have the same sparsity characterization when A is strong Hall. We then show that this characterization can be extended to any weak Hall matrix that has been permuted into block upper triangular form. Finally, we show that permuting to block triangular form never increases the fill incurred during the factorization.« less

A real-space stochastic density matrix approach for density functional electronic structure.

PubMed

Beck, Thomas L

2015-12-21

The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.

Physics of the Lorentz Group

NASA Astrophysics Data System (ADS)

Başkal, Sibel

2015-11-01

This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincaré sphere on polarization optics.

Measurement of the matrix elements for the decays η'→η π+π- and η'→η π0π0

NASA Astrophysics Data System (ADS)

Ablikim, M.; Achasov, M. N.; Ahmed, S.; Albrecht, M.; Amoroso, A.; An, F. F.; An, Q.; Bai, J. Z.; Bai, Y.; Bakina, O.; Baldini Ferroli, R.; Ban, Y.; Bennett, D. W.; Bennett, J. V.; Berger, N.; Bertani, M.; Bettoni, D.; Bian, J. M.; Bianchi, F.; Boger, E.; Boyko, I.; Briere, R. A.; Cai, H.; Cai, X.; Cakir, O.; Calcaterra, A.; Cao, G. F.; Cetin, S. A.; Chai, J.; Chang, J. F.; Chelkov, G.; Chen, G.; Chen, H. S.; Chen, J. C.; Chen, M. L.; Chen, S. J.; Chen, X. R.; Chen, Y. B.; Chu, X. K.; Cibinetto, G.; Dai, H. L.; Dai, J. P.; Dbeyssi, A.; Dedovich, D.; Deng, Z. Y.; Denig, A.; Denysenko, I.; Destefanis, M.; de Mori, F.; Ding, Y.; Dong, C.; Dong, J.; Dong, L. Y.; Dong, M. Y.; Dorjkhaidav, O.; Dou, Z. L.; Du, S. X.; Duan, P. F.; Fang, J.; Fang, S. S.; Fang, X.; Fang, Y.; Farinelli, R.; Fava, L.; Fegan, S.; Feldbauer, F.; Felici, G.; Feng, C. Q.; Fioravanti, E.; Fritsch, M.; Fu, C. D.; Gao, Q.; Gao, X. L.; Gao, Y.; Gao, Y. G.; Gao, Z.; Garzia, I.; Goetzen, K.; Gong, L.; Gong, W. X.; Gradl, W.; Greco, M.; Gu, M. H.; Gu, S.; Gu, Y. T.; Guo, A. Q.; Guo, L. B.; Guo, R. P.; Guo, Y. P.; Haddadi, Z.; Han, S.; Hao, X. Q.; Harris, F. A.; He, K. L.; He, X. Q.; Heinsius, F. H.; Held, T.; Heng, Y. K.; Holtmann, T.; Hou, Z. L.; Hu, C.; Hu, H. M.; Hu, T.; Hu, Y.; Huang, G. S.; Huang, J. S.; Huang, X. T.; Huang, X. Z.; Huang, Z. L.; Hussain, T.; Ikegami Andersson, W.; Ji, Q.; Ji, Q. P.; Ji, X. B.; Ji, X. L.; Jiang, X. S.; Jiang, X. Y.; Jiao, J. B.; Jiao, Z.; Jin, D. P.; Jin, S.; Jin, Y.; Johansson, T.; Julin, A.; Kalantar-Nayestanaki, N.; Kang, X. L.; Kang, X. S.; Kavatsyuk, M.; Ke, B. C.; Khan, T.; Khoukaz, A.; Kiese, P.; Kliemt, R.; Koch, L.; Kolcu, O. B.; Kopf, B.; Kornicer, M.; Kuemmel, M.; Kuhlmann, M.; Kupsc, A.; Kühn, W.; Lange, J. S.; Lara, M.; Larin, P.; Lavezzi, L.; Leithoff, H.; Leng, C.; Li, C.; Li, Cheng; Li, D. M.; Li, F.; Li, F. Y.; Li, G.; Li, H. B.; Li, H. J.; Li, J. C.; Li, Jin; Li, K.; Li, K.; Li, K. J.; Li, Lei; Li, P. L.; Li, P. R.; Li, Q. Y.; Li, T.; Li, W. D.; Li, W. G.; Li, X. L.; Li, X. N.; Li, X. Q.; Li, Z. B.; Liang, H.; Liang, Y. F.; Liang, Y. T.; Liao, G. R.; Lin, D. X.; Liu, B.; Liu, B. J.; Liu, C. X.; Liu, D.; Liu, F. H.; Liu, Fang; Liu, Feng; Liu, H. B.; Liu, H. H.; Liu, H. H.; Liu, H. M.; Liu, J. B.; Liu, J. P.; Liu, J. Y.; Liu, K.; Liu, K. Y.; Liu, Ke; Liu, L. D.; Liu, P. L.; Liu, Q.; Liu, S. B.; Liu, X.; Liu, Y. B.; Liu, Z. A.; Liu, Zhiqing; Long, Y. F.; Lou, X. C.; Lu, H. J.; Lu, J. G.; Lu, Y.; Lu, Y. P.; Luo, C. L.; Luo, M. X.; Luo, X. L.; Lyu, X. R.; Ma, F. C.; Ma, H. L.; Ma, L. L.; Ma, M. M.; Ma, Q. M.; Ma, T.; Ma, X. N.; Ma, X. Y.; Ma, Y. M.; Maas, F. E.; Maggiora, M.; Magnoni, A. S.; Malik, Q. A.; Mao, Y. J.; Mao, Z. P.; Marcello, S.; Meng, Z. X.; Messchendorp, J. G.; Mezzadri, G.; Min, J.; Min, T. J.; Mitchell, R. E.; Mo, X. H.; Mo, Y. J.; Morales Morales, C.; Morello, G.; Muchnoi, N. Yu.; Muramatsu, H.; Mustafa, A.; Nefedov, Y.; Nerling, F.; Nikolaev, I. B.; Ning, Z.; Nisar, S.; Niu, S. L.; Niu, X. Y.; Olsen, S. L.; Ouyang, Q.; Pacetti, S.; Pan, Y.; Papenbrock, M.; Patteri, P.; Pelizaeus, M.; Pellegrino, J.; Peng, H. P.; Peters, K.; Pettersson, J.; Ping, J. L.; Ping, R. G.; Poling, R.; Prasad, V.; Qi, H. R.; Qi, M.; Qian, S.; Qiao, C. F.; Qin, N.; Qin, X.; Qin, X. S.; Qin, Z. H.; Qiu, J. F.; Rashid, K. H.; Redmer, C. F.; Richter, M.; Ripka, M.; Rolo, M.; Rong, G.; Rosner, Ch.; Ruan, X. D.; Sarantsev, A.; Savrié, M.; Schnier, C.; Schoenning, K.; Shan, W.; Shao, M.; Shen, C. P.; Shen, P. X.; Shen, X. Y.; Sheng, H. Y.; Song, J. J.; Song, W. M.; Song, X. Y.; Sosio, S.; Sowa, C.; Spataro, S.; Sun, G. X.; Sun, J. F.; Sun, L.; Sun, S. S.; Sun, X. H.; Sun, Y. J.; Sun, Y. K.; Sun, Y. Z.; Sun, Z. J.; Sun, Z. T.; Tang, C. J.; Tang, G. Y.; Tang, X.; Tapan, I.; Tiemens, M.; Tsednee, B. T.; Uman, I.; Varner, G. S.; Wang, B.; Wang, B. L.; Wang, D.; Wang, D. Y.; Wang, Dan; Wang, K.; Wang, L. L.; Wang, L. S.; Wang, M.; Wang, P.; Wang, P. L.; Wang, W. P.; Wang, X. F.; Wang, Y.; Wang, Y. D.; Wang, Y. F.; Wang, Y. Q.; Wang, Z.; Wang, Z. G.; Wang, Z. H.; Wang, Z. Y.; Wang, Z. Y.; Weber, T.; Wei, D. H.; Wei, J. H.; Weidenkaff, P.; Wen, S. P.; Wiedner, U.; Wolke, M.; Wu, L. H.; Wu, L. J.; Wu, Z.; Xia, L.; Xia, Y.; Xiao, D.; Xiao, H.; Xiao, Y. J.; Xiao, Z. J.; Xie, Y. G.; Xie, Y. H.; Xiong, X. A.; Xiu, Q. L.; Xu, G. F.; Xu, J. J.; Xu, L.; Xu, Q. J.; Xu, Q. N.; Xu, X. P.; Yan, L.; Yan, W. B.; Yan, W. C.; Yan, Y. H.; Yang, H. J.; Yang, H. X.; Yang, L.; Yang, Y. H.; Yang, Y. X.; Ye, M.; Ye, M. H.; Yin, J. H.; You, Z. Y.; Yu, B. X.; Yu, C. X.; Yu, J. S.; Yuan, C. Z.; Yuan, Y.; Yuncu, A.; Zafar, A. A.; Zeng, Y.; Zeng, Z.; Zhang, B. X.; Zhang, B. Y.; Zhang, C. C.; Zhang, D. H.; Zhang, H. H.; Zhang, H. Y.; Zhang, J.; Zhang, J. L.; Zhang, J. Q.; Zhang, J. W.; Zhang, J. Y.; Zhang, J. Z.; Zhang, K.; Zhang, L.; Zhang, S. Q.; Zhang, X. Y.; Zhang, Y.; Zhang, Y.; Zhang, Y. H.; Zhang, Y. T.; Zhang, Yu; Zhang, Z. H.; Zhang, Z. P.; Zhang, Z. Y.; Zhao, G.; Zhao, J. W.; Zhao, J. Y.; Zhao, J. Z.; Zhao, Lei; Zhao, Ling; Zhao, M. G.; Zhao, Q.; Zhao, S. J.; Zhao, T. C.; Zhao, Y. B.; Zhao, Z. G.; Zhemchugov, A.; Zheng, B.; Zheng, J. P.; Zheng, W. J.; Zheng, Y. H.; Zhong, B.; Zhou, L.; Zhou, X.; Zhou, X. K.; Zhou, X. R.; Zhou, X. Y.; Zhou, Y. X.; Zhu, J.; Zhu, K.; Zhu, K. J.; Zhu, S.; Zhu, S. H.; Zhu, X. L.; Zhu, Y. C.; Zhu, Y. S.; Zhu, Z. A.; Zhuang, J.; Zou, B. S.; Zou, J. H.; Besiii Collaboration

2018-01-01

Based on a sample of 1.31 ×109 J /ψ events collected with the BESIII detector, the matrix elements for the decays η'→η π+π- and η'→η π0π0 are determined using 351,016 η'→(η →γ γ )π+π- and 56,249 η'→(η →γ γ )π0π0 events with background levels less than 1%. Two commonly used representations are used to describe the Dalitz plot density. We find that an assumption of a linear amplitude does not describe the data well. A small deviation of the obtained matrix elements between η'→η π+π- and η'→η π0π0 is probably caused by the mass difference between charged and neutral pions or radiative corrections. No cusp structure in η'→η π0π0 is observed.

Ultraviolet Spectroscopy of Matrix-isolated Amorphous Carbon Particles

NASA Astrophysics Data System (ADS)

Schnaiter, M.; Mutschke, H.; Henning, Th.; Lindackers, D.; Strecker, M.; Roth, P.

1996-06-01

In view of the interstellar 217.5 nm and the circumstellar 230--250 nm extinction features, the UV extinction behavior of small matrix-isolated amorphous carbon grains is investigated experimentally. The particles were produced in a flame by burning acetylene with oxygen at low pressure. To prevent coagulation, the condensing primary soot grains (average diameter ~6 nm) were extracted by a molecular beam technique into a high-vacuum chamber. There they were deposited into a layer of solid argon, isolated from each other. The particle mass and size were controlled using a particle mass spectrometer. The measured UV extinction of the matrix-isolated particles is compared with measurements on samples produced in the conventional way by collecting carbon smoke on substrate as well as with scattering calculations for small spheres and ellipsoides. The laboratory data give a good representation of the circumstellar extinction feature observed in the spectrum of V348 Sgr.

Complex Langevin simulation of a random matrix model at nonzero chemical potential

NASA Astrophysics Data System (ADS)

Bloch, J.; Glesaaen, J.; Verbaarschot, J. J. M.; Zafeiropoulos, S.

2018-03-01

In this paper we test the complex Langevin algorithm for numerical simulations of a random matrix model of QCD with a first order phase transition to a phase of finite baryon density. We observe that a naive implementation of the algorithm leads to phase quenched results, which were also derived analytically in this article. We test several fixes for the convergence issues of the algorithm, in particular the method of gauge cooling, the shifted representation, the deformation technique and reweighted complex Langevin, but only the latter method reproduces the correct analytical results in the region where the quark mass is inside the domain of the eigenvalues. In order to shed more light on the issues of the methods we also apply them to a similar random matrix model with a milder sign problem and no phase transition, and in that case gauge cooling solves the convergence problems as was shown before in the literature.

Approximate equiangular tight frames for compressed sensing and CDMA applications

NASA Astrophysics Data System (ADS)

Tsiligianni, Evaggelia; Kondi, Lisimachos P.; Katsaggelos, Aggelos K.

