Reduced Wiener Chaos representation of random fields via basis adaptation and projection

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

Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu; Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089; Ghanem, Roger G., E-mail: ghanem@usc.edu

2017-07-15

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

NASA Astrophysics Data System (ADS)

Tsilifis, Panagiotis; Ghanem, Roger G.

2017-07-01

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Covariant harmonic oscillators: 1973 revisited

NASA Technical Reports Server (NTRS)

Noz, M. E.

1993-01-01

Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated.

Total recall in distributive associative memories

NASA Technical Reports Server (NTRS)

Danforth, Douglas G.

1991-01-01

Iterative error correction of asymptotically large associative memories is equivalent to a one-step learning rule. This rule is the inverse of the activation function of the memory. Spectral representations of nonlinear activation functions are used to obtain the inverse in closed form for Sparse Distributed Memory, Selected-Coordinate Design, and Radial Basis Functions.

Constructing diabatic representations using adiabatic and approximate diabatic data--Coping with diabolical singularities.

PubMed

Zhu, Xiaolei; Yarkony, David R

2016-01-28

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H(d), and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility, has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H(d) individually provides a starting point (seed) from which convergence of the full H(d) construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4(1)A states of phenol and the 1,2(1)A states of NH3, states which are coupled by conical intersections.

Experimental Design and Interpretation of Functional Neuroimaging Studies of Cognitive Processes

PubMed Central

Caplan, David

2008-01-01

This article discusses how the relation between experimental and baseline conditions in functional neuroimaging studies affects the conclusions that can be drawn from a study about the neural correlates of components of the cognitive system and about the nature and organization of those components. I argue that certain designs in common use—in particular the contrast of qualitatively different representations that are processed at parallel stages of a functional architecture—can never identify the neural basis of a cognitive operation and have limited use in providing information about the nature of cognitive systems. Other types of designs—such as ones that contrast representations that are computed in immediately sequential processing steps and ones that contrast qualitatively similar representations that are parametrically related within a single processing stage—are more easily interpreted. PMID:17979122

Variational nonadiabatic dynamics in the moving crude adiabatic representation: Further merging of nuclear dynamics and electronic structure

NASA Astrophysics Data System (ADS)

Joubert-Doriol, Loïc; Izmaylov, Artur F.

2018-03-01

A new methodology of simulating nonadiabatic dynamics using frozen-width Gaussian wavepackets within the moving crude adiabatic representation with the on-the-fly evaluation of electronic structure is presented. The main feature of the new approach is the elimination of any global or local model representation of electronic potential energy surfaces; instead, the electron-nuclear interaction is treated explicitly using the Gaussian integration. As a result, the new scheme does not introduce any uncontrolled approximations. The employed variational principle ensures the energy conservation and leaves the number of electronic and nuclear basis functions as the only parameter determining the accuracy. To assess performance of the approach, a model with two electronic and two nuclear spacial degrees of freedom containing conical intersections between potential energy surfaces has been considered. Dynamical features associated with nonadiabatic transitions and nontrivial geometric (or Berry) phases were successfully reproduced within a limited basis expansion.

Image restoration for three-dimensional fluorescence microscopy using an orthonormal basis for efficient representation of depth-variant point-spread functions

PubMed Central

Patwary, Nurmohammed; Preza, Chrysanthe

2015-01-01

A depth-variant (DV) image restoration algorithm for wide field fluorescence microscopy, using an orthonormal basis decomposition of DV point-spread functions (PSFs), is investigated in this study. The efficient PSF representation is based on a previously developed principal component analysis (PCA), which is computationally intensive. We present an approach developed to reduce the number of DV PSFs required for the PCA computation, thereby making the PCA-based approach computationally tractable for thick samples. Restoration results from both synthetic and experimental images show consistency and that the proposed algorithm addresses efficiently depth-induced aberration using a small number of principal components. Comparison of the PCA-based algorithm with a previously-developed strata-based DV restoration algorithm demonstrates that the proposed method improves performance by 50% in terms of accuracy and simultaneously reduces the processing time by 64% using comparable computational resources. PMID:26504634

Electric transition dipole moment in pre-Born-Oppenheimer molecular structure theory.

PubMed

Simmen, Benjamin; Mátyus, Edit; Reiher, Markus

2014-10-21

This paper presents the calculation of the electric transition dipole moment in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally in terms of the parametrization of the non-relativistic total wave function, which is written as a linear combination of basis functions constructed from explicitly correlated Gaussian functions and the global vector representation. The integrals of the electric transition dipole moment are derived corresponding to these basis functions in both the length and the velocity representation. The calculations are performed in laboratory-fixed Cartesian coordinates without relying on coordinates which separate the center of mass from the translationally invariant degrees of freedom. The effect of the overall motion is eliminated through translationally invariant integral expressions. The electric transition dipole moment is calculated between two rovibronic levels of the H2 molecule assignable to the lowest rovibrational states of the X (1)Σ(g)(+) and B (1)Σ(u)(+) electronic states in the clamped-nuclei framework. This is the first evaluation of this quantity in a full quantum mechanical treatment without relying on the Born-Oppenheimer approximation.

Constructing diabatic representations using adiabatic and approximate diabatic data – Coping with diabolical singularities

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

Zhu, Xiaolei, E-mail: virtualzx@gmail.com; Yarkony, David R., E-mail: yarkony@jhu.edu

2016-01-28

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H{sup d}, and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility,more » has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H{sup d} individually provides a starting point (seed) from which convergence of the full H{sup d} construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4{sup 1}A states of phenol and the 1,2{sup 1}A states of NH{sub 3}, states which are coupled by conical intersections.« less

Unconstrained handwritten numeral recognition based on radial basis competitive and cooperative networks with spatio-temporal feature representation.

PubMed

Lee, S; Pan, J J

1996-01-01

This paper presents a new approach to representation and recognition of handwritten numerals. The approach first transforms a two-dimensional (2-D) spatial representation of a numeral into a three-dimensional (3-D) spatio-temporal representation by identifying the tracing sequence based on a set of heuristic rules acting as transformation operators. A multiresolution critical-point segmentation method is then proposed to extract local feature points, at varying degrees of scale and coarseness. A new neural network architecture, referred to as radial-basis competitive and cooperative network (RCCN), is presented especially for handwritten numeral recognition. RCCN is a globally competitive and locally cooperative network with the capability of self-organizing hidden units to progressively achieve desired network performance, and functions as a universal approximator of arbitrary input-output mappings. Three types of RCCNs are explored: input-space RCCN (IRCCN), output-space RCCN (ORCCN), and bidirectional RCCN (BRCCN). Experiments against handwritten zip code numerals acquired by the U.S. Postal Service indicated that the proposed method is robust in terms of variations, deformations, transformations, and corruption, achieving about 97% recognition rate.

Attention during natural vision warps semantic representation across the human brain.

PubMed

Çukur, Tolga; Nishimoto, Shinji; Huth, Alexander G; Gallant, Jack L

2013-06-01

Little is known about how attention changes the cortical representation of sensory information in humans. On the basis of neurophysiological evidence, we hypothesized that attention causes tuning changes to expand the representation of attended stimuli at the cost of unattended stimuli. To investigate this issue, we used functional magnetic resonance imaging to measure how semantic representation changed during visual search for different object categories in natural movies. We found that many voxels across occipito-temporal and fronto-parietal cortex shifted their tuning toward the attended category. These tuning shifts expanded the representation of the attended category and of semantically related, but unattended, categories, and compressed the representation of categories that were semantically dissimilar to the target. Attentional warping of semantic representation occurred even when the attended category was not present in the movie; thus, the effect was not a target-detection artifact. These results suggest that attention dynamically alters visual representation to optimize processing of behaviorally relevant objects during natural vision.

Bayesian image reconstruction - The pixon and optimal image modeling

NASA Technical Reports Server (NTRS)

Pina, R. K.; Puetter, R. C.

1993-01-01

In this paper we describe the optimal image model, maximum residual likelihood method (OptMRL) for image reconstruction. OptMRL is a Bayesian image reconstruction technique for removing point-spread function blurring. OptMRL uses both a goodness-of-fit criterion (GOF) and an 'image prior', i.e., a function which quantifies the a priori probability of the image. Unlike standard maximum entropy methods, which typically reconstruct the image on the data pixel grid, OptMRL varies the image model in order to find the optimal functional basis with which to represent the image. We show how an optimal basis for image representation can be selected and in doing so, develop the concept of the 'pixon' which is a generalized image cell from which this basis is constructed. By allowing both the image and the image representation to be variable, the OptMRL method greatly increases the volume of solution space over which the image is optimized. Hence the likelihood of the final reconstructed image is greatly increased. For the goodness-of-fit criterion, OptMRL uses the maximum residual likelihood probability distribution introduced previously by Pina and Puetter (1992). This GOF probability distribution, which is based on the spatial autocorrelation of the residuals, has the advantage that it ensures spatially uncorrelated image reconstruction residuals.

Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation

NASA Astrophysics Data System (ADS)

Rim, Chaiho; Zhang, Hong

2017-06-01

AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate representation, q being the instanton expansion parameter. Based on AFLT basis together with intertwiners we construct gauge conformal state and demonstrate its equivalence to the Liouville conformal state, with careful attention to the proper scaling behavior of the state. Using the colliding limit of regular states, we obtain the formal expression of irregular conformal states corresponding to Argyres-Douglas theory, which involves summation of functions over Young diagrams.

Polarization ellipse and Stokes parameters in geometric algebra.

PubMed

Santos, Adler G; Sugon, Quirino M; McNamara, Daniel J

2012-01-01

In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.

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.

The interval testing procedure: A general framework for inference in functional data analysis.

PubMed

Pini, Alessia; Vantini, Simone

2016-09-01

We introduce in this work the Interval Testing Procedure (ITP), a novel inferential technique for functional data. The procedure can be used to test different functional hypotheses, e.g., distributional equality between two or more functional populations, equality of mean function of a functional population to a reference. ITP involves three steps: (i) the representation of data on a (possibly high-dimensional) functional basis; (ii) the test of each possible set of consecutive basis coefficients; (iii) the computation of the adjusted p-values associated to each basis component, by means of a new strategy here proposed. We define a new type of error control, the interval-wise control of the family wise error rate, particularly suited for functional data. We show that ITP is provided with such a control. A simulation study comparing ITP with other testing procedures is reported. ITP is then applied to the analysis of hemodynamical features involved with cerebral aneurysm pathology. ITP is implemented in the fdatest R package. © 2016, The International Biometric Society.

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.

A new single-particle basis for nuclear many-body calculations

NASA Astrophysics Data System (ADS)

Puddu, G.

2017-10-01

Predominantly, harmonic oscillator single-particle wave functions are the preferred choice for a basis in ab initio nuclear many-body calculations. These wave-functions, although very convenient in order to evaluate the matrix elements of the interaction in the laboratory frame, have too fast a fall-off at large distances. In the past, as an alternative to the harmonic oscillator, other single-particle wave functions have been proposed. In this work, we propose a new single-particle basis, directly linked to nucleon-nucleon interaction. This new basis is orthonormal and complete, has the proper asymptotic behavior at large distances and does not contain the continuum which would pose severe convergence problems in nuclear many body calculations. We consider the newly proposed NNLO-opt nucleon-nucleon interaction, without any renormalization. We show that, unlike other bases, this single-particle representation has a computational cost similar to the harmonic oscillator basis with the same space truncation and it gives lower energies for 6He and 6Li.

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.

KARHUNEN-LOÈVE Basis Functions of Kolmogorov Turbulence in the Sphere

NASA Astrophysics Data System (ADS)

Mathar, Richard J.

In support of modeling atmospheric turbulence, the statistically independent Karhunen-Loève modes of refractive indices with isotropic Kolmogorov spectrum of the covariance are calculated inside a sphere of fixed radius, rendered as series of 3D Zernike functions. Many of the symmetry arguments of the well-known associated 2D problem for the circular input pupil remain valid. The technique of efficient diagonalization of the eigenvalue problem in wavenumber space is founded on the Fourier representation of the 3D Zernike basis, and extensible to the von-Kármán power spectrum.

Individual differences in long-range time representation.

PubMed

Agostino, Camila S; Caetano, Marcelo S; Balci, Fuat; Claessens, Peter M E; Zana, Yossi

2017-04-01

On the basis of experimental data, long-range time representation has been proposed to follow a highly compressed power function, which has been hypothesized to explain the time inconsistency found in financial discount rate preferences. The aim of this study was to evaluate how well linear and power function models explain empirical data from individual participants tested in different procedural settings. The line paradigm was used in five different procedural variations with 35 adult participants. Data aggregated over the participants showed that fitted linear functions explained more than 98% of the variance in all procedures. A linear regression fit also outperformed a power model fit for the aggregated data. An individual-participant-based analysis showed better fits of a linear model to the data of 14 participants; better fits of a power function with an exponent β > 1 to the data of 12 participants; and better fits of a power function with β < 1 to the data of the remaining nine participants. Of the 35 volunteers, the null hypothesis β = 1 was rejected for 20. The dispersion of the individual β values was approximated well by a normal distribution. These results suggest that, on average, humans perceive long-range time intervals not in a highly compressed, biased manner, but rather in a linear pattern. However, individuals differ considerably in their subjective time scales. This contribution sheds new light on the average and individual psychophysical functions of long-range time representation, and suggests that any attribution of deviation from exponential discount rates in intertemporal choice to the compressed nature of subjective time must entail the characterization of subjective time on an individual-participant basis.

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.

LETTER TO THE EDITOR: Two-centre exchange integrals for complex exponent Slater orbitals

NASA Astrophysics Data System (ADS)

Kuang, Jiyun; Lin, C. D.

1996-12-01

The one-dimensional integral representation for the Fourier transform of a two-centre product of B functions (finite linear combinations of Slater orbitals) with real parameters is generalized to include B functions with complex parameters. This one-dimensional integral representation allows for an efficient method of calculating two-centre exchange integrals with plane-wave electronic translational factors (ETF) over Slater orbitals of real/complex exponents. This method is a significant improvement on the previous two-dimensional quadrature method of the integrals. A new basis set of the form 0953-4075/29/24/005/img1 is proposed to improve the description of pseudo-continuum states in the close-coupling treatment of ion - atom collisions.

Basic statistics with Microsoft Excel: a review.

PubMed

Divisi, Duilio; Di Leonardo, Gabriella; Zaccagna, Gino; Crisci, Roberto

2017-06-01

The scientific world is enriched daily with new knowledge, due to new technologies and continuous discoveries. The mathematical functions explain the statistical concepts particularly those of mean, median and mode along with those of frequency and frequency distribution associated to histograms and graphical representations, determining elaborative processes on the basis of the spreadsheet operations. The aim of the study is to highlight the mathematical basis of statistical models that regulate the operation of spreadsheets in Microsoft Excel.

Basic statistics with Microsoft Excel: a review

PubMed Central

Di Leonardo, Gabriella; Zaccagna, Gino; Crisci, Roberto

2017-01-01

The scientific world is enriched daily with new knowledge, due to new technologies and continuous discoveries. The mathematical functions explain the statistical concepts particularly those of mean, median and mode along with those of frequency and frequency distribution associated to histograms and graphical representations, determining elaborative processes on the basis of the spreadsheet operations. The aim of the study is to highlight the mathematical basis of statistical models that regulate the operation of spreadsheets in Microsoft Excel. PMID:28740690

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

Maiolo, M., E-mail: massimo.maiolo@zhaw.ch; ZHAW, Institut für Angewandte Simulation, Grüental, CH-8820 Wädenswil; Vancheri, A., E-mail: alberto.vancheri@supsi.ch

In this paper, we apply Multiresolution Analysis (MRA) to develop sparse but accurate representations for the Multiscale Coarse-Graining (MSCG) approximation to the many-body potential of mean force. We rigorously framed the MSCG method into MRA so that all the instruments of this theory become available together with a multitude of new basis functions, namely the wavelets. The coarse-grained (CG) force field is hierarchically decomposed at different resolution levels enabling to choose the most appropriate wavelet family for each physical interaction without requiring an a priori knowledge of the details localization. The representation of the CG potential in this new efficientmore » orthonormal basis leads to a compression of the signal information in few large expansion coefficients. The multiresolution property of the wavelet transform allows to isolate and remove the noise from the CG force-field reconstruction by thresholding the basis function coefficients from each frequency band independently. We discuss the implementation of our wavelet-based MSCG approach and demonstrate its accuracy using two different condensed-phase systems, i.e. liquid water and methanol. Simulations of liquid argon have also been performed using a one-to-one mapping between atomistic and CG sites. The latter model allows to verify the accuracy of the method and to test different choices of wavelet families. Furthermore, the results of the computer simulations show that the efficiency and sparsity of the representation of the CG force field can be traced back to the mathematical properties of the chosen family of wavelets. This result is in agreement with what is known from the theory of multiresolution analysis of signals.« less

Executive Control in Bilingual Language Processing

ERIC Educational Resources Information Center

Rodriguez-Fornells, A.; Balaguer, R. De Deigo; Munte, T. F.

2006-01-01

Little is known in cognitive neuroscience about the brain mechanisms and brain representations involved in bilingual language processing. On the basis of previous studies on switching and bilingualism, it has been proposed that executive functions are engaged in the control and regulation of the languages in use. Here, we review the existing…

Metaphor, Simile, Analogy and the Brain

ERIC Educational Resources Information Center

Riddell, Patricia

2016-01-01

Fox argues that the poetic function of language fulfils the human need to symbolise. Metaphor, simile and analogy provide examples of the ways in which symbolic language can be used creatively. The neural representations of these processes therefore provide a means to determine the neurological basis of creative language. Neuro-imaging has…

Cerebral localization in the nineteenth century--the birth of a science and its modern consequences.

PubMed

Steinberg, David A

2009-07-01

Although many individuals contributed to the development of the science of cerebral localization, its conceptual framework is the work of a single man--John Hughlings Jackson (1835-1911), a Victorian physician practicing in London. Hughlings Jackson's formulation of a neurological science consisted of an axiomatic basis, an experimental methodology, and a clinical neurophysiology. His axiom--that the brain is an exclusively sensorimotor machine--separated neurology from psychiatry and established a rigorous and sophisticated structure for the brain and mind. Hughlings Jackson's experimental method utilized the focal lesion as a probe of brain function and created an evolutionary structure of somatotopic representation to explain clinical neurophysiology. His scientific theory of cerebral localization can be described as a weighted ordinal representation. Hughlings Jackson's theory of weighted ordinal representation forms the scientific basis for modern neurology. Though this science is utilized daily by every neurologist and forms the basis of neuroscience, the consequences of Hughlings Jackson's ideas are still not generally appreciated. For example, they imply the intrinsic inconsistency of some modern fields of neuroscience and neurology. Thus, "cognitive imaging" and the "neurology of art"--two topics of modern interest--are fundamentally oxymoronic according to the science of cerebral localization. Neuroscientists, therefore, still have much to learn from John Hughlings Jackson.

Orthogonal bases of invariants in tensor models

NASA Astrophysics Data System (ADS)

Diaz, Pablo; Rey, Soo-Jong

2018-02-01

Representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry G d = U( N 1) ⊗ · · · ⊗ U( N d ) . We show that there are two natural ways of counting invariants, one for arbitrary G d and another valid for large rank of G d . We construct basis of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of G d diagonalizes two-point function. It is analogous to the restricted Schur basis used in matrix models. We comment on future directions for investigation.

Sparse regularization for force identification using dictionaries

NASA Astrophysics Data System (ADS)

Qiao, Baijie; Zhang, Xingwu; Wang, Chenxi; Zhang, Hang; Chen, Xuefeng

2016-04-01

The classical function expansion method based on minimizing l2-norm of the response residual employs various basis functions to represent the unknown force. Its difficulty lies in determining the optimum number of basis functions. Considering the sparsity of force in the time domain or in other basis space, we develop a general sparse regularization method based on minimizing l1-norm of the coefficient vector of basis functions. The number of basis functions is adaptively determined by minimizing the number of nonzero components in the coefficient vector during the sparse regularization process. First, according to the profile of the unknown force, the dictionary composed of basis functions is determined. Second, a sparsity convex optimization model for force identification is constructed. Third, given the transfer function and the operational response, Sparse reconstruction by separable approximation (SpaRSA) is developed to solve the sparse regularization problem of force identification. Finally, experiments including identification of impact and harmonic forces are conducted on a cantilever thin plate structure to illustrate the effectiveness and applicability of SpaRSA. Besides the Dirac dictionary, other three sparse dictionaries including Db6 wavelets, Sym4 wavelets and cubic B-spline functions can also accurately identify both the single and double impact forces from highly noisy responses in a sparse representation frame. The discrete cosine functions can also successfully reconstruct the harmonic forces including the sinusoidal, square and triangular forces. Conversely, the traditional Tikhonov regularization method with the L-curve criterion fails to identify both the impact and harmonic forces in these cases.

Cognition and procedure representational requirements for predictive human performance models

NASA Technical Reports Server (NTRS)

Corker, K.

1992-01-01

Models and modeling environments for human performance are becoming significant contributors to early system design and analysis procedures. Issues of levels of automation, physical environment, informational environment, and manning requirements are being addressed by such man/machine analysis systems. The research reported here investigates the close interaction between models of human cognition and models that described procedural performance. We describe a methodology for the decomposition of aircrew procedures that supports interaction with models of cognition on the basis of procedures observed; that serves to identify cockpit/avionics information sources and crew information requirements; and that provides the structure to support methods for function allocation among crew and aiding systems. Our approach is to develop an object-oriented, modular, executable software representation of the aircrew, the aircraft, and the procedures necessary to satisfy flight-phase goals. We then encode in a time-based language, taxonomies of the conceptual, relational, and procedural constraints among the cockpit avionics and control system and the aircrew. We have designed and implemented a goals/procedures hierarchic representation sufficient to describe procedural flow in the cockpit. We then execute the procedural representation in simulation software and calculate the values of the flight instruments, aircraft state variables and crew resources using the constraints available from the relationship taxonomies. The system provides a flexible, extensible, manipulative and executable representation of aircrew and procedures that is generally applicable to crew/procedure task-analysis. The representation supports developed methods of intent inference, and is extensible to include issues of information requirements and functional allocation. We are attempting to link the procedural representation to models of cognitive functions to establish several intent inference methods including procedural backtracking with concurrent search, temporal reasoning, and constraint checking for partial ordering of procedures. Finally, the representation is being linked to models of human decision making processes that include heuristic, propositional and prescriptive judgement models that are sensitive to the procedural content in which the valuative functions are being performed.

Optimal color coding for compression of true color images

NASA Astrophysics Data System (ADS)

Musatenko, Yurij S.; Kurashov, Vitalij N.

1998-11-01

In the paper we present the method that improves lossy compression of the true color or other multispectral images. The essence of the method is to project initial color planes into Karhunen-Loeve (KL) basis that gives completely decorrelated representation for the image and to compress basis functions instead of the planes. To do that the new fast algorithm of true KL basis construction with low memory consumption is suggested and our recently proposed scheme for finding optimal losses of Kl functions while compression is used. Compare to standard JPEG compression of the CMYK images the method provides the PSNR gain from 0.2 to 2 dB for the convenient compression ratios. Experimental results are obtained for high resolution CMYK images. It is demonstrated that presented scheme could work on common hardware.

Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments.

PubMed

Choi, Ji Yeh; Hwang, Heungsun; Timmerman, Marieke E

2018-03-01

Parallel factor analysis (PARAFAC) is a useful multivariate method for decomposing three-way data that consist of three different types of entities simultaneously. This method estimates trilinear components, each of which is a low-dimensional representation of a set of entities, often called a mode, to explain the maximum variance of the data. Functional PARAFAC permits the entities in different modes to be smooth functions or curves, varying over a continuum, rather than a collection of unconnected responses. The existing functional PARAFAC methods handle functions of a one-dimensional argument (e.g., time) only. In this paper, we propose a new extension of functional PARAFAC for handling three-way data whose responses are sequenced along both a two-dimensional domain (e.g., a plane with x- and y-axis coordinates) and a one-dimensional argument. Technically, the proposed method combines PARAFAC with basis function expansion approximations, using a set of piecewise quadratic finite element basis functions for estimating two-dimensional smooth functions and a set of one-dimensional basis functions for estimating one-dimensional smooth functions. In a simulation study, the proposed method appeared to outperform the conventional PARAFAC. We apply the method to EEG data to demonstrate its empirical usefulness.

Game Theory of Mind

PubMed Central

Yoshida, Wako; Dolan, Ray J.; Friston, Karl J.

2008-01-01

This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. Critically, the joint value functions and ensuing behaviour are optimised recursively, under the assumption that I represent your value function, your representation of mine, your representation of my representation of yours, and so on ad infinitum. However, if we assume that the degree of recursion is bounded, then players need to estimate the opponent's degree of recursion (i.e., sophistication) to respond optimally. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. We show it is possible to deduce whether players make inferences about each other and quantify their sophistication on the basis of choices in sequential games. This rests on comparing generative models of choices with, and without, inference. Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’. Finally, we note that exactly the same sophisticated behaviour can be achieved by optimising the utility function itself (through prosocial utility), producing unsophisticated but apparently altruistic agents. This may be relevant ethologically in hierarchal game theory and coevolution. PMID:19112488

Linking Neural and Symbolic Representation and Processing of Conceptual Structures

PubMed Central

van der Velde, Frank; Forth, Jamie; Nazareth, Deniece S.; Wiggins, Geraint A.

2017-01-01

We compare and discuss representations in two cognitive architectures aimed at representing and processing complex conceptual (sentence-like) structures. First is the Neural Blackboard Architecture (NBA), which aims to account for representation and processing of complex and combinatorial conceptual structures in the brain. Second is IDyOT (Information Dynamics of Thinking), which derives sentence-like structures by learning statistical sequential regularities over a suitable corpus. Although IDyOT is designed at a level more abstract than the neural, so it is a model of cognitive function, rather than neural processing, there are strong similarities between the composite structures developed in IDyOT and the NBA. We hypothesize that these similarities form the basis of a combined architecture in which the individual strengths of each architecture are integrated. We outline and discuss the characteristics of this combined architecture, emphasizing the representation and processing of conceptual structures. PMID:28848460

Projected Hybrid Orbitals: A General QM/MM Method

PubMed Central

2015-01-01

A projected hybrid orbital (PHO) method was described to model the covalent boundary in a hybrid quantum mechanical and molecular mechanical (QM/MM) system. The PHO approach can be used in ab initio wave function theory and in density functional theory with any basis set without introducing system-dependent parameters. In this method, a secondary basis set on the boundary atom is introduced to formulate a set of hybrid atomic orbtials. The primary basis set on the boundary atom used for the QM subsystem is projected onto the secondary basis to yield a representation that provides a good approximation to the electron-withdrawing power of the primary basis set to balance electronic interactions between QM and MM subsystems. The PHO method has been tested on a range of molecules and properties. Comparison with results obtained from QM calculations on the entire system shows that the present PHO method is a robust and balanced QM/MM scheme that preserves the structural and electronic properties of the QM region. PMID:25317748

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

Exponentially accurate approximations to piece-wise smooth periodic functions

NASA Technical Reports Server (NTRS)

Greer, James; Banerjee, Saheb

1995-01-01

A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.

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

Liakh, Dmitry I

While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent-particle level and, recently, second-order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many-particle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scale-adaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of many-body operators via the local adjustment of the basis set quality. Given a series of locallymore » supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated many-body methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).« less

Sparsest representations and approximations of an underdetermined linear system

NASA Astrophysics Data System (ADS)

Tardivel, Patrick J. C.; Servien, Rémi; Concordet, Didier

2018-05-01

In an underdetermined linear system of equations, constrained l 1 minimization methods such as the basis pursuit or the lasso are often used to recover one of the sparsest representations or approximations of the system. The null space property is a sufficient and ‘almost’ necessary condition to recover a sparsest representation with the basis pursuit. Unfortunately, this property cannot be easily checked. On the other hand, the mutual coherence is an easily checkable sufficient condition insuring the basis pursuit to recover one of the sparsest representations. Because the mutual coherence condition is too strong, it is hardly met in practice. Even if one of these conditions holds, to our knowledge, there is no theoretical result insuring that the lasso solution is one of the sparsest approximations. In this article, we study a novel constrained problem that gives, without any condition, one of the sparsest representations or approximations. To solve this problem, we provide a numerical method and we prove its convergence. Numerical experiments show that this approach gives better results than both the basis pursuit problem and the reweighted l 1 minimization problem.

Chiral symmetry breaking and the spin content of hadrons

NASA Astrophysics Data System (ADS)

Glozman, L. Ya.; Lang, C. B.; Limmer, M.

2012-04-01

From the parton distributions in the infinite momentum frame, one finds that only about 30% of the nucleon spin is carried by spins of the valence quarks, which gave rise to the term “spin crisis”. Similar results hold for the lowest mesons, as it follows from the lattice simulations. We define the spin content of a meson in the rest frame and use a complete and orthogonal q¯q chiral basis and a unitary transformation from the chiral basis to the 2LJ basis. Then, given a mixture of different allowed chiral representations in the meson wave function at a given resolution scale, one can obtain its spin content at this scale. To obtain the mixture of the chiral representations in the meson, we measure in dynamical lattice simulations a ratio of couplings of interpolators with different chiral structure. For the ρ meson, we obtain practically the 3S1 state with no trace of the spin crisis. Then a natural question arises: which definition does reflect the spin content of a hadron?

I See What You Mean: Theta Power Increases Are Involved in the Retrieval of Lexical Semantic Information

ERIC Educational Resources Information Center

Bastiaansen, Marcel C. M.; Oostenveld, Robert; Jensen, Ole; Hagoort, Peter

2008-01-01

An influential hypothesis regarding the neural basis of the mental lexicon is that semantic representations are neurally implemented as distributed networks carrying sensory, motor and/or more abstract functional information. This work investigates whether the semantic properties of words partly determine the topography of such networks. Subjects…

On the suitability of different representations of solid catalysts for combinatorial library design by genetic algorithms.

PubMed

Gobin, Oliver C; Schüth, Ferdi

2008-01-01

Genetic algorithms are widely used to solve and optimize combinatorial problems and are more often applied for library design in combinatorial chemistry. Because of their flexibility, however, their implementation can be challenging. In this study, the influence of the representation of solid catalysts on the performance of genetic algorithms was systematically investigated on the basis of a new, constrained, multiobjective, combinatorial test problem with properties common to problems in combinatorial materials science. Constraints were satisfied by penalty functions, repair algorithms, or special representations. The tests were performed using three state-of-the-art evolutionary multiobjective algorithms by performing 100 optimization runs for each algorithm and test case. Experimental data obtained during the optimization of a noble metal-free solid catalyst system active in the selective catalytic reduction of nitric oxide with propene was used to build up a predictive model to validate the results of the theoretical test problem. A significant influence of the representation on the optimization performance was observed. Binary encodings were found to be the preferred encoding in most of the cases, and depending on the experimental test unit, repair algorithms or penalty functions performed best.

Multiscale geometric modeling of macromolecules II: Lagrangian representation

PubMed Central

Feng, Xin; Xia, Kelin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei

2013-01-01

Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR and cryo-EM, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger’s functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, while our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions. PMID:23813599

iQIST v0.7: An open source continuous-time quantum Monte Carlo impurity solver toolkit

NASA Astrophysics Data System (ADS)

Huang, Li

2017-12-01

In this paper, we present a new version of the iQIST software package, which is capable of solving various quantum impurity models by using the hybridization expansion (or strong coupling expansion) continuous-time quantum Monte Carlo algorithm. In the revised version, the software architecture is completely redesigned. New basis (intermediate representation or singular value decomposition representation) for the single-particle and two-particle Green's functions is introduced. A lot of useful physical observables are added, such as the charge susceptibility, fidelity susceptibility, Binder cumulant, and autocorrelation time. Especially, we optimize measurement for the two-particle Green's functions. Both the particle-hole and particle-particle channels are supported. In addition, the block structure of the two-particle Green's functions is exploited to accelerate the calculation. Finally, we fix some known bugs and limitations. The computational efficiency of the code is greatly enhanced.

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.

Improved Classification of Lung Cancer Using Radial Basis Function Neural Network with Affine Transforms of Voss Representation.

PubMed

Adetiba, Emmanuel; Olugbara, Oludayo O

2015-01-01

Lung cancer is one of the diseases responsible for a large number of cancer related death cases worldwide. The recommended standard for screening and early detection of lung cancer is the low dose computed tomography. However, many patients diagnosed die within one year, which makes it essential to find alternative approaches for screening and early detection of lung cancer. We present computational methods that can be implemented in a functional multi-genomic system for classification, screening and early detection of lung cancer victims. Samples of top ten biomarker genes previously reported to have the highest frequency of lung cancer mutations and sequences of normal biomarker genes were respectively collected from the COSMIC and NCBI databases to validate the computational methods. Experiments were performed based on the combinations of Z-curve and tetrahedron affine transforms, Histogram of Oriented Gradient (HOG), Multilayer perceptron and Gaussian Radial Basis Function (RBF) neural networks to obtain an appropriate combination of computational methods to achieve improved classification of lung cancer biomarker genes. Results show that a combination of affine transforms of Voss representation, HOG genomic features and Gaussian RBF neural network perceptibly improves classification accuracy, specificity and sensitivity of lung cancer biomarker genes as well as achieving low mean square error.

The NATO thesaurus project

NASA Technical Reports Server (NTRS)

Krueger, Jonathan

1990-01-01

This document describes functionality to be developed to support the NATO technical thesaurus. Described are the specificity of the thesaurus structure and function; the distinction between the thesaurus information and its representation in a given online, machine readable, or printed form; the enhancement of the thesaurus with the assignment of COSATI codes (fields and groups) to posting terms, the integration of DTIC DRIT and NASA thesauri related terminology, translation of posting terms into French; and the provision of a basis for system design.

A Bayesian spatial model for neuroimaging data based on biologically informed basis functions.

PubMed

Huertas, Ismael; Oldehinkel, Marianne; van Oort, Erik S B; Garcia-Solis, David; Mir, Pablo; Beckmann, Christian F; Marquand, Andre F

2017-11-01

The dominant approach to neuroimaging data analysis employs the voxel as the unit of computation. While convenient, voxels lack biological meaning and their size is arbitrarily determined by the resolution of the image. Here, we propose a multivariate spatial model in which neuroimaging data are characterised as a linearly weighted combination of multiscale basis functions which map onto underlying brain nuclei or networks or nuclei. In this model, the elementary building blocks are derived to reflect the functional anatomy of the brain during the resting state. This model is estimated using a Bayesian framework which accurately quantifies uncertainty and automatically finds the most accurate and parsimonious combination of basis functions describing the data. We demonstrate the utility of this framework by predicting quantitative SPECT images of striatal dopamine function and we compare a variety of basis sets including generic isotropic functions, anatomical representations of the striatum derived from structural MRI, and two different soft functional parcellations of the striatum derived from resting-state fMRI (rfMRI). We found that a combination of ∼50 multiscale functional basis functions accurately represented the striatal dopamine activity, and that functional basis functions derived from an advanced parcellation technique known as Instantaneous Connectivity Parcellation (ICP) provided the most parsimonious models of dopamine function. Importantly, functional basis functions derived from resting fMRI were more accurate than both structural and generic basis sets in representing dopamine function in the striatum for a fixed model order. We demonstrate the translational validity of our framework by constructing classification models for discriminating parkinsonian disorders and their subtypes. Here, we show that ICP approach is the only basis set that performs well across all comparisons and performs better overall than the classical voxel-based approach. This spatial model constitutes an elegant alternative to voxel-based approaches in neuroimaging studies; not only are their atoms biologically informed, they are also adaptive to high resolutions, represent high dimensions efficiently, and capture long-range spatial dependencies, which are important and challenging objectives for neuroimaging data. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

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.

Inhibition of quantum transport due to 'scars' of unstable periodic orbits

NASA Technical Reports Server (NTRS)

Jensen, R. V.; Sanders, M. M.; Saraceno, M.; Sundaram, B.

1989-01-01

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.

High-resolution time-frequency representation of EEG data using multi-scale wavelets

NASA Astrophysics Data System (ADS)

Li, Yang; Cui, Wei-Gang; Luo, Mei-Lin; Li, Ke; Wang, Lina

2017-09-01

An efficient time-varying autoregressive (TVAR) modelling scheme that expands the time-varying parameters onto the multi-scale wavelet basis functions is presented for modelling nonstationary signals and with applications to time-frequency analysis (TFA) of electroencephalogram (EEG) signals. In the new parametric modelling framework, the time-dependent parameters of the TVAR model are locally represented by using a novel multi-scale wavelet decomposition scheme, which can allow the capability to capture the smooth trends as well as track the abrupt changes of time-varying parameters simultaneously. A forward orthogonal least square (FOLS) algorithm aided by mutual information criteria are then applied for sparse model term selection and parameter estimation. Two simulation examples illustrate that the performance of the proposed multi-scale wavelet basis functions outperforms the only single-scale wavelet basis functions or Kalman filter algorithm for many nonstationary processes. Furthermore, an application of the proposed method to a real EEG signal demonstrates the new approach can provide highly time-dependent spectral resolution capability.

Teaching structure: student use of software tools for understanding macromolecular structure in an undergraduate biochemistry course.

PubMed

Jaswal, Sheila S; O'Hara, Patricia B; Williamson, Patrick L; Springer, Amy L

2013-01-01

Because understanding the structure of biological macromolecules is critical to understanding their function, students of biochemistry should become familiar not only with viewing, but also with generating and manipulating structural representations. We report a strategy from a one-semester undergraduate biochemistry course to integrate use of structural representation tools into both laboratory and homework activities. First, early in the course we introduce the use of readily available open-source software for visualizing protein structure, coincident with modules on amino acid and peptide bond properties. Second, we use these same software tools in lectures and incorporate images and other structure representations in homework tasks. Third, we require a capstone project in which teams of students examine a protein-nucleic acid complex and then use the software tools to illustrate for their classmates the salient features of the structure, relating how the structure helps explain biological function. To ensure engagement with a range of software and database features, we generated a detailed template file that can be used to explore any structure, and that guides students through specific applications of many of the software tools. In presentations, students demonstrate that they are successfully interpreting structural information, and using representations to illustrate particular points relevant to function. Thus, over the semester students integrate information about structural features of biological macromolecules into the larger discussion of the chemical basis of function. Together these assignments provide an accessible introduction to structural representation tools, allowing students to add these methods to their biochemical toolboxes early in their scientific development. © 2013 by The International Union of Biochemistry and Molecular Biology.

Factors controlling high-frequency radiation from extended ruptures

NASA Astrophysics Data System (ADS)

Beresnev, Igor A.

2017-09-01

Small-scale slip heterogeneity or variations in rupture velocity on the fault plane are often invoked to explain the high-frequency radiation from earthquakes. This view has no theoretical basis, which follows, for example, from the representation integral of elasticity, an exact solution for the radiated wave field. The Fourier transform, applied to the integral, shows that the seismic spectrum is fully controlled by that of the source time function, while the distribution of final slip and rupture acceleration/deceleration only contribute to directivity. This inference is corroborated by the precise numerical computation of the full radiated field from the representation integral. We compare calculated radiation from four finite-fault models: (1) uniform slip function with low slip velocity, (2) slip function spatially modulated by a sinusoidal function, (3) slip function spatially modulated by a sinusoidal function with random roughness added, and (4) uniform slip function with high slip velocity. The addition of "asperities," both regular and irregular, does not cause any systematic increase in the spectral level of high-frequency radiation, except for the creation of maxima due to constructive interference. On the other hand, an increase in the maximum rate of slip on the fault leads to highly amplified high frequencies, in accordance with the prediction on the basis of a simple point-source treatment of the fault. Hence, computations show that the temporal rate of slip, not the spatial heterogeneity on faults, is the predominant factor forming the high-frequency radiation and thus controlling the velocity and acceleration of the resulting ground motions.

A study of different modeling choices for simulating platelets within the immersed boundary method

PubMed Central

Shankar, Varun; Wright, Grady B.; Fogelson, Aaron L.; Kirby, Robert M.

2012-01-01

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid–structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations – radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations – for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations. PMID:23585704

Rhetorical Interpretation of Abstracts in Sci-Tech Theses Based on Burke's Identification Theory

ERIC Educational Resources Information Center

Zhong, Jihong

2017-01-01

Abstract of a thesis is the brief and accurate representation of the thesis, with the important function of persuading readers to read on the thesis. So how the writer constructs the abstract and wins readers' recognition is our main focus. On the basis of Burke's Identification Theory, this paper analyzed 10 abstracts from "Nature" from…

Two-step superresolution approach for surveillance face image through radial basis function-partial least squares regression and locality-induced sparse representation

NASA Astrophysics Data System (ADS)

Jiang, Junjun; Hu, Ruimin; Han, Zhen; Wang, Zhongyuan; Chen, Jun

2013-10-01

Face superresolution (SR), or face hallucination, refers to the technique of generating a high-resolution (HR) face image from a low-resolution (LR) one with the help of a set of training examples. It aims at transcending the limitations of electronic imaging systems. Applications of face SR include video surveillance, in which the individual of interest is often far from cameras. A two-step method is proposed to infer a high-quality and HR face image from a low-quality and LR observation. First, we establish the nonlinear relationship between LR face images and HR ones, according to radial basis function and partial least squares (RBF-PLS) regression, to transform the LR face into the global face space. Then, a locality-induced sparse representation (LiSR) approach is presented to enhance the local facial details once all the global faces for each LR training face are constructed. A comparison of some state-of-the-art SR methods shows the superiority of the proposed two-step approach, RBF-PLS global face regression followed by LiSR-based local patch reconstruction. Experiments also demonstrate the effectiveness under both simulation conditions and some real conditions.

Development of Fast Deterministic Physically Accurate Solvers for Kinetic Collision Integral for Applications of Near Space Flight and Control Devices

DTIC Science & Technology

2015-08-31

following functions were used: where are the Legendre polynomials of degree . It is assumed that the coefficient standing with has the form...enforce relaxation rates of high order moments, higher order polynomial basis functions are used. The use of high order polynomials results in strong...enforced while only polynomials up to second degree were used in the representation of the collision frequency. It can be seen that the new model

Visual management of large scale data mining projects.

PubMed

Shah, I; Hunter, L

2000-01-01

This paper describes a unified framework for visualizing the preparations for, and results of, hundreds of machine learning experiments. These experiments were designed to improve the accuracy of enzyme functional predictions from sequence, and in many cases were successful. Our system provides graphical user interfaces for defining and exploring training datasets and various representational alternatives, for inspecting the hypotheses induced by various types of learning algorithms, for visualizing the global results, and for inspecting in detail results for specific training sets (functions) and examples (proteins). The visualization tools serve as a navigational aid through a large amount of sequence data and induced knowledge. They provided significant help in understanding both the significance and the underlying biological explanations of our successes and failures. Using these visualizations it was possible to efficiently identify weaknesses of the modular sequence representations and induction algorithms which suggest better learning strategies. The context in which our data mining visualization toolkit was developed was the problem of accurately predicting enzyme function from protein sequence data. Previous work demonstrated that approximately 6% of enzyme protein sequences are likely to be assigned incorrect functions on the basis of sequence similarity alone. In order to test the hypothesis that more detailed sequence analysis using machine learning techniques and modular domain representations could address many of these failures, we designed a series of more than 250 experiments using information-theoretic decision tree induction and naive Bayesian learning on local sequence domain representations of problematic enzyme function classes. In more than half of these cases, our methods were able to perfectly discriminate among various possible functions of similar sequences. We developed and tested our visualization techniques on this application.

Diffusion Forecasting Model with Basis Functions from QR-Decomposition

NASA Astrophysics Data System (ADS)

Harlim, John; Yang, Haizhao

2018-06-01

The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to Itô diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the Fokker-Planck equation with a discrete representation of the shift (Koopman) operator on a set of basis functions generated via the diffusion maps algorithm. While the choice of these basis functions is provably optimal under appropriate conditions, computing these basis functions is quite expensive since it requires the eigendecomposition of an N× N diffusion matrix, where N denotes the data size and could be very large. For large-scale forecasting problems, only a few leading eigenvectors are computationally achievable. To overcome this computational bottleneck, a new set of basis functions constructed by orthonormalizing selected columns of the diffusion matrix and its leading eigenvectors is proposed. This computation can be carried out efficiently via the unpivoted Householder QR factorization. The efficiency and effectiveness of the proposed algorithm will be shown in both deterministically chaotic and stochastic dynamical systems; in the former case, the superiority of the proposed basis functions over purely eigenvectors is significant, while in the latter case forecasting accuracy is improved relative to using a purely small number of eigenvectors. Supporting arguments will be provided on three- and six-dimensional chaotic ODEs, a three-dimensional SDE that mimics turbulent systems, and also on the two spatial modes associated with the boreal winter Madden-Julian Oscillation obtained from applying the Nonlinear Laplacian Spectral Analysis on the measured Outgoing Longwave Radiation.

Diffusion Forecasting Model with Basis Functions from QR-Decomposition

NASA Astrophysics Data System (ADS)

Harlim, John; Yang, Haizhao

2017-12-01

The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to Itô diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the Fokker-Planck equation with a discrete representation of the shift (Koopman) operator on a set of basis functions generated via the diffusion maps algorithm. While the choice of these basis functions is provably optimal under appropriate conditions, computing these basis functions is quite expensive since it requires the eigendecomposition of an N× N diffusion matrix, where N denotes the data size and could be very large. For large-scale forecasting problems, only a few leading eigenvectors are computationally achievable. To overcome this computational bottleneck, a new set of basis functions constructed by orthonormalizing selected columns of the diffusion matrix and its leading eigenvectors is proposed. This computation can be carried out efficiently via the unpivoted Householder QR factorization. The efficiency and effectiveness of the proposed algorithm will be shown in both deterministically chaotic and stochastic dynamical systems; in the former case, the superiority of the proposed basis functions over purely eigenvectors is significant, while in the latter case forecasting accuracy is improved relative to using a purely small number of eigenvectors. Supporting arguments will be provided on three- and six-dimensional chaotic ODEs, a three-dimensional SDE that mimics turbulent systems, and also on the two spatial modes associated with the boreal winter Madden-Julian Oscillation obtained from applying the Nonlinear Laplacian Spectral Analysis on the measured Outgoing Longwave Radiation.

Spectral properties from Matsubara Green's function approach: Application to molecules

NASA Astrophysics Data System (ADS)

Schüler, M.; Pavlyukh, Y.

2018-03-01

We present results for many-body perturbation theory for the one-body Green's function at finite temperatures using the Matsubara formalism. Our method relies on the accurate representation of the single-particle states in standard Gaussian basis sets, allowing to efficiently compute, among other observables, quasiparticle energies and Dyson orbitals of atoms and molecules. In particular, we challenge the second-order treatment of the Coulomb interaction by benchmarking its accuracy for a well-established test set of small molecules, which includes also systems where the usual Hartree-Fock treatment encounters difficulties. We discuss different schemes how to extract quasiparticle properties and assess their range of applicability. With an accurate solution and compact representation, our method is an ideal starting point to study electron dynamics in time-resolved experiments by the propagation of the Kadanoff-Baym equations.

Inverse Thermal Analysis of Titanium GTA Welds Using Multiple Constraints

NASA Astrophysics Data System (ADS)

Lambrakos, S. G.; Shabaev, A.; Huang, L.

2015-06-01

Inverse thermal analysis of titanium gas-tungsten-arc welds using multiple constraint conditions is presented. This analysis employs a methodology that is in terms of numerical-analytical basis functions for inverse thermal analysis of steady-state energy deposition in plate structures. The results of this type of analysis provide parametric representations of weld temperature histories that can be adopted as input data to various types of computational procedures, such as those for prediction of solid-state phase transformations. In addition, these temperature histories can be used to construct parametric function representations for inverse thermal analysis of welds corresponding to other process parameters or welding processes whose process conditions are within similar regimes. The present study applies an inverse thermal analysis procedure that provides for the inclusion of constraint conditions associated with both solidification and phase transformation boundaries.

Self-consistent pseudopotential calculation of the bulk properties of Mo and W

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

Zunger, A.; Cohen, M.L.

The bulk properties of Mo and W are calculated using the recently developed momentum-space approach for calculating total energy via a nonlocal pseudopotential. This approach avoids any shape approximation to the variational charge density (e.g., muffin tins), is fully self-consistent, and replaces the multidimensional and multicenter integrals akin to real-space representations by simple and readily convergent reciprocal-space lattice sums. We use first-principles atomic pseudopotentials which have been previously demonstrated to yield band structures and charge densities for both semiconductors and transition metals in good agreement with experiment and all-electron calculations. Using a mixed-basis representation for the crystalline wave function, wemore » are able to accurately reproduce both the localized and itinerant features of the electronic states in these systems. These first-principles pseudopotentials, together with the self-consistent density-functional representation for both the exchange and the correlation screening, yields agreement with experiment of 0.2% in the lattice parameters, 2% and 11% for the binding energies of Mo and W, respectively, and 12% and 7% for the bulk moduli of Mo and W, respectively.« less

Ab Initio and Analytic Intermolecular Potentials for Ar-CF₄

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

Vayner, Grigoriy; Alexeev, Yuri; Wang, Jiangping

2006-03-09

Ab initio calculations at the CCSD(T) level of theory are performed to characterize the Ar + CF ₄ intermolecular potential. Extensive calculations, with and without a correction for basis set superposition error (BSSE), are performed with the cc-pVTZ basis set. Additional calculations are performed with other correlation consistent (cc) basis sets to extrapolate the Ar---CF₄potential energy minimum to the complete basis set (CBS) limit. Both the size of the basis set and BSSE have substantial effects on the Ar + CF₄ potential. Calculations with the cc-pVTZ basis set and without a BSSE correction, appear to give a good representation ofmore » the potential at the CBS limit and with a BSSE correction. In addition, MP2 theory is found to give potential energies in very good agreement with those determined by the much higher level CCSD(T) theory. Two analytic potential energy functions were determined for Ar + CF₄by fitting the cc-pVTZ calculations both with and without a BSSE correction. These analytic functions were written as a sum of two body potentials and excellent fits to the ab initio potentials were obtained by representing each two body interaction as a Buckingham potential.« less

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.

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.

The validity of multiphase DNS initialized on the basis of single--point statistics

NASA Astrophysics Data System (ADS)

Subramaniam, Shankar

1999-11-01

A study of the point--process statistical representation of a spray reveals that single--point statistical information contained in the droplet distribution function (ddf) is related to a sequence of single surrogate--droplet pdf's, which are in general different from the physical single--droplet pdf's. The results of this study have important consequences for the initialization and evolution of direct numerical simulations (DNS) of multiphase flows, which are usually initialized on the basis of single--point statistics such as the average number density in physical space. If multiphase DNS are initialized in this way, this implies that even the initial representation contains certain implicit assumptions concerning the complete ensemble of realizations, which are invalid for general multiphase flows. Also the evolution of a DNS initialized in this manner is shown to be valid only if an as yet unproven commutation hypothesis holds true. Therefore, it is questionable to what extent DNS that are initialized in this manner constitute a direct simulation of the physical droplets.

Comparison of Flux-Surface Aligned Curvilinear Coordinate Systems and Neoclassical Magnetic Field Predictions

NASA Astrophysics Data System (ADS)

Collart, T. G.; Stacey, W. M.

2015-11-01

Several methods are presented for extending the traditional analytic ``circular'' representation of flux-surface aligned curvilinear coordinate systems to more accurately describe equilibrium plasma geometry and magnetic fields in DIII-D. The formalism originally presented by Miller is extended to include different poloidal variations in the upper and lower hemispheres. A coordinate system based on separate Fourier expansions of major radius and vertical position greatly improves accuracy in edge plasma structure representation. Scale factors and basis vectors for a system formed by expanding the circular model minor radius can be represented using linear combinations of Fourier basis functions. A general method for coordinate system orthogonalization is presented and applied to all curvilinear models. A formalism for the magnetic field structure in these curvilinear models is presented, and the resulting magnetic field predictions are compared against calculations performed in a Cartesian system using an experimentally based EFIT prediction for the Grad-Shafranov equilibrium. Supported by: US DOE under DE-FG02-00ER54538.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

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

Pinski, Peter; Riplinger, Christoph; Neese, Frank, E-mail: evaleev@vt.edu, E-mail: frank.neese@cec.mpg.de

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implementsmore » sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.« less

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals.

PubMed

Pinski, Peter; Riplinger, Christoph; Valeev, Edward F; Neese, Frank

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

Vector-based navigation using grid-like representations in artificial agents.