2017-12-01

Performance guarantees for recovery algorithms employed in sparse representations, and compressed sensing highlights the importance of incoherence. Optimal bounds of incoherence are attained by equiangular unit norm tight frames (ETFs). Although ETFs are important in many applications, they do not exist for all dimensions, while their construction has been proven extremely difficult. In this paper, we construct frames that are close to ETFs. According to results from frame and graph theory, the existence of an ETF depends on the existence of its signature matrix, that is, a symmetric matrix with certain structure and spectrum consisting of two distinct eigenvalues. We view the construction of a signature matrix as an inverse eigenvalue problem and propose a method that produces frames of any dimensions that are close to ETFs. Due to the achieved equiangularity property, the so obtained frames can be employed as spreading sequences in synchronous code-division multiple access (s-CDMA) systems, besides compressed sensing.

Matrix-vector multiplication using digital partitioning for more accurate optical computing

NASA Technical Reports Server (NTRS)

Gary, C. K.

1992-01-01

Digital partitioning offers a flexible means of increasing the accuracy of an optical matrix-vector processor. This algorithm can be implemented with the same architecture required for a purely analog processor, which gives optical matrix-vector processors the ability to perform high-accuracy calculations at speeds comparable with or greater than electronic computers as well as the ability to perform analog operations at a much greater speed. Digital partitioning is compared with digital multiplication by analog convolution, residue number systems, and redundant number representation in terms of the size and the speed required for an equivalent throughput as well as in terms of the hardware requirements. Digital partitioning and digital multiplication by analog convolution are found to be the most efficient alogrithms if coding time and hardware are considered, and the architecture for digital partitioning permits the use of analog computations to provide the greatest throughput for a single processor.

Lattice Symmetry and Identification-The Fundamental Role of Reduced Cells in Materials Characterization.

PubMed

Mighell, A D

2001-01-01

In theory, physical crystals can be represented by idealized mathematical lattices. Under appropriate conditions, these representations can be used for a variety of purposes such as identifying, classifying, and understanding the physical properties of materials. Critical to these applications is the ability to construct a unique representation of the lattice. The vital link that enabled this theory to be realized in practice was provided by the 1970 paper on the determination of reduced cells. This seminal paper led to a mathematical approach to lattice analysis initially based on systematic reduction procedures and the use of standard cells. Subsequently, the process evolved to a matrix approach based on group theory and linear algebra that offered a more abstract and powerful way to look at lattices and their properties. Application of the reduced cell to both database work and laboratory research at NIST was immediately successful. Currently, this cell and/or procedures based on reduction are widely and routinely used by the general scientific community: (i) for calculating standard cells for the reporting of crystalline materials, (ii) for classifying materials, (iii) in crystallographic database work (iv) in routine x-ray and neutron diffractometry, and (v) in general crystallographic research. Especially important is its use in symmetry determination and in identification. The focus herein is on the role of the reduced cell in lattice symmetry determination.

Identification of vehicle suspension parameters by design optimization

NASA Astrophysics Data System (ADS)

Tey, J. Y.; Ramli, R.; Kheng, C. W.; Chong, S. Y.; Abidin, M. A. Z.

2014-05-01

The design of a vehicle suspension system through simulation requires accurate representation of the design parameters. These parameters are usually difficult to measure or sometimes unavailable. This article proposes an efficient approach to identify the unknown parameters through optimization based on experimental results, where the covariance matrix adaptation-evolutionary strategy (CMA-es) is utilized to improve the simulation and experimental results against the kinematic and compliance tests. This speeds up the design and development cycle by recovering all the unknown data with respect to a set of kinematic measurements through a single optimization process. A case study employing a McPherson strut suspension system is modelled in a multi-body dynamic system. Three kinematic and compliance tests are examined, namely, vertical parallel wheel travel, opposite wheel travel and single wheel travel. The problem is formulated as a multi-objective optimization problem with 40 objectives and 49 design parameters. A hierarchical clustering method based on global sensitivity analysis is used to reduce the number of objectives to 30 by grouping correlated objectives together. Then, a dynamic summation of rank value is used as pseudo-objective functions to reformulate the multi-objective optimization to a single-objective optimization problem. The optimized results show a significant improvement in the correlation between the simulated model and the experimental model. Once accurate representation of the vehicle suspension model is achieved, further analysis, such as ride and handling performances, can be implemented for further optimization.

Lattice Symmetry and Identification—The Fundamental Role of Reduced Cells in Materials Characterization

PubMed Central

Mighell, Alan D.

2001-01-01

In theory, physical crystals can be represented by idealized mathematical lattices. Under appropriate conditions, these representations can be used for a variety of purposes such as identifying, classifying, and understanding the physical properties of materials. Critical to these applications is the ability to construct a unique representation of the lattice. The vital link that enabled this theory to be realized in practice was provided by the 1970 paper on the determination of reduced cells. This seminal paper led to a mathematical approach to lattice analysis initially based on systematic reduction procedures and the use of standard cells. Subsequently, the process evolved to a matrix approach based on group theory and linear algebra that offered a more abstract and powerful way to look at lattices and their properties. Application of the reduced cell to both database work and laboratory research at NIST was immediately successful. Currently, this cell and/or procedures based on reduction are widely and routinely used by the general scientific community: (i) for calculating standard cells for the reporting of crystalline materials, (ii) for classifying materials, (iii) in crystallographic database work (iv) in routine x-ray and neutron diffractometry, and (v) in general crystallographic research. Especially important is its use in symmetry determination and in identification. The focus herein is on the role of the reduced cell in lattice symmetry determination. PMID:27500059

Signal Sampling for Efficient Sparse Representation of Resting State FMRI Data

PubMed Central

Ge, Bao; Makkie, Milad; Wang, Jin; Zhao, Shijie; Jiang, Xi; Li, Xiang; Lv, Jinglei; Zhang, Shu; Zhang, Wei; Han, Junwei; Guo, Lei; Liu, Tianming

2015-01-01

As the size of brain imaging data such as fMRI grows explosively, it provides us with unprecedented and abundant information about the brain. How to reduce the size of fMRI data but not lose much information becomes a more and more pressing issue. Recent literature studies tried to deal with it by dictionary learning and sparse representation methods, however, their computation complexities are still high, which hampers the wider application of sparse representation method to large scale fMRI datasets. To effectively address this problem, this work proposes to represent resting state fMRI (rs-fMRI) signals of a whole brain via a statistical sampling based sparse representation. First we sampled the whole brain’s signals via different sampling methods, then the sampled signals were aggregate into an input data matrix to learn a dictionary, finally this dictionary was used to sparsely represent the whole brain’s signals and identify the resting state networks. Comparative experiments demonstrate that the proposed signal sampling framework can speed-up by ten times in reconstructing concurrent brain networks without losing much information. The experiments on the 1000 Functional Connectomes Project further demonstrate its effectiveness and superiority. PMID:26646924

Model representations of kerogen structures: An insight from density functional theory calculations and spectroscopic measurements

DOE PAGES

Weck, Philippe F.; Kim, Eunja; Wang, Yifeng; ...

2017-08-01

Molecular structures of kerogen control hydrocarbon production in unconventional reservoirs. Significant progress has been made in developing model representations of various kerogen structures. These models have been widely used for the prediction of gas adsorption and migration in shale matrix. However, using density functional perturbation theory (DFPT) calculations and vibrational spectroscopic measurements, we here show that a large gap may still remain between the existing model representations and actual kerogen structures, therefore calling for new model development. Using DFPT, we calculated Fourier transform infrared (FTIR) spectra for six most widely used kerogen structure models. The computed spectra were then systematicallymore » compared to the FTIR absorption spectra collected for kerogen samples isolated from Mancos, Woodford and Marcellus formations representing a wide range of kerogen origin and maturation conditions. Limited agreement between the model predictions and the measurements highlights that the existing kerogen models may still miss some key features in structural representation. A combination of DFPT calculations with spectroscopic measurements may provide a useful diagnostic tool for assessing the adequacy of a proposed structural model as well as for future model development. This approach may eventually help develop comprehensive infrared (IR)-fingerprints for tracing kerogen evolution.« less

Model representations of kerogen structures: An insight from density functional theory calculations and spectroscopic measurements.

PubMed

Weck, Philippe F; Kim, Eunja; Wang, Yifeng; Kruichak, Jessica N; Mills, Melissa M; Matteo, Edward N; Pellenq, Roland J-M

2017-08-01

Molecular structures of kerogen control hydrocarbon production in unconventional reservoirs. Significant progress has been made in developing model representations of various kerogen structures. These models have been widely used for the prediction of gas adsorption and migration in shale matrix. However, using density functional perturbation theory (DFPT) calculations and vibrational spectroscopic measurements, we here show that a large gap may still remain between the existing model representations and actual kerogen structures, therefore calling for new model development. Using DFPT, we calculated Fourier transform infrared (FTIR) spectra for six most widely used kerogen structure models. The computed spectra were then systematically compared to the FTIR absorption spectra collected for kerogen samples isolated from Mancos, Woodford and Marcellus formations representing a wide range of kerogen origin and maturation conditions. Limited agreement between the model predictions and the measurements highlights that the existing kerogen models may still miss some key features in structural representation. A combination of DFPT calculations with spectroscopic measurements may provide a useful diagnostic tool for assessing the adequacy of a proposed structural model as well as for future model development. This approach may eventually help develop comprehensive infrared (IR)-fingerprints for tracing kerogen evolution.

Model representations of kerogen structures: An insight from density functional theory calculations and spectroscopic measurements

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

Weck, Philippe F.; Kim, Eunja; Wang, Yifeng

Molecular structures of kerogen control hydrocarbon production in unconventional reservoirs. Significant progress has been made in developing model representations of various kerogen structures. These models have been widely used for the prediction of gas adsorption and migration in shale matrix. However, using density functional perturbation theory (DFPT) calculations and vibrational spectroscopic measurements, we here show that a large gap may still remain between the existing model representations and actual kerogen structures, therefore calling for new model development. Using DFPT, we calculated Fourier transform infrared (FTIR) spectra for six most widely used kerogen structure models. The computed spectra were then systematicallymore » compared to the FTIR absorption spectra collected for kerogen samples isolated from Mancos, Woodford and Marcellus formations representing a wide range of kerogen origin and maturation conditions. Limited agreement between the model predictions and the measurements highlights that the existing kerogen models may still miss some key features in structural representation. A combination of DFPT calculations with spectroscopic measurements may provide a useful diagnostic tool for assessing the adequacy of a proposed structural model as well as for future model development. This approach may eventually help develop comprehensive infrared (IR)-fingerprints for tracing kerogen evolution.« less

An embedded system for face classification in infrared video using sparse representation

NASA Astrophysics Data System (ADS)

Saavedra M., Antonio; Pezoa, Jorge E.; Zarkesh-Ha, Payman; Figueroa, Miguel

2017-09-01

We propose a platform for robust face recognition in Infrared (IR) images using Compressive Sensing (CS). In line with CS theory, the classification problem is solved using a sparse representation framework, where test images are modeled by means of a linear combination of the training set. Because the training set constitutes an over-complete dictionary, we identify new images by finding their sparsest representation based on the training set, using standard l1-minimization algorithms. Unlike conventional face-recognition algorithms, we feature extraction is performed using random projections with a precomputed binary matrix, as proposed in the CS literature. This random sampling reduces the effects of noise and occlusions such as facial hair, eyeglasses, and disguises, which are notoriously challenging in IR images. Thus, the performance of our framework is robust to these noise and occlusion factors, achieving an average accuracy of approximately 90% when the UCHThermalFace database is used for training and testing purposes. We implemented our framework on a high-performance embedded digital system, where the computation of the sparse representation of IR images was performed by a dedicated hardware using a deeply pipelined architecture on an Field-Programmable Gate Array (FPGA).

Algebro-geometric approach for a centrally extended Uq[sl(2|2)] R-matrix

NASA Astrophysics Data System (ADS)

Martins, M. J.

2017-04-01

In this paper we investigate the algebraic geometric nature of a solution of the Yang-Baxter equation based on the quantum deformation of the centrally extended sl (2 | 2) superalgebra proposed by Beisert and Koroteev [1]. We derive an alternative representation for the R-matrix in which the matrix elements are given in terms of rational functions depending on weights sited on a degree six surface. For generic gauge the weights geometry are governed by a genus one ruled surface while for a symmetric gauge choice the weights lie instead on a genus five curve. We have written down the polynomial identities satisfied by the R-matrix entries needed to uncover the corresponding geometric properties. For arbitrary gauge the R-matrix geometry is argued to be birational to the direct product CP1 ×CP1 × A where A is an Abelian surface. For the symmetric gauge we present evidences that the geometric content is that of a surface of general type lying on the so-called Severi line with irregularity two and geometric genus nine. We discuss potential geometric degenerations when the two free couplings are restricted to certain one-dimensional subspaces.

Half a century of "the nuclear matrix".

PubMed

Pederson, T

2000-03-01

A cell fraction that would today be termed "the nuclear matrix" was first described and patented in 1948 by Russian investigators. In 1974 this fraction was rediscovered and promoted as a fundamental organizing principle of eukaryotic gene expression. Yet, convincing evidence for this functional role of the nuclear matrix has been elusive and has recently been further challenged. What do we really know about the nonchromatin elements (if any) of internal nuclear structure? Are there objective reasons (as opposed to thinly veiled disdain) to question experiments that use harsh nuclear extraction steps and precipitation-prone conditions? Are the known biophysical properties of the nucleoplasm in vivo consistent with the existence of an extensive network of anastomosing filaments coursing dendritically throughout the interchromatin space? To what extent may the genome itself contribute information for its own quarternary structure in the interphase nucleus? These questions and recent work that bears on the mystique of the nuclear matrix are addressed in this essay. The degree to which gene expression literally depends on nonchromatin nuclear structure as a facilitating organizational format remains an intriguing but unsolved issue in eukaryotic cell biology, and considerable skepticism continues to surround the nuclear matrix fraction as an accurate representation of the in vivo situation.