PubMed

Banino, Andrea; Barry, Caswell; Uria, Benigno; Blundell, Charles; Lillicrap, Timothy; Mirowski, Piotr; Pritzel, Alexander; Chadwick, Martin J; Degris, Thomas; Modayil, Joseph; Wayne, Greg; Soyer, Hubert; Viola, Fabio; Zhang, Brian; Goroshin, Ross; Rabinowitz, Neil; Pascanu, Razvan; Beattie, Charlie; Petersen, Stig; Sadik, Amir; Gaffney, Stephen; King, Helen; Kavukcuoglu, Koray; Hassabis, Demis; Hadsell, Raia; Kumaran, Dharshan

2018-05-01

Deep neural networks have achieved impressive successes in fields ranging from object recognition to complex games such as Go 1,2 . Navigation, however, remains a substantial challenge for artificial agents, with deep neural networks trained by reinforcement learning 3-5 failing to rival the proficiency of mammalian spatial behaviour, which is underpinned by grid cells in the entorhinal cortex 6 . Grid cells are thought to provide a multi-scale periodic representation that functions as a metric for coding space 7,8 and is critical for integrating self-motion (path integration) 6,7,9 and planning direct trajectories to goals (vector-based navigation) 7,10,11 . Here we set out to leverage the computational functions of grid cells to develop a deep reinforcement learning agent with mammal-like navigational abilities. We first trained a recurrent network to perform path integration, leading to the emergence of representations resembling grid cells, as well as other entorhinal cell types 12 . We then showed that this representation provided an effective basis for an agent to locate goals in challenging, unfamiliar, and changeable environments-optimizing the primary objective of navigation through deep reinforcement learning. The performance of agents endowed with grid-like representations surpassed that of an expert human and comparison agents, with the metric quantities necessary for vector-based navigation derived from grid-like units within the network. Furthermore, grid-like representations enabled agents to conduct shortcut behaviours reminiscent of those performed by mammals. Our findings show that emergent grid-like representations furnish agents with a Euclidean spatial metric and associated vector operations, providing a foundation for proficient navigation. As such, our results support neuroscientific theories that see grid cells as critical for vector-based navigation 7,10,11 , demonstrating that the latter can be combined with path-based strategies to support navigation in challenging environments.

Space-time VMS computation of wind-turbine rotor and tower aerodynamics

NASA Astrophysics Data System (ADS)

Takizawa, Kenji; Tezduyar, Tayfun E.; McIntyre, Spenser; Kostov, Nikolay; Kolesar, Ryan; Habluetzel, Casey

2014-01-01

We present the space-time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called "DSD/SST-VMST" method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of flows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this "ST/NURBS Mesh Update Method (STNMUM)." The STNMUM increases computational efficiency in terms of computer time and storage, and computational flexibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion.

Space-Time VMS Computation of Wind-Turbine Rotor and Tower Aerodynamics

NASA Astrophysics Data System (ADS)

McIntyre, Spenser W.

This thesis is on the space{time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent ows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called "DSD/SST-VMST" method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of ows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this "ST/NURBS Mesh Update Method (STNMUM)." The STNMUM increases computational efficiency in terms of computer time and storage, and computational exibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion.

Comparison of Ionospheric Vertical Total Electron Content modelling approaches using spline based representations

NASA Astrophysics Data System (ADS)

Krypiak-Gregorczyk, Anna; Wielgosz, Pawel; Borkowski, Andrzej; Schmidt, Michael; Erdogan, Eren; Goss, Andreas

2017-04-01

Since electromagnetic measurements show dispersive characteristics, accurate modelling of the ionospheric electron content plays an important role for positioning and navigation applications to mitigate the effect of the ionospheric disturbances. Knowledge about the ionosphere contributes to a better understanding of space weather events as well as to forecast these events to enable protective measures in advance for electronic systems and satellite missions. In the last decades, advances in satellite technologies, data analysis techniques and models together with a rapidly growing number of analysis centres allow modelling the ionospheric electron content with an unprecedented accuracy in (near) real-time. In this sense, the representation of electron content variations in time and space with spline basis functions has gained practical importance in global and regional ionosphere modelling. This is due to their compact support and their flexibility to handle unevenly distributed observations and data gaps. In this contribution, the performances of two ionosphere models from UWM and DGFI-TUM, which are developed using spline functions are evaluated. The VTEC model of DGFI-TUM is based on tensor products of trigonometric B-spline functions in longitude and polynomial B-spline functions in latitude for a global representation. The UWM model uses two dimensional planar thin plate spline (TPS) with the Universal Transverse Mercator representation of ellipsoidal coordinates. In order to provide a smooth VTEC model, the TPS minimizes both, the squared norm of the Hessian matrix and deviations between data points and the model. In the evaluations, the differenced STEC analysis method and Jason-2 altimetry comparisons are applied.

Grobner Basis Representations of Sudoku

ERIC Educational Resources Information Center

Taalman, Laura; Arnold, Elizabeth; Lucas, Stephen

2010-01-01

This paper uses Grobner bases to explore the inherent structure of Sudoku puzzles and boards. In particular, we develop three different ways of representing the constraints of Sudoku puzzles with a system of polynomial equations. In one case, we explicitly show how a Grobner basis can be used to obtain a more meaningful representation of the…

Opaque models: Using drugs and dreams to explore the neurobiological basis of mental phenomena.

PubMed

Langlitz, Nicolas

2017-01-01

On the basis of four historical and ethnographic case studies of modeling in neuroscience laboratories, this chapter introduces a distinction between transparent and opaque models. A transparent model is a simplified representation of a real world phenomenon. If it is not patently clear, it is at least much better comprehended than its objects of representation. An opaque model, by contrast, looks at one only partially understood phenomenon to stand in for another partially understood phenomenon. Here, the model is often just as complex as its target. Examples of such opaque models discussed in this chapter are the use of hallucinogen intoxication in humans and animals as well as the dreaming brain as models of psychosis as well as the dreaming brain as a model of consciousness in general. Several functions of opaque models are discussed, ranging from the generation of funding to the formulation of new research questions. While science studies scholars have often emphasized the epistemic fertility of failures of representation, the opacity of hallucinogen intoxications and dreams seems to have diminished the potential to produce positive knowledge from the representational relationship between the supposed models and their targets. Bidirectional comparisons between inebriation, dreaming, and psychosis, however, proved to be generative on the level of basic science. Moreover, the opaque models discussed in this chapter implicated cosmologies that steered research endeavors into certain directions rather than others. © 2017 Elsevier B.V. All rights reserved.

Multimodal representation of limb endpoint position in the posterior parietal cortex.

PubMed

Shi, Ying; Apker, Gregory; Buneo, Christopher A

2013-04-01

Understanding the neural representation of limb position is important for comprehending the control of limb movements and the maintenance of body schema, as well as for the development of neuroprosthetic systems designed to replace lost limb function. Multiple subcortical and cortical areas contribute to this representation, but its multimodal basis has largely been ignored. Regarding the parietal cortex, previous results suggest that visual information about arm position is not strongly represented in area 5, although these results were obtained under conditions in which animals were not using their arms to interact with objects in their environment, which could have affected the relative weighting of relevant sensory signals. Here we examined the multimodal basis of limb position in the superior parietal lobule (SPL) as monkeys reached to and actively maintained their arm position at multiple locations in a frontal plane. On half of the trials both visual and nonvisual feedback of the endpoint of the arm were available, while on the other trials visual feedback was withheld. Many neurons were tuned to arm position, while a smaller number were modulated by the presence/absence of visual feedback. Visual modulation generally took the form of a decrease in both firing rate and variability with limb vision and was associated with more accurate decoding of position at the population level under these conditions. These findings support a multimodal representation of limb endpoint position in the SPL but suggest that visual signals are relatively weakly represented in this area, and only at the population level.

Grey-box state-space identification of nonlinear mechanical vibrations

NASA Astrophysics Data System (ADS)

Noël, J. P.; Schoukens, J.

2018-05-01

The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.

Distributed representations in memory: Insights from functional brain imaging

PubMed Central

Rissman, Jesse; Wagner, Anthony D.

2015-01-01

Forging new memories for facts and events, holding critical details in mind on a moment-to-moment basis, and retrieving knowledge in the service of current goals all depend on a complex interplay between neural ensembles throughout the brain. Over the past decade, researchers have increasingly leveraged powerful analytical tools (e.g., multi-voxel pattern analysis) to decode the information represented within distributed fMRI activity patterns. In this review, we discuss how these methods can sensitively index neural representations of perceptual and semantic content, and how leverage on the engagement of distributed representations provides unique insights into distinct aspects of memory-guided behavior. We emphasize that, in addition to characterizing the contents of memories, analyses of distributed patterns shed light on the processes that influence how information is encoded, maintained, or retrieved, and thus inform memory theory. We conclude by highlighting open questions about memory that can be addressed through distributed pattern analyses. PMID:21943171

Multivariate Patterns in the Human Object-Processing Pathway Reveal a Shift from Retinotopic to Shape Curvature Representations in Lateral Occipital Areas, LO-1 and LO-2.

PubMed

Vernon, Richard J W; Gouws, André D; Lawrence, Samuel J D; Wade, Alex R; Morland, Antony B

2016-05-25

Representations in early visual areas are organized on the basis of retinotopy, but this organizational principle appears to lose prominence in the extrastriate cortex. Nevertheless, an extrastriate region, such as the shape-selective lateral occipital cortex (LO), must still base its activation on the responses from earlier retinotopic visual areas, implying that a transition from retinotopic to "functional" organizations should exist. We hypothesized that such a transition may lie in LO-1 or LO-2, two visual areas lying between retinotopically defined V3d and functionally defined LO. Using a rapid event-related fMRI paradigm, we measured neural similarity in 12 human participants between pairs of stimuli differing along dimensions of shape exemplar and shape complexity within both retinotopically and functionally defined visual areas. These neural similarity measures were then compared with low-level and more abstract (curvature-based) measures of stimulus similarity. We found that low-level, but not abstract, stimulus measures predicted V1-V3 responses, whereas the converse was true for LO, a double dissociation. Critically, abstract stimulus measures were most predictive of responses within LO-2, akin to LO, whereas both low-level and abstract measures were predictive for responses within LO-1, perhaps indicating a transitional point between those two organizational principles. Similar transitions to abstract representations were not observed in the more ventral stream passing through V4 and VO-1/2. The transition we observed in LO-1 and LO-2 demonstrates that a more "abstracted" representation, typically considered the preserve of "category-selective" extrastriate cortex, can nevertheless emerge in retinotopic regions. Visual areas are typically identified either through retinotopy (e.g., V1-V3) or from functional selectivity [e.g., shape-selective lateral occipital complex (LOC)]. We combined these approaches to explore the nature of shape representations through the visual hierarchy. Two different representations emerged: the first reflected low-level shape properties (dependent on the spatial layout of the shape outline), whereas the second captured more abstract curvature-related shape features. Critically, early visual cortex represented low-level information but this diminished in the extrastriate cortex (LO-1/LO-2/LOC), in which the abstract representation emerged. Therefore, this work further elucidates the nature of shape representations in the LOC, provides insight into how those representations emerge from early retinotopic cortex, and crucially demonstrates that retinotopically tuned regions (LO-1/LO-2) are not necessarily constrained to retinotopic representations. Copyright © 2016 Vernon et al.

Classification of three-particle states according to an orthonormal SU(3) ⊃ SO(3) basis

NASA Astrophysics Data System (ADS)

del Aguila, F.

1980-09-01

In this paper we generalize Dragt's approach to classifying three-particle states. Using his formalism of creation and annihilation operators, we obtain explicitly a complete set of orthonormal functions YλμRLM on S5. This set of functions carries all the irreducible representations of the group SU(3) reduced according to SO(3). The YλμRLM, which are eigenvectors of the togetherness and angular momentum operators, have very simple properties under three-particle permutations. We obtain also explicitly the coefficients ''3ν'' which reduce the products of these functions.

Synthesis of atmospheric turbulence point spread functions by sparse and redundant representations

NASA Astrophysics Data System (ADS)

Hunt, Bobby R.; Iler, Amber L.; Bailey, Christopher A.; Rucci, Michael A.

2018-02-01

Atmospheric turbulence is a fundamental problem in imaging through long slant ranges, horizontal-range paths, or uplooking astronomical cases through the atmosphere. An essential characterization of atmospheric turbulence is the point spread function (PSF). Turbulence images can be simulated to study basic questions, such as image quality and image restoration, by synthesizing PSFs of desired properties. In this paper, we report on a method to synthesize PSFs of atmospheric turbulence. The method uses recent developments in sparse and redundant representations. From a training set of measured atmospheric PSFs, we construct a dictionary of "basis functions" that characterize the atmospheric turbulence PSFs. A PSF can be synthesized from this dictionary by a properly weighted combination of dictionary elements. We disclose an algorithm to synthesize PSFs from the dictionary. The algorithm can synthesize PSFs in three orders of magnitude less computing time than conventional wave optics propagation methods. The resulting PSFs are also shown to be statistically representative of the turbulence conditions that were used to construct the dictionary.

The representation of object viewpoint in human visual cortex.

PubMed

Andresen, David R; Vinberg, Joakim; Grill-Spector, Kalanit

2009-04-01

Understanding the nature of object representations in the human brain is critical for understanding the neural basis of invariant object recognition. However, the degree to which object representations are sensitive to object viewpoint is unknown. Using fMRI we employed a parametric approach to examine the sensitivity to object view as a function of rotation (0 degrees-180 degrees ), category (animal/vehicle) and fMRI-adaptation paradigm (short or long-lagged). For both categories and fMRI-adaptation paradigms, object-selective regions recovered from adaptation when a rotated view of an object was shown after adaptation to a specific view of that object, suggesting that representations are sensitive to object rotation. However, we found evidence for differential representations across categories and ventral stream regions. Rotation cross-adaptation was larger for animals than vehicles, suggesting higher sensitivity to vehicle than animal rotation, and was largest in the left fusiform/occipito-temporal sulcus (pFUS/OTS), suggesting that this region has low sensitivity to rotation. Moreover, right pFUS/OTS and FFA responded more strongly to front than back views of animals (without adaptation) and rotation cross-adaptation depended both on the level of rotation and the adapting view. This result suggests a prevalence of neurons that prefer frontal views of animals in fusiform regions. Using a computational model of view-tuned neurons, we demonstrate that differential neural view tuning widths and relative distributions of neural-tuned populations in fMRI voxels can explain the fMRI results. Overall, our findings underscore the utility of parametric approaches for studying the neural basis of object invariance and suggest that there is no complete invariance to object view in the human ventral stream.

Adequate representation of charge polarization effects leads to a successful treatment of the CF4 + SiCl4 → CCl4 + SiF4 reaction by density functional theory.

PubMed

Li, Ruifang; Zhao, Yan; Truhlar, Donald G

2011-02-28

Adequate polarization functions reduce the error of density functional theory (DFT) for the heat of reaction for CF(4) + SiCl(4) from ∼9-12 kcal mol(-1) to ∼2-4 kcal mol(-1), and using an improved density functional further reduces it to ∼1 kcal mol(-1). This reaction was previously identified as a stumbling block for DFT, but we show that the problem with the previous calculations was not DFT but rather inadequate basis sets to account for intramolecular charge polarization.

Inverse Thermal Analysis of Ti-6Al-4V Friction Stir Welds Using Numerical-Analytical Basis Functions with Pseudo-Advection

NASA Astrophysics Data System (ADS)

Lambrakos, S. G.

2018-04-01

Inverse thermal analysis of Ti-6Al-4V friction stir welds is presented that demonstrates application of a methodology using numerical-analytical basis functions and temperature-field constraint conditions. This analysis provides parametric representation of friction-stir-weld temperature histories that can be adopted as input data to computational procedures for prediction of solid-state phase transformations and mechanical response. These parameterized temperature histories can be used for inverse thermal analysis of friction stir welds having process conditions similar those considered here. Case studies are presented for inverse thermal analysis of friction stir welds that use three-dimensional constraint conditions on calculated temperature fields, which are associated with experimentally measured transformation boundaries and weld-stir-zone cross sections.

Balkanizing the primate orbitofrontal cortex: Distinct subregions for comparing and contrasting values

PubMed Central

Rudebeck, Peter H.; Murray, Elisabeth A.

2014-01-01

The primate orbitofrontal cortex (OFC) is often treated as a single entity, but architectonic and connectional neuroanatomy indicates that it has distinguishable parts. Nevertheless, few studies have attempted to dissociate the functions of its subregions. Here we review findings from recent neuropsychological and neurophysiological studies that do so. The lateral OFC seems to be important for learning, representing and updating specific object–reward associations. Medial OFC seems to be important for value comparisons and choosing among objects on that basis. Rather than viewing this dissociation of function in terms of learning versus choosing, however, we suggest that it reflects the distinction between contrasts and comparisons: differences versus similarities. Making use of high-dimensional representations that arise from the convergence of several sensory modalities, the lateral OFC encodes contrasts among outcomes. The medial MFC reduces these contrasting representations of value to a single dimension, a common currency, in order to compare alternative choices. PMID:22145870

Exploring the Neural Representation of Novel Words Learned through Enactment in a Word Recognition Task

PubMed Central

Macedonia, Manuela; Mueller, Karsten

2016-01-01

Vocabulary learning in a second language is enhanced if learners enrich the learning experience with self-performed iconic gestures. This learning strategy is called enactment. Here we explore how enacted words are functionally represented in the brain and which brain regions contribute to enhance retention. After an enactment training lasting 4 days, participants performed a word recognition task in the functional Magnetic Resonance Imaging (fMRI) scanner. Data analysis suggests the participation of different and partially intertwined networks that are engaged in higher cognitive processes, i.e., enhanced attention and word recognition. Also, an experience-related network seems to map word representation. Besides core language regions, this latter network includes sensory and motor cortices, the basal ganglia, and the cerebellum. On the basis of its complexity and the involvement of the motor system, this sensorimotor network might explain superior retention for enactment. PMID:27445918

Rényi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems.

PubMed

Varga, Imre; Pipek, János

2003-08-01

We discuss some properties of the generalized entropies, called Rényi entropies, and their application to the case of continuous distributions. In particular, it is shown that these measures of complexity can be divergent; however, their differences are free from these divergences, thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions. We apply this formalism to the projection of wave functions onto the coherent state basis, i.e., to the Husimi representation. We also show how the localization properties of the Husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure, i.e., no classical limit can be defined. Numerical simulations on a one-dimensional disordered system corroborate our expectations.

Differences in the emergent coding properties of cortical and striatal ensembles

PubMed Central

Ma, L.; Hyman, J.M.; Lindsay, A.J.; Phillips, A.G.; Seamans, J.K.

2016-01-01

The function of a given brain region is often defined by the coding properties of its individual neurons, yet how this information is combined at the ensemble level is an equally important consideration. In the present study, multiple neurons from the anterior cingulate cortex (ACC) and the dorsal striatum (DS) were recorded simultaneously as rats performed different sequences of the same three actions. Sequence and lever decoding was remarkably similar on a per-neuron basis in the two regions. At the ensemble level, sequence-specific representations in the DS appeared synchronously but transiently along with the representation of lever location, while these two streams of information appeared independently and asynchronously in the ACC. As a result the ACC achieved superior ensemble decoding accuracy overall. Thus, the manner in which information was combined across neurons in an ensemble determined the functional separation of the ACC and DS on this task. PMID:24974796

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.

Discrete variable representation in electronic structure theory: quadrature grids for least-squares tensor hypercontraction.

PubMed

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

2013-05-21

We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes.

Background noise exerts diverse effects on the cortical encoding of foreground sounds.

PubMed

Malone, B J; Heiser, Marc A; Beitel, Ralph E; Schreiner, Christoph E

2017-08-01

In natural listening conditions, many sounds must be detected and identified in the context of competing sound sources, which function as background noise. Traditionally, noise is thought to degrade the cortical representation of sounds by suppressing responses and increasing response variability. However, recent studies of neural network models and brain slices have shown that background synaptic noise can improve the detection of signals. Because acoustic noise affects the synaptic background activity of cortical networks, it may improve the cortical responses to signals. We used spike train decoding techniques to determine the functional effects of a continuous white noise background on the responses of clusters of neurons in auditory cortex to foreground signals, specifically frequency-modulated sweeps (FMs) of different velocities, directions, and amplitudes. Whereas the addition of noise progressively suppressed the FM responses of some cortical sites in the core fields with decreasing signal-to-noise ratios (SNRs), the stimulus representation remained robust or was even significantly enhanced at specific SNRs in many others. Even though the background noise level was typically not explicitly encoded in cortical responses, significant information about noise context could be decoded from cortical responses on the basis of how the neural representation of the foreground sweeps was affected. These findings demonstrate significant diversity in signal in noise processing even within the core auditory fields that could support noise-robust hearing across a wide range of listening conditions. NEW & NOTEWORTHY The ability to detect and discriminate sounds in background noise is critical for our ability to communicate. The neural basis of robust perceptual performance in noise is not well understood. We identified neuronal populations in core auditory cortex of squirrel monkeys that differ in how they process foreground signals in background noise and that may contribute to robust signal representation and discrimination in acoustic environments with prominent background noise. Copyright © 2017 the American Physiological Society.

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

PubMed

Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

2017-12-01

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion

NASA Astrophysics Data System (ADS)

Alexandrov, A.; Chapuy, G.; Eynard, B.; Harnad, J.

2017-12-01

A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2D Toda {τ} -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel-Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers.

Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion

NASA Astrophysics Data System (ADS)

Alexandrov, A.; Chapuy, G.; Eynard, B.; Harnad, J.

2018-06-01

A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2 D Toda {τ} -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel-Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers.

From Semantics to Syntax and Back Again: Argument Structure in the Third Year of Life

ERIC Educational Resources Information Center

Fernandes, Keith J.; Marcus, Gary F.; Di Nubila, Jennifer A.; Vouloumanos, Athena

2006-01-01

An essential part of the human capacity for language is the ability to link conceptual or semantic representations with syntactic representations. On the basis of data from spontaneous production, Tomasello (2000) suggested that young children acquire such links on a verb-by-verb basis, with little in the way of a general understanding of…

Reverse engineering of aircraft wing data using a partial differential equation surface model

NASA Astrophysics Data System (ADS)

Huband, Jacalyn Mann

Reverse engineering is a multi-step process used in industry to determine a production representation of an existing physical object. This representation is in the form of mathematical equations that are compatible with computer-aided design and computer-aided manufacturing (CAD/CAM) equipment. The four basic steps to the reverse engineering process are data acquisition, data separation, surface or curve fitting, and CAD/CAM production. The surface fitting step determines the design representation of the object, and thus is critical to the success or failure of the reverse engineering process. Although surface fitting methods described in the literature are used to model a variety of surfaces, they are not suitable for reversing aircraft wings. In this dissertation, we develop and demonstrate a new strategy for reversing a mathematical representation of an aircraft wing. The basis of our strategy is to take an aircraft design model and determine if an inverse model can be derived. A candidate design model for this research is the partial differential equation (PDE) surface model, proposed by Bloor and Wilson and used in the Rapid Airplane Parameter Input Design (RAPID) tool at the NASA-LaRC Geolab. There are several basic mathematical problems involved in reversing the PDE surface model: (i) deriving a computational approximation of the surface function; (ii) determining a radial parametrization of the wing; (iii) choosing mathematical models or classes of functions for representation of the boundary functions; (iv) fitting the boundary data points by the chosen boundary functions; and (v) simultaneously solving for the axial parameterization and the derivative boundary functions. The study of the techniques to solve the above mathematical problems has culminated in a reverse PDE surface model and two reverse PDE surface algorithms. One reverse PDE surface algorithm recovers engineering design parameters for the RAPID tool from aircraft wing data and the other generates a PDE surface model with spline boundary functions from an arbitrary set of grid points. Our numerical tests show that the reverse PDE surface model and the reverse PDE surface algorithms can be used for the reverse engineering of aircraft wing data.

Advances in Quantum Trajectory Approaches to Dynamics

NASA Astrophysics Data System (ADS)

Askar, Attila

2001-03-01

The quantum fluid dynamics (QFD) formulation is based on the separation of the amplitude and phase of the complex wave function in Schrodinger's equation. The approach leads to conservation laws for an equivalent "gas continuum". The Lagrangian [1] representation corresponds to following the particles of the fluid continuum, i. e. calculating "quantum trajectories". The Eulerian [2] representation on the other hand, amounts to observing the dynamics of the gas continuum at the points of a fixed coordinate frame. The combination of several factors leads to a most encouraging computational efficiency. QFD enables the numerical analysis to deal with near monotonic amplitude and phase functions. The Lagrangian description concentrates the computation effort to regions of highest probability as an optimal adaptive grid. The Eulerian representation allows the study of multi-coordinate problems as a set of one-dimensional problems within an alternating direction methodology. An explicit time integrator limits the increase in computational effort with the number of discrete points to linear. Discretization of the space via local finite elements [1,2] and global radial functions [3] will be discussed. Applications include wave packets in four-dimensional quadratic potentials and two coordinate photo-dissociation problems for NOCl and NO2. [1] "Quantum fluid dynamics (QFD) in the Lagrangian representation with applications to photo-dissociation problems", F. Sales, A. Askar and H. A. Rabitz, J. Chem. Phys. 11, 2423 (1999) [2] "Multidimensional wave-packet dynamics within the fluid dynamical formulation of the Schrodinger equation", B. Dey, A. Askar and H. A. Rabitz, J. Chem. Phys. 109, 8770 (1998) [3] "Solution of the quantum fluid dynamics equations with radial basis function interpolation", Xu-Guang Hu, Tak-San Ho, H. A. Rabitz and A. Askar, Phys. Rev. E. 61, 5967 (2000)

The cognitive nature of action - functional links between cognitive psychology, movement science, and robotics.

PubMed

Schack, Thomas; Ritter, Helge

2009-01-01

This paper examines the cognitive architecture of human action, showing how it is organized over several levels and how it is built up. Basic action concepts (BACs) are identified as major building blocks on a representation level. These BACs are cognitive tools for mastering the functional demands of movement tasks. Results from different lines of research showed that not only the structure formation of mental representations in long-term memory but also chunk formation in working memory are built up on BACs and relate systematically to movement structures. It is concluded that such movement representations might provide the basis for action implementation and action control in skilled voluntary movements in the form of cognitive reference structures. To simulate action implementation we discuss challenges and issues that arise when we try to replicate complex movement abilities in robots. Among the key issues to be addressed is the question how structured representations can arise during skill acquisition and how the underlying processes can be understood sufficiently succinctly to replicate them on robot platforms. Working towards this goal, we translate our findings in studies of motor control in humans into models that can guide the implementation of cognitive robot architectures. Focusing on the issue of manual action control, we illustrate some results in the context of grasping with a five-fingered anthropomorphic robot hand.

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

Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

In this paper, we present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support ourmore » construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Lastly, our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.« less

Infinite occupation number basis of bosons: Solving a numerical challenge

NASA Astrophysics Data System (ADS)

Geißler, Andreas; Hofstetter, Walter

2017-06-01

In any bosonic lattice system, which is not dominated by local interactions and thus "frozen" in a Mott-type state, numerical methods have to cope with the infinite size of the corresponding Hilbert space even for finite lattice sizes. While it is common practice to restrict the local occupation number basis to Nc lowest occupied states, the presence of a finite condensate fraction requires the complete number basis for an exact representation of the many-body ground state. In this work we present a truncation scheme to account for contributions from higher number states. By simply adding a single coherent-tail state to this common truncation, we demonstrate increased numerical accuracy and the possible increase in numerical efficiency of this method for the Gutzwiller variational wave function and within dynamical mean-field theory.

Basis adaptation and domain decomposition for steady partial differential equations with random coefficients

DOE PAGES

Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

2017-09-04

In this paper, we present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support ourmore » construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Lastly, our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.« less

Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients

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

Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support our construction with numericalmore » experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.« less

Method for the Direct Solve of the Many-Body Schrödinger Wave Equation

NASA Astrophysics Data System (ADS)

Jerke, Jonathan; Tymczak, C. J.; Poirier, Bill

We report on theoretical and computational developments towards a computationally efficient direct solve of the many-body Schrödinger wave equation for electronic systems. This methodology relies on two recent developments pioneered by the authors: 1) the development of a Cardinal Sine basis for electronic structure calculations; and 2) the development of a highly efficient and compact representation of multidimensional functions using the Canonical tensor rank representation developed by Belykin et. al. which we have adapted to electronic structure problems. We then show several relevant examples of the utility and accuracy of this methodology, scaling with system size, and relevant convergence issues of the methodology. Method for the Direct Solve of the Many-Body Schrödinger Wave Equation.

Visual feature extraction from voxel-weighted averaging of stimulus images in 2 fMRI studies.

PubMed

Hart, Corey B; Rose, William J

2013-11-01

Multiple studies have provided evidence for distributed object representation in the brain, with several recent experiments leveraging basis function estimates for partial image reconstruction from fMRI data. Using a novel combination of statistical decomposition, generalized linear models, and stimulus averaging on previously examined image sets and Bayesian regression of recorded fMRI activity during presentation of these data sets, we identify a subset of relevant voxels that appear to code for covarying object features. Using a technique we term "voxel-weighted averaging," we isolate image filters that these voxels appear to implement. The results, though very cursory, appear to have significant implications for hierarchical and deep-learning-type approaches toward the understanding of neural coding and representation.

An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach

DOE PAGES

Yu, Hua-Gen

2002-01-01

We present a full dimensional variational algorithm to calculate vibrational energies of penta-atomic molecules. The quantum mechanical Hamiltonian of the system for J=0 is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame without any dynamical approximation. Moreover, the vibrational Hamiltonian has been obtained in an explicitly Hermitian form. Variational calculations are performed in a direct product discrete variable representation basis set. The sine functions are used for the radial coordinates, whereas the Legendre polynomials are employed for the polar angles. For the azimuthal angles, the symmetrically adapted Fourier–Chebyshev basis functions are utilized. The eigenvalue problem ismore » solved by a Lanczos iterative diagonalization algorithm. The preliminary application to methane is given. Ultimately, we made a comparison with previous results.« less

A coherent discrete variable representation method on a sphere

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

Yu, Hua -Gen

Here, the coherent discrete variable representation (ZDVR) has been extended for construct- ing a multidimensional potential-optimized DVR basis on a sphere. In order to deal with the non-constant Jacobian in spherical angles, two direct product primitive basis methods are proposed so that the original ZDVR technique can be properly implemented. The method has been demonstrated by computing the lowest states of a two dimensional (2D) vibrational model. Results show that the extended ZDVR method gives accurate eigenval- ues and exponential convergence with increasing ZDVR basis size.

A coherent discrete variable representation method on a sphere

DOE PAGES

Yu, Hua -Gen

2017-09-05

Here, the coherent discrete variable representation (ZDVR) has been extended for construct- ing a multidimensional potential-optimized DVR basis on a sphere. In order to deal with the non-constant Jacobian in spherical angles, two direct product primitive basis methods are proposed so that the original ZDVR technique can be properly implemented. The method has been demonstrated by computing the lowest states of a two dimensional (2D) vibrational model. Results show that the extended ZDVR method gives accurate eigenval- ues and exponential convergence with increasing ZDVR basis size.

Weak solution concept and Galerkin's matrix for the exterior of an oblate ellipsoid of revolution in the representation of the Earth's gravity potential by buried masses

NASA Astrophysics Data System (ADS)

Holota, Petr; Nesvadba, Otakar

2017-04-01

The paper is motivated by the role of boundary value problems in Earth's gravity field studies. The discussion focuses on Neumann's problem formulated for the exterior of an oblate ellipsoid of revolution as this is considered a basis for an iteration solution of the linear gravimetric boundary value problem in the determination of the disturbing potential. The approach follows the concept of the weak solution and Galerkin's approximations are applied. This means that the solution of the problem is approximated by linear combinations of basis functions with scalar coefficients. The construction of Galerkin's matrix for basis functions generated by elementary potentials (point masses) is discussed. Ellipsoidal harmonics are used as a natural tool and the elementary potentials are expressed by means of series of ellipsoidal harmonics. The problem, however, is the summation of the series that represent the entries of Galerkin's matrix. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no analogue to the addition theorem known for spherical harmonics. Therefore, the straightforward application of series of ellipsoidal harmonics is complemented by deeper relations contained in the theory of ordinary differential equations of second order and in the theory of Legendre's functions. Subsequently, also hypergeometric functions and series are used. Moreover, within some approximations the entries are split into parts. Some of the resulting series may be summed relatively easily, apart from technical tricks. For the remaining series the summation was converted to elliptic integrals. The approach made it possible to deduce a closed (though approximate) form representation of the entries in Galerkin's matrix. The result rests on concepts and methods of mathematical analysis. In the paper it is confronted with a direct numerical approach applied for the implementation of Legendre's functions. The computation of the entries is more demanding in this case, but conceptually it avoids approximations. Finally, some specific features associated with function bases generated by elementary potentials in case the ellipsoidal solution domain are illustrated and discussed.

Experimental evaluation and basis function optimization of the spatially variant image-space PSF on the Ingenuity PET/MR scanner

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

Kotasidis, Fotis A., E-mail: Fotis.Kotasidis@unige.ch; Zaidi, Habib; Geneva Neuroscience Centre, Geneva University, CH-1205 Geneva

2014-06-15

Purpose: The Ingenuity time-of-flight (TF) PET/MR is a recently developed hybrid scanner combining the molecular imaging capabilities of PET with the excellent soft tissue contrast of MRI. It is becoming common practice to characterize the system's point spread function (PSF) and understand its variation under spatial transformations to guide clinical studies and potentially use it within resolution recovery image reconstruction algorithms. Furthermore, due to the system's utilization of overlapping and spherical symmetric Kaiser-Bessel basis functions during image reconstruction, its image space PSF and reconstructed spatial resolution could be affected by the selection of the basis function parameters. Hence, a detailedmore » investigation into the multidimensional basis function parameter space is needed to evaluate the impact of these parameters on spatial resolution. Methods: Using an array of 12 × 7 printed point sources, along with a custom made phantom, and with the MR magnet on, the system's spatially variant image-based PSF was characterized in detail. Moreover, basis function parameters were systematically varied during reconstruction (list-mode TF OSEM) to evaluate their impact on the reconstructed resolution and the image space PSF. Following the spatial resolution optimization, phantom, and clinical studies were subsequently reconstructed using representative basis function parameters. Results: Based on the analysis and under standard basis function parameters, the axial and tangential components of the PSF were found to be almost invariant under spatial transformations (∼4 mm) while the radial component varied modestly from 4 to 6.7 mm. Using a systematic investigation into the basis function parameter space, the spatial resolution was found to degrade for basis functions with a large radius and small shape parameter. However, it was found that optimizing the spatial resolution in the reconstructed PET images, while having a good basis function superposition and keeping the image representation error to a minimum, is feasible, with the parameter combination range depending upon the scanner's intrinsic resolution characteristics. Conclusions: Using the printed point source array as a MR compatible methodology for experimentally measuring the scanner's PSF, the system's spatially variant resolution properties were successfully evaluated in image space. Overall the PET subsystem exhibits excellent resolution characteristics mainly due to the fact that the raw data are not under-sampled/rebinned, enabling the spatial resolution to be dictated by the scanner's intrinsic resolution and the image reconstruction parameters. Due to the impact of these parameters on the resolution properties of the reconstructed images, the image space PSF varies both under spatial transformations and due to basis function parameter selection. Nonetheless, for a range of basis function parameters, the image space PSF remains unaffected, with the range depending on the scanner's intrinsic resolution properties.« less

Unconventional Signal Processing Using the Cone Kernel Time-Frequency Representation.

DTIC Science & Technology

1992-10-30

Wigner - Ville distribution ( WVD ), the Choi- Williams distribution , and the cone kernel distribution were compared with the spectrograms. Results were...ambiguity function. Figures A-18(c) and (d) are the Wigner - Ville Distribution ( WVD ) and CK-TFR Doppler maps. In this noiseless case all three exhibit...kernel is the basis for the well known Wigner - Ville distribution . In A-9(2), the cone kernel defined by Zhao, Atlas and Marks [21 is described

On vector-valued Poincaré series of weight 2

NASA Astrophysics Data System (ADS)

Meneses, Claudio

2017-10-01

Given a pair (Γ , ρ) of a Fuchsian group of the first kind, and a unitary representation ρ of Γ of arbitrary rank, the problem of construction of vector-valued Poincaré series of weight 2 is considered. Implications in the theory of parabolic bundles are discussed. When the genus of the group is zero, it is shown how an explicit basis for the space of these functions can be constructed.

Graphical Representation and Origin of Piezoresistance Effect in Germanium

NASA Astrophysics Data System (ADS)

Matsuda, K.; Nagaoka, S.; Kanda, Y.

2017-06-01

The longitudinal and transverse piezoresistance coefficients of Ge at room temperature are represented graphically as a function of the crystal directions for orientation (001), (110) and (211) planes. Many valley model of conduction band and stress decoupling decoupling of the degenerate valence band into two bands of prolate and oblate ellipsoidal energy surface are shown to explain origin of the piezoresistance. One this basis, comparison between piezoresistance coefficient and theoretical model is discussed.

Spherical harmonics and rigged Hilbert spaces

NASA Astrophysics Data System (ADS)

Celeghini, E.; Gadella, M.; del Olmo, M. A.

2018-05-01

This paper is devoted to study discrete and continuous bases for spaces supporting representations of SO(3) and SO(3, 2) where the spherical harmonics are involved. We show how discrete and continuous bases coexist on appropriate choices of rigged Hilbert spaces. We prove the continuity of relevant operators and the operators in the algebras spanned by them using appropriate topologies on our spaces. Finally, we discuss the properties of the functionals that form the continuous basis.

Shared action spaces: a basis function framework for social re-calibration of sensorimotor representations supporting joint action

PubMed Central

Pezzulo, Giovanni; Iodice, Pierpaolo; Ferraina, Stefano; Kessler, Klaus

2013-01-01

The article explores the possibilities of formalizing and explaining the mechanisms that support spatial and social perspective alignment sustained over the duration of a social interaction. The basic proposed principle is that in social contexts the mechanisms for sensorimotor transformations and multisensory integration (learn to) incorporate information relative to the other actor(s), similar to the “re-calibration” of visual receptive fields in response to repeated tool use. This process aligns or merges the co-actors’ spatial representations and creates a “Shared Action Space” (SAS) supporting key computations of social interactions and joint actions; for example, the remapping between the coordinate systems and frames of reference of the co-actors, including perspective taking, the sensorimotor transformations required for lifting jointly an object, and the predictions of the sensory effects of such joint action. The social re-calibration is proposed to be based on common basis function maps (BFMs) and could constitute an optimal solution to sensorimotor transformation and multisensory integration in joint action or more in general social interaction contexts. However, certain situations such as discrepant postural and viewpoint alignment and associated differences in perspectives between the co-actors could constrain the process quite differently. We discuss how alignment is achieved in the first place, and how it is maintained over time, providing a taxonomy of various forms and mechanisms of space alignment and overlap based, for instance, on automaticity vs. control of the transformations between the two agents. Finally, we discuss the link between low-level mechanisms for the sharing of space and high-level mechanisms for the sharing of cognitive representations. PMID:24324425

Development and neurophysiology of mentalizing.

PubMed Central

Frith, Uta; Frith, Christopher D

2003-01-01

The mentalizing (theory of mind) system of the brain is probably in operation from ca. 18 months of age, allowing implicit attribution of intentions and other mental states. Between the ages of 4 and 6 years explicit mentalizing becomes possible, and from this age children are able to explain the misleading reasons that have given rise to a false belief. Neuroimaging studies of mentalizing have so far only been carried out in adults. They reveal a system with three components consistently activated during both implicit and explicit mentalizing tasks: medial prefrontal cortex (MPFC), temporal poles and posterior superior temporal sulcus (STS). The functions of these components can be elucidated, to some extent, from their role in other tasks used in neuroimaging studies. Thus, the MPFC region is probably the basis of the decoupling mechanism that distinguishes mental state representations from physical state representations; the STS region is probably the basis of the detection of agency, and the temporal poles might be involved in access to social knowledge in the form of scripts. The activation of these components in concert appears to be critical to mentalizing. PMID:12689373

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.

The Cognitive and Perceptual Laws of the Inclined Plane.

PubMed

Masin, Sergio Cesare

2016-09-01

The study explored whether laypersons correctly tacitly know Galileo's law of the inclined plane and what the basis of such knowledge could be. Participants predicted the time a ball would take to roll down a slope with factorial combination of ball travel distance and slope angle. The resulting pattern of factorial curves relating the square of predicted time to travel distance for each slope angle was identical to that implied by Galileo's law, indicating a correct cognitive representation of this law. Intuitive physics research suggests that this cognitive representation may result from memories of past perceptions of objects rolling down a slope. Such a basis and the correct cognitive representation of Galileo's law led to the hypothesis that Galileo's law is also perceptually represented correctly. To test this hypothesis, participants were asked to judge the perceived travel time of a ball actually rolling down a slope, with perceived travel distance and perceived slope angle varied in a factorial design. The obtained pattern of factorial curves was equal to that implied by Galileo's law, indicating that the functional relationships defined in this law were perceptually represented correctly. The results foster the idea that laypersons may tacitly know both linear and nonlinear multiplicative physical laws of the everyday world. As a practical implication, the awareness of this conclusion may help develop more effective methods for teaching physics and for improving human performance in the physical environment.

Variational treatment of electron-polyatomic-molecule scattering calculations using adaptive overset grids

NASA Astrophysics Data System (ADS)

Greenman, Loren; Lucchese, Robert R.; McCurdy, C. William

2017-11-01

The complex Kohn variational method for electron-polyatomic-molecule scattering is formulated using an overset-grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free-particle Green's function and potential Ĝ0+V ̂ on the overset grid in a Born-Arnoldi solution of the working equations. The theory is shown to be equivalent to a specific Padé approximant to the T matrix and has rapid convergence properties, in both the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF4 in the static-exchange approximation and compared in detail with calculations performed with the numerical Schwinger variational approach based on single-center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described.

Multivariate Patterns in the Human Object-Processing Pathway Reveal a Shift from Retinotopic to Shape Curvature Representations in Lateral Occipital Areas, LO-1 and LO-2

PubMed Central

Vernon, Richard J. W.; Gouws, André D.; Lawrence, Samuel J. D.; Wade, Alex R.

2016-01-01

Representations in early visual areas are organized on the basis of retinotopy, but this organizational principle appears to lose prominence in the extrastriate cortex. Nevertheless, an extrastriate region, such as the shape-selective lateral occipital cortex (LO), must still base its activation on the responses from earlier retinotopic visual areas, implying that a transition from retinotopic to “functional” organizations should exist. We hypothesized that such a transition may lie in LO-1 or LO-2, two visual areas lying between retinotopically defined V3d and functionally defined LO. Using a rapid event-related fMRI paradigm, we measured neural similarity in 12 human participants between pairs of stimuli differing along dimensions of shape exemplar and shape complexity within both retinotopically and functionally defined visual areas. These neural similarity measures were then compared with low-level and more abstract (curvature-based) measures of stimulus similarity. We found that low-level, but not abstract, stimulus measures predicted V1–V3 responses, whereas the converse was true for LO, a double dissociation. Critically, abstract stimulus measures were most predictive of responses within LO-2, akin to LO, whereas both low-level and abstract measures were predictive for responses within LO-1, perhaps indicating a transitional point between those two organizational principles. Similar transitions to abstract representations were not observed in the more ventral stream passing through V4 and VO-1/2. The transition we observed in LO-1 and LO-2 demonstrates that a more “abstracted” representation, typically considered the preserve of “category-selective” extrastriate cortex, can nevertheless emerge in retinotopic regions. SIGNIFICANCE STATEMENT Visual areas are typically identified either through retinotopy (e.g., V1–V3) or from functional selectivity [e.g., shape-selective lateral occipital complex (LOC)]. We combined these approaches to explore the nature of shape representations through the visual hierarchy. Two different representations emerged: the first reflected low-level shape properties (dependent on the spatial layout of the shape outline), whereas the second captured more abstract curvature-related shape features. Critically, early visual cortex represented low-level information but this diminished in the extrastriate cortex (LO-1/LO-2/LOC), in which the abstract representation emerged. Therefore, this work further elucidates the nature of shape representations in the LOC, provides insight into how those representations emerge from early retinotopic cortex, and crucially demonstrates that retinotopically tuned regions (LO-1/LO-2) are not necessarily constrained to retinotopic representations. PMID:27225766

Finite basis representations with nondirect product basis functions having structure similar to that of spherical harmonics.

PubMed

Czakó, Gábor; Szalay, Viktor; Császár, Attila G

2006-01-07

The currently most efficient finite basis representation (FBR) method [Corey et al., in Numerical Grid Methods and Their Applications to Schrodinger Equation, NATO ASI Series C, edited by C. Cerjan (Kluwer Academic, New York, 1993), Vol. 412, p. 1; Bramley et al., J. Chem. Phys. 100, 6175 (1994)] designed specifically to deal with nondirect product bases of structures phi(n) (l)(s)f(l)(u), chi(m) (l)(t)phi(n) (l)(s)f(l)(u), etc., employs very special l-independent grids and results in a symmetric FBR. While highly efficient, this method is not general enough. For instance, it cannot deal with nondirect product bases of the above structure efficiently if the functions phi(n) (l)(s) [and/or chi(m) (l)(t)] are discrete variable representation (DVR) functions of the infinite type. The optimal-generalized FBR(DVR) method [V. Szalay, J. Chem. Phys. 105, 6940 (1996)] is designed to deal with general, i.e., direct and/or nondirect product, bases and grids. This robust method, however, is too general, and its direct application can result in inefficient computer codes [Czako et al., J. Chem. Phys. 122, 024101 (2005)]. It is shown here how the optimal-generalized FBR method can be simplified in the case of nondirect product bases of structures phi(n) (l)(s)f(l)(u), chi(m) (l)(t)phi(n) (l)(s)f(l)(u), etc. As a result the commonly used symmetric FBR is recovered and simplified nonsymmetric FBRs utilizing very special l-dependent grids are obtained. The nonsymmetric FBRs are more general than the symmetric FBR in that they can be employed efficiently even when the functions phi(n) (l)(s) [and/or chi(m) (l)(t)] are DVR functions of the infinite type. Arithmetic operation counts and a simple numerical example presented show unambiguously that setting up the Hamiltonian matrix requires significantly less computer time when using one of the proposed nonsymmetric FBRs than that in the symmetric FBR. Therefore, application of this nonsymmetric FBR is more efficient than that of the symmetric FBR when one wants to diagonalize the Hamiltonian matrix either by a direct or via a basis-set contraction method. Enormous decrease of computer time can be achieved, with respect to a direct application of the optimal-generalized FBR, by employing one of the simplified nonsymmetric FBRs as is demonstrated in noniterative calculations of the low-lying vibrational energy levels of the H3+ molecular ion. The arithmetic operation counts of the Hamiltonian matrix vector products and the properties of a recently developed diagonalization method [Andreozzi et al., J. Phys. A Math. Gen. 35, L61 (2002)] suggest that the nonsymmetric FBR applied along with this particular diagonalization method is suitable to large scale iterative calculations. Whether or not the nonsymmetric FBR is competitive with the symmetric FBR in large-scale iterative calculations still has to be investigated numerically.

Derivation of Rigid Body Analysis Models from Vehicle Architecture Abstractions

DTIC Science & Technology

2011-06-17

models of every type have their basis in some type of physical representation of the design domain. Rather than describing three-dimensional continua of...arrangement, while capturing just enough physical detail to be used as the basis for a meaningful representation of the design , and eventually, analyses that...permit architecture assessment. The design information captured by the abstractions is available at the very earliest stages of the vehicle

Neural signatures of attention: insights from decoding population activity patterns.

PubMed

Sapountzis, Panagiotis; Gregoriou, Georgia G

2018-01-01

Understanding brain function and the computations that individual neurons and neuronal ensembles carry out during cognitive functions is one of the biggest challenges in neuroscientific research. To this end, invasive electrophysiological studies have provided important insights by recording the activity of single neurons in behaving animals. To average out noise, responses are typically averaged across repetitions and across neurons that are usually recorded on different days. However, the brain makes decisions on short time scales based on limited exposure to sensory stimulation by interpreting responses of populations of neurons on a moment to moment basis. Recent studies have employed machine-learning algorithms in attention and other cognitive tasks to decode the information content of distributed activity patterns across neuronal ensembles on a single trial basis. Here, we review results from studies that have used pattern-classification decoding approaches to explore the population representation of cognitive functions. These studies have offered significant insights into population coding mechanisms. Moreover, we discuss how such advances can aid the development of cognitive brain-computer interfaces.

Fuzziness In Approximate And Common-Sense Reasoning In Knowledge-Based Robotics Systems

NASA Astrophysics Data System (ADS)

Dodds, David R.

1987-10-01

Fuzzy functions, a major key to inexact reasoning, are described as they are applied to the fuzzification of robot co-ordinate systems. Linguistic-variables, a means of labelling ranges in fuzzy sets, are used as computationally pragmatic means of representing spatialization metaphors, themselves an extraordinarily rich basis for understanding concepts in orientational terms. Complex plans may be abstracted and simplified in a system which promotes conceptual planning by means of the orientational representation.

Neural network representation and learning of mappings and their derivatives

NASA Technical Reports Server (NTRS)

White, Halbert; Hornik, Kurt; Stinchcombe, Maxwell; Gallant, A. Ronald

1991-01-01

Discussed here are recent theorems proving that artificial neural networks are capable of approximating an arbitrary mapping and its derivatives as accurately as desired. This fact forms the basis for further results establishing the learnability of the desired approximations, using results from non-parametric statistics. These results have potential applications in robotics, chaotic dynamics, control, and sensitivity analysis. An example involving learning the transfer function and its derivatives for a chaotic map is discussed.

3-dimensional orthodontics visualization system with dental study models and orthopantomograms

NASA Astrophysics Data System (ADS)

Zhang, Hua; Ong, S. H.; Foong, K. W. C.; Dhar, T.

2005-04-01

The aim of this study is to develop a system that provides 3-dimensional visualization of orthodontic treatments. Dental plaster models and corresponding orthopantomogram (dental panoramic tomogram) are first digitized and fed into the system. A semi-auto segmentation technique is applied to the plaster models to detect the dental arches, tooth interstices and gum margins, which are used to extract individual crown models. 3-dimensional representation of roots, generated by deforming generic tooth models with orthopantomogram using radial basis functions, is attached to corresponding crowns to enable visualization of complete teeth. An optional algorithm to close the gaps between deformed roots and actual crowns by using multi-quadratic radial basis functions is also presented, which is capable of generating smooth mesh representation of complete 3-dimensional teeth. User interface is carefully designed to achieve a flexible system with as much user friendliness as possible. Manual calibration and correction is possible throughout the data processing steps to compensate occasional misbehaviors of automatic procedures. By allowing the users to move and re-arrange individual teeth (with their roots) on a full dentition, this orthodontic visualization system provides an easy and accurate way of simulation and planning of orthodontic treatment. Its capability of presenting 3-dimensional root information with only study models and orthopantomogram is especially useful for patients who do not undergo CT scanning, which is not a routine procedure in most orthodontic cases.

The shared neural basis of empathy and facial imitation accuracy.

PubMed

Braadbaart, L; de Grauw, H; Perrett, D I; Waiter, G D; Williams, J H G

2014-01-01

Empathy involves experiencing emotion vicariously, and understanding the reasons for those emotions. It may be served partly by a motor simulation function, and therefore share a neural basis with imitation (as opposed to mimicry), as both involve sensorimotor representations of intentions based on perceptions of others' actions. We recently showed a correlation between imitation accuracy and Empathy Quotient (EQ) using a facial imitation task and hypothesised that this relationship would be mediated by the human mirror neuron system. During functional Magnetic Resonance Imaging (fMRI), 20 adults observed novel 'blends' of facial emotional expressions. According to instruction, they either imitated (i.e. matched) the expressions or executed alternative, pre-prescribed mismatched actions as control. Outside the scanner we replicated the association between imitation accuracy and EQ. During fMRI, activity was greater during mismatch compared to imitation, particularly in the bilateral insula. Activity during imitation correlated with EQ in somatosensory cortex, intraparietal sulcus and premotor cortex. Imitation accuracy correlated with activity in insula and areas serving motor control. Overlapping voxels for the accuracy and EQ correlations occurred in premotor cortex. We suggest that both empathy and facial imitation rely on formation of action plans (or a simulation of others' intentions) in the premotor cortex, in connection with representations of emotional expressions based in the somatosensory cortex. In addition, the insula may play a key role in the social regulation of facial expression. © 2013.

Mecanismos de plasticidad (funcional y dependiente de actividad) en el cerebro auditivo adulto y en desarrollo

PubMed Central

Izquierdo, M.A.; Oliver, D.L.; Malmierca, M.S.