Towards an Effective Theory of Reformulation. Part 1; Semantics

NASA Technical Reports Server (NTRS)

Benjamin, D. Paul

1992-01-01

This paper describes an investigation into the structure of representations of sets of actions, utilizing semigroup theory. The goals of this project are twofold: to shed light on the relationship between tasks and representations, leading to a classification of tasks according to the representations they admit; and to develop techniques for automatically transforming representations so as to improve problem-solving performance. A method is demonstrated for automatically generating serial algorithms for representations whose actions form a finite group. This method is then extended to representations whose actions form a finite inverse semigroup.

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

PubMed

Greene, Samuel M; Batista, Victor S

2017-09-12

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

Using anthropomorphic avatars resembling sedentary older individuals as models to enhance self-efficacy and adherence to physical activity: psychophysiological correlates.

PubMed

Ruiz, Jorge G; Andrade, Allen D; Anam, Ramankumar; Aguiar, Rudxandra; Sun, Huaping; Roos, Bernard A

2012-01-01

The prevalence of obesity and associated health complications are currently at unprecedented levels. Physical activity in this population can improve patient outcomes. Virtual reality (VR) self-modeling may improve self-efficacy and adherence to physical activity. We conducted a comparative study of 30 participants randomized to 3 versions of a 3D avatar-based VR intervention about exercise: virtual representation of the self exercising condition; virtual representation of other person exercising and control condition. Participants in the virtual representation of the self group significantly increased their levels of physical activity. The improvement in physical activity for participants in the visual representation of other person exercising was marginal. The improvement for the control group was not significant. However, the effect sizes for comparing the pre and post intervention physical activity levels were quite large for all three groups. We did not find any group difference in the improvements of physical activity levels and self-efficacy among sedentary, overweight or obese individuals.

Positron collisions with acetylene calculated using the R-matrix with pseudo-states method

NASA Astrophysics Data System (ADS)

Zhang, Rui; Galiatsatos, Pavlos G.; Tennyson, Jonathan

2011-10-01

Eigenphase sums, total cross sections and differential cross sections are calculated for low-energy collisions of positrons with C2H2. The calculations demonstrate that the use of appropriate pseudo-state expansions very significantly improves the representation of this process giving both realistic eigenphases and cross sections. Differential cross sections are strongly forward peaked in agreement with the measurements. These calculations are computationally very demanding; even with improved procedures for matrix diagonalization, fully converged calculations are too expensive with current computer resources. Nonetheless, the calculations show clear evidence for the formation of a virtual state but no indication that acetylene actually binds a positron at its equilibrium geometry.

1-norm support vector novelty detection and its sparseness.

PubMed

Zhang, Li; Zhou, WeiDa

2013-12-01

This paper proposes a 1-norm support vector novelty detection (SVND) method and discusses its sparseness. 1-norm SVND is formulated as a linear programming problem and uses two techniques for inducing sparseness, or the 1-norm regularization and the hinge loss function. We also find two upper bounds on the sparseness of 1-norm SVND, or exact support vector (ESV) and kernel Gram matrix rank bounds. The ESV bound indicates that 1-norm SVND has a sparser representation model than SVND. The kernel Gram matrix rank bound can loosely estimate the sparseness of 1-norm SVND. Experimental results show that 1-norm SVND is feasible and effective. Copyright © 2013 Elsevier Ltd. All rights reserved.

Experimental and numerical characterization of the sound pressure in standing wave acoustic levitators

NASA Astrophysics Data System (ADS)

Stindt, A.; Andrade, M. A. B.; Albrecht, M.; Adamowski, J. C.; Panne, U.; Riedel, J.

2014-01-01

A novel method for predictions of the sound pressure distribution in acoustic levitators is based on a matrix representation of the Rayleigh integral. This method allows for a fast calculation of the acoustic field within the resonator. To make sure that the underlying assumptions and simplifications are justified, this approach was tested by a direct comparison to experimental data. The experimental sound pressure distributions were recorded by high spatially resolved frequency selective microphone scanning. To emphasize the general applicability of the two approaches, the comparative studies were conducted for four different resonator geometries. In all cases, the results show an excellent agreement, demonstrating the accuracy of the matrix method.

Representations of Nets of C*-Algebras over S 1

NASA Astrophysics Data System (ADS)

Ruzzi, Giuseppe; Vasselli, Ezio

2012-11-01

In recent times a new kind of representations has been used to describe superselection sectors of the observable net over a curved spacetime, taking into account the effects of the fundamental group of the spacetime. Using this notion of representation, we prove that any net of C*-algebras over S 1 admits faithful representations, and when the net is covariant under Diff( S 1), it admits representations covariant under any amenable subgroup of Diff( S 1).

Decomposition of the polynomial kernel of arbitrary higher spin Dirac operators

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

Eelbode, D., E-mail: David.Eelbode@ua.ac.be; Raeymaekers, T., E-mail: Tim.Raeymaekers@UGent.be; Van der Jeugt, J., E-mail: Joris.VanderJeugt@UGent.be

2015-10-15

In a series of recent papers, we have introduced higher spin Dirac operators, which are generalisations of the classical Dirac operator. Whereas the latter acts on spinor-valued functions, the former acts on functions taking values in arbitrary irreducible half-integer highest weight representations for the spin group. In this paper, we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group. We will hereby make use of results from representation theory.

A combined representation method for use in band structure calculations. 1: Method

NASA Technical Reports Server (NTRS)

Friedli, C.; Ashcroft, N. W.

1975-01-01

A representation was described whose basis levels combine the important physical aspects of a finite set of plane waves with those of a set of Bloch tight-binding levels. The chosen combination has a particularly simple dependence on the wave vector within the Brillouin Zone, and its use in reducing the standard one-electron band structure problem to the usual secular equation has the advantage that the lattice sums involved in the calculation of the matrix elements are actually independent of the wave vector. For systems with complicated crystal structures, for which the Korringa-Kohn-Rostoker (KKR), Augmented-Plane Wave (APW) and Orthogonalized-Plane Wave (OPW) methods are difficult to apply, the present method leads to results with satisfactory accuracy and convergence.

"Everyone Has to Find Themselves in the Story": Exploring Minority Group Representation in the Citizenship Curriculum in Northern Ireland and Israel

ERIC Educational Resources Information Center

Hanna, Helen

2016-01-01

This article explores understandings of minority group representation in citizenship education in Northern Ireland and Israel, from the point of view of students, teachers, and policy makers. It is set against the background of the minority-majority group dichotomy within societies divided along ethnonational lines, and the challenge of delivering…

[Social representations of illness: Comparison of "expert" knowledge and "naïve" knowledge].

PubMed

Jeoffrion, C; Dupont, P; Tripodi, D; Roland-Lévy, C

2016-06-01

The link between social practices and representations is now well known. But while many studies have focused on the social representation of mental illness, in various populations, few studies have focused on the notion of disease/illness by comparing professionals and non-professionals health workers representations. Indeed, the disease is both a reality described, explained and treated by medicine; for those who are affected by a disease, it is an individual experience with psychological, social and cultural impacts. The social representation is determined by the structure of the social groups in which it develops; therefore, it is a form of knowledge socially shaped and shared by the members of a social group. Several theoretical extensions have been elaborated and particularly, the structural approach and the central core theory. These approaches sustain the arguments of a hierarchical organization of a social representation with a central core surrounded by peripheral zones. The central core is common and shared by the majority of the members of a given group, whereas the peripheral zones provide space for the individualization of the social knowledge. The main goal of our study is to highlight the social representations of disease in health professionals (HP) and in non-health professionals (NHP). The group of HP has been differentiated into three subgroups: "medical doctors", "nurses" and "pharmacists", while that of NHP in two subgroups: those submitted to a "long period medical treatment" and those "without treatment". Our aim is to show that there are different social and professional Representations of disease. The professional representations are specific social representations related to professional contexts. We formulate the following assumptions (a) that the social representations of HP and NHP will be articulated around a common central core. Nevertheless, we expect to find specific peripheral elements related to professional status, based on different knowledge and a differentiated "practice"; (b) the HP should refer to more descriptive aspects of the disease and monitoring of patients, while (c) NHP should refer more to the experience of illness around emotional aspects. Our sample is composed of 270 participants (135 HP and 135 HNP). Representations are measured by a free association task based on the target term: disease. The data have been submitted to prototypical and categorical analyses in agreement with the central core theory. The results confirm that there is a common social representation of disease shared by the two groups, which refers essentially to suffering and pain. The analysis of each group brings to light two different registers: the one of the HP with more descriptive words referring to the nature and the illness's characteristics, and the other ones of the HNP with more words connected to emotions and referring to personal real experience of the illness. As expected, the social representation of the HP is referring to the "professional representations" of the disease, while the one for the HNP is linked to "practices" of an illness. An analysis of intra-group differences shows specificities for each of the questioned subgroups. In the HP, medical doctors focus on the diagnosis and consequences of the disease, pharmacists refer to the treatment of the disease and its management, while nurses focus on the treatment and on the relation while monitoring patients. In the NHP, people submitted to a "long period medical treatment" refer to the emotional aspects and to the consequences of the illness on their live, while those without treatment use more descriptive and formal terms. These results suggest to the PS to expand exchanges related to the disease in order to facilitate communication centered on taking care of the patient, considered in its wholeness and not only as an actual or potential patient. This is an important step in improving the health of the patient. Copyright © 2015 L'Encéphale, Paris. Published by Elsevier Masson SAS. All rights reserved.

Practical implementation of tetrahedral mesh reconstruction in emission tomography

PubMed Central

Boutchko, R.; Sitek, A.; Gullberg, G. T.

2014-01-01

This paper presents a practical implementation of image reconstruction on tetrahedral meshes optimized for emission computed tomography with parallel beam geometry. Tetrahedral mesh built on a point cloud is a convenient image representation method, intrinsically three-dimensional and with a multi-level resolution property. Image intensities are defined at the mesh nodes and linearly interpolated inside each tetrahedron. For the given mesh geometry, the intensities can be computed directly from tomographic projections using iterative reconstruction algorithms with a system matrix calculated using an exact analytical formula. The mesh geometry is optimized for a specific patient using a two stage process. First, a noisy image is reconstructed on a finely-spaced uniform cloud. Then, the geometry of the representation is adaptively transformed through boundary-preserving node motion and elimination. Nodes are removed in constant intensity regions, merged along the boundaries, and moved in the direction of the mean local intensity gradient in order to provide higher node density in the boundary regions. Attenuation correction and detector geometric response are included in the system matrix. Once the mesh geometry is optimized, it is used to generate the final system matrix for ML-EM reconstruction of node intensities and for visualization of the reconstructed images. In dynamic PET or SPECT imaging, the system matrix generation procedure is performed using a quasi-static sinogram, generated by summing projection data from multiple time frames. This system matrix is then used to reconstruct the individual time frame projections. Performance of the new method is evaluated by reconstructing simulated projections of the NCAT phantom and the method is then applied to dynamic SPECT phantom and patient studies and to a dynamic microPET rat study. Tetrahedral mesh-based images are compared to the standard voxel-based reconstruction for both high and low signal-to-noise ratio projection datasets. The results demonstrate that the reconstructed images represented as tetrahedral meshes based on point clouds offer image quality comparable to that achievable using a standard voxel grid while allowing substantial reduction in the number of unknown intensities to be reconstructed and reducing the noise. PMID:23588373

Practical implementation of tetrahedral mesh reconstruction in emission tomography

NASA Astrophysics Data System (ADS)

Boutchko, R.; Sitek, A.; Gullberg, G. T.

2013-05-01

This paper presents a practical implementation of image reconstruction on tetrahedral meshes optimized for emission computed tomography with parallel beam geometry. Tetrahedral mesh built on a point cloud is a convenient image representation method, intrinsically three-dimensional and with a multi-level resolution property. Image intensities are defined at the mesh nodes and linearly interpolated inside each tetrahedron. For the given mesh geometry, the intensities can be computed directly from tomographic projections using iterative reconstruction algorithms with a system matrix calculated using an exact analytical formula. The mesh geometry is optimized for a specific patient using a two stage process. First, a noisy image is reconstructed on a finely-spaced uniform cloud. Then, the geometry of the representation is adaptively transformed through boundary-preserving node motion and elimination. Nodes are removed in constant intensity regions, merged along the boundaries, and moved in the direction of the mean local intensity gradient in order to provide higher node density in the boundary regions. Attenuation correction and detector geometric response are included in the system matrix. Once the mesh geometry is optimized, it is used to generate the final system matrix for ML-EM reconstruction of node intensities and for visualization of the reconstructed images. In dynamic PET or SPECT imaging, the system matrix generation procedure is performed using a quasi-static sinogram, generated by summing projection data from multiple time frames. This system matrix is then used to reconstruct the individual time frame projections. Performance of the new method is evaluated by reconstructing simulated projections of the NCAT phantom and the method is then applied to dynamic SPECT phantom and patient studies and to a dynamic microPET rat study. Tetrahedral mesh-based images are compared to the standard voxel-based reconstruction for both high and low signal-to-noise ratio projection datasets. The results demonstrate that the reconstructed images represented as tetrahedral meshes based on point clouds offer image quality comparable to that achievable using a standard voxel grid while allowing substantial reduction in the number of unknown intensities to be reconstructed and reducing the noise.

Multi-representation based on scientific investigation for enhancing students’ representation skills

NASA Astrophysics Data System (ADS)

Siswanto, J.; Susantini, E.; Jatmiko, B.

2018-03-01

This research aims to implementation learning physics with multi-representation based on the scientific investigation for enhancing students’ representation skills, especially on the magnetic field subject. The research design is one group pretest-posttest. This research was conducted in the department of mathematics education, Universitas PGRI Semarang, with the sample is students of class 2F who take basic physics courses. The data were obtained by representation skills test and documentation of multi-representation worksheet. The Results show gain analysis value of .64 which means some medium improvements. The result of t-test (α = .05) is shows p-value = .001. This learning significantly improves students representation skills.

Perceptually relevant grouping of image tokens on the basis of constraint propagation from local binary patterns

NASA Astrophysics Data System (ADS)

Behlim, Sadaf Iqbal; Syed, Tahir Qasim; Malik, Muhammad Yameen; Vigneron, Vincent

2016-11-01

Grouping image tokens is an intermediate step needed to arrive at meaningful image representation and summarization. Usually, perceptual cues, for instance, gestalt properties inform token grouping. However, they do not take into account structural continuities that could be derived from other tokens belonging to similar structures irrespective of their location. We propose an image representation that encodes structural constraints emerging from local binary patterns (LBP), which provides a long-distance measure of similarity but in a structurally connected way. Our representation provides a grouping of pixels or larger image tokens that is free of numeric similarity measures and could therefore be extended to nonmetric spaces. The representation lends itself nicely to ubiquitous image processing applications such as connected component labeling and segmentation. We test our proposed representation on the perceptual grouping or segmentation task on the popular Berkeley segmentation dataset (BSD500) that with respect to human segmented images achieves an average F-measure of 0.559. Our algorithm achieves a high average recall of 0.787 and is therefore well-suited to other applications such as object retrieval and category-independent object recognition. The proposed merging heuristic based on levels of singular tree component has shown promising results on the BSD500 dataset and currently ranks 12th among all benchmarked algorithms, but contrary to the others, it requires no data-driven training or specialized preprocessing.

The crypto-Hermitian smeared-coordinate representation of wave functions

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2011-08-01

In discrete-coordinate quantum models the kinematical observable of position need not necessarily be chosen local (i.e., diagonal). Its smearing is selected in the nearest-neighbor form of a real asymmetric (i.e., crypto-Hermitian) tridiagonal matrix Qˆ. Via Gauss-Hermite illustrative example we show how such an option restricts the class of admissible dynamical observables (sampled here just by the Hamiltonian).

Development of the Nuclear-Electronic Orbital Approach and Applications to Ionic Liquids and Tunneling Processes

DTIC Science & Technology

2010-02-24

electronic Schrodinger equation . In previous grant cycles, we implemented the NEO approach at the Hartree-Fock (NEO-HF),13 configuration interaction...electronic and nuclear molecular orbitals. The resulting electronic and nuclear Hartree-Fock-Roothaan equations are solved iteratively until self...directly into the standard Hartree- Fock-Roothaan equations , which are solved iteratively to self-consistency. The density matrix representation

Coupling between shear and bending in the analysis of beam problems: Planar case

NASA Astrophysics Data System (ADS)

Shabana, Ahmed A.; Patel, Mohil

2018-04-01

The interpretation of invariants, such as curvatures which uniquely define the bending and twist of space curves and surfaces, is fundamental in the formulation of the beam and plate elastic forces. Accurate representations of curve and surface invariants, which enter into the definition of the strain energy equations, is particularly important in the case of large displacement analysis. This paper discusses this important subject in view of the fact that shear and bending are independent modes of deformation and do not have kinematic coupling; this is despite the fact that kinetic coupling may exist. The paper shows, using simple examples, that shear without bending and bending without shear at an arbitrary point and along a certain direction are scenarios that higher-order finite elements (FE) can represent with a degree of accuracy that depends on the order of interpolation and/or mesh size. The FE representation of these two kinematically uncoupled modes of deformation is evaluated in order to examine the effect of the order of the polynomial interpolation on the accuracy of representing these two independent modes. It is also shown in this paper that not all the curvature vectors contribute to bending deformation. In view of the conclusions drawn from the analysis of simple beam problems, the material curvature used in several previous investigations is evaluated both analytically and numerically. The problems associated with the material curvature matrix, obtained using the rotation of the beam cross-section, and the fundamental differences between this material curvature matrix and the Serret-Frenet curvature matrix are discussed.

Modular invariant representations of infinite-dimensional Lie algebras and superalgebras

PubMed Central

Kac, Victor G.; Wakimoto, Minoru

1988-01-01

In this paper, we launch a program to describe and classify modular invariant representations of infinite-dimensional Lie algebras and superalgebras. We prove a character formula for a large class of highest weight representations L(λ) of a Kac-Moody algebra [unk] with a symmetrizable Cartan matrix, generalizing the Weyl-Kac character formula [Kac, V. G. (1974) Funct. Anal. Appl. 8, 68-70]. In the case of an affine [unk], this class includes modular invariant representations of arbitrary rational level m = t/u, where t [unk] Z and u [unk] N are relatively prime and m + g ≥ g/u (g is the dual Coxeter number). We write the characters of these representations in terms of theta functions and calculate their asymptotics, generalizing the results of Kac and Peterson [Kac, V. G. & Peterson, D. H. (1984) Adv. Math. 53, 125-264] and of Kac and Wakimoto [Kac, V. G. & Wakimoto, M. (1988) Adv. Math. 70, 156-234] for the u = 1 (integrable) case. We work out in detail the case [unk] = A1(1), in particular classifying all its modular invariant representations. Furthermore, we show that the modular invariant representations of the Virasoro algebra Vir are precisely the “minimal series” of Belavin et al. [Belavin, A. A., Polyakov, A. M. & Zamolodchikov, A. B. (1984) Nucl. Phys. B 241, 333-380] using the character formulas of Feigin and Fuchs [Feigin, B. L. & Fuchs, D. B. (1984) Lect. Notes Math. 1060, 230-245]. We show that tensoring the basic representation and modular invariant representations of A1(1) produces all modular invariant representations of Vir generalizing the results of Goddard et al. [Goddard P., Kent, A. & Olive, D. (1986) Commun. Math. Phys. 103, 105-119] and of Kac and Wakimoto [Kac, V. G. & Wakimoto, M. (1986) Lect. Notes Phys. 261, 345-371] in the unitary case. We study the general branching functions as well. All these results are generalized to the Kac-Moody superalgebras introduced by Kac [Kac, V. G. (1978) Adv. Math. 30, 85-136] and to N = 1 super Virasoro algebras. We work out in detail the case of the superalgebra B(0, 1)(1), showing, in particular, that restricting to its even part produces again all modular invariant representations of Vir. These results lead to general conjectures about asymptotic behavior of positive energy representations and classification of modular invariant representations. PMID:16593954

Estimation of genetic connectedness diagnostics based on prediction errors without the prediction error variance-covariance matrix.

PubMed

Holmes, John B; Dodds, Ken G; Lee, Michael A

2017-03-02

An important issue in genetic evaluation is the comparability of random effects (breeding values), particularly between pairs of animals in different contemporary groups. This is usually referred to as genetic connectedness. While various measures of connectedness have been proposed in the literature, there is general agreement that the most appropriate measure is some function of the prediction error variance-covariance matrix. However, obtaining the prediction error variance-covariance matrix is computationally demanding for large-scale genetic evaluations. Many alternative statistics have been proposed that avoid the computational cost of obtaining the prediction error variance-covariance matrix, such as counts of genetic links between contemporary groups, gene flow matrices, and functions of the variance-covariance matrix of estimated contemporary group fixed effects. In this paper, we show that a correction to the variance-covariance matrix of estimated contemporary group fixed effects will produce the exact prediction error variance-covariance matrix averaged by contemporary group for univariate models in the presence of single or multiple fixed effects and one random effect. We demonstrate the correction for a series of models and show that approximations to the prediction error matrix based solely on the variance-covariance matrix of estimated contemporary group fixed effects are inappropriate in certain circumstances. Our method allows for the calculation of a connectedness measure based on the prediction error variance-covariance matrix by calculating only the variance-covariance matrix of estimated fixed effects. Since the number of fixed effects in genetic evaluation is usually orders of magnitudes smaller than the number of random effect levels, the computational requirements for our method should be reduced.

Geometry of matrix product states: Metric, parallel transport, and curvature

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

Haegeman, Jutho, E-mail: jutho.haegeman@gmail.com; Verstraete, Frank; Faculty of Physics and Astronomy, University of Ghent, Krijgslaan 281 S9, 9000 Gent

2014-02-15

We study the geometric properties of the manifold of states described as (uniform) matrix product states. Due to the parameter redundancy in the matrix product state representation, matrix product states have the mathematical structure of a (principal) fiber bundle. The total space or bundle space corresponds to the parameter space, i.e., the space of tensors associated to every physical site. The base manifold is embedded in Hilbert space and can be given the structure of a Kähler manifold by inducing the Hilbert space metric. Our main interest is in the states living in the tangent space to the base manifold,more » which have recently been shown to be interesting in relation to time dependence and elementary excitations. By lifting these tangent vectors to the (tangent space) of the bundle space using a well-chosen prescription (a principal bundle connection), we can define and efficiently compute an inverse metric, and introduce differential geometric concepts such as parallel transport (related to the Levi-Civita connection) and the Riemann curvature tensor.« less

Multipole expansions and Fock symmetry of the hydrogen atom

NASA Astrophysics Data System (ADS)

Meremianin, A. V.; Rost, J.-M.

2006-10-01

The main difficulty in utilizing the O(4) symmetry of the hydrogen atom in practical calculations is the dependence of the Fock stereographic projection on energy. This is due to the fact that the wavefunctions of the states with different energies are proportional to the hyperspherical harmonics (HSH) corresponding to different points on the hypersphere. Thus, the calculation of the matrix elements reduces to the problem of re-expanding HSH in terms of HSH depending on different points on the hypersphere. We solve this problem by applying the technique of multipole expansions for four-dimensional HSH. As a result, we obtain the multipole expansions whose coefficients are the matrix elements of the boost operator taken between hydrogen wavefunctions (i.e., hydrogen form factors). The explicit expressions for those coefficients are derived. It is shown that the hydrogen matrix elements can be presented as derivatives of an elementary function. Such an operator representation is convenient for the derivation of recurrence relations connecting matrix elements between states corresponding to different values of the quantum numbers n and l.

Kernel analysis of partial least squares (PLS) regression models.

PubMed

Shinzawa, Hideyuki; Ritthiruangdej, Pitiporn; Ozaki, Yukihiro

2011-05-01

An analytical technique based on kernel matrix representation is demonstrated to provide further chemically meaningful insight into partial least squares (PLS) regression models. The kernel matrix condenses essential information about scores derived from PLS or principal component analysis (PCA). Thus, it becomes possible to establish the proper interpretation of the scores. A PLS model for the total nitrogen (TN) content in multiple Thai fish sauces is built with a set of near-infrared (NIR) transmittance spectra of the fish sauce samples. The kernel analysis of the scores effectively reveals that the variation of the spectral feature induced by the change in protein content is substantially associated with the total water content and the protein hydration. Kernel analysis is also carried out on a set of time-dependent infrared (IR) spectra representing transient evaporation of ethanol from a binary mixture solution of ethanol and oleic acid. A PLS model to predict the elapsed time is built with the IR spectra and the kernel matrix is derived from the scores. The detailed analysis of the kernel matrix provides penetrating insight into the interaction between the ethanol and the oleic acid.

Performance of low-rank QR approximation of the finite element Biot-Savart law

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

White, D; Fasenfest, B

2006-10-16

In this paper we present a low-rank QR method for evaluating the discrete Biot-Savart law. Our goal is to develop an algorithm that is easily implemented on parallel computers. It is assumed that the known current density and the unknown magnetic field are both expressed in a finite element expansion, and we wish to compute the degrees-of-freedom (DOF) in the basis function expansion of the magnetic field. The matrix that maps the current DOF to the field DOF is full, but if the spatial domain is properly partitioned the matrix can be written as a block matrix, with blocks representingmore » distant interactions being low rank and having a compressed QR representation. While an octree partitioning of the matrix may be ideal, for ease of parallel implementation we employ a partitioning based on number of processors. The rank of each block (i.e. the compression) is determined by the specific geometry and is computed dynamically. In this paper we provide the algorithmic details and present computational results for large-scale computations.« less

Combinatorial approach to the representation of the Schur-Weyl duality in one-dimensional spin systems

NASA Astrophysics Data System (ADS)

Jakubczyk, Dorota; Jakubczyk, Paweł

2018-02-01

We propose combinatorial approach to the representation of Schur-Weyl duality in physical systems on the example of one-dimensional spin chains. Exploiting the Robinson-Schensted-Knuth algorithm, we perform decomposition of the dual group representations into irreducible representations in a fully combinatorial way. As representation space, we choose the Hilbert space of the spin chains, but this approach can be easily generalized to an arbitrary physical system where the Schur-Weyl duality works.