2010-01-01

Summary Introduction and development Sensory systems show a topographic representation of the sensory epithelium in the central nervous system. In the auditory system this representation originates tonotopic maps. For the last four decades these changes in tonotopic maps have been widely studied either after peripheral mechanical lesions or by exposing animals to an augmented acoustic environment. These sensory manipulations induce plastic reorganizations in the tonotopic map of the auditory cortex. By contrast, acoustic trauma does not seem to induce functional plasticity at subcortical nuclei. Mechanisms that generate these changes differ in their molecular basis and temporal course and we can distinguish two different mechanisms: those involving an active reorganization process, and those that show a simple reflection of the loss of peripheral afferences. Only the former involve a genuine process of plastic reorganization. Neuronal plasticity is critical for the normal development and function of the adult auditory system, as well as for the rehabilitation needed after the implantation of auditory prostheses. However, development of plasticity can also generate abnormal sensation like tinnitus. Recently, a new concept in neurobiology so-called ‘neuronal stability’ has emerged and its implications and conceptual basis could help to improve the treatments of hearing loss. Conclusion A combination of neuronal plasticity and stability is suggested as a powerful and promising future strategy in the design of new treatments of hearing loss. PMID:19340783

Balkanizing the primate orbitofrontal cortex: distinct subregions for comparing and contrasting values.

PubMed

Rudebeck, Peter H; Murray, Elisabeth A

2011-12-01

The primate orbitofrontal cortex (OFC) is often treated as a single entity, but architectonic and connectional neuroanatomy indicate that it has distinguishable parts. Nevertheless, few studies have attempted to dissociate the functions of its subregions. Here we review findings from recent neuropsychological and neurophysiological studies that do so. The lateral OFC seems to be important for learning, representing, and updating specific object-reward associations. The medial OFC seems to be important for value comparisons and choosing among objects on that basis. Rather than viewing this dissociation of function in terms of learning versus choosing, however, we suggest that it reflects the distinction between contrasts and comparisons: differences versus similarities. Making use of high-dimensional representations that arise from the convergence of several sensory modalities, the lateral OFC encodes contrasts among outcomes. The medial OFC reduces these contrasting representations of value to a single dimension, a common currency, in order to compare alternative choices. © 2011 New York Academy of Sciences.

Representation of Students in Solving Simultaneous Linear Equation Problems Based on Multiple Intelligence

NASA Astrophysics Data System (ADS)

Yanti, Y. R.; Amin, S. M.; Sulaiman, R.

2018-01-01

This study described representation of students who have musical, logical-mathematic and naturalist intelligence in solving a problem. Subjects were selected on the basis of multiple intelligence tests (TPM) consists of 108 statements, with 102 statements adopted from Chislet and Chapman and 6 statements equal to eksistensial intelligences. Data were analyzed based on problem-solving tests (TPM) and interviewing. See the validity of the data then problem-solving tests (TPM) and interviewing is given twice with an analyzed using the representation indikator and the problem solving step. The results showed that: the stage of presenting information known, stage of devising a plan, and stage of carrying out the plan those three subjects were using same form of representation. While he stage of presenting information asked and stage of looking back, subject of logical-mathematic was using different forms of representation with subjects of musical and naturalist intelligence. From this research is expected to provide input to the teacher in determining the learning strategy that will be used by considering the representation of students with the basis of multiple intelligences.

4D Hyperspherical Harmonic (HyperSPHARM) Representation of Multiple Disconnected Brain Subcortical Structures

PubMed Central

Hosseinbor, A. Pasha; Chung, Moo K.; Schaefer, Stacey M.; van Reekum, Carien M.; Peschke-Schmitz, Lara; Sutterer, Matt; Alexander, Andrew L.; Davidson, Richard J.

2014-01-01

We present a novel surface parameterization technique using hyperspherical harmonics (HSH) in representing compact, multiple, disconnected brain subcortical structures as a single analytic function. The proposed hyperspherical harmonic representation (HyperSPHARM) has many advantages over the widely used spherical harmonic (SPHARM) parameterization technique. SPHARM requires flattening 3D surfaces to 3D sphere which can be time consuming for large surface meshes, and can’t represent multiple disconnected objects with single parameterization. On the other hand, HyperSPHARM treats 3D object, via simple stereographic projection, as a surface of 4D hypersphere with extremely large radius, hence avoiding the computationally demanding flattening process. HyperSPHARM is shown to achieve a better reconstruction with only 5 basis compared to SPHARM that requires more than 441. PMID:24505716

Unfolding energy spectra of double-periodicity two-dimensional systems: Twisted bilayer graphene and MoS2 on graphene

NASA Astrophysics Data System (ADS)

Matsushita, Yu-ichiro; Nishi, Hirofumi; Iwata, Jun-ichi; Kosugi, Taichi; Oshiyama, Atsushi

2018-01-01

We propose an unfolding scheme to analyze energy spectra of complex large-scale systems which are inherently of double periodicity on the basis of the density-functional theory. Applying our method to a twisted bilayer graphene (tBLG) and a stack of monolayer MoS2 on graphene (MoS2/graphene) as examples, we first show that the conventional unfolding scheme in the past using a single primitive-cell representation causes serious problems in analyses of the energy spectra. We then introduce our multispace representation scheme in the unfolding method and clarify its validity. Velocity renormalization of Dirac electrons in tBLG and mini gaps of Dirac cones in MoS2/graphene are elucidated in the present unfolding scheme.

Parameter dimension of turbulence-induced phase errors and its effects on estimation in phase diversity

NASA Technical Reports Server (NTRS)

Thelen, Brian J.; Paxman, Richard G.

1994-01-01

The method of phase diversity has been used in the context of incoherent imaging to estimate jointly an object that is being imaged and phase aberrations induced by atmospheric turbulence. The method requires a parametric model for the phase-aberration function. Typically, the parameters are coefficients to a finite set of basis functions. Care must be taken in selecting a parameterization that properly balances accuracy in the representation of the phase-aberration function with stability in the estimates. It is well known that over parameterization can result in unstable estimates. Thus a certain amount of model mismatch is often desirable. We derive expressions that quantify the bias and variance in object and aberration estimates as a function of parameter dimension.

From plane waves to local Gaussians for the simulation of correlated periodic systems

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

Booth, George H., E-mail: george.booth@kcl.ac.uk; Tsatsoulis, Theodoros; Grüneis, Andreas, E-mail: a.grueneis@fkf.mpg.de

2016-08-28

We present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of themore » basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller–Plesset perturbation theory.« less

Statistical representation of a spray as a point process

NASA Astrophysics Data System (ADS)

Subramaniam, S.

2000-10-01

The statistical representation of a spray as a finite point process is investigated. One objective is to develop a better understanding of how single-point statistical information contained in descriptions such as the droplet distribution function (ddf), relates to the probability density functions (pdfs) associated with the droplets themselves. Single-point statistical information contained in the droplet distribution function (ddf) is shown to be related to a sequence of single surrogate-droplet pdfs, which are in general different from the physical single-droplet pdfs. It is shown that the ddf contains less information than the fundamental single-point statistical representation of the spray, which is also described. The analysis shows which events associated with the ensemble of spray droplets can be characterized by the ddf, and which cannot. The implications of these findings for the ddf approach to spray modeling are discussed. The results of this study also have important consequences for the initialization and evolution of direct numerical simulations (DNS) of multiphase flows, which are usually initialized on the basis of single-point statistics such as the droplet number density in physical space. If multiphase DNS are initialized in this way, this implies that even the initial representation contains certain implicit assumptions concerning the complete ensemble of realizations, which are invalid for general multiphase flows. Also the evolution of a DNS initialized in this manner is shown to be valid only if an as yet unproven commutation hypothesis holds true. Therefore, it is questionable to what extent DNS that are initialized in this manner constitute a direct simulation of the physical droplets. Implications of these findings for large eddy simulations of multiphase flows are also discussed.

Accurate donor electron wave functions from a multivalley effective mass theory.

NASA Astrophysics Data System (ADS)

Pendo, Luke; Hu, Xuedong

Multivalley effective mass (MEM) theories combine physical intuition with a marginal need for computational resources, but they tend to be insensitive to variations in the wavefunction. However, recent papers suggest full Bloch functions and suitable central cell donor potential corrections are essential to replicating qualitative and quantitative features of the wavefunction. In this talk, we consider a variational MEM method that can accurately predict both spectrum and wavefunction of isolated phosphorus donors. As per Gamble et. al, we employ a truncated series representation of the Bloch function with a tetrahedrally symmetric central cell correction. We use a dynamic dielectric constant, a feature commonly seen in tight-binding methods. Uniquely, we use a freely extensible basis of either all Slater- or all Gaussian-type functions. With a large basis able to capture the influence of higher energy eigenstates, this method is well positioned to consider the influence of external perturbations, such as electric field or applied strain, on the charge density. This work is supported by the US Army Research Office (W911NF1210609).

The role of the hippocampus in memory and mental construction.

PubMed

Sheldon, Signy; Levine, Brian

2016-04-01

Much has been learned about the processes that support the remembrance of past autobiographical episodes and their importance for a number of cognitive tasks. This work has focused on hippocampal contributions to constructing coherent mental representations of scenarios for these tasks, which has opened up new questions about the underlying hippocampal mechanisms. We propose a new framework to answer these questions, which incorporates task demands that prompt hippocampal contributions to mental construction, the online formation of such mental representations, and how these demands relate to the functional organization of the hippocampus. Synthesizing findings from autobiographical memory research, our framework suggests that the interaction of two task characteristics influences the recruitment of the hippocampus: (1) the degree of task open-endedness (quantified by the presence/absence of a retrieval framework) and (2) the degree to which the integration of perceptual details is required. These characteristics inform the relative weighting of anterior and posterior hippocampal involvement, following an organizational model in which the anterior and posterior hippocampus support constructions on the basis of conceptual and perceptual representations, respectively. The anticipated outcome of our framework is a refined understanding of hippocampal contributions to memory and to the host of related cognitive functions. © 2016 New York Academy of Sciences.

High-order nonlinear susceptibilities of He

NASA Astrophysics Data System (ADS)

Liu, W.-C.; Clark, Charles W.

1996-05-01

High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. We have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s^2, within the framework of Rayleigh-Schrödinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Pont and Shakeshaft (M. Pont and R. Shakeshaft, Phy. Rev. A 51), 257 (1995), and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used(J. D. Baker, Master thesis, U. Delaware (1988); J. D. Baker, R. N. Hill, and J. D. Morgan, AIP Conference Proceedings 189) 123(1989); the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals.

Analytic model of a multi-electron atom

NASA Astrophysics Data System (ADS)

Skoromnik, O. D.; Feranchuk, I. D.; Leonau, A. U.; Keitel, C. H.

2017-12-01

A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis completeness allows us to employ the secondary-quantized representation for the construction of regular perturbation theory, which includes in a natural way correlation effects, converges fast and enables an effective calculation of the subsequent corrections. The hydrogen-like basis set provides a possibility to perform all summations over intermediate states in closed form, including both the discrete and continuous spectra. This is achieved with the help of the decomposition of the multi-particle Green function in a convolution of single-electronic Coulomb Green functions. We demonstrate that our fully analytical zeroth-order approximation describes the whole spectrum of the system, provides accuracy, which is independent of the number of electrons and is important for applications where the Thomas-Fermi model is still utilized. In addition already in second-order perturbation theory our results become comparable with those via a multi-configuration Hartree-Fock approach.

Vibrational spectra, DFT quantum chemical calculations and conformational analysis of P-iodoanisole.

PubMed

Arivazhagan, M; Anitha Rexalin, D; Geethapriya, J

2013-09-01

The solid phase FT-IR and FT-Raman spectra of P-iodoanisole (P-IA) have been recorded in the regions 400-4000 and 50-4000 cm(-1), respectively. The spectra were interpreted in terms of fundamentals modes, combination and overtone bands. The structure of the molecule was optimized and the structural characteristics were determined by ab initio (HF) and density functional theory (B3LYP) methods with LanL2DZ as basis set. The potential energy surface scan for the selected dihedral angle of P-IA has been performed to identify stable conformer. The optimized structure parameters and vibrational wavenumbers of stable conformer have been predicted by density functional B3LYP method with LanL2DZ (with effective core potential representations of electrons near the nuclei for post-third row atoms) basis set. The nucleophilic and electrophilic sites obtained from the molecular electrostatic potential (MEP) surface were calculated. The temperature dependence of thermodynamic properties has been analyzed. Several thermodynamic parameters have been calculated using B3LYP with LanL2DZ basis set. Copyright © 2013 Elsevier B.V. All rights reserved.

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.

Linking Passive and Active Representation: A Review of the Literature and a Model for Testing the Linkage for Women Representatives.

ERIC Educational Resources Information Center

Robinson, Ted P.; And Others

Most research efforts concerning minority politics have focused on descriptive representation, which emphasizes (1) counting the minority or female persons in office, and (2) explaining representative levels on the basis of political, social and economic determinants. Descriptive representation, however, is passive and focuses on "being something"…

A Cross-Talk between Brain-Damage Patients and Infants on Action and Language

ERIC Educational Resources Information Center

Papeo, Liuba; Hochmann, Jean-Remy

2012-01-01

Sensorimotor representations in the brain encode the sensory and motor aspects of one's own bodily activity. It is highly debated whether sensorimotor representations are the core basis for the representation of action-related knowledge and, in particular, action words, such as verbs. In this review, we will address this question by bringing to…

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.

Group-theoretical analysis of two-dimensional hexagonal materials

NASA Astrophysics Data System (ADS)

Minami, Susumu; Sugita, Itaru; Tomita, Ryosuke; Oshima, Hiroyuki; Saito, Mineo

2017-10-01

Two-dimensional hexagonal materials such as graphene and silicene have highly symmetric crystal structures and Dirac cones at the K point, which induce novel electronic properties. In this report, we calculate their electronic structures by using density functional theory and analyze their band structures on the basis of the group theory. Dirac cones frequently appear when the symmetry at the K point is high; thus, two-dimensional irreducible representations are included. We discuss the relationship between symmetry and the appearance of the Dirac cone.

Another Function for Language and its Theoretical Consequences

NASA Astrophysics Data System (ADS)

Barahona da Fonseca, Isabel; Barahona da Fonseca, José; Simões da Fonseca, José

2006-06-01

Our proposal is that when they exercise the faculty of "parole" subjects use strategies characterized by an internal reconstruction of objects which acquire a status similar to the imperative believe in the representation of reality as it occurs in visual or auditory perception. The referent of verbal expressions acquires a greater importance for the subject who uses it according more to rhetoric principles than through logical critical analysis. Consequences concerning psychopathology, namely the phenomena of hallucination are explained on that basis.

Distinguishing Representations as Origin and Representations as Input: Roles for Individual Neurons.

PubMed

Edwards, Jonathan C W

2016-01-01

It is widely perceived that there is a problem in giving a naturalistic account of mental representation that deals adequately with the issue of meaning, interpretation, or significance (semantic content). It is suggested here that this problem may arise partly from the conflation of two vernacular senses of representation: representation-as-origin and representation-as-input. The flash of a neon sign may in one sense represent a popular drink, but to function as a representation it must provide an input to a 'consumer' in the street. The arguments presented draw on two principles - the neuron doctrine and the need for a venue for 'presentation' or 'reception' of a representation at a specified site, consistent with the locality principle. It is also argued that domains of representation cannot be defined by signal traffic, since they can be expected to include 'null' elements based on non-firing cells. In this analysis, mental representations-as-origin are distributed patterns of cell firing. Each firing cell is given semantic value in its own right - some form of atomic propositional significance - since different axonal branches may contribute to integration with different populations of signals at different downstream sites. Representations-as-input are patterns of local co-arrival of signals in the form of synaptic potentials in dendrites. Meaning then draws on the relationships between active and null inputs, forming 'scenarios' comprising a molecular combination of 'premises' from which a new output with atomic propositional significance is generated. In both types of representation, meaning, interpretation or significance pivots on events in an individual cell. (This analysis only applies to 'occurrent' representations based on current neural activity.) The concept of representations-as-input emphasizes the need for an internal 'consumer' of a representation and the dependence of meaning on the co-relationships involved in an input interaction between signals and consumer. The acceptance of this necessity provides a basis for resolving the problem that representations appear both as distributed (representation-as-origin) and as local (representation-as-input). The key implications are that representations in the brain are massively multiple both in series and in parallel, and that individual cells play specific semantic roles. These roles are discussed in relation to traditional concepts of 'gnostic' cell types.

Distinguishing Representations as Origin and Representations as Input: Roles for Individual Neurons

PubMed Central

Edwards, Jonathan C. W.

2016-01-01

It is widely perceived that there is a problem in giving a naturalistic account of mental representation that deals adequately with the issue of meaning, interpretation, or significance (semantic content). It is suggested here that this problem may arise partly from the conflation of two vernacular senses of representation: representation-as-origin and representation-as-input. The flash of a neon sign may in one sense represent a popular drink, but to function as a representation it must provide an input to a ‘consumer’ in the street. The arguments presented draw on two principles – the neuron doctrine and the need for a venue for ‘presentation’ or ‘reception’ of a representation at a specified site, consistent with the locality principle. It is also argued that domains of representation cannot be defined by signal traffic, since they can be expected to include ‘null’ elements based on non-firing cells. In this analysis, mental representations-as-origin are distributed patterns of cell firing. Each firing cell is given semantic value in its own right – some form of atomic propositional significance – since different axonal branches may contribute to integration with different populations of signals at different downstream sites. Representations-as-input are patterns of local co-arrival of signals in the form of synaptic potentials in dendrites. Meaning then draws on the relationships between active and null inputs, forming ‘scenarios’ comprising a molecular combination of ‘premises’ from which a new output with atomic propositional significance is generated. In both types of representation, meaning, interpretation or significance pivots on events in an individual cell. (This analysis only applies to ‘occurrent’ representations based on current neural activity.) The concept of representations-as-input emphasizes the need for an internal ‘consumer’ of a representation and the dependence of meaning on the co-relationships involved in an input interaction between signals and consumer. The acceptance of this necessity provides a basis for resolving the problem that representations appear both as distributed (representation-as-origin) and as local (representation-as-input). The key implications are that representations in the brain are massively multiple both in series and in parallel, and that individual cells play specific semantic roles. These roles are discussed in relation to traditional concepts of ‘gnostic’ cell types. PMID:27746760

GRACE L1b inversion through a self-consistent modified radial basis function approach

NASA Astrophysics Data System (ADS)

Yang, Fan; Kusche, Juergen; Rietbroek, Roelof; Eicker, Annette

2016-04-01

Implementing a regional geopotential representation such as mascons or, more general, RBFs (radial basis functions) has been widely accepted as an efficient and flexible approach to recover the gravity field from GRACE (Gravity Recovery and Climate Experiment), especially at higher latitude region like Greenland. This is since RBFs allow for regionally specific regularizations over areas which have sufficient and dense GRACE observations. Although existing RBF solutions show a better resolution than classical spherical harmonic solutions, the applied regularizations cause spatial leakage which should be carefully dealt with. It has been shown that leakage is a main error source which leads to an evident underestimation of yearly trend of ice-melting over Greenland. Unlike some popular post-processing techniques to mitigate leakage signals, this study, for the first time, attempts to reduce the leakage directly in the GRACE L1b inversion by constructing an innovative modified (MRBF) basis in place of the standard RBFs to retrieve a more realistic temporal gravity signal along the coastline. Our point of departure is that the surface mass loading associated with standard RBF is smooth but disregards physical consistency between continental mass and passive ocean response. In this contribution, based on earlier work by Clarke et al.(2007), a physically self-consistent MRBF representation is constructed from standard RBFs, with the help of the sea level equation: for a given standard RBF basis, the corresponding MRBF basis is first obtained by keeping the surface load over the continent unchanged, but imposing global mass conservation and equilibrium response of the oceans. Then, the updated set of MRBFs as well as standard RBFs are individually employed as the basis function to determine the temporal gravity field from GRACE L1b data. In this way, in the MRBF GRACE solution, the passive (e.g. ice melting and land hydrology response) sea level is automatically separated from ocean dynamic effects, and our hypothesis is that in this way we improve the partitioning of the GRACE signals into land and ocean contributions along the coastline. In particular, we inspect the ice-melting over Greenland from real GRACE data, and we evaluate the ability of the MRBF approach to recover true mass variations along the coastline. Finally, using independent measurements from multiple techniques including GPS vertical motion and altimetry, a validation will be presented to quantify to what extent it is possible to reduce the leakage through the MRBF approach.

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

NASA Technical Reports Server (NTRS)

Solakiewicz, Richard; Attele, Rohan; Koshak, William

2011-01-01

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.

Neural basis for dynamic updating of object representation in visual working memory.

PubMed

Takahama, Sachiko; Miyauchi, Satoru; Saiki, Jun

2010-02-15

In real world, objects have multiple features and change dynamically. Thus, object representations must satisfy dynamic updating and feature binding. Previous studies have investigated the neural activity of dynamic updating or feature binding alone, but not both simultaneously. We investigated the neural basis of feature-bound object representation in a dynamically updating situation by conducting a multiple object permanence tracking task, which required observers to simultaneously process both the maintenance and dynamic updating of feature-bound objects. Using an event-related design, we separated activities during memory maintenance and change detection. In the search for regions showing selective activation in dynamic updating of feature-bound objects, we identified a network during memory maintenance that was comprised of the inferior precentral sulcus, superior parietal lobule, and middle frontal gyrus. In the change detection period, various prefrontal regions, including the anterior prefrontal cortex, were activated. In updating object representation of dynamically moving objects, the inferior precentral sulcus closely cooperates with a so-called "frontoparietal network", and subregions of the frontoparietal network can be decomposed into those sensitive to spatial updating and feature binding. The anterior prefrontal cortex identifies changes in object representation by comparing memory and perceptual representations rather than maintaining object representations per se, as previously suggested. Copyright 2009 Elsevier Inc. All rights reserved.

A projection-free method for representing plane-wave DFT results in an atom-centered basis

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

Dunnington, Benjamin D.; Schmidt, J. R., E-mail: schmidt@chem.wisc.edu

2015-09-14

Plane wave density functional theory (DFT) is a powerful tool for gaining accurate, atomic level insight into bulk and surface structures. Yet, the delocalized nature of the plane wave basis set hinders the application of many powerful post-computation analysis approaches, many of which rely on localized atom-centered basis sets. Traditionally, this gap has been bridged via projection-based techniques from a plane wave to atom-centered basis. We instead propose an alternative projection-free approach utilizing direct calculation of matrix elements of the converged plane wave DFT Hamiltonian in an atom-centered basis. This projection-free approach yields a number of compelling advantages, including strictmore » orthonormality of the resulting bands without artificial band mixing and access to the Hamiltonian matrix elements, while faithfully preserving the underlying DFT band structure. The resulting atomic orbital representation of the Kohn-Sham wavefunction and Hamiltonian provides a gateway to a wide variety of analysis approaches. We demonstrate the utility of the approach for a diverse set of chemical systems and example analysis approaches.« less

Wissensstrukturierung im Unterricht: Neuere Forschung zur Wissensreprasentation und ihre Anwendung in der Didaktik (Knowledge Structuring in Instruction: Recent Research on Knowledge Representation and Its Application in the Classroom).

ERIC Educational Resources Information Center

Einsiedler, Wolfgang

1996-01-01

Asks whether theories of knowledge representation provide a basis for the development of theories of knowledge structuring in instruction. Discusses codes of knowledge, surface versus deep structures, semantic networks, and multiple memory systems. Reviews research on teaching, external representation of cognitive structures, hierarchical…

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.

Neural basis of individualistic and collectivistic views of self.

PubMed

Chiao, Joan Y; Harada, Tokiko; Komeda, Hidetsugu; Li, Zhang; Mano, Yoko; Saito, Daisuke; Parrish, Todd B; Sadato, Norihiro; Iidaka, Tetsuya

2009-09-01

Individualism and collectivism refer to cultural values that influence how people construe themselves and their relation to the world. Individualists perceive themselves as stable entities, autonomous from other people and their environment, while collectivists view themselves as dynamic entities, continually defined by their social context and relationships. Despite rich understanding of how individualism and collectivism influence social cognition at a behavioral level, little is known about how these cultural values modulate neural representations underlying social cognition. Using cross-cultural functional magnetic resonance imaging (fMRI), we examined whether the cultural values of individualism and collectivism modulate neural activity within medial prefrontal cortex (MPFC) during processing of general and contextual self judgments. Here, we show that neural activity within the anterior rostral portion of the MPFC during processing of general and contextual self judgments positively predicts how individualistic or collectivistic a person is across cultures. These results reveal two kinds of neural representations of self (eg, a general self and a contextual self) within MPFC and demonstrate how cultural values of individualism and collectivism shape these neural representations. 2008 Wiley-Liss, Inc.

Galaxy halo expansions: a new biorthogonal family of potential-density pairs

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn; Erkal, Denis

2018-05-01

Efficient expansions of the gravitational field of (dark) haloes have two main uses in the modelling of galaxies: first, they provide a compact representation of numerically constructed (or real) cosmological haloes, incorporating the effects of triaxiality, lopsidedness or other distortion. Secondly, they provide the basis functions for self-consistent field expansion algorithms used in the evolution of N-body systems. We present a new family of biorthogonal potential-density pairs constructed using the Hankel transform of the Laguerre polynomials. The lowest order density basis functions are double-power-law profiles cusped like ρ ˜ r-2+1/α at small radii with asymptotic density fall-off like ρ ˜ r-3-1/(2α). Here, α is a parameter satisfying α ≥ 1/2. The family therefore spans the range of inner density cusps found in numerical simulations, but has much shallower - and hence more realistic - outer slopes than the corresponding members of the only previously known family deduced by Zhao and exemplified by Hernquist & Ostriker. When α = 1, the lowest order density profile has an inner density cusp of ρ ˜ r-1 and an outer density slope of ρ ˜ r-3.5, similar to the famous Navarro, Frenk & White (NFW) model. For this reason, we demonstrate that our new expansion provides a more accurate representation of flattened NFW haloes than the competing Hernquist-Ostriker expansion. We utilize our new expansion by analysing a suite of numerically constructed haloes and providing the distributions of the expansion coefficients.

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

P, C and T: Different Properties on the Kinematical Level

NASA Astrophysics Data System (ADS)

Dvoeglazov, Valeriy V.

2018-04-01

We study the discrete symmetries (P,C and T) on the kinematical level within the extended Poincaré Group. On the basis of the Silagadze research, we investigate the question of the definitions of the discrete symmetry operators both on the classical level, and in the secondary-quantization scheme. We study the physical contents within several bases: light-front formulation, helicity basis, angular momentum basis, and so on, on several practical examples. We analize problems in construction of the neutral particles in the the (1/2, 0) + (0, 1/2) representation, the (1, 0) + (0, 1) and the (1/2, 1/2) representations of the Lorentz Group. As well known, the photon has the quantum numbers 1‑, so the (1, 0) + (0, 1) representation of the Lorentz group is relevant to its description. We have ambiguities in the definitions of the corresponding operators P, C; T, which lead to different physical consequences. It appears that the answers are connected with the helicity basis properties, and commutations/anticommutations of the corresponding operators, P, C, T, and C 2, P 2, (CP)2 properties. This contribution is the review paper of my previous work [2, 3].

On the mapping associated with the complex representation of functions and processes.

NASA Technical Reports Server (NTRS)

Harger, R. O.

1972-01-01

The mapping between function spaces that is implied by the representation of a real 'bandpass' function by a complex 'low-pass' function is explicitly accepted. The discussion is extended to the representation of stationary random processes where the mapping is between spaces of random processes. This approach clarifies the nature of the complex representation, especially in the case of random processes and, in addition, derives the properties of the complex representation.-

Internal representations for face detection: an application of noise-based image classification to BOLD responses.

PubMed

Nestor, Adrian; Vettel, Jean M; Tarr, Michael J

2013-11-01

What basic visual structures underlie human face detection and how can we extract such structures directly from the amplitude of neural responses elicited by face processing? Here, we address these issues by investigating an extension of noise-based image classification to BOLD responses recorded in high-level visual areas. First, we assess the applicability of this classification method to such data and, second, we explore its results in connection with the neural processing of faces. To this end, we construct luminance templates from white noise fields based on the response of face-selective areas in the human ventral cortex. Using behaviorally and neurally-derived classification images, our results reveal a family of simple but robust image structures subserving face representation and detection. Thus, we confirm the role played by classical face selective regions in face detection and we help clarify the representational basis of this perceptual function. From a theory standpoint, our findings support the idea of simple but highly diagnostic neurally-coded features for face detection. At the same time, from a methodological perspective, our work demonstrates the ability of noise-based image classification in conjunction with fMRI to help uncover the structure of high-level perceptual representations. Copyright © 2012 Wiley Periodicals, Inc.

Vocal Tract Images Reveal Neural Representations of Sensorimotor Transformation During Speech Imitation

PubMed Central

Carey, Daniel; Miquel, Marc E.; Evans, Bronwen G.; Adank, Patti; McGettigan, Carolyn

2017-01-01

Abstract Imitating speech necessitates the transformation from sensory targets to vocal tract motor output, yet little is known about the representational basis of this process in the human brain. Here, we address this question by using real-time MR imaging (rtMRI) of the vocal tract and functional MRI (fMRI) of the brain in a speech imitation paradigm. Participants trained on imitating a native vowel and a similar nonnative vowel that required lip rounding. Later, participants imitated these vowels and an untrained vowel pair during separate fMRI and rtMRI runs. Univariate fMRI analyses revealed that regions including left inferior frontal gyrus were more active during sensorimotor transformation (ST) and production of nonnative vowels, compared with native vowels; further, ST for nonnative vowels activated somatomotor cortex bilaterally, compared with ST of native vowels. Using test representational similarity analysis (RSA) models constructed from participants’ vocal tract images and from stimulus formant distances, we found that RSA searchlight analyses of fMRI data showed either type of model could be represented in somatomotor, temporal, cerebellar, and hippocampal neural activation patterns during ST. We thus provide the first evidence of widespread and robust cortical and subcortical neural representation of vocal tract and/or formant parameters, during prearticulatory ST. PMID:28334401

New perspectives on the auditory cortex: learning and memory.

PubMed

Weinberger, Norman M

2015-01-01

Primary ("early") sensory cortices have been viewed as stimulus analyzers devoid of function in learning, memory, and cognition. However, studies combining sensory neurophysiology and learning protocols have revealed that associative learning systematically modifies the encoding of stimulus dimensions in the primary auditory cortex (A1) to accentuate behaviorally important sounds. This "representational plasticity" (RP) is manifest at different levels. The sensitivity and selectivity of signal tones increase near threshold, tuning above threshold shifts toward the frequency of acoustic signals, and their area of representation can increase within the tonotopic map of A1. The magnitude of area gain encodes the level of behavioral stimulus importance and serves as a substrate of memory strength. RP has the same characteristics as behavioral memory: it is associative, specific, develops rapidly, consolidates, and can last indefinitely. Pairing tone with stimulation of the cholinergic nucleus basalis induces RP and implants specific behavioral memory, while directly increasing the representational area of a tone in A1 produces matching behavioral memory. Thus, RP satisfies key criteria for serving as a substrate of auditory memory. The findings suggest a basis for posttraumatic stress disorder in abnormally augmented cortical representations and emphasize the need for a new model of the cerebral cortex. © 2015 Elsevier B.V. All rights reserved.

Vocal Tract Images Reveal Neural Representations of Sensorimotor Transformation During Speech Imitation.

PubMed

Carey, Daniel; Miquel, Marc E; Evans, Bronwen G; Adank, Patti; McGettigan, Carolyn

2017-05-01

Imitating speech necessitates the transformation from sensory targets to vocal tract motor output, yet little is known about the representational basis of this process in the human brain. Here, we address this question by using real-time MR imaging (rtMRI) of the vocal tract and functional MRI (fMRI) of the brain in a speech imitation paradigm. Participants trained on imitating a native vowel and a similar nonnative vowel that required lip rounding. Later, participants imitated these vowels and an untrained vowel pair during separate fMRI and rtMRI runs. Univariate fMRI analyses revealed that regions including left inferior frontal gyrus were more active during sensorimotor transformation (ST) and production of nonnative vowels, compared with native vowels; further, ST for nonnative vowels activated somatomotor cortex bilaterally, compared with ST of native vowels. Using test representational similarity analysis (RSA) models constructed from participants' vocal tract images and from stimulus formant distances, we found that RSA searchlight analyses of fMRI data showed either type of model could be represented in somatomotor, temporal, cerebellar, and hippocampal neural activation patterns during ST. We thus provide the first evidence of widespread and robust cortical and subcortical neural representation of vocal tract and/or formant parameters, during prearticulatory ST. © The Author 2017. Published by Oxford University Press.

The field representation language.

PubMed

Tsafnat, Guy

2008-02-01

The complexity of quantitative biomedical models, and the rate at which they are published, is increasing to a point where managing the information has become all but impossible without automation. International efforts are underway to standardise representation languages for a number of mathematical entities that represent a wide variety of physiological systems. This paper presents the Field Representation Language (FRL), a portable representation of values that change over space and/or time. FRL is an extensible mark-up language (XML) derivative with support for large numeric data sets in Hierarchical Data Format version 5 (HDF5). Components of FRL can be reused through unified resource identifiers (URI) that point to external resources such as custom basis functions, boundary geometries and numerical data. To demonstrate the use of FRL as an interchange we present three models that study hyperthermia cancer treatment: a fractal model of liver tumour microvasculature; a probabilistic model simulating the deposition of magnetic microspheres throughout it; and a finite element model of hyperthermic treatment. The microsphere distribution field was used to compute the heat generation rate field around the tumour. We used FRL to convey results from the microsphere simulation to the treatment model. FRL facilitated the conversion of the coordinate systems and approximated the integral over regions of the microsphere deposition field.

Resolution-of-identity stochastic time-dependent configuration interaction for dissipative electron dynamics in strong fields.

PubMed

Klinkusch, Stefan; Tremblay, Jean Christophe

2016-05-14

In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.

Resolution-of-identity stochastic time-dependent configuration interaction for dissipative electron dynamics in strong fields

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

Klinkusch, Stefan; Tremblay, Jean Christophe

In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electronmore » ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.« less

The free-energy self: a predictive coding account of self-recognition.

PubMed

Apps, Matthew A J; Tsakiris, Manos

2014-04-01

Recognising and representing one's self as distinct from others is a fundamental component of self-awareness. However, current theories of self-recognition are not embedded within global theories of cortical function and therefore fail to provide a compelling explanation of how the self is processed. We present a theoretical account of the neural and computational basis of self-recognition that is embedded within the free-energy account of cortical function. In this account one's body is processed in a Bayesian manner as the most likely to be "me". Such probabilistic representation arises through the integration of information from hierarchically organised unimodal systems in higher-level multimodal areas. This information takes the form of bottom-up "surprise" signals from unimodal sensory systems that are explained away by top-down processes that minimise the level of surprise across the brain. We present evidence that this theoretical perspective may account for the findings of psychological and neuroimaging investigations into self-recognition and particularly evidence that representations of the self are malleable, rather than fixed as previous accounts of self-recognition might suggest. Copyright © 2013 Elsevier Ltd. All rights reserved.

Estimation of signal-dependent noise level function in transform domain via a sparse recovery model.

PubMed

Yang, Jingyu; Gan, Ziqiao; Wu, Zhaoyang; Hou, Chunping

2015-05-01

This paper proposes a novel algorithm to estimate the noise level function (NLF) of signal-dependent noise (SDN) from a single image based on the sparse representation of NLFs. Noise level samples are estimated from the high-frequency discrete cosine transform (DCT) coefficients of nonlocal-grouped low-variation image patches. Then, an NLF recovery model based on the sparse representation of NLFs under a trained basis is constructed to recover NLF from the incomplete noise level samples. Confidence levels of the NLF samples are incorporated into the proposed model to promote reliable samples and weaken unreliable ones. We investigate the behavior of the estimation performance with respect to the block size, sampling rate, and confidence weighting. Simulation results on synthetic noisy images show that our method outperforms existing state-of-the-art schemes. The proposed method is evaluated on real noisy images captured by three types of commodity imaging devices, and shows consistently excellent SDN estimation performance. The estimated NLFs are incorporated into two well-known denoising schemes, nonlocal means and BM3D, and show significant improvements in denoising SDN-polluted images.

The free-energy self: A predictive coding account of self-recognition

PubMed Central

Apps, Matthew A.J.; Tsakiris, Manos

2013-01-01

Recognising and representing one’s self as distinct from others is a fundamental component of self-awareness. However, current theories of self-recognition are not embedded within global theories of cortical function and therefore fail to provide a compelling explanation of how the self is processed. We present a theoretical account of the neural and computational basis of self-recognition that is embedded within the free-energy account of cortical function. In this account one’s body is processed in a Bayesian manner as the most likely to be “me”. Such probabilistic representation arises through the integration of information from hierarchically organised unimodal systems in higher-level multimodal areas. This information takes the form of bottom-up “surprise” signals from unimodal sensory systems that are explained away by top-down processes that minimise the level of surprise across the brain. We present evidence that this theoretical perspective may account for the findings of psychological and neuroimaging investigations into self-recognition and particularly evidence that representations of the self are malleable, rather than fixed as previous accounts of self-recognition might suggest. PMID:23416066

The structure and energetics of Cr(CO)6 and Cr(CO)5

NASA Technical Reports Server (NTRS)

Barnes, Leslie A.; Liu, Bowen; Lindh, Roland

1992-01-01

The geometric structure of Cr(CO)6 is optimized at the modified coupled pair functional (MCPF), single and double excitation coupled-cluster (CCSD) and CCSD(T) levels of theory (including a perturbational estimate for connected triple excitations), and the force constants for the totally symmetric representation are determined. The geometry of Cr(CO)5 is partially optimized at the MCPF, CCSD, and CCSD(T) levels of theory. Comparison with experimental data shows that the CCSD(T) method gives the best results for the structures and force constants, and that remaining errors are probably due to deficiencies in the one-particle basis sets used for CO. The total binding energies of Cr(CO)6 and Cr(CO)5 are also determined at the MCPF, CCSD, and CCSD(T) levels of theory. The CCSD(T) method gives a much larger total binding energy than either the MCPF or CCSD methods. An analysis of the basis set superposition error (BSSE) at the MCPF level of treatment points out limitations in the one-particle basis used. Calculations using larger basis sets reduce the BSSE, but the total binding energy of Cr(CO)6 is still significantly smaller than the experimental value, although the first CO bond dissociation energy of Cr(CO)6 is well described. An investigation of 3s3p correlation reveals only a small effect. In the largest basis set, the total CO binding energy of Cr(CO)6 is estimated to be 140 kcal/mol at the CCSD(T) level of theory, or about 86 percent of the experimental value. The remaining discrepancy between the experimental and theoretical value is probably due to limitations in the one-particle basis, rather than limitations in the correlation treatment. In particular an additional d function and an f function on each C and O are needed to obtain quantitative results. This is underscored by the fact that even using a very large primitive set (1042 primitive functions contracted to 300 basis functions), the superposition error for the total binding energy of Cr(CO)6 is 22 kcal/mol at the MCPF level of treatment.

Finite-Time Attitude Tracking Control for Spacecraft Using Terminal Sliding Mode and Chebyshev Neural Network.

PubMed

An-Min Zou; Kumar, K D; Zeng-Guang Hou; Xi Liu

2011-08-01

A finite-time attitude tracking control scheme is proposed for spacecraft using terminal sliding mode and Chebyshev neural network (NN) (CNN). The four-parameter representations (quaternion) are used to describe the spacecraft attitude for global representation without singularities. The attitude state (i.e., attitude and velocity) error dynamics is transformed to a double integrator dynamics with a constraint on the spacecraft attitude. With consideration of this constraint, a novel terminal sliding manifold is proposed for the spacecraft. In order to guarantee that the output of the NN used in the controller is bounded by the corresponding bound of the approximated unknown function, a switch function is applied to generate a switching between the adaptive NN control and the robust controller. Meanwhile, a CNN, whose basis functions are implemented using only desired signals, is introduced to approximate the desired nonlinear function and bounded external disturbances online, and the robust term based on the hyperbolic tangent function is applied to counteract NN approximation errors in the adaptive neural control scheme. Most importantly, the finite-time stability in both the reaching phase and the sliding phase can be guaranteed by a Lyapunov-based approach. Finally, numerical simulations on the attitude tracking control of spacecraft in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, and control input constraints are presented to demonstrate the performance of the proposed controller.

Representation and Exchange of Knowledge as a Basis of Information Processes. Proceedings of the International Research Forum in Information Science (5th, Heidelberg, West Germany, September 5-7, 1983).

ERIC Educational Resources Information Center

Dietschmann, Hans, Ed.

This 22-paper collection addresses a variety of issues related to representation and transfer of knowledge. Individual papers include an explanation of the usefulness of general scientific models versus case-specific approaches and a discussion of different empirical approaches to the general problem of knowledge representation for information…

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.

Some comparisons of complexity in dictionary-based and linear computational models.

PubMed

Gnecco, Giorgio; Kůrková, Věra; Sanguineti, Marcello

2011-03-01

Neural networks provide a more flexible approximation of functions than traditional linear regression. In the latter, one can only adjust the coefficients in linear combinations of fixed sets of functions, such as orthogonal polynomials or Hermite functions, while for neural networks, one may also adjust the parameters of the functions which are being combined. However, some useful properties of linear approximators (such as uniqueness, homogeneity, and continuity of best approximation operators) are not satisfied by neural networks. Moreover, optimization of parameters in neural networks becomes more difficult than in linear regression. Experimental results suggest that these drawbacks of neural networks are offset by substantially lower model complexity, allowing accuracy of approximation even in high-dimensional cases. We give some theoretical results comparing requirements on model complexity for two types of approximators, the traditional linear ones and so called variable-basis types, which include neural networks, radial, and kernel models. We compare upper bounds on worst-case errors in variable-basis approximation with lower bounds on such errors for any linear approximator. Using methods from nonlinear approximation and integral representations tailored to computational units, we describe some cases where neural networks outperform any linear approximator. Copyright © 2010 Elsevier Ltd. All rights reserved.

Host genetic determinants of microbiota-dependent nutrition revealed by genome-wide analysis of Drosophila melanogaster

PubMed Central

Dobson, Adam J.; Chaston, John M.; Newell, Peter D.; Donahue, Leanne; Hermann, Sara L.; Sannino, David R.; Westmiller, Stephanie; Wong, Adam C.-N.; Clark, Andrew G.; Lazzaro, Brian P.; Douglas, Angela E.

2015-01-01

Animals bear communities of gut microorganisms with substantial effects on animal nutrition, but the host genetic basis of these effects is unknown. Here, we use Drosophila to demonstrate substantial among-genotype variation in the effects of eliminating the gut microbiota on five host nutritional indices (weight, and protein, lipid, glucose and glycogen contents); this includes variation in both the magnitude and direction of microbiota-dependent effects. Genome-wide associations to identify the genetic basis of the microbiota-dependent variation reveal polymorphisms in largely non-overlapping sets of genes associated with variation in the nutritional traits, including strong representation of conserved genes functioning in signaling. Key genes identified by the GWA study are validated by loss-of-function mutations that altered microbiota-dependent nutritional effects. We conclude that the microbiota interacts with the animal at multiple points in the signaling and regulatory networks that determine animal nutrition. These interactions with the microbiota are likely conserved across animals, including humans. PMID:25692519

[Formula: see text] regularity properties of singular parameterizations in isogeometric analysis.

PubMed

Takacs, T; Jüttler, B

2012-11-01

Isogeometric analysis (IGA) is a numerical simulation method which is directly based on the NURBS-based representation of CAD models. It exploits the tensor-product structure of 2- or 3-dimensional NURBS objects to parameterize the physical domain. Hence the physical domain is parameterized with respect to a rectangle or to a cube. Consequently, singularly parameterized NURBS surfaces and NURBS volumes are needed in order to represent non-quadrangular or non-hexahedral domains without splitting, thereby producing a very compact and convenient representation. The Galerkin projection introduces finite-dimensional spaces of test functions in the weak formulation of partial differential equations. In particular, the test functions used in isogeometric analysis are obtained by composing the inverse of the domain parameterization with the NURBS basis functions. In the case of singular parameterizations, however, some of the resulting test functions do not necessarily fulfill the required regularity properties. Consequently, numerical methods for the solution of partial differential equations cannot be applied properly. We discuss the regularity properties of the test functions. For one- and two-dimensional domains we consider several important classes of singularities of NURBS parameterizations. For specific cases we derive additional conditions which guarantee the regularity of the test functions. In addition we present a modification scheme for the discretized function space in case of insufficient regularity. It is also shown how these results can be applied for computational domains in higher dimensions that can be parameterized via sweeping.

Dopamine Reward Prediction Error Responses Reflect Marginal Utility

PubMed Central

Stauffer, William R.; Lak, Armin; Schultz, Wolfram

2014-01-01

Summary Background Optimal choices require an accurate neuronal representation of economic value. In economics, utility functions are mathematical representations of subjective value that can be constructed from choices under risk. Utility usually exhibits a nonlinear relationship to physical reward value that corresponds to risk attitudes and reflects the increasing or decreasing marginal utility obtained with each additional unit of reward. Accordingly, neuronal reward responses coding utility should robustly reflect this nonlinearity. Results In two monkeys, we measured utility as a function of physical reward value from meaningful choices under risk (that adhered to first- and second-order stochastic dominance). The resulting nonlinear utility functions predicted the certainty equivalents for new gambles, indicating that the functions’ shapes were meaningful. The monkeys were risk seeking (convex utility function) for low reward and risk avoiding (concave utility function) with higher amounts. Critically, the dopamine prediction error responses at the time of reward itself reflected the nonlinear utility functions measured at the time of choices. In particular, the reward response magnitude depended on the first derivative of the utility function and thus reflected the marginal utility. Furthermore, dopamine responses recorded outside of the task reflected the marginal utility of unpredicted reward. Accordingly, these responses were sufficient to train reinforcement learning models to predict the behaviorally defined expected utility of gambles. Conclusions These data suggest a neuronal manifestation of marginal utility in dopamine neurons and indicate a common neuronal basis for fundamental explanatory constructs in animal learning theory (prediction error) and economic decision theory (marginal utility). PMID:25283778

Toward a general theory of conical intersections in systems of identical nuclei

NASA Astrophysics Data System (ADS)

Keating, Sean P.; Mead, C. Alden

1987-02-01

It has been shown previously that the Herzberg-Longuet-Higgins sign change produced in Born-Oppenheimer electronic wave functions when the nuclei traverse a closed path around a conical intersection has implications for the symmetry of wave functions under permutations of identical nuclei. For systems of three or four identical nuclei, there are special features present which have facilitated the detailed analysis. The present paper reports progress toward a general theory for systems of n nuclei. For n=3 or 4, the two key functions which locate conical intersections and define compensating phase factors can conveniently be defined so as to transform under permutations according to a two-dimensional irreducible representation of the permutation group. Since such representations do not exist for n>4, we have chosen to develop a formalism in terms of lab-fixed electronic basis functions, and we show how to define the two key functions in principle. The functions so defined both turn out to be totally symmetric under permutations. We show how they can be used to define compensating phase factors so that all modified electronic wave functions are either totally symmetric or totally antisymmetric under permutations. A detailed analysis is made to cyclic permutations in the neighborhood of Dnh symmetry, which can be extended by continuity arguments to more general configurations, and criteria are obtained for sign changes. There is a qualitative discussion of the treatment of more general permutations.

Contour Curvature As an Invariant Code for Objects in Visual Area V4

PubMed Central

Pasupathy, Anitha

2016-01-01

Size-invariant object recognition—the ability to recognize objects across transformations of scale—is a fundamental feature of biological and artificial vision. To investigate its basis in the primate cerebral cortex, we measured single neuron responses to stimuli of varying size in visual area V4, a cornerstone of the object-processing pathway, in rhesus monkeys (Macaca mulatta). Leveraging two competing models for how neuronal selectivity for the bounding contours of objects may depend on stimulus size, we show that most V4 neurons (∼70%) encode objects in a size-invariant manner, consistent with selectivity for a size-independent parameter of boundary form: for these neurons, “normalized” curvature, rather than “absolute” curvature, provided a better account of responses. Our results demonstrate the suitability of contour curvature as a basis for size-invariant object representation in the visual cortex, and posit V4 as a foundation for behaviorally relevant object codes. SIGNIFICANCE STATEMENT Size-invariant object recognition is a bedrock for many perceptual and cognitive functions. Despite growing neurophysiological evidence for invariant object representations in the primate cortex, we still lack a basic understanding of the encoding rules that govern them. Classic work in the field of visual shape theory has long postulated that a representation of objects based on information about their bounding contours is well suited to mediate such an invariant code. In this study, we provide the first empirical support for this hypothesis, and its instantiation in single neurons of visual area V4. PMID:27194333

Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

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

Chen, Ray -Bing; Wang, Weichung; Jeff Wu, C. F.

A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction ofmore » sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.« less

Comparison of deep neural networks to spatio-temporal cortical dynamics of human visual object recognition reveals hierarchical correspondence

PubMed Central

Cichy, Radoslaw Martin; Khosla, Aditya; Pantazis, Dimitrios; Torralba, Antonio; Oliva, Aude

2016-01-01

The complex multi-stage architecture of cortical visual pathways provides the neural basis for efficient visual object recognition in humans. However, the stage-wise computations therein remain poorly understood. Here, we compared temporal (magnetoencephalography) and spatial (functional MRI) visual brain representations with representations in an artificial deep neural network (DNN) tuned to the statistics of real-world visual recognition. We showed that the DNN captured the stages of human visual processing in both time and space from early visual areas towards the dorsal and ventral streams. Further investigation of crucial DNN parameters revealed that while model architecture was important, training on real-world categorization was necessary to enforce spatio-temporal hierarchical relationships with the brain. Together our results provide an algorithmically informed view on the spatio-temporal dynamics of visual object recognition in the human visual brain. PMID:27282108

Comparison of deep neural networks to spatio-temporal cortical dynamics of human visual object recognition reveals hierarchical correspondence.

PubMed

Cichy, Radoslaw Martin; Khosla, Aditya; Pantazis, Dimitrios; Torralba, Antonio; Oliva, Aude

2016-06-10

The complex multi-stage architecture of cortical visual pathways provides the neural basis for efficient visual object recognition in humans. However, the stage-wise computations therein remain poorly understood. Here, we compared temporal (magnetoencephalography) and spatial (functional MRI) visual brain representations with representations in an artificial deep neural network (DNN) tuned to the statistics of real-world visual recognition. We showed that the DNN captured the stages of human visual processing in both time and space from early visual areas towards the dorsal and ventral streams. Further investigation of crucial DNN parameters revealed that while model architecture was important, training on real-world categorization was necessary to enforce spatio-temporal hierarchical relationships with the brain. Together our results provide an algorithmically informed view on the spatio-temporal dynamics of visual object recognition in the human visual brain.

Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

DOE PAGES

Chen, Ray -Bing; Wang, Weichung; Jeff Wu, C. F.

2017-04-12

A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction ofmore » sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.« less

Symbolism in prehistoric man.

PubMed

Facchini, F

2000-12-01

The aptitude for symbolization, characteristic of man, is revealed not only in artistic representations and funerary practices. It is exhibited by every manifestation of human activity or representation of natural phenomena that assumes or refers to a meaning. We can recognize functional symbolism (tool-making, habitative or food technology), social symbolism, (language and social communication) and spiritual symbolism (funerary practices and artistic expressions). On the basis of these concepts, research into symbolism in prehistoric man allows us to recognize forms of symbolism already in the manifestations of the most ancient humans, starting with Homo habilis (or rudolfensis). Toolmaking, social organization and organization of the territory are oriented toward survival and the life of the family group. They attest to symbolic behaviors and constitute symbolic systems by means of which man expresses himself, lives and transmits his symbolic world. The diverse forms of symbolism are discussed with reference to the different phases of prehistoric humanity.

Towards spinning Mellin amplitudes

NASA Astrophysics Data System (ADS)

Chen, Heng-Yu; Kuo, En-Jui; Kyono, Hideki

2018-06-01

We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the exchange of symmetric traceless primaries, we generalize the Mellin transform for scalar case to introduce discrete Mellin variables for incorporating spin degrees of freedom. Based on the structures about spinning three and four point Witten diagrams, we also obtain a generalization of the Mack polynomial which can be regarded as a natural kinematical polynomial basis for computing spinning Mellin amplitudes using different choices of interaction vertices.

Application of neural networks to autonomous rendezvous and docking of space vehicles

NASA Technical Reports Server (NTRS)

Dabney, Richard W.

1992-01-01

NASA-Marshall has investigated the feasibility of numerous autonomous rendezvous and docking (ARD) candidate techniques. Neural networks have been studied as a viable basis for such systems' implementation, due to their intrinsic representation of such nonlinear functions as those for which analytical solutions are either difficult or nonexistent. Neural networks are also able to recognize and adapt to changes in their dynamic environment, thereby enhancing redundancy and fault tolerance. Outstanding performance has been obtained from ARD azimuth, elevation, and roll networks of this type.

Altered neural reward representations in pathological gamblers revealed by delay and probability discounting.