Wigner functions for noncommutative quantum mechanics: A group representation based construction

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

Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com; Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8; Ali, S. Twareque, E-mail: twareque.ali@concordia.ca

This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and thosemore » of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.« less

Improved Estimation and Interpretation of Correlations in Neural Circuits

PubMed Central

Yatsenko, Dimitri; Josić, Krešimir; Ecker, Alexander S.; Froudarakis, Emmanouil; Cotton, R. James; Tolias, Andreas S.

2015-01-01

Ambitious projects aim to record the activity of ever larger and denser neuronal populations in vivo. Correlations in neural activity measured in such recordings can reveal important aspects of neural circuit organization. However, estimating and interpreting large correlation matrices is statistically challenging. Estimation can be improved by regularization, i.e. by imposing a structure on the estimate. The amount of improvement depends on how closely the assumed structure represents dependencies in the data. Therefore, the selection of the most efficient correlation matrix estimator for a given neural circuit must be determined empirically. Importantly, the identity and structure of the most efficient estimator informs about the types of dominant dependencies governing the system. We sought statistically efficient estimators of neural correlation matrices in recordings from large, dense groups of cortical neurons. Using fast 3D random-access laser scanning microscopy of calcium signals, we recorded the activity of nearly every neuron in volumes 200 μm wide and 100 μm deep (150–350 cells) in mouse visual cortex. We hypothesized that in these densely sampled recordings, the correlation matrix should be best modeled as the combination of a sparse graph of pairwise partial correlations representing local interactions and a low-rank component representing common fluctuations and external inputs. Indeed, in cross-validation tests, the covariance matrix estimator with this structure consistently outperformed other regularized estimators. The sparse component of the estimate defined a graph of interactions. These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive ‘excitatory’ interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative ‘inhibitory’ interactions were less selective. Because of its superior performance, this ‘sparse+latent’ estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix. PMID:25826696

Comparing student understanding of quantum physics when embedding multimodal representations into two different writing formats: Presentation format versus summary report format

NASA Astrophysics Data System (ADS)

Gunel, Murat; Hand, Brian; Gunduz, Sevket

2006-11-01

Physics as a subject for school students requires an understanding and ability to move between different modes of representation for the concepts under review. However, the inability of students to have a multimodal understanding of the concepts is seen as restricting their understandings of the concepts. The aim of this study was to explore the effectiveness of using writing-to-learn strategies that required students to embed multimodal representations of the concepts. In particular, the study compared a presentation format with a summary report format for students learning quantum theory. A pre-post test design was used to compare performances of these two groups across two units. For unit 1, students' scores from groups that completed either a presentation format (PowerPoint presentation) or a summary report format (chapter summary) were compared. No limits were placed on the amount of text or the number of representations used. For unit 2, products of both groups were constructed for an audience of year 10 students. The presentation format group (PowerPoint) was limited to 15 slides, with a maximum of 10 words displayed per slide; a script was written to accompany the presentation. Slides could include graphical and mathematical formulae; however, the text could not. The summary report format group that wrote out its explanations was limited to four pages and was required to incorporate multimodal representations. Results indicated that for both units students using the presentation format group scored significantly better on tests than the summary report format group. The effect size difference between the groups increased for the second unit, indicating that more practice was leading to better student understanding of the physics concepts.

A Simple Method for Calculating Clebsch-Gordan Coefficients

ERIC Educational Resources Information Center

Klink, W. H.; Wickramasekara, S.

2010-01-01

This paper presents a simple method for calculating Clebsch-Gordan coefficients for the tensor product of two unitary irreducible representations (UIRs) of the rotation group. The method also works for multiplicity-free irreducible representations appearing in the tensor product of any number of UIRs of the rotation group. The generalization to…

Perturbation theory from automorphic forms

NASA Astrophysics Data System (ADS)

Lambert, Neil; West, Peter

2010-05-01

Using our previous construction of Eisenstein-like automorphic forms we derive formulae for the perturbative and non-perturbative parts for any group and representation. The result is written in terms of the weights of the representation and the derivation is largely group theoretical. Specialising to the E n+1 groups relevant to type II string theory and the representation associated with node n + 1 of the E n+1 Dynkin diagram we explicitly find the perturbative part in terms of String Theory variables, such as the string coupling g d and volume V n . For dimensions seven and higher we find that the perturbation theory involves only two terms. In six dimensions we construct the SO(5, 5) automorphic form using the vector representation. Although these automorphic forms are generally compatible with String Theory, the one relevant to R 4 involves terms with g d -6 and so is problematic. We then study a constrained SO(5, 5) automorphic form, obtained by summing over null vectors, and compute its perturbative part. We find that it is consistent with String Theory and makes precise predictions for the perturbative results. We also study the unconstrained automorphic forms for E 6 in the 27 representation and E 7 in the 133 representation, giving their perturbative part and commenting on their role in String Theory.

The continuous spin representations of the Poincare and super-Poincare groups and their construction by the Inonu-Wigner group contraction

NASA Astrophysics Data System (ADS)

Khan, Abu M. A. S.

We study the continuous spin representation (CSR) of the Poincare group in arbitrary dimensions. In d dimensions, the CSRs are characterized by the length of the light-cone vector and the Dynkin labels of the SO(d-3) short little group which leaves the light-cone vector invariant. In addition to these, a solid angle Od-3 which specifies the direction of the light-cone vector is also required to label the states. We also find supersymmetric generalizations of the CSRs. In four dimensions, the supermultiplet contains one bosonic and one fermionic CSRs which transform into each other under the action of the supercharges. In a five dimensional case, the supermultiplet contains two bosonic and two fermionic CSRs which is like N = 2 supersymmetry in four dimensions. When constructed using Grassmann parameters, the light-cone vector becomes nilpotent. This makes the representation finite dimensional, but at the expense of introducing central charges even though the representation is massless. This leads to zero or negative norm states. The nilpotent constructions are valid only for even dimensions. We also show how the CSRs in four dimensions can be obtained from five dimensions by the combinations of Kaluza-Klein (KK) dimensional reduction and the Inonu-Wigner group contraction. The group contraction is a singular transformation. We show that the group contraction is equivalent to imposing periodic boundary condition along one direction and taking a double singular limit. In this form the contraction parameter is interpreted as the inverse KK radius. We apply this technique to both five dimensional regular massless and massive representations. For the regular massless case, we find that the contraction gives the CSR in four dimensions under a double singular limit and the representation wavefunction is the Bessel function. For the massive case, we use Majorana's infinite component theory as a model for the SO(4) little group. In this case, a triple singular limit is required to yield any CSR in four dimensions. The representation wavefunction is the Bessel function, as expected, but the scale factor is not the length of the light-cone vector. The amplitude and the scale factor are implicit functions of the parameter y which is a ratio of the internal and external coordinates. We also state under what conditions our solutions become identical to Wigner's solution.

Visual memory transformations in dyslexia.

PubMed

Barnes, James; Hinkley, Lisa; Masters, Stuart; Boubert, Laura

2007-06-01

Representational Momentum refers to observers' distortion of recognition memory for pictures that imply motion because of an automatic mental process which extrapolates along the implied trajectory of the picture. Neuroimaging evidence suggests that activity in the magnocellular visual pathway is necessary for representational momentum to occur. It has been proposed that individuals with dyslexia have a magnocellular deficit, so it was hypothesised that these individuals would show reduced or absent representational momentum. In this study, 30 adults with dyslexia and 30 age-matched controls were compared on two tasks, one linear and one rotation, which had previously elicited the representational momentum effect. Analysis indicated significant differences in the performance of the two groups, with the dyslexia group having a reduced susceptibility to representational momentum in both linear and rotational directions. The findings highlight that deficits in temporal spatial processing may contribute to the perceptual profile of dyslexia.

Coherent States for Kronecker Products of Non Compact Groups: Formulation and Applications

NASA Technical Reports Server (NTRS)

Bambah, Bindu A.; Agarwal, Girish S.

1996-01-01

We introduce and study the properties of a class of coherent states for the group SU(1,1) X SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the discrete series representations of SU(1,1). These are the generalization of the 'Barut Girardello' coherent states to the Kronecker Product of two non-compact groups. The resolution of the identity and the analytic phase space representation of these states is presented. This phase space representation is based on the basis of products of 'pair coherent states' rather than the standard number state canonical basis. We discuss the utility of the resulting 'bi-pair coherent states' in the context of four-mode interactions in quantum optics.

The temporal evolution of conceptual object representations revealed through models of behavior, semantics and deep neural networks.

PubMed

Bankson, B B; Hebart, M N; Groen, I I A; Baker, C I

2018-05-17

Visual object representations are commonly thought to emerge rapidly, yet it has remained unclear to what extent early brain responses reflect purely low-level visual features of these objects and how strongly those features contribute to later categorical or conceptual representations. Here, we aimed to estimate a lower temporal bound for the emergence of conceptual representations by defining two criteria that characterize such representations: 1) conceptual object representations should generalize across different exemplars of the same object, and 2) these representations should reflect high-level behavioral judgments. To test these criteria, we compared magnetoencephalography (MEG) recordings between two groups of participants (n = 16 per group) exposed to different exemplar images of the same object concepts. Further, we disentangled low-level from high-level MEG responses by estimating the unique and shared contribution of models of behavioral judgments, semantics, and different layers of deep neural networks of visual object processing. We find that 1) both generalization across exemplars as well as generalization of object-related signals across time increase after 150 ms, peaking around 230 ms; 2) representations specific to behavioral judgments emerged rapidly, peaking around 160 ms. Collectively, these results suggest a lower bound for the emergence of conceptual object representations around 150 ms following stimulus onset. Copyright © 2018 Elsevier Inc. All rights reserved.

Learning with Multiple Representations: Extending Multimedia Learning beyond the Lab

ERIC Educational Resources Information Center

Eilam, Billie; Poyas, Yael

2008-01-01

The present study extended multimedia learning principles beyond the lab to an ecologically valid setting (homework). Eighteen information cards were used to perform three homework tasks. The control group students learned from single representation (SR) cards that presented all information as printed text. The multiple representation (MR) group…

Sparsity-Based Representation for Classification Algorithms and Comparison Results for Transient Acoustic Signals

DTIC Science & Technology

2016-05-01

large but correlated noise and signal interference (i.e., low -rank interference). Another contribution is the implementation of deep learning...representation, low rank, deep learning 52 Tung-Duong Tran-Luu 301-394-3082Unclassified Unclassified Unclassified UU ii Approved for public release; distribution...Classification of Acoustic Transients 6 3.2 Joint Sparse Representation with Low -Rank Interference 7 3.3 Simultaneous Group-and-Joint Sparse Representation

Quantum dressing orbits on compact groups

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Šťovíček, Pavel

1993-02-01

The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decompositon in the general case. Quantum dressing orbits are described explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient “coherent states” are introduced and a correspondence between classical and quantum observables is given.

N300 indexes deficient integration of orthographic and phonological representations in children with dyslexia.

PubMed

Hasko, Sandra; Bruder, Jennifer; Bartling, Jürgen; Schulte-Körne, Gerd

2012-04-01

In transparent orthographies, like German, children with developmental dyslexia (DD) are mainly characterized by a reading fluency deficit. The reading fluency deficit might be traced back to a scarce integration of orthographic and phonological representations. In order to address this question, the present study used EEG to investigate the N300, an ERP component which has been associated with the integration of orthographic and phonological representations. Twenty children without DD and 18 children with DD performed a phonological (P)-orthographic (O) matching task (P-O condition), which tapped the integration of orthographic and phonological representations. A control task was applied which did not require the integration of orthographic and phonological representations and consisted only of orthographic information (O-O condition). The O-O condition revealed a similar N300 distribution between groups with a bilateral activity over fronto-temporal electrodes. However, in the P-O condition N300 differentiated the 2 groups of children. The control group revealed greater activity over left fronto-temporal electrodes, whereas the N300 was distributed bilaterally in the group of children with DD suggesting deficient integration of orthographic and phonological representations. These findings might be related to the reading fluency deficit as it was also observed that better reading fluency was correlated with higher (r=-.36) and earlier peaking (r=-.33) N300 amplitudes in the left hemisphere and attenuated N300 amplitudes (r=.45) in the right hemisphere. Standardized low-resolution electromagnetic tomography analysis (sLORETA) revealed that children with DD rely more on right temporo-parietal brain areas compared to children without DD. Furthermore, in order to rule out that earlier deficient processes might influence the group differences found in the N300, we analyzed the N170 for group differences. We did not find significant differences between children without DD and children with DD. In conclusion the results suggest deficient integration of orthographic and phonological representations in dyslexia, as indexed by the N300, and further highlight how this activity is relevant for fluent reading. Copyright © 2012 Elsevier Ltd. All rights reserved.

The time course of the competition between grouping organizations.