PubMed

Miedl, Stephan F; Peters, Jan; Büchel, Christian

2012-02-01

The neural basis of excessive delay discounting and reduced risk sensitivity of pathological gamblers with a particular focus on subjective neural reward representations has not been previously examined. To examine how pathological gamblers represent subjective reward value at a neural level and how this is affected by gambling severity. Model-based functional magnetic resonance imaging study with patients and control subjects. Department of Systems Neuroscience, University Medical Center Hamburg-Eppendorf. Participants were recruited from the local community by advertisement and through self-help groups. A sample of 16 pathological gamblers (according to the DSM-IV definition) was matched by age, sex, smoking status, income, educational level, and handedness to 16 healthy controls. Pathological gamblers showed increased discounting of delayed rewards and a trend toward decreased discounting of probabilistic rewards compared with matched controls. At the neural level, a significant group × condition interaction indicated that reward representations in the gamblers were modulated in a condition-specific manner, such that they exhibited increased (delay discounting) and decreased (probability discounting) neural value correlations in the reward system. In addition, throughout the reward system, neuronal value signals for delayed rewards were negatively correlated with gambling severity. The results extend previous reports of a generally hypoactive reward system in pathological gamblers by showing that, even when subjective reward valuation is accounted for, gamblers still show altered reward representations. Furthermore, results point toward a gradual degradation of mesolimbic reward representations for delayed rewards during the course of pathological gambling.

Neural Basis of Self and Other Representation in Autism: An fMRI Study of Self-Face Recognition

PubMed Central

Uddin, Lucina Q.; Davies, Mari S.; Scott, Ashley A.; Zaidel, Eran; Bookheimer, Susan Y.; Iacoboni, Marco; Dapretto, Mirella

2008-01-01

Background Autism is a developmental disorder characterized by decreased interest and engagement in social interactions and by enhanced self-focus. While previous theoretical approaches to understanding autism have emphasized social impairments and altered interpersonal interactions, there is a recent shift towards understanding the nature of the representation of the self in individuals with autism spectrum disorders (ASD). Still, the neural mechanisms subserving self-representations in ASD are relatively unexplored. Methodology/Principal Findings We used event-related fMRI to investigate brain responsiveness to images of the subjects' own face and to faces of others. Children with ASD and typically developing (TD) children viewed randomly presented digital morphs between their own face and a gender-matched other face, and made “self/other” judgments. Both groups of children activated a right premotor/prefrontal system when identifying images containing a greater percentage of the self face. However, while TD children showed activation of this system during both self- and other-processing, children with ASD only recruited this system while viewing images containing mostly their own face. Conclusions/Significance This functional dissociation between the representation of self versus others points to a potential neural substrate for the characteristic self-focus and decreased social understanding exhibited by these individuals, and suggests that individuals with ASD lack the shared neural representations for self and others that TD children and adults possess and may use to understand others. PMID:18958161

A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

PubMed

Wapenaar, Kees

2017-06-01

A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

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

Meek, Garrett A.; Levine, Benjamin G., E-mail: levine@chemistry.msu.edu

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplingsmore » at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.« less

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-05-01

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

PubMed

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

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.

Contribution of frontal and temporal lobe function to memory interference from divided attention at retrieval.

PubMed

Fernandes, Myra A; Davidson, Patrick S R; Glisky, Elizabeth L; Moscovitch, Morris

2004-07-01

On the basis of their scores on composite measures of frontal and temporal lobe function, derived from neuropsychological testing, seniors were divided preexperimentally into 4 groups. Participants studied a list of unrelated words under full attention and recalled them while concurrently performing an animacy decision task to words, an odd-digit identification task to numbers, or no distracting task. Large interference effects on memory were produced by the animacy but not by the odd-digit distracting task, and this pattern was not influenced by level of frontal or temporal lobe function. Results show associative retrieval is largely disrupted by competition for common representations, and it is not affected by a reduction in general processing resources, attentional capacity, or competition for memory structures in the temporal lobe.

A critical review of the allocentric spatial representation and its neural underpinnings: toward a network-based perspective

PubMed Central

Ekstrom, Arne D.; Arnold, Aiden E. G. F.; Iaria, Giuseppe

2014-01-01

While the widely studied allocentric spatial representation holds a special status in neuroscience research, its exact nature and neural underpinnings continue to be the topic of debate, particularly in humans. Here, based on a review of human behavioral research, we argue that allocentric representations do not provide the kind of map-like, metric representation one might expect based on past theoretical work. Instead, we suggest that almost all tasks used in past studies involve a combination of egocentric and allocentric representation, complicating both the investigation of the cognitive basis of an allocentric representation and the task of identifying a brain region specifically dedicated to it. Indeed, as we discuss in detail, past studies suggest numerous brain regions important to allocentric spatial memory in addition to the hippocampus, including parahippocampal, retrosplenial, and prefrontal cortices. We thus argue that although allocentric computations will often require the hippocampus, particularly those involving extracting details across temporally specific routes, the hippocampus is not necessary for all allocentric computations. We instead suggest that a non-aggregate network process involving multiple interacting brain areas, including hippocampus and extra-hippocampal areas such as parahippocampal, retrosplenial, prefrontal, and parietal cortices, better characterizes the neural basis of spatial representation during navigation. According to this model, an allocentric representation does not emerge from the computations of a single brain region (i.e., hippocampus) nor is it readily decomposable into additive computations performed by separate brain regions. Instead, an allocentric representation emerges from computations partially shared across numerous interacting brain regions. We discuss our non-aggregate network model in light of existing data and provide several key predictions for future experiments. PMID:25346679

Representational analysis of extended disorder in atomistic ensembles derived from total scattering data

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

Neilson, James R.; McQueen, Tyrel M.

With the increased availability of high-intensity time-of-flight neutron and synchrotron X-ray scattering sources that can access wide ranges of momentum transfer, the pair distribution function method has become a standard analysis technique for studying disorder of local coordination spheres and at intermediate atomic separations. In some cases, rational modeling of the total scattering data (Bragg and diffuse) becomes intractable with least-squares approaches, necessitating reverse Monte Carlo simulations using large atomistic ensembles. However, the extraction of meaningful information from the resulting atomistic ensembles is challenging, especially at intermediate length scales. Representational analysis is used here to describe the displacements of atomsmore » in reverse Monte Carlo ensembles from an ideal crystallographic structure in an approach analogous to tight-binding methods. Rewriting the displacements in terms of a local basis that is descriptive of the ideal crystallographic symmetry provides a robust approach to characterizing medium-range order (and disorder) and symmetry breaking in complex and disordered crystalline materials. Lastly, this method enables the extraction of statistically relevant displacement modes (orientation, amplitude and distribution) of the crystalline disorder and provides directly meaningful information in a locally symmetry-adapted basis set that is most descriptive of the crystal chemistry and physics.« less

Representational analysis of extended disorder in atomistic ensembles derived from total scattering data

DOE PAGES

Neilson, James R.; McQueen, Tyrel M.

2015-09-20

With the increased availability of high-intensity time-of-flight neutron and synchrotron X-ray scattering sources that can access wide ranges of momentum transfer, the pair distribution function method has become a standard analysis technique for studying disorder of local coordination spheres and at intermediate atomic separations. In some cases, rational modeling of the total scattering data (Bragg and diffuse) becomes intractable with least-squares approaches, necessitating reverse Monte Carlo simulations using large atomistic ensembles. However, the extraction of meaningful information from the resulting atomistic ensembles is challenging, especially at intermediate length scales. Representational analysis is used here to describe the displacements of atomsmore » in reverse Monte Carlo ensembles from an ideal crystallographic structure in an approach analogous to tight-binding methods. Rewriting the displacements in terms of a local basis that is descriptive of the ideal crystallographic symmetry provides a robust approach to characterizing medium-range order (and disorder) and symmetry breaking in complex and disordered crystalline materials. Lastly, this method enables the extraction of statistically relevant displacement modes (orientation, amplitude and distribution) of the crystalline disorder and provides directly meaningful information in a locally symmetry-adapted basis set that is most descriptive of the crystal chemistry and physics.« less

Relation of exact Gaussian basis methods to the dephasing representation: Theory and application to time-resolved electronic spectra

NASA Astrophysics Data System (ADS)

Sulc, Miroslav; Hernandez, Henar; Martinez, Todd J.; Vanicek, Jiri

2014-03-01

We recently showed that the Dephasing Representation (DR) provides an efficient tool for computing ultrafast electronic spectra and that cellularization yields further acceleration [M. Šulc and J. Vaníček, Mol. Phys. 110, 945 (2012)]. Here we focus on increasing its accuracy by first implementing an exact Gaussian basis method (GBM) combining the accuracy of quantum dynamics and efficiency of classical dynamics. The DR is then derived together with ten other methods for computing time-resolved spectra with intermediate accuracy and efficiency. These include the Gaussian DR (GDR), an exact generalization of the DR, in which trajectories are replaced by communicating frozen Gaussians evolving classically with an average Hamiltonian. The methods are tested numerically on time correlation functions and time-resolved stimulated emission spectra in the harmonic potential, pyrazine S0 /S1 model, and quartic oscillator. Both the GBM and the GDR are shown to increase the accuracy of the DR. Surprisingly, in chaotic systems the GDR can outperform the presumably more accurate GBM, in which the two bases evolve separately. This research was supported by the Swiss NSF Grant No. 200021_124936/1 and NCCR Molecular Ultrafast Science & Technology (MUST), and by the EPFL.

Geometric and computer-aided spline hob modeling

NASA Astrophysics Data System (ADS)

Brailov, I. G.; Myasoedova, T. M.; Panchuk, K. L.; Krysova, I. V.; Rogoza, YU A.

2018-03-01

The paper considers acquiring the spline hob geometric model. The objective of the research is the development of a mathematical model of spline hob for spline shaft machining. The structure of the spline hob is described taking into consideration the motion in parameters of the machine tool system of cutting edge positioning and orientation. Computer-aided study is performed with the use of CAD and on the basis of 3D modeling methods. Vector representation of cutting edge geometry is accepted as the principal method of spline hob mathematical model development. The paper defines the correlations described by parametric vector functions representing helical cutting edges designed for spline shaft machining with consideration for helical movement in two dimensions. An application for acquiring the 3D model of spline hob is developed on the basis of AutoLISP for AutoCAD environment. The application presents the opportunity for the use of the acquired model for milling process imitation. An example of evaluation, analytical representation and computer modeling of the proposed geometrical model is reviewed. In the mentioned example, a calculation of key spline hob parameters assuring the capability of hobbing a spline shaft of standard design is performed. The polygonal and solid spline hob 3D models are acquired by the use of imitational computer modeling.

Indigenous Representation and Alternative Schooling: Prioritising an Epistemology of Relationality

ERIC Educational Resources Information Center

Keddie, Amanda

2014-01-01

This paper draws on a case study of a small alternative Indigenous school in Queensland, Australia. From the perspective of several of the school's Indigenous Elders, the paper foregrounds the significance of group differentiation at the school on the basis of Indigenous representation. However, it also considers how such…

Computational studies of metal-metal and metal-ligand interactions

NASA Technical Reports Server (NTRS)

Barnes, Leslie A.

1992-01-01

The geometric structure of Cr(CO)6 is optimized at the modified coupled-pair functional (MCPF), single and double excitation coupled-cluster (CCSD) and CCSD(T) levels of theory (including a perturbational estimate for connected triple excitations), and the force constants for the totally symmetric representation are determined. The geometry of Cr(CO)5 is partially optimized at the MCPF, CCSD and CCSD(T) levels of theory. Comparison with experimental data shows that the CCSD(T) method gives the best results for the structures and force constants, and that remaining errors are probably due to deficiencies in the one-particle basis sets used for CO. A detailed comparison of the properties of free CO is therefore given, at both the MCPF and CCSD/CCSD(T) levels of treatment, using a variety of basis sets. With very large one-particle basis sets, the SSCD(T) method gives excellent results for the bond distance, dipole moment and harmonic frequency of free CO. The total binding energies of Cr(CO)6 and Cr(CO)5 are also determined at the MCPF, CCSD and CCSD(T) levels of theory. The CCSD(T) method gives a much larger total binding energy than either the MCPF or CCSD methods. An analysis of the basis set superposition error (BSSE) at the MCPF level of treatment points out limitations in the one-particle basis used here and in a previous study. Calculations using larger basis sets reduced the BSSE, but the total binding energy of Cr(CO)6 is still significantly smaller than the experimental value, although the first CO bond dissociation energy of Cr(CO)6 is well described. An investigation of 3s3p correlation reveals only a small effect. The remaining discrepancy between the experimental and theoretical total binding energy of Cr(CO)6 is probably due to limitations in the one-particle basis, rather than limitations in the correlation treatment. In particular an additional d function and an f function on each C and O are needed to obtain quantitative results. This is underscored by the fact that even using a very large primitive se (1042 primitive functions contracted to 300 basis functions), the superposition error for the total binding energy of Cr(CO)6 is 22 kcal/mol at the MCPF level of treatment.

A Sparsity-Promoted Method Based on Majorization-Minimization for Weak Fault Feature Enhancement

PubMed Central

Hao, Yansong; Song, Liuyang; Tang, Gang; Yuan, Hongfang

2018-01-01

Fault transient impulses induced by faulty components in rotating machinery usually contain substantial interference. Fault features are comparatively weak in the initial fault stage, which renders fault diagnosis more difficult. In this case, a sparse representation method based on the Majorzation-Minimization (MM) algorithm is proposed to enhance weak fault features and extract the features from strong background noise. However, the traditional MM algorithm suffers from two issues, which are the choice of sparse basis and complicated calculations. To address these challenges, a modified MM algorithm is proposed in which a sparse optimization objective function is designed firstly. Inspired by the Basis Pursuit (BP) model, the optimization function integrates an impulsive feature-preserving factor and a penalty function factor. Second, a modified Majorization iterative method is applied to address the convex optimization problem of the designed function. A series of sparse coefficients can be achieved through iterating, which only contain transient components. It is noteworthy that there is no need to select the sparse basis in the proposed iterative method because it is fixed as a unit matrix. Then the reconstruction step is omitted, which can significantly increase detection efficiency. Eventually, envelope analysis of the sparse coefficients is performed to extract weak fault features. Simulated and experimental signals including bearings and gearboxes are employed to validate the effectiveness of the proposed method. In addition, comparisons are made to prove that the proposed method outperforms the traditional MM algorithm in terms of detection results and efficiency. PMID:29597280

A Sparsity-Promoted Method Based on Majorization-Minimization for Weak Fault Feature Enhancement.

PubMed

Ren, Bangyue; Hao, Yansong; Wang, Huaqing; Song, Liuyang; Tang, Gang; Yuan, Hongfang

2018-03-28

Fault transient impulses induced by faulty components in rotating machinery usually contain substantial interference. Fault features are comparatively weak in the initial fault stage, which renders fault diagnosis more difficult. In this case, a sparse representation method based on the Majorzation-Minimization (MM) algorithm is proposed to enhance weak fault features and extract the features from strong background noise. However, the traditional MM algorithm suffers from two issues, which are the choice of sparse basis and complicated calculations. To address these challenges, a modified MM algorithm is proposed in which a sparse optimization objective function is designed firstly. Inspired by the Basis Pursuit (BP) model, the optimization function integrates an impulsive feature-preserving factor and a penalty function factor. Second, a modified Majorization iterative method is applied to address the convex optimization problem of the designed function. A series of sparse coefficients can be achieved through iterating, which only contain transient components. It is noteworthy that there is no need to select the sparse basis in the proposed iterative method because it is fixed as a unit matrix. Then the reconstruction step is omitted, which can significantly increase detection efficiency. Eventually, envelope analysis of the sparse coefficients is performed to extract weak fault features. Simulated and experimental signals including bearings and gearboxes are employed to validate the effectiveness of the proposed method. In addition, comparisons are made to prove that the proposed method outperforms the traditional MM algorithm in terms of detection results and efficiency.

Eulerian formulation of the interacting particle representation model of homogeneous turbulence

DOE PAGES

Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca

2016-10-21

The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the con nes of a one-point model. In the original formulation [Kassinos & Reynolds, Center for Turbulence Research: Annual Research Briefs, 31{51, (1996)], the IPRM was developed in a Lagrangian setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is re-formulated in an Eulerian framework and evolution equations are developed for the marginal PDFs. Eulerian methods avoid the issues associated with statistical estimators used by Lagrangian approaches, such as slow convergence. Amore » specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with Eulerian simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new Eulerian solution method are thoroughly analyzed. The sensitivity of the Eulerian simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between Eulerian and Lagrangian simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new Eulerian solution method and the original Lagrangian approach.« less

Convergence to equilibrium under a random Hamiltonian.

PubMed

Brandão, Fernando G S L; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K; Mozrzymas, Marek

2012-09-01

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

Convergence to equilibrium under a random Hamiltonian

NASA Astrophysics Data System (ADS)

Brandão, Fernando G. S. L.; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K.; Mozrzymas, Marek

2012-09-01

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

Dopamine reward prediction error responses reflect marginal utility.

PubMed

Stauffer, William R; Lak, Armin; Schultz, Wolfram

2014-11-03

Optimal choices require an accurate neuronal representation of economic value. In economics, utility functions are mathematical representations of subjective value that can be constructed from choices under risk. Utility usually exhibits a nonlinear relationship to physical reward value that corresponds to risk attitudes and reflects the increasing or decreasing marginal utility obtained with each additional unit of reward. Accordingly, neuronal reward responses coding utility should robustly reflect this nonlinearity. In two monkeys, we measured utility as a function of physical reward value from meaningful choices under risk (that adhered to first- and second-order stochastic dominance). The resulting nonlinear utility functions predicted the certainty equivalents for new gambles, indicating that the functions' shapes were meaningful. The monkeys were risk seeking (convex utility function) for low reward and risk avoiding (concave utility function) with higher amounts. Critically, the dopamine prediction error responses at the time of reward itself reflected the nonlinear utility functions measured at the time of choices. In particular, the reward response magnitude depended on the first derivative of the utility function and thus reflected the marginal utility. Furthermore, dopamine responses recorded outside of the task reflected the marginal utility of unpredicted reward. Accordingly, these responses were sufficient to train reinforcement learning models to predict the behaviorally defined expected utility of gambles. These data suggest a neuronal manifestation of marginal utility in dopamine neurons and indicate a common neuronal basis for fundamental explanatory constructs in animal learning theory (prediction error) and economic decision theory (marginal utility). Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

PubMed

Khoromskaia, Venera; Khoromskij, Boris N

2015-12-21

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

A hexagonal orthogonal-oriented pyramid as a model of image representation in visual cortex

NASA Technical Reports Server (NTRS)

Watson, Andrew B.; Ahumada, Albert J., Jr.

1989-01-01

Retinal ganglion cells represent the visual image with a spatial code, in which each cell conveys information about a small region in the image. In contrast, cells of the primary visual cortex use a hybrid space-frequency code in which each cell conveys information about a region that is local in space, spatial frequency, and orientation. A mathematical model for this transformation is described. The hexagonal orthogonal-oriented quadrature pyramid (HOP) transform, which operates on a hexagonal input lattice, uses basis functions that are orthogonal, self-similar, and localized in space, spatial frequency, orientation, and phase. The basis functions, which are generated from seven basic types through a recursive process, form an image code of the pyramid type. The seven basis functions, six bandpass and one low-pass, occupy a point and a hexagon of six nearest neighbors on a hexagonal lattice. The six bandpass basis functions consist of three with even symmetry, and three with odd symmetry. At the lowest level, the inputs are image samples. At each higher level, the input lattice is provided by the low-pass coefficients computed at the previous level. At each level, the output is subsampled in such a way as to yield a new hexagonal lattice with a spacing square root of 7 larger than the previous level, so that the number of coefficients is reduced by a factor of seven at each level. In the biological model, the input lattice is the retinal ganglion cell array. The resulting scheme provides a compact, efficient code of the image and generates receptive fields that resemble those of the primary visual cortex.

Coherent orthogonal polynomials

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

Celeghini, E., E-mail: celeghini@fi.infn.it; Olmo, M.A. del, E-mail: olmo@fta.uva.es

2013-08-15

We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we include thus–in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions–Lie algebra theory. We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard uncountable basis (|x〉), for an alternative countable basis (|n〉). The matrix elements that relatemore » these two bases are essentially the orthogonal polynomials: Hermite polynomials for the line and Laguerre and Legendre polynomials for the half-line and the line interval, respectively. Differential recurrence relations of orthogonal polynomials allow us to realize that they determine an infinite-dimensional irreducible representation of a non-compact Lie algebra, whose second order Casimir C gives rise to the second order differential equation that defines the corresponding family of orthogonal polynomials. Thus, the Weyl–Heisenberg algebra h(1) with C=0 for Hermite polynomials and su(1,1) with C=−1/4 for Laguerre and Legendre polynomials are obtained. Starting from the orthogonal polynomials the Lie algebra is extended both to the whole space of the L{sup 2} functions and to the corresponding Universal Enveloping Algebra and transformation group. Generalized coherent states from each vector in the space L{sup 2} and, in particular, generalized coherent polynomials are thus obtained. -- Highlights: •Fundamental characteristic of orthogonal polynomials (OP): existence of a Lie algebra. •Differential recurrence relations of OP determine a unitary representation of a non-compact Lie group. •2nd order Casimir originates a 2nd order differential equation that defines the corresponding OP family. •Generalized coherent polynomials are obtained from OP.« less

Specialization along the left superior temporal sulcus for auditory categorization.

PubMed

Liebenthal, Einat; Desai, Rutvik; Ellingson, Michael M; Ramachandran, Brinda; Desai, Anjali; Binder, Jeffrey R

2010-12-01

The affinity and temporal course of functional fields in middle and posterior superior temporal cortex for the categorization of complex sounds was examined using functional magnetic resonance imaging (fMRI) and event-related potentials (ERPs) recorded simultaneously. Data were compared before and after subjects were trained to categorize a continuum of unfamiliar nonphonemic auditory patterns with speech-like properties (NP) and a continuum of familiar phonemic patterns (P). fMRI activation for NP increased after training in left posterior superior temporal sulcus (pSTS). The ERP P2 response to NP also increased with training, and its scalp topography was consistent with left posterior superior temporal generators. In contrast, the left middle superior temporal sulcus (mSTS) showed fMRI activation only for P, and this response was not affected by training. The P2 response to P was also independent of training, and its estimated source was more anterior in left superior temporal cortex. Results are consistent with a role for left pSTS in short-term representation of relevant sound features that provide the basis for identifying newly acquired sound categories. Categorization of highly familiar phonemic patterns is mediated by long-term representations in left mSTS. Results provide new insight regarding the function of ventral and dorsal auditory streams.

Empirical Orthogonal Function (EOF) Analysis of Storm-Time GPS Total Electron Content Variations

NASA Astrophysics Data System (ADS)

Thomas, E. G.; Coster, A. J.; Zhang, S.; McGranaghan, R. M.; Shepherd, S. G.; Baker, J. B.; Ruohoniemi, J. M.

2016-12-01

Large perturbations in ionospheric density are known to occur during geomagnetic storms triggered by dynamic structures in the solar wind. These ionospheric storm effects have long attracted interest due to their impact on the propagation characteristics of radio wave communications. Over the last two decades, maps of vertically-integrated total electron content (TEC) based on data collected by worldwide networks of Global Positioning System (GPS) receivers have dramatically improved our ability to monitor the spatiotemporal dynamics of prominent storm-time features such as polar cap patches and storm enhanced density (SED) plumes. In this study, we use an empirical orthogonal function (EOF) decomposition technique to identify the primary modes of spatial and temporal variability in the storm-time GPS TEC response at midlatitudes over North America during more than 100 moderate geomagnetic storms from 2001-2013. We next examine the resulting time-varying principal components and their correlation with various geophysical indices and parameters in order to derive an analytical representation. Finally, we use a truncated reconstruction of the EOF basis functions and parameterization of the principal components to produce an empirical representation of the geomagnetic storm-time response of GPS TEC for all magnetic local times local times and seasons at midlatitudes in the North American sector.

Reformulation of Density Functional Theory for N-Representable Densities and the Resolution of the v-Representability Problem

DOE PAGES

Gonis, A.; Zhang, X. G.; Stocks, G. M.; ...

2015-10-23

Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide a complete solution of the v-representability problem by establishing a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of themore » density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism.« less

Toward an understanding of the cerebral substrates of woman's orgasm.

PubMed

Bianchi-Demicheli, Francesco; Ortigue, Stephanie

2007-09-20

The way women experience orgasm is of interest to scientists, clinicians, and laypeople. Whereas the origin and the function of a woman's orgasm remains controversial, the current models of sexual function acknowledge a combined role of central (spinal and cerebral) and peripheral processes during orgasm experience. At the central level, although it is accepted that the spinal cord drives orgasm, the cerebral involvement and cognitive representation of a woman's orgasm has not been extensively investigated. Important gaps in our knowledge remain. Recently, the astonishing advances of neuroimaging techniques applied in parallel with a neuropsychological approach allowed the unravelling of specific functional neuroanatomy of a woman's orgasm. Here, clinical and experimental findings on the cortico-subcortical pathway of a woman's orgasm are reviewed and compared with the neural basis of a man's orgasm. By defining the specific brain areas that sustain the assumed higher-order representation of a woman's orgasm, this review provides a foundation for future studies. The next challenge of functional imaging and neuropsychological studies is to understand the hierarchical interactions between these multiple cortical areas, not only with a correlation analysis but also with high spatio-temporal resolution techniques demonstrating the causal necessity, the temporal time course and the direction of the causality. Further studies using a multi-disciplinary approach are needed to identify the spatio-temporal dynamic of a woman's orgasm, its dysfunctions and possible new treatments.

A functional analysis of photo-object matching skills of severely retarded adolescents.

PubMed

Dixon, L S

1981-01-01

Matching-to-sample procedures were used to assess picture representation skills of severely retarded, nonverbal adolescents. Identity matching within the classes of objects and life-size, full-color photos of the objects was first used to assess visual discrimination, a necessary condition for picture representation. Picture representation was then assessed through photo-object matching tasks. Five students demonstrated visual discrimination (identity matching) within the two classes of photos and the objects. Only one student demonstrated photo-object matching. The results of the four students who failed to demonstrate photo-object matching suggested that physical properties of photos (flat, rectangular) and depth dimensions of objects may exert more control over matching than the similarities of the objects and images within the photos. An analysis of figure-ground variables was conducted to provide an empirical basis for program development in the use of pictures. In one series of tests, rectangular shape and background were removed by cutting out the figures in the photos. The edge shape of the photo and the edge shape of the image were then identical. The results suggest that photo-object matching may be facilitated by using cut-out figures rather than the complete rectangular photo.