PubMed

Rashal, Einat; Yeshurun, Yaffa; Kimchi, Ruth

2017-03-01

Previous research on the competition between grouping organizations focused mainly on their relative strength as measured by subjective reports of the final percept. Considerably less is known about the underlying representations of the competing organizations. We hypothesized that when more than 1 organization is possible, multiple representations are constructed for the alternative organizations. We tested this hypothesis using the primed-matching paradigm. Our primes depicted either a single grouping principle (grouping into columns or rows by brightness similarity, connectedness, or proximity) or 2 grouping principles (brightness similarity and connectedness, or brightness similarity and proximity) that led to competing organizations (e.g., grouping into columns by brightness similarity and into rows by connectedness, or vice versa). The time course of representation construction was examined by varying prime duration. Significant priming effects of similar magnitude were found for the individual grouping organizations. These effects were modified when 2 competing organizations were present in the prime, indicating that both organizations were represented and competed for dominancy. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Human action recognition with group lasso regularized-support vector machine

NASA Astrophysics Data System (ADS)

Luo, Huiwu; Lu, Huanzhang; Wu, Yabei; Zhao, Fei

2016-05-01

The bag-of-visual-words (BOVW) and Fisher kernel are two popular models in human action recognition, and support vector machine (SVM) is the most commonly used classifier for the two models. We show two kinds of group structures in the feature representation constructed by BOVW and Fisher kernel, respectively, since the structural information of feature representation can be seen as a prior for the classifier and can improve the performance of the classifier, which has been verified in several areas. However, the standard SVM employs L2-norm regularization in its learning procedure, which penalizes each variable individually and cannot express the structural information of feature representation. We replace the L2-norm regularization with group lasso regularization in standard SVM, and a group lasso regularized-support vector machine (GLRSVM) is proposed. Then, we embed the group structural information of feature representation into GLRSVM. Finally, we introduce an algorithm to solve the optimization problem of GLRSVM by alternating directions method of multipliers. The experiments evaluated on KTH, YouTube, and Hollywood2 datasets show that our method achieves promising results and improves the state-of-the-art methods on KTH and YouTube datasets.

Modelling the backscatter from spherical cavities in a solid matrix: Can an effective medium layer model mimic the scattering response?

NASA Astrophysics Data System (ADS)

Pinfield, Valerie J.; Challis, Richard E.

2011-01-01

Industrial applications are increasingly turning to modern composite layered materials to satisfy strength requirements whilst reducing component weight. An important group of such materials are fibre/resin composites in which long fibres are laid down in layers in a resin matrix. Whilst delamination flaws, where layers separate from each other, are detectable using traditional ultrasonic techniques, the presence of porosity in any particular layer is harder to detect. The reflected signal from a layered material can already be modelled successfully by using the acoustic impedance of the layers and summing reflections from layer boundaries. However, it is not yet known how to incorporate porosity into such a model. The aim of the work reported here was to model the backscatter from randomly distributed spherical cavities within one layer, and to establish whether an effective medium, with a derived acoustic impedance, could reproduce the characteristics of that scattering. Since effective medium models are much more readily implemented in simulations of multi-layer structures than scattering per se, it was felt desirable to simplify the scattering response into an effective medium representation. A model was constructed in which spherical cavities were placed randomly in a solid continuous matrix and the system backscattering response was calculated. The scattering from the cavities was determined by using the Rayleigh partial-wave method, and taking the received signal at the transducer to be equivalent to the far field limit. It was concluded that even at relatively low porosity levels, the received signal was still "layer-like" and an effective medium model was a good approximation for the scattering behaviour.

Fully constrained Majorana neutrino mass matrices using \\varvec{Σ(72× 3)}

NASA Astrophysics Data System (ADS)

Krishnan, R.; Harrison, P. F.; Scott, W. G.

2018-01-01

In 2002, two neutrino mixing ansatze having trimaximally mixed middle (ν _2) columns, namely tri-chi-maximal mixing ( {T}χ {M}) and tri-phi-maximal mixing ( {T}φ {M}), were proposed. In 2012, it was shown that {T}χ {M} with χ =± π /16 as well as {T}φ {M} with φ = ± π /16 leads to the solution, sin ^2 θ _{13} = 2/3 sin ^2 π /16, consistent with the latest measurements of the reactor mixing angle, θ _{13}. To obtain {T}χ {M}_{(χ =± π /16)} and {T}φ {M}_{(φ =± π /16)}, the type I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, m_1:m_2:m_3=( 2+√{2}) /1+√{2(2+√{2)}}:1:( 2+√{2}) /-1+√{2(2+√{2)}}. In this paper we construct a flavour model based on the discrete group Σ (72× 3) and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric 3× 3 matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of Σ (72× 3). Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.

Information Geometry for Landmark Shape Analysis: Unifying Shape Representation and Deformation

PubMed Central

Peter, Adrian M.; Rangarajan, Anand

2010-01-01

Shape matching plays a prominent role in the comparison of similar structures. We present a unifying framework for shape matching that uses mixture models to couple both the shape representation and deformation. The theoretical foundation is drawn from information geometry wherein information matrices are used to establish intrinsic distances between parametric densities. When a parameterized probability density function is used to represent a landmark-based shape, the modes of deformation are automatically established through the information matrix of the density. We first show that given two shapes parameterized by Gaussian mixture models (GMMs), the well-known Fisher information matrix of the mixture model is also a Riemannian metric (actually, the Fisher-Rao Riemannian metric) and can therefore be used for computing shape geodesics. The Fisher-Rao metric has the advantage of being an intrinsic metric and invariant to reparameterization. The geodesic—computed using this metric—establishes an intrinsic deformation between the shapes, thus unifying both shape representation and deformation. A fundamental drawback of the Fisher-Rao metric is that it is not available in closed form for the GMM. Consequently, shape comparisons are computationally very expensive. To address this, we develop a new Riemannian metric based on generalized ϕ-entropy measures. In sharp contrast to the Fisher-Rao metric, the new metric is available in closed form. Geodesic computations using the new metric are considerably more efficient. We validate the performance and discriminative capabilities of these new information geometry-based metrics by pairwise matching of corpus callosum shapes. We also study the deformations of fish shapes that have various topological properties. A comprehensive comparative analysis is also provided using other landmark-based distances, including the Hausdorff distance, the Procrustes metric, landmark-based diffeomorphisms, and the bending energies of the thin-plate (TPS) and Wendland splines. PMID:19110497

Application of Quaternion in improving the quality of global sequence alignment scores for an ambiguous sequence target in Streptococcus pneumoniae DNA

NASA Astrophysics Data System (ADS)

Lestari, D.; Bustamam, A.; Novianti, T.; Ardaneswari, G.

2017-07-01

DNA sequence can be defined as a succession of letters, representing the order of nucleotides within DNA, using a permutation of four DNA base codes including adenine (A), guanine (G), cytosine (C), and thymine (T). The precise code of the sequences is determined using DNA sequencing methods and technologies, which have been developed since the 1970s and currently become highly developed, advanced and highly throughput sequencing technologies. So far, DNA sequencing has greatly accelerated biological and medical research and discovery. However, in some cases DNA sequencing could produce any ambiguous and not clear enough sequencing results that make them quite difficult to be determined whether these codes are A, T, G, or C. To solve these problems, in this study we can introduce other representation of DNA codes namely Quaternion Q = (PA, PT, PG, PC), where PA, PT, PG, PC are the probability of A, T, G, C bases that could appear in Q and PA + PT + PG + PC = 1. Furthermore, using Quaternion representations we are able to construct the improved scoring matrix for global sequence alignment processes, by applying a dot product method. Moreover, this scoring matrix produces better and higher quality of the match and mismatch score between two DNA base codes. In implementation, we applied the Needleman-Wunsch global sequence alignment algorithm using Octave, to analyze our target sequence which contains some ambiguous sequence data. The subject sequences are the DNA sequences of Streptococcus pneumoniae families obtained from the Genebank, meanwhile the target DNA sequence are received from our collaborator database. As the results we found the Quaternion representations improve the quality of the sequence alignment score and we can conclude that DNA sequence target has maximum similarity with Streptococcus pneumoniae.

Internal representations reveal cultural diversity in expectations of facial expressions of emotion.

PubMed

Jack, Rachael E; Caldara, Roberto; Schyns, Philippe G

2012-02-01

Facial expressions have long been considered the "universal language of emotion." Yet consistent cultural differences in the recognition of facial expressions contradict such notions (e.g., R. E. Jack, C. Blais, C. Scheepers, P. G. Schyns, & R. Caldara, 2009). Rather, culture--as an intricate system of social concepts and beliefs--could generate different expectations (i.e., internal representations) of facial expression signals. To investigate, they used a powerful psychophysical technique (reverse correlation) to estimate the observer-specific internal representations of the 6 basic facial expressions of emotion (i.e., happy, surprise, fear, disgust, anger, and sad) in two culturally distinct groups (i.e., Western Caucasian [WC] and East Asian [EA]). Using complementary statistical image analyses, cultural specificity was directly revealed in these representations. Specifically, whereas WC internal representations predominantly featured the eyebrows and mouth, EA internal representations showed a preference for expressive information in the eye region. Closer inspection of the EA observer preference revealed a surprising feature: changes of gaze direction, shown primarily among the EA group. For the first time, it is revealed directly that culture can finely shape the internal representations of common facial expressions of emotion, challenging notions of a biologically hardwired "universal language of emotion."

Exploring the Structure of Spatial Representations

PubMed Central

Madl, Tamas; Franklin, Stan; Chen, Ke; Trappl, Robert; Montaldi, Daniela

2016-01-01

It has been suggested that the map-like representations that support human spatial memory are fragmented into sub-maps with local reference frames, rather than being unitary and global. However, the principles underlying the structure of these ‘cognitive maps’ are not well understood. We propose that the structure of the representations of navigation space arises from clustering within individual psychological spaces, i.e. from a process that groups together objects that are close in these spaces. Building on the ideas of representational geometry and similarity-based representations in cognitive science, we formulate methods for learning dissimilarity functions (metrics) characterizing participants’ psychological spaces. We show that these learned metrics, together with a probabilistic model of clustering based on the Bayesian cognition paradigm, allow prediction of participants’ cognitive map structures in advance. Apart from insights into spatial representation learning in human cognition, these methods could facilitate novel computational tools capable of using human-like spatial concepts. We also compare several features influencing spatial memory structure, including spatial distance, visual similarity and functional similarity, and report strong correlations between these dimensions and the grouping probability in participants’ spatial representations, providing further support for clustering in spatial memory. PMID:27347681

Cohomologie des Groupes Localement Compacts et Produits Tensoriels Continus de Representations

ERIC Educational Resources Information Center

Guichardet, A.

1976-01-01

Contains few and sometimes incomplete proofs on continuous tensor products of Hilbert spaces and of group representations, and on the irreducibility of the latter. Theory of continuous tensor products of Hilbert Spaces is closely related to that of conditionally positive definite functions; it relies on the technique of symmetric Hilbert spaces,…

Effect of Algorithms' Multiple Representations in the Context of Programming Education

ERIC Educational Resources Information Center

Siozou, Stefania; Tselios, Nikolaos; Komis, Vassilis

2008-01-01

Purpose: The purpose of this paper is to compare the effect of different representations while teaching basic algorithmic concepts to novice programmers. Design/methodology/approach: A learning activity was designed and mediated with two conceptually different learning environments, each one used by a different group. The first group used the…

On coherent states for the simplest quantum groups

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1991-01-01

The coherent states for the simplest quantum groups ( q-Heisenberg-Weyl, SU q (2) and the discrete series of representations of SU q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on ℂ, a sphere, and the Lobatchevsky plane are discussed.

76 FR 39974 - Delegation by the Deputy Secretary of State Regarding Department Representation on the Investment...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-07-07

... DEPARTMENT OF STATE [Delegation of Authority No. 337] Delegation by the Deputy Secretary of State Regarding Department Representation on the Investment Working Group Established by the SelectUSA Executive... Group established by the SelectUSA Executive Order of June 15, 2011. The Under Secretary or Assistant...

A general non-Abelian density matrix renormalization group algorithm with application to the C{sub 2} dimer

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

Sharma, Sandeep, E-mail: sanshar@gmail.com

2015-01-14

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve ofmore » the C{sub 2} dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10{sup 12} many-body states. While our calculated energy lies within the 0.3 mE{sub h} error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mE{sub h}, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (T{sub e}) of eight lowest lying excited states: a{sup 3}Π{sub u}, b{sup 3}Σ{sub g}{sup −}, A{sup 1}Π{sub u}, c{sup 3}Σ{sub u}{sup +}, B{sup 1}Δ{sub g}, B{sup ′1}Σ{sub g}{sup +}, d{sup 3}Π{sub g}, and C{sup 1}Π{sub g} are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations {sup 1}Σ{sub g}{sup +}, {sup 1}Σ{sub u}{sup +}, {sup 1}Σ{sub g}{sup −}, and {sup 1}Σ{sub u}{sup −}, to an estimated accuracy of 0.1 mE{sub h} of the exact result in this basis.« less

Discriminative Transfer Subspace Learning via Low-Rank and Sparse Representation.

PubMed

Xu, Yong; Fang, Xiaozhao; Wu, Jian; Li, Xuelong; Zhang, David

2016-02-01

In this paper, we address the problem of unsupervised domain transfer learning in which no labels are available in the target domain. We use a transformation matrix to transfer both the source and target data to a common subspace, where each target sample can be represented by a combination of source samples such that the samples from different domains can be well interlaced. In this way, the discrepancy of the source and target domains is reduced. By imposing joint low-rank and sparse constraints on the reconstruction coefficient matrix, the global and local structures of data can be preserved. To enlarge the margins between different classes as much as possible and provide more freedom to diminish the discrepancy, a flexible linear classifier (projection) is obtained by learning a non-negative label relaxation matrix that allows the strict binary label matrix to relax into a slack variable matrix. Our method can avoid a potentially negative transfer by using a sparse matrix to model the noise and, thus, is more robust to different types of noise. We formulate our problem as a constrained low-rankness and sparsity minimization problem and solve it by the inexact augmented Lagrange multiplier method. Extensive experiments on various visual domain adaptation tasks show the superiority of the proposed method over the state-of-the art methods. The MATLAB code of our method will be publicly available at http://www.yongxu.org/lunwen.html.

Wilson loops and its correlators with chiral operators in N = 2, 4 SCFT at large N

NASA Astrophysics Data System (ADS)

Sysoeva, E.

2018-03-01

In this paper we compute the vacuum expectation value of the Wilson loop and its correlators with chiral primary operators in N = 2, 4 superconformal U( N ) gauge theories at large N . After localization these quantities can be computed in terms of a deformed U( N ) matrix model. The Wilson loops we deal with are in the fundamental and symmetric representations.

Context as the Building Blocks of Meaning: A Retrieval Model for the Semantic Representation of Words

DTIC Science & Technology

2003-04-01

8 Deconstructing the model’s output................................................................................ 9 Implications of the ideas...identified characters of a word are used as a probe to retrieve a word’s identity (its spelling and phonology ) from memory. In addition to the...document matrix has been reduced by the SVD. Deconstructing the model’s output Why do semantic relationships between words emerge from the model? Is the

Consistent Alignment of World Embedding Models

DTIC Science & Technology

2017-03-02

propose a solution that aligns variations of the same model (or different models) in a joint low-dimensional la- tent space leveraging carefully...representations of linguistic enti- ties, most often referred to as embeddings. This includes techniques that rely on matrix factoriza- tion (Levy & Goldberg ...higher, the variation is much higher as well. As we increase the size of the neighborhood, or improve the quality of our sample by only picking the most

Matrix approach to land carbon cycle modeling: A case study with the Community Land Model.

PubMed

Huang, Yuanyuan; Lu, Xingjie; Shi, Zheng; Lawrence, David; Koven, Charles D; Xia, Jianyang; Du, Zhenggang; Kluzek, Erik; Luo, Yiqi

2018-03-01

The terrestrial carbon (C) cycle has been commonly represented by a series of C balance equations to track C influxes into and effluxes out of individual pools in earth system models (ESMs). This representation matches our understanding of C cycle processes well but makes it difficult to track model behaviors. It is also computationally expensive, limiting the ability to conduct comprehensive parametric sensitivity analyses. To overcome these challenges, we have developed a matrix approach, which reorganizes the C balance equations in the original ESM into one matrix equation without changing any modeled C cycle processes and mechanisms. We applied the matrix approach to the Community Land Model (CLM4.5) with vertically-resolved biogeochemistry. The matrix equation exactly reproduces litter and soil organic carbon (SOC) dynamics of the standard CLM4.5 across different spatial-temporal scales. The matrix approach enables effective diagnosis of system properties such as C residence time and attribution of global change impacts to relevant processes. We illustrated, for example, the impacts of CO 2 fertilization on litter and SOC dynamics can be easily decomposed into the relative contributions from C input, allocation of external C into different C pools, nitrogen regulation, altered soil environmental conditions, and vertical mixing along the soil profile. In addition, the matrix tool can accelerate model spin-up, permit thorough parametric sensitivity tests, enable pool-based data assimilation, and facilitate tracking and benchmarking of model behaviors. Overall, the matrix approach can make a broad range of future modeling activities more efficient and effective. © 2017 John Wiley & Sons Ltd.

Estimating the Volterra Series Transfer Function over coherent optical OFDM for efficient monitoring of the fiber channel nonlinearity.

PubMed

Shulkind, Gal; Nazarathy, Moshe

2012-12-17

We present an efficient method for system identification (nonlinear channel estimation) of third order nonlinear Volterra Series Transfer Function (VSTF) characterizing the four-wave-mixing nonlinear process over a coherent OFDM fiber link. Despite the seemingly large number of degrees of freedom in the VSTF (cubic in the number of frequency points) we identified a compressed VSTF representation which does not entail loss of information. Additional slightly lossy compression may be obtained by discarding very low power VSTF coefficients associated with regions of destructive interference in the FWM phased array effect. Based on this two-staged VSTF compressed representation, we develop a robust and efficient algorithm of nonlinear system identification (optical performance monitoring) estimating the VSTF by transmission of an extended training sequence over the OFDM link, performing just a matrix-vector multiplication at the receiver by a pseudo-inverse matrix which is pre-evaluated offline. For 512 (1024) frequency samples per channel, the VSTF measurement takes less than 1 (10) msec to complete with computational complexity of one real-valued multiply-add operation per time sample. Relative to a naïve exhaustive three-tone-test, our algorithm is far more tolerant of ASE additive noise and its acquisition time is orders of magnitude faster.

Individual movement behavior, matrix heterogeneity, and the dynamics of spatially structured populations.

PubMed

Revilla, Eloy; Wiegand, Thorsten

2008-12-09

The dynamics of spatially structured populations is characterized by within- and between-patch processes. The available theory describes the latter with simple distance-dependent functions that depend on landscape properties such as interpatch distance or patch size. Despite its potential role, we lack a good mechanistic understanding of how the movement of individuals between patches affects the dynamics of these populations. We used the theoretical framework provided by movement ecology to make a direct representation of the processes determining how individuals connect local populations in a spatially structured population of Iberian lynx. Interpatch processes depended on the heterogeneity of the matrix where patches are embedded and the parameters defining individual movement behavior. They were also very sensitive to the dynamic demographic variables limiting the time moving, the within-patch dynamics of available settlement sites (both spatiotemporally heterogeneous) and the response of individuals to the perceived risk while moving. These context-dependent dynamic factors are an inherent part of the movement process, producing connectivities and dispersal kernels whose variability is affected by other demographic processes. Mechanistic representations of interpatch movements, such as the one provided by the movement-ecology framework, permit the dynamic interaction of birth-death processes and individual movement behavior, thus improving our understanding of stochastic spatially structured populations.

Discriminative Relational Topic Models.

PubMed

Chen, Ning; Zhu, Jun; Xia, Fei; Zhang, Bo

2015-05-01

Relational topic models (RTMs) provide a probabilistic generative process to describe both the link structure and document contents for document networks, and they have shown promise on predicting network structures and discovering latent topic representations. However, existing RTMs have limitations in both the restricted model expressiveness and incapability of dealing with imbalanced network data. To expand the scope and improve the inference accuracy of RTMs, this paper presents three extensions: 1) unlike the common link likelihood with a diagonal weight matrix that allows the-same-topic interactions only, we generalize it to use a full weight matrix that captures all pairwise topic interactions and is applicable to asymmetric networks; 2) instead of doing standard Bayesian inference, we perform regularized Bayesian inference (RegBayes) with a regularization parameter to deal with the imbalanced link structure issue in real networks and improve the discriminative ability of learned latent representations; and 3) instead of doing variational approximation with strict mean-field assumptions, we present collapsed Gibbs sampling algorithms for the generalized relational topic models by exploring data augmentation without making restricting assumptions. Under the generic RegBayes framework, we carefully investigate two popular discriminative loss functions, namely, the logistic log-loss and the max-margin hinge loss. Experimental results on several real network datasets demonstrate the significance of these extensions on improving prediction performance.

Direct Retrieval of Exterior Orientation Parameters Using A 2-D Projective Transformation

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

Seedahmed, Gamal H.

2006-09-01

Direct solutions are very attractive because they obviate the need for initial approximations associated with non-linear solutions. The Direct Linear Transformation (DLT) establishes itself as a method of choice for direct solutions in photogrammetry and other fields. The use of the DLT with coplanar object space points leads to a rank deficient model. This rank deficient model leaves the DLT defined up to a 2-D projective transformation, which makes the direct retrieval of the exterior orientation parameters (EOPs) a non-trivial task. This paper presents a novel direct algorithm to retrieve the EOPs from the 2-D projective transformation. It is basedmore » on a direct relationship between the 2-D projective transformation and the collinearity model using homogeneous coordinates representation. This representation offers a direct matrix correspondence between the 2-D projective transformation parameters and the collinearity model parameters. This correspondence lends itself to a direct matrix factorization to retrieve the EOPs. An important step in the proposed algorithm is a normalization process that provides the actual link between the 2-D projective transformation and the collinearity model. This paper explains the theoretical basis of the proposed algorithm as well as the necessary steps for its practical implementation. In addition, numerical examples are provided to demonstrate its validity.« less

Green's function of multi-layered poroelastic half-space for models of ground vibration due to railway traffic

NASA Astrophysics Data System (ADS)

Wang, Futong; Tao, Xiaxin; Xie, Lili; Raj, Siddharthan

2017-04-01

This study proposes a Green's function, an essential representation of water-saturated ground under moving excitation, to simulate ground borne vibration from trains. First, general solutions to the governing equations of poroelastic medium are derived by means of integral transform. Secondly, the transmission and reflection matrix approach is used to formulate the relationship between displacement and stress of the stratified ground, which results in the matrix of the Green's function. Then the Green's function is combined into a train-track-ground model, and is verified by typical examples and a field test. Additional simulations show that the computed ground vibration attenuates faster in the immediate vicinity of the track than in the surrounding area. The wavelength of wheel-rail unevenness has a notable effect on computed displacement and pore pressure. The variation of vibration intensity with the depth of ground is significantly influenced by the layering of the strata soil. When the train speed is equal to the velocity of the Rayleigh wave, the Mach cone appears in the simulated wave field. The proposed Green's function is an appropriate representation for a layered ground with shallow ground water table, and will be helpful to understand the dynamic responses of the ground to complicated moving excitation.

Quantum groups, roots of unity and particles on quantized Anti-de Sitter space

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

Steinacker, Harold

1997-05-23

Quantum groups in general and the quantum Anti-de Sitter group U q(so(2,3)) in particular are studied from the point of view of quantum field theory. The author shows that if q is a suitable root of unity, there exist finite-dimensional, unitary representations corresponding to essentially all the classical one-particle representations with (half) integer spin, with the same structure at low energies as in the classical case. In the massless case for spin ≥ 1, "naive" representations are unitarizable only after factoring out a subspace of "pure gauges", as classically. Unitary many-particle representations are defined, with the correct classical limit. Furthermore,more » the author identifies a remarkable element Q in the center of U q(g), which plays the role of a BRST operator in the case of U q(so(2,3)) at roots of unity, for any spin ≥ 1. The associated ghosts are an intrinsic part of the indecomposable representations. The author shows how to define an involution on algebras of creation and anihilation operators at roots of unity, in an example corresponding to non-identical particles. It is shown how nonabelian gauge fields appear naturally in this framework, without having to define connections on fiber bundles. Integration on Quantum Euclidean space and sphere and on Anti-de Sitter space is studied as well. The author gives a conjecture how Q can be used in general to analyze the structure of indecomposable representations, and to define a new, completely reducible associative (tensor) product of representations at roots of unity, which generalizes the standard "truncated" tensor product as well as many-particle representations.« less

Stabilization of Taylor-Couette flow due to time-periodic outer cylinder oscillation

NASA Technical Reports Server (NTRS)

Murray, B. T.; Mcfadden, G. B.; Coriell, S. R.

1990-01-01

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case when the inner cylinder is rotated at a constant angular velocity and the outer cylinder is driven sinusoidally in time with zero mean rotation. This configuration was studied experimentally by Walsh and Donnelly. The critical Reynolds numbers calculated from linear stability theory agree well with the experimental values, except at large modulation amplitudes and small frequencies. The theoretical values are obtained using Floquet theory implemented in two distinct approaches: a truncated Fourier series representation in time, and a fundamental solution matrix based on a Chebyshev pseudospectral representation in space. For large amplitude, low frequency modulation, the linear eigenfunctions are temporally complex, consisting of a quiescent region followed by rapid change in the perturbed flow velocities.

Geometrical eigen-subspace framework based molecular conformation representation for efficient structure recognition and comparison

NASA Astrophysics Data System (ADS)

Li, Xiao-Tian; Yang, Xiao-Bao; Zhao, Yu-Jun

2017-04-01

We have developed an extended distance matrix approach to study the molecular geometric configuration through spectral decomposition. It is shown that the positions of all atoms in the eigen-space can be specified precisely by their eigen-coordinates, while the refined atomic eigen-subspace projection array adopted in our approach is demonstrated to be a competent invariant in structure comparison. Furthermore, a visual eigen-subspace projection function (EPF) is derived to characterize the surrounding configuration of an atom naturally. A complete set of atomic EPFs constitute an intrinsic representation of molecular conformation, based on which the interatomic EPF distance and intermolecular EPF distance can be reasonably defined. Exemplified with a few cases, the intermolecular EPF distance shows exceptional rationality and efficiency in structure recognition and comparison.

Torus Knot Polynomials and Susy Wilson Loops

NASA Astrophysics Data System (ADS)

Giasemidis, Georgios; Tierz, Miguel

2014-12-01

We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987), a basic hypergeometric representation of the HOMFLY polynomial of ( n, m) torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result, the symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilson loop of 2d Yang-Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang-Mills theory, which is known to give averages of Wilson loops in = 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones-Rosso representation in terms of q-harmonic oscillators.

40 CFR 97.620 - Establishment of compliance accounts, assurance accounts, and general accounts.

Code of Federal Regulations, 2013 CFR

2013-07-01

... representation under § 97.616, the Administrator will establish a compliance account for the TR SO2 Group 1 source for which the certificate of representation was submitted, unless the source already has a... such persons and that each such person shall be fully bound by my representations, actions, inactions...

40 CFR 97.720 - Establishment of compliance accounts, assurance accounts, and general accounts.

Code of Federal Regulations, 2013 CFR

2013-07-01

... representation under § 97.716, the Administrator will establish a compliance account for the TR SO2 Group 2 source for which the certificate of representation was submitted, unless the source already has a... such persons and that each such person shall be fully bound by my representations, actions, inactions...

Using Multiple Representations to Promote Grade 11 Students' Scientific Understanding of the Particle Theory of Matter

ERIC Educational Resources Information Center

Adadan, Emine

2013-01-01

This study explored two groups of Grade 11 (age 16-17) students' conceptual understandings about aspects of particle theory before, immediately after, and 3 months after instruction with multiple representations (IMR) and instruction with verbal representations (IVR). Data sources included open-ended questionnaires, interviews, and student…

Applying the Common Sense Model to Understand Representations of Arsenic Contaminated Well Water

PubMed Central

Severtson, Dolores J.; Baumann, Linda C.; Brown, Roger L.

2015-01-01

Theory-based research is needed to understand how people respond to environmental health risk information. The common sense model of self-regulation and the mental models approach propose that information shapes individual’s personal understandings that influence their decisions and actions. We compare these frameworks and explain how the common sense model (CSM) was applied to describe and measure mental representations of arsenic contaminated well water. Educational information, key informant interviews, and environmental risk literature were used to develop survey items to measure dimensions of cognitive representations (identity, cause, timeline, consequences, control) and emotional representations. Surveys mailed to 1067 private well users with moderate and elevated arsenic levels yielded an 84% response rate (n=897). Exploratory and confirmatory factor analyses of data from the elevated arsenic group identified a factor structure that retained the CSM representational structure and was consistent across moderate and elevated arsenic groups. The CSM has utility for describing and measuring representations of environmental health risks thus supporting its application to environmental health risk communication research. PMID:18726811

Attachment security representations in institutionalized children and children living with their families: links to problem behaviour.

PubMed

Torres, Nuno; Maia, Joana; Veríssimo, Manuela; Fernandes, Marilia; Silva, Filipa

2012-01-01

The present work analyses differences in the attachment representations of institutionalized children as compared with children from low and high educational level living with their natural families. Participants were 91 Portuguese children, 52% girls, aged 48-96 months. There were three different groups: 19 institutionalized children, 16 low educational level families' children and 56 from high educational level families'. Attachment representations were assessed for Security of the narratives of the Attachment Story Completion Task (ASCT). Psychopathological symptoms were assessed using the Child Behaviour Checklist for parents and caretakers. Verbal skills were assessed using the Wechsler Preschool and Primary Scale of Intelligence--Revised. Results show that institutionalized children have significantly lower security of attachment representations, less verbal skills and higher aggressive behaviour than the other two groups. Attachment representations were associated with social/withdrawal and aggression, independently of age, verbal skills and parents' education. The main effect of institutionalization on externalizing aggressive behaviour was completely mediated by the security of attachment representations.  Copyright © 2010 John Wiley & Sons, Ltd.

Sparse representation based image interpolation with nonlocal autoregressive modeling.

PubMed

Dong, Weisheng; Zhang, Lei; Lukac, Rastislav; Shi, Guangming

2013-04-01

Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without blurring, the super-resolution problem becomes an image interpolation problem. In such cases, however, the conventional sparse representation models (SRM) become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, fortunately, many nonlocal similar patches to a given patch could provide nonlocal constraint to the local structure. In this paper, we incorporate the image nonlocal self-similarity into SRM for image interpolation. More specifically, a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in SRM. We show that the NARM-induced sampling matrix is less coherent with the representation dictionary, and consequently makes SRM more effective for image interpolation. Our extensive experimental results demonstrate that the proposed NARM-based image interpolation method can effectively reconstruct the edge structures and suppress the jaggy/ringing artifacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as SSIM and FSIM.

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

Koenig, Robert; Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125; Mitchison, Graeme

In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's 'exponential' approximation by 'almost-product' states, a theorem which deals with certain triples of representations of the unitary group, and the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choicemore » of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states and leads to some new results, including an exponential theorem for infinite-dimensional systems.« less

Right ventricular function after repair of tetralogy of Fallot: a comparison between bovine pericardium and porcine small intestinal extracellular matrix.

PubMed

Naik, Ronak; Johnson, Jason; Kumar, T K S; Philip, Ranjit; Boston, Umar; Knott-Craig, Christopher J

2017-05-29

The porcine small intestinal extracellular matrix reportedly has the potential to differentiate into viable myocardial cells. When used in tetralogy of Fallot repair, it may improve right ventricular function. We evaluated right ventricular function after repair of tetralogy of Fallot with extracellular matrix versus bovine pericardium. Subjects with non-transannular repair of tetralogy of Fallot with at least 1 year of follow-up were selected. The extracellular matrix and bovine pericardium groups were compared. We used three-dimensional right ventricular ejection fraction, right ventricle global longitudinal strain, and tricuspid annular plane systolic excursion to assess right ventricular function. The extracellular matrix group had 11 patients, whereas the bovine pericardium group had 10 patients. No differences between the groups were found regarding sex ratio, age at surgery, and cardiopulmonary bypass time. The follow-up period was 28±12.6 months in the extracellular matrix group and 50.05±17.6 months in the bovine pericardium group (p=0.001). The mean three-dimensional right ventricular ejection fraction (55.7±5.0% versus 55.3±5.2%, p=0.73), right ventricular global longitudinal strain (-18.5±3.0% versus -18.0±2.2%, p=0.44), and tricuspid annular plane systolic excursions (1.59±0.16 versus 1.59±0.2, p=0.93) were similar in the extracellular matrix group and in the bovine pericardium group, respectively. Right ventricular global longitudinal strain in healthy children is reported at -29±3% in literature. In a small cohort of the patients undergoing non-transannular repair of tetralogy of Fallot, there was no significant difference in right ventricular function between groups having extracellular matrix versus bovine pericardium patches followed-up for more than 1 year. Lower right ventricular longitudinal strain noted in both the groups compared to healthy children.

Self-other disturbance in borderline personality disorder: Neural, self-report, and performance-based evidence.

PubMed

Beeney, Joseph E; Hallquist, Michael N; Ellison, William D; Levy, Kenneth N

2016-01-01

Individuals with borderline personality disorder (BPD) display an impoverished sense of self and representations of self and others that shift between positive and negative poles. However, little research has investigated the nature of representational disturbance in BPD. The present study takes a multimodal approach. A card sort task was used to investigate complexity, integration, and valence of self-representation in BPD. Impairment in maintenance of self and other representations was assessed using a personality representational maintenance task. Finally, functional MRI (fMRI) was used to assess whether individuals with BPD show neural abnormalities related specifically to the self and what brain areas may be related to poor representational maintenance. Individuals with BPD sorted self-aspects suggesting more complexity of self-representation, but also less integration and more negative valence overall. On the representational maintenance task, individuals with BPD showed less consistency in their representations of self and others over the 3-hr period, but only for abstract, personality-based representations. Performance on this measure mediated between-groups brain activation in several areas supporting social cognition. We found no evidence for social-cognitive disturbance specific to the self. Additionally, the BPD group showed main effects, insensitive to condition, of hyperactivation in the medial prefrontal cortex, temporal parietal junction, several regions of the frontal pole, the precuneus and middle temporal gyrus, all areas crucial social cognition. In contrast, controls evidenced greater activation in visual, sensory, motor, and mirror neuron regions. These findings are discussed in relation to research regarding hypermentalization and the overlap between self- and other-disturbance. (c) 2016 APA, all rights reserved).

Associating Animations with Concrete Models to Enhance Students' Comprehension of Different Visual Representations in Organic Chemistry

ERIC Educational Resources Information Center

Al-Balushi, Sulaiman M.; Al-Hajri, Sheikha H.

2014-01-01

The purpose of the current study is to explore the impact of associating animations with concrete models on eleventh-grade students' comprehension of different visual representations in organic chemistry. The study used a post-test control group quasi-experimental design. The experimental group (N = 28) used concrete models, submicroscopic…

Creating Joint Representations of Collaborative Problem Solving with Multi-Touch Technology

ERIC Educational Resources Information Center

Mercier, E.; Higgins, S.

2014-01-01

Multi-touch surfaces have the potential to change the nature of computer-supported collaborative learning, allowing more equitable access to shared digital content. In this paper, we explore how large multi-touch tables can be used by groups of students as an external representation of their group interaction processes. Video data from 24 groups…

Covariant fields on anti-de Sitter spacetimes

NASA Astrophysics Data System (ADS)

Cotăescu, Ion I.

2018-02-01

The covariant free fields of any spin on anti-de Sitter (AdS) spacetimes are studied, pointing out that these transform under isometries according to covariant representations (CRs) of the AdS isometry group, induced by those of the Lorentz group. Applying the method of ladder operators, it is shown that the CRs with unique spin are equivalent with discrete unitary irreducible representations (UIRs) of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations (reps.) may depend on the mass and spin of the covariant field. The conclusion is that on AdS spacetime, one cannot formulate a universal mass condition as in special relativity.

Quasiprobability Representations of Quantum Mechanics with Minimal Negativity

NASA Astrophysics Data System (ADS)

Zhu, Huangjun

2016-09-01

Quasiprobability representations, such as the Wigner function, play an important role in various research areas. The inevitable appearance of negativity in such representations is often regarded as a signature of nonclassicality, which has profound implications for quantum computation. However, little is known about the minimal negativity that is necessary in general quasiprobability representations. Here we focus on a natural class of quasiprobability representations that is distinguished by simplicity and economy. We introduce three measures of negativity concerning the representations of quantum states, unitary transformations, and quantum channels, respectively. Quite surprisingly, all three measures lead to the same representations with minimal negativity, which are in one-to-one correspondence with the elusive symmetric informationally complete measurements. In addition, most representations with minimal negativity are automatically covariant with respect to the Heisenberg-Weyl groups. Furthermore, our study reveals an interesting tradeoff between negativity and symmetry in quasiprobability representations.

A rough set approach for determining weights of decision makers in group decision making.

PubMed

Yang, Qiang; Du, Ping-An; Wang, Yong; Liang, Bin

2017-01-01

This study aims to present a novel approach for determining the weights of decision makers (DMs) based on rough group decision in multiple attribute group decision-making (MAGDM) problems. First, we construct a rough group decision matrix from all DMs' decision matrixes on the basis of rough set theory. After that, we derive a positive ideal solution (PIS) founded on the average matrix of rough group decision, and negative ideal solutions (NISs) founded on the lower and upper limit matrixes of rough group decision. Then, we obtain the weight of each group member and priority order of alternatives by using relative closeness method, which depends on the distances from each individual group member' decision to the PIS and NISs. Through comparisons with existing methods and an on-line business manager selection example, the proposed method show that it can provide more insights into the subjectivity and vagueness of DMs' evaluations and selections.

Trunk Robot Rehabilitation Training with Active Stepping Reorganizes and Enriches Trunk Motor Cortex Representations in Spinal Transected Rats

PubMed Central

Oza, Chintan S.

2015-01-01

Trunk motor control is crucial for postural stability and propulsion after low thoracic spinal cord injury (SCI) in animals and humans. Robotic rehabilitation aimed at trunk shows promise in SCI animal models and patients. However, little is known about the effect of SCI and robot rehabilitation of trunk on cortical motor representations. We previously showed reorganization of trunk motor cortex after adult SCI. Non-stepping training also exacerbated some SCI-driven plastic changes. Here we examine effects of robot rehabilitation that promotes recovery of hindlimb weight support functions on trunk motor cortex representations. Adult rats spinal transected as neonates (NTX rats) at the T9/10 level significantly improve function with our robot rehabilitation paradigm, whereas treadmill-only trained do not. We used intracortical microstimulation to map motor cortex in two NTX groups: (1) treadmill trained (control group); and (2) robot-assisted treadmill trained (improved function group). We found significant robot rehabilitation-driven changes in motor cortex: (1) caudal trunk motor areas expanded; (2) trunk coactivation at cortex sites increased; (3) richness of trunk cortex motor representations, as examined by cumulative entropy and mutual information for different trunk representations, increased; (4) trunk motor representations in the cortex moved toward more normal topography; and (5) trunk and forelimb motor representations that SCI-driven plasticity and compensations had caused to overlap were segregated. We conclude that effective robot rehabilitation training induces significant reorganization of trunk motor cortex and partially reverses some plastic changes that may be adaptive in non-stepping paraplegia after SCI. PMID:25948267

Adinkra (in)equivalence from Coxeter group representations: A case study

NASA Astrophysics Data System (ADS)

Chappell, Isaac; Gates, S. James; Hübsch, T.

2014-02-01

Using a MathematicaTM code, we present a straightforward numerical analysis of the 384-dimensional solution space of signed permutation 4×4 matrices, which in sets of four, provide representations of the 𝒢ℛ(4, 4) algebra, closely related to the 𝒩 = 1 (simple) supersymmetry algebra in four-dimensional space-time. Following after ideas discussed in previous papers about automorphisms and classification of adinkras and corresponding supermultiplets, we make a new and alternative proposal to use equivalence classes of the (unsigned) permutation group S4 to define distinct representations of higher-dimensional spin bundles within the context of adinkras. For this purpose, the definition of a dual operator akin to the well-known Hodge star is found to partition the space of these 𝒢ℛ(4, 4) representations into three suggestive classes.

Towards topological quantum computer

NASA Astrophysics Data System (ADS)

Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.

2018-01-01

Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.