Music as Environment: An Ecological and Biosemiotic Approach

PubMed Central

Reybrouck, Mark

2014-01-01

This paper provides an attempt to conceive of music in terms of a sounding environment. Starting from a definition of music as a collection of vibrational events, it introduces the distinction between discrete-symbolic representations as against analog-continuous representations of the sounds. The former makes it possible to conceive of music in terms of a Humboldt system, the latter in terms of an experiential approach. Both approaches, further, are not opposed to each other, but are complementary to some extent. There is, however, a distinction to be drawn between the bottom-up approach to auditory processing of environmental sounds and music, which is continuous and proceeding in real time, as against the top-down approach, which is proceeding at a level of mental representation by applying discrete symbolic labels to vibrational events. The distinction is discussed against the background of phylogenetic and ontogenetic claims, with a major focus on the innate auditory capabilities of the fetus and neonate and the gradual evolution from mere sensory perception of sound to sense-making and musical meaning. The latter, finally, is elaborated on the basis of the operational concepts of affordance and functional tone, thus bringing together some older contributions from ecology and biosemiotics. PMID:25545707

Toroidal gyro-Landau fluid model turbulence simulations in a nonlinear ballooning mode representation with radial modes

NASA Astrophysics Data System (ADS)

Waltz, R. E.; Kerbel, G. D.; Milovich, J.

1994-07-01

The method of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] to model Landau damping has been recently applied to the moments of the gyrokinetic equation with curvature drift by Waltz, Dominguez, and Hammett [Phys. Fluids B 4, 3138 (1992)]. The higher moments are truncated in terms of the lower moments (density, parallel velocity, and parallel and perpendicular pressure) by modeling the deviation from a perturbed Maxwellian to fit the kinetic response function at all values of the kinetic parameters: k∥vth/ω, b=(k⊥ρ)2/2, and ωD/ω. Here the resulting gyro-Landau fluid equations are applied to the simulation of ion temperature gradient (ITG) mode turbulence in toroidal geometry using a novel three-dimensional (3-D) nonlinear ballooning mode representation. The representation is a Fourier transform of a field line following basis (ky',kx',z') with periodicity in toroidal and poloidal angles. Particular emphasis is given to the role of nonlinearly generated n=0 (ky' = 0, kx' ≠ 0) ``radial modes'' in stabilizing the transport from the finite-n ITG ballooning modes. Detailing the parametric dependence of toroidal ITG turbulence is a key result.

Toroidal turbulence simulations with gyro-Landau fluid models in a nonlinear ballooning mode representation

NASA Astrophysics Data System (ADS)

Waltz, R. E.; Kerbel, G. D.

1994-05-01

The method of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] to model Landau damping has been recently applied to the moments of the gyro-kinetic equation with curvature drift by Waltz, Dominguez, and Hammett [Phys. Fluids B 4, 3138 (1992)]. The higher moments are truncated in terms of the lower moments (density, parallel velocity, and parallel and perpendicular pressure) by modeling the deviation from a perturbed Maxwellian to fit the kinetic response function at all values of the kinetic parameters: k∥vth/ω, b=(k⊥ρ)2/2, and ωD/ω. Here the resulting gyro-Landau fluid equations are applied to the simulation of ion temperature gradient (ITG) mode turbulence in toroidal geometry using a novel 3D nonlinear ballooning mode representation. The representation is a Fourier transform of the Cowley et al. [Phys. Fluids B 3, 2767 (1991)] field line following twisted eddy basis (kx',ky',z') with periodicity in toroidal and poloidal angles. Particular emphasis is given to the role of nonlinearly generated n=0 (ky'=0, kx'≠0) ``radial modes'' in stabilizing the transport from the finite-n ITG ballooning modes.

Space-Time and Architecture

NASA Astrophysics Data System (ADS)

Field, F.; Goodbun, J.; Watson, V.

Architects have a role to play in interplanetary space that has barely yet been explored. The architectural community is largely unaware of this new territory, for which there is still no agreed method of practice. There is moreover a general confusion, in scientific and related fields, over what architects might actually do there today. Current extra-planetary designs generally fail to explore the dynamic and relational nature of space-time, and often reduce human habitation to a purely functional problem. This is compounded by a crisis over the representation (drawing) of space-time. The present work returns to first principles of architecture in order to realign them with current socio-economic and technological trends surrounding the space industry. What emerges is simultaneously the basis for an ecological space architecture, and the representational strategies necessary to draw it. We explore this approach through a work of design-based research that describes the construction of Ocean; a huge body of water formed by the collision of two asteroids at the Translunar Lagrange Point (L2), that would serve as a site for colonisation, and as a resource to fuel future missions. Ocean is an experimental model for extra-planetary space design and its representation, within the autonomous discipline of architecture.

Reflected ray retrieval from radio occultation data using radio holographic filtering of wave fields in ray space

NASA Astrophysics Data System (ADS)

Gorbunov, Michael E.; Cardellach, Estel; Lauritsen, Kent B.

2018-03-01

Linear and non-linear representations of wave fields constitute the basis of modern algorithms for analysis of radio occultation (RO) data. Linear representations are implemented by Fourier Integral Operators, which allow for high-resolution retrieval of bending angles. Non-linear representations include Wigner Distribution Function (WDF), which equals the pseudo-density of energy in the ray space. Representations allow for filtering wave fields by suppressing some areas of the ray space and mapping the field back from the transformed space to the initial one. We apply this technique to the retrieval of reflected rays from RO observations. The use of reflected rays may increase the accuracy of the retrieval of the atmospheric refractivity. Reflected rays can be identified by the visual inspection of WDF or spectrogram plots. Numerous examples from COSMIC data indicate that reflections are mostly observed over oceans or snow, in particular over Antarctica. We introduce the reflection index that characterizes the relative intensity of the reflected ray with respect to the direct ray. The index allows for the automatic identification of events with reflections. We use the radio holographic estimate of the errors of the retrieved bending angle profiles of reflected rays. A comparison of indices evaluated for a large base of events including the visual identification of reflections indicated a good agreement with our definition of reflection index.

Perceptual Learning Selectively Refines Orientation Representations in Early Visual Cortex

PubMed Central

Jehee, Janneke F.M.; Ling, Sam; Swisher, Jascha D.; van Bergen, Ruben S.; Tong, Frank

2013-01-01

Although practice has long been known to improve perceptual performance, the neural basis of this improvement in humans remains unclear. Using fMRI in conjunction with a novel signal detection-based analysis, we show that extensive practice selectively enhances the neural representation of trained orientations in the human visual cortex. Twelve observers practiced discriminating small changes in the orientation of a laterally presented grating over 20 or more daily one-hour training sessions. Training on average led to a two-fold improvement in discrimination sensitivity, specific to the trained orientation and the trained location, with minimal improvement found for untrained orthogonal orientations or for orientations presented in the untrained hemifield. We measured the strength of orientation-selective responses in individual voxels in early visual areas (V1–V4) using signal detection measures, both pre- and post-training. Although the overall amplitude of the BOLD response was no greater after training, practice nonetheless specifically enhanced the neural representation of the trained orientation at the trained location. This training-specific enhancement of orientation-selective responses was observed in the primary visual cortex (V1) as well as higher extrastriate visual areas V2–V4, and moreover, reliably predicted individual differences in the behavioral effects of perceptual learning. These results demonstrate that extensive training can lead to targeted functional reorganization of the human visual cortex, refining the cortical representation of behaviorally relevant information. PMID:23175828

Perceptual learning selectively refines orientation representations in early visual cortex.

PubMed

Jehee, Janneke F M; Ling, Sam; Swisher, Jascha D; van Bergen, Ruben S; Tong, Frank

2012-11-21

Although practice has long been known to improve perceptual performance, the neural basis of this improvement in humans remains unclear. Using fMRI in conjunction with a novel signal detection-based analysis, we show that extensive practice selectively enhances the neural representation of trained orientations in the human visual cortex. Twelve observers practiced discriminating small changes in the orientation of a laterally presented grating over 20 or more daily 1 h training sessions. Training on average led to a twofold improvement in discrimination sensitivity, specific to the trained orientation and the trained location, with minimal improvement found for untrained orthogonal orientations or for orientations presented in the untrained hemifield. We measured the strength of orientation-selective responses in individual voxels in early visual areas (V1-V4) using signal detection measures, both before and after training. Although the overall amplitude of the BOLD response was no greater after training, practice nonetheless specifically enhanced the neural representation of the trained orientation at the trained location. This training-specific enhancement of orientation-selective responses was observed in the primary visual cortex (V1) as well as higher extrastriate visual areas V2-V4, and moreover, reliably predicted individual differences in the behavioral effects of perceptual learning. These results demonstrate that extensive training can lead to targeted functional reorganization of the human visual cortex, refining the cortical representation of behaviorally relevant information.

Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI.

PubMed

Cheng, Jian; Deriche, Rachid; Jiang, Tianzi; Shen, Dinggang; Yap, Pew-Thian

2014-11-01

Spherical Deconvolution (SD) is commonly used for estimating fiber Orientation Distribution Functions (fODFs) from diffusion-weighted signals. Existing SD methods can be classified into two categories: 1) Continuous Representation based SD (CR-SD), where typically Spherical Harmonic (SH) representation is used for convenient analytical solutions, and 2) Discrete Representation based SD (DR-SD), where the signal profile is represented by a discrete set of basis functions uniformly oriented on the unit sphere. A feasible fODF should be non-negative and should integrate to unity throughout the unit sphere S(2). However, to our knowledge, most existing SH-based SD methods enforce non-negativity only on discretized points and not the whole continuum of S(2). Maximum Entropy SD (MESD) and Cartesian Tensor Fiber Orientation Distributions (CT-FOD) are the only SD methods that ensure non-negativity throughout the unit sphere. They are however computational intensive and are susceptible to errors caused by numerical spherical integration. Existing SD methods are also known to overestimate the number of fiber directions, especially in regions with low anisotropy. DR-SD introduces additional error in peak detection owing to the angular discretization of the unit sphere. This paper proposes a SD framework, called Non-Negative SD (NNSD), to overcome all the limitations above. NNSD is significantly less susceptible to the false-positive peaks, uses SH representation for efficient analytical spherical deconvolution, and allows accurate peak detection throughout the whole unit sphere. We further show that NNSD and most existing SD methods can be extended to work on multi-shell data by introducing a three-dimensional fiber response function. We evaluated NNSD in comparison with Constrained SD (CSD), a quadratic programming variant of CSD, MESD, and an L1-norm regularized non-negative least-squares DR-SD. Experiments on synthetic and real single-/multi-shell data indicate that NNSD improves estimation performance in terms of mean difference of angles, peak detection consistency, and anisotropy contrast between isotropic and anisotropic regions. Copyright © 2014 Elsevier Inc. All rights reserved.

Structure and energetics of Cr(CO)6 and Cr(CO)5

NASA Technical Reports Server (NTRS)

Barnes, Leslie A.; Liu, Bowen; Lindh, Roland

1993-01-01

The geometric structures and energetics of Cr(CO)6 and Cr(CO)5 are determined at the modified coupled-pair functional, single and double excitation coupled-cluster (CCSD), and CCSD(T) levels of theory. For Cr(CO)6, the structure and force constants for the totally symmetric representation are in good agreement with experimental data once basis set constants are taken into account. In the largest basis set at the CCSD(T) level of theory, the total binding energy of CR(CO)6 is estimated at around 140 kcal/mol, or about 86 percent of the experimental value. In contrast, the first bond energy of Cr(CO)6 is very well described at the CCSD(T) level of theory, with the best estimated value of 38 kcal/mol being within the experimental uncertainty.

Distributed Compressive Sensing

DTIC Science & Technology

2009-01-01

example, smooth signals are sparse in the Fourier basis, and piecewise smooth signals are sparse in a wavelet basis [8]; the commercial coding standards MP3...including wavelets [8], Gabor bases [8], curvelets [35], etc., are widely used for representation and compression of natural signals, images, and...spikes and the sine waves of a Fourier basis, or the Fourier basis and wavelets . Signals that are sparsely represented in frames or unions of bases can

A Unified Graphical Representation of Chemical Thermodynamics and Equilibrium

ERIC Educational Resources Information Center

Hanson, Robert M.

2012-01-01

During the years 1873-1879, J. Willard Gibbs published his now-famous set of articles that form the basis of the current perspective on chemical thermodynamics. The second article of this series, "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces," published in 1873, is particularly notable…

Attractor Dynamics and Semantic Neighborhood Density: Processing Is Slowed by Near Neighbors and Speeded by Distant Neighbors

ERIC Educational Resources Information Center

Mirman, Daniel; Magnuson, James S.

2008-01-01

The authors investigated semantic neighborhood density effects on visual word processing to examine the dynamics of activation and competition among semantic representations. Experiment 1 validated feature-based semantic representations as a basis for computing semantic neighborhood density and suggested that near and distant neighbors have…

Forming Tool Use Representations: A Neurophysiological Investigation into Tool Exposure

ERIC Educational Resources Information Center

Mizelle, John Christopher; Tang, Teresa; Pirouz, Nikta; Wheaton, Lewis A.

2011-01-01

Prior work has identified a common left parietofrontal network for storage of tool-related information for various tasks. How these representations become established within this network on the basis of different modes of exposure is unclear. Here, healthy subjects engaged in physical practice (direct exposure) with familiar and unfamiliar tools.…

The Representation of Bilingual Mental Lexicon and English Vocabulary Acquisition

ERIC Educational Resources Information Center

Ying, Zhang

2017-01-01

This paper provides an overview of the theories on the organization and development of L1 mental lexicon and the representation mode of bilingual mental lexicon. It analyzes the structure and characteristics of Chinese EFL learners and their problems in English vocabulary acquisition. On the basis of this, it suggests that English vocabulary…

Neural representation of consciously imperceptible speech sound differences.

PubMed

Allen, J; Kraus, N; Bradlow, A

2000-10-01

The concept of subliminal perception has been a subject of interest and controversy for decades. Of interest in the present investigation was whether a neurophysiologic index of stimulus change could be elicited to speech sound contrasts that were consciously indiscriminable. The stimuli were chosen on the basis of each individual subject's discrimination threshold. The speech stimuli (which varied along an F3 onset frequency continuum from /da/ to /ga/) were synthesized so that the acoustical properties of the stimuli could be tightly controlled. Subthreshold and suprathreshold stimuli were chosen on the basis of behavioral ability demonstrated during psychophysical testing. A significant neural representation of stimulus change, reflected by the mismatch negativity response, was obtained in all but 1 subject in response to subthreshold stimuli. Grand average responses differed significantly from responses obtained in a control condition consisting of physiologic responses elicited by physically identical stimuli. Furthermore, responses to suprathreshold stimuli (close to threshold) did not differ significantly from subthreshold responses with respect to latency, amplitude, or area. These results suggest that neural representation of consciously imperceptible stimulus differences occurs and that this representation occurs at a preattentive level.

An unbiased Hessian representation for Monte Carlo PDFs.

PubMed

Carrazza, Stefano; Forte, Stefano; Kassabov, Zahari; Latorre, José Ignacio; Rojo, Juan

We develop a methodology for the construction of a Hessian representation of Monte Carlo sets of parton distributions, based on the use of a subset of the Monte Carlo PDF replicas as an unbiased linear basis, and of a genetic algorithm for the determination of the optimal basis. We validate the methodology by first showing that it faithfully reproduces a native Monte Carlo PDF set (NNPDF3.0), and then, that if applied to Hessian PDF set (MMHT14) which was transformed into a Monte Carlo set, it gives back the starting PDFs with minimal information loss. We then show that, when applied to a large Monte Carlo PDF set obtained as combination of several underlying sets, the methodology leads to a Hessian representation in terms of a rather smaller set of parameters (MC-H PDFs), thereby providing an alternative implementation of the recently suggested Meta-PDF idea and a Hessian version of the recently suggested PDF compression algorithm (CMC-PDFs). The mc2hessian conversion code is made publicly available together with (through LHAPDF6) a Hessian representations of the NNPDF3.0 set, and the MC-H PDF set.

ODF Maxima Extraction in Spherical Harmonic Representation via Analytical Search Space Reduction

PubMed Central

Aganj, Iman; Lenglet, Christophe; Sapiro, Guillermo

2015-01-01

By revealing complex fiber structure through the orientation distribution function (ODF), q-ball imaging has recently become a popular reconstruction technique in diffusion-weighted MRI. In this paper, we propose an analytical dimension reduction approach to ODF maxima extraction. We show that by expressing the ODF, or any antipodally symmetric spherical function, in the common fourth order real and symmetric spherical harmonic basis, the maxima of the two-dimensional ODF lie on an analytically derived one-dimensional space, from which we can detect the ODF maxima. This method reduces the computational complexity of the maxima detection, without compromising the accuracy. We demonstrate the performance of our technique on both artificial and human brain data. PMID:20879302

Novel Spectral Representations and Sparsity-Driven Algorithms for Shape Modeling and Analysis

NASA Astrophysics Data System (ADS)

Zhong, Ming

In this dissertation, we focus on extending classical spectral shape analysis by incorporating spectral graph wavelets and sparsity-seeking algorithms. Defined with the graph Laplacian eigenbasis, the spectral graph wavelets are localized both in the vertex domain and graph spectral domain, and thus are very effective in describing local geometry. With a rich dictionary of elementary vectors and forcing certain sparsity constraints, a real life signal can often be well approximated by a very sparse coefficient representation. The many successful applications of sparse signal representation in computer vision and image processing inspire us to explore the idea of employing sparse modeling techniques with dictionary of spectral basis to solve various shape modeling problems. Conventional spectral mesh compression uses the eigenfunctions of mesh Laplacian as shape bases, which are highly inefficient in representing local geometry. To ameliorate, we advocate an innovative approach to 3D mesh compression using spectral graph wavelets as dictionary to encode mesh geometry. The spectral graph wavelets are locally defined at individual vertices and can better capture local shape information than Laplacian eigenbasis. The multi-scale SGWs form a redundant dictionary as shape basis, so we formulate the compression of 3D shape as a sparse approximation problem that can be readily handled by greedy pursuit algorithms. Surface inpainting refers to the completion or recovery of missing shape geometry based on the shape information that is currently available. We devise a new surface inpainting algorithm founded upon the theory and techniques of sparse signal recovery. Instead of estimating the missing geometry directly, our novel method is to find this low-dimensional representation which describes the entire original shape. More specifically, we find that, for many shapes, the vertex coordinate function can be well approximated by a very sparse coefficient representation with respect to the dictionary comprising its Laplacian eigenbasis, and it is then possible to recover this sparse representation from partial measurements of the original shape. Taking advantage of the sparsity cue, we advocate a novel variational approach for surface inpainting, integrating data fidelity constraints on the shape domain with coefficient sparsity constraints on the transformed domain. Because of the powerful properties of Laplacian eigenbasis, the inpainting results of our method tend to be globally coherent with the remaining shape. Informative and discriminative feature descriptors are vital in qualitative and quantitative shape analysis for a large variety of graphics applications. We advocate novel strategies to define generalized, user-specified features on shapes. Our new region descriptors are primarily built upon the coefficients of spectral graph wavelets that are both multi-scale and multi-level in nature, consisting of both local and global information. Based on our novel spectral feature descriptor, we developed a user-specified feature detection framework and a tensor-based shape matching algorithm. Through various experiments, we demonstrate the competitive performance of our proposed methods and the great potential of spectral basis and sparsity-driven methods for shape modeling.

Goal-Function Tree Modeling for Systems Engineering and Fault Management

NASA Technical Reports Server (NTRS)

Patterson, Jonathan D.; Johnson, Stephen B.

2013-01-01

The draft NASA Fault Management (FM) Handbook (2012) states that Fault Management (FM) is a "part of systems engineering", and that it "demands a system-level perspective" (NASAHDBK- 1002, 7). What, exactly, is the relationship between systems engineering and FM? To NASA, systems engineering (SE) is "the art and science of developing an operable system capable of meeting requirements within often opposed constraints" (NASA/SP-2007-6105, 3). Systems engineering starts with the elucidation and development of requirements, which set the goals that the system is to achieve. To achieve these goals, the systems engineer typically defines functions, and the functions in turn are the basis for design trades to determine the best means to perform the functions. System Health Management (SHM), by contrast, defines "the capabilities of a system that preserve the system's ability to function as intended" (Johnson et al., 2011, 3). Fault Management, in turn, is the operational subset of SHM, which detects current or future failures, and takes operational measures to prevent or respond to these failures. Failure, in turn, is the "unacceptable performance of intended function." (Johnson 2011, 605) Thus the relationship of SE to FM is that SE defines the functions and the design to perform those functions to meet system goals and requirements, while FM detects the inability to perform those functions and takes action. SHM and FM are in essence "the dark side" of SE. For every function to be performed (SE), there is the possibility that it is not successfully performed (SHM); FM defines the means to operationally detect and respond to this lack of success. We can also describe this in terms of goals: for every goal to be achieved, there is the possibility that it is not achieved; FM defines the means to operationally detect and respond to this inability to achieve the goal. This brief description of relationships between SE, SHM, and FM provide hints to a modeling approach to provide formal connectivity between the nominal (SE), and off-nominal (SHM and FM) aspects of functions and designs. This paper describes a formal modeling approach to the initial phases of the development process that integrates the nominal and off-nominal perspectives in a model that unites SE goals and functions of with the failure to achieve goals and functions (SHM/FM). This methodology and corresponding model, known as a Goal-Function Tree (GFT), provides a means to represent, decompose, and elaborate system goals and functions in a rigorous manner that connects directly to design through use of state variables that translate natural language requirements and goals into logical-physical state language. The state variable-based approach also provides the means to directly connect FM to the design, by specifying the range in which state variables must be controlled to achieve goals, and conversely, the failures that exist if system behavior go out-of-range. This in turn allows for the systems engineers and SHM/FM engineers to determine which state variables to monitor, and what action(s) to take should the system fail to achieve that goal. In sum, the GFT representation provides a unified approach to early-phase SE and FM development. This representation and methodology has been successfully developed and implemented using Systems Modeling Language (SysML) on the NASA Space Launch System (SLS) Program. It enabled early design trade studies of failure detection coverage to ensure complete detection coverage of all crew-threatening failures. The representation maps directly both to FM algorithm designs, and to failure scenario definitions needed for design analysis and testing. The GFT representation provided the basis for mapping of abort triggers into scenarios, both needed for initial, and successful quantitative analyses of abort effectiveness (detection and response to crew-threatening events).

Animacy and real-world size shape object representations in the human medial temporal lobes.

PubMed

Blumenthal, Anna; Stojanoski, Bobby; Martin, Chris B; Cusack, Rhodri; Köhler, Stefan

2018-06-26

Identifying what an object is, and whether an object has been encountered before, is a crucial aspect of human behavior. Despite this importance, we do not yet have a complete understanding of the neural basis of these abilities. Investigations into the neural organization of human object representations have revealed category specific organization in the ventral visual stream in perceptual tasks. Interestingly, these categories fall within broader domains of organization, with reported distinctions between animate, inanimate large, and inanimate small objects. While there is some evidence for category specific effects in the medial temporal lobe (MTL), in particular in perirhinal and parahippocampal cortex, it is currently unclear whether domain level organization is also present across these structures. To this end, we used fMRI with a continuous recognition memory task. Stimuli were images of objects from several different categories, which were either animate or inanimate, or large or small within the inanimate domain. We employed representational similarity analysis (RSA) to test the hypothesis that object-evoked responses in MTL structures during recognition-memory judgments also show evidence for domain-level organization along both dimensions. Our data support this hypothesis. Specifically, object representations were shaped by either animacy, real-world size, or both, in perirhinal and parahippocampal cortex, and the hippocampus. While sensitivity to these dimensions differed across structures when probed individually, hinting at interesting links to functional differentiation, similarities in organization across MTL structures were more prominent overall. These results argue for continuity in the organization of object representations in the ventral visual stream and the MTL. © 2018 Wiley Periodicals, Inc.

Gaussian Process Regression (GPR) Representation in Predictive Model Markup Language (PMML)

PubMed Central

Lechevalier, D.; Ak, R.; Ferguson, M.; Law, K. H.; Lee, Y.-T. T.; Rachuri, S.

2017-01-01

This paper describes Gaussian process regression (GPR) models presented in predictive model markup language (PMML). PMML is an extensible-markup-language (XML) -based standard language used to represent data-mining and predictive analytic models, as well as pre- and post-processed data. The previous PMML version, PMML 4.2, did not provide capabilities for representing probabilistic (stochastic) machine-learning algorithms that are widely used for constructing predictive models taking the associated uncertainties into consideration. The newly released PMML version 4.3, which includes the GPR model, provides new features: confidence bounds and distribution for the predictive estimations. Both features are needed to establish the foundation for uncertainty quantification analysis. Among various probabilistic machine-learning algorithms, GPR has been widely used for approximating a target function because of its capability of representing complex input and output relationships without predefining a set of basis functions, and predicting a target output with uncertainty quantification. GPR is being employed to various manufacturing data-analytics applications, which necessitates representing this model in a standardized form for easy and rapid employment. In this paper, we present a GPR model and its representation in PMML. Furthermore, we demonstrate a prototype using a real data set in the manufacturing domain. PMID:29202125

Gaussian Process Regression (GPR) Representation in Predictive Model Markup Language (PMML).

PubMed

Park, J; Lechevalier, D; Ak, R; Ferguson, M; Law, K H; Lee, Y-T T; Rachuri, S

2017-01-01

This paper describes Gaussian process regression (GPR) models presented in predictive model markup language (PMML). PMML is an extensible-markup-language (XML) -based standard language used to represent data-mining and predictive analytic models, as well as pre- and post-processed data. The previous PMML version, PMML 4.2, did not provide capabilities for representing probabilistic (stochastic) machine-learning algorithms that are widely used for constructing predictive models taking the associated uncertainties into consideration. The newly released PMML version 4.3, which includes the GPR model, provides new features: confidence bounds and distribution for the predictive estimations. Both features are needed to establish the foundation for uncertainty quantification analysis. Among various probabilistic machine-learning algorithms, GPR has been widely used for approximating a target function because of its capability of representing complex input and output relationships without predefining a set of basis functions, and predicting a target output with uncertainty quantification. GPR is being employed to various manufacturing data-analytics applications, which necessitates representing this model in a standardized form for easy and rapid employment. In this paper, we present a GPR model and its representation in PMML. Furthermore, we demonstrate a prototype using a real data set in the manufacturing domain.

A Deterministic Transport Code for Space Environment Electrons

NASA Technical Reports Server (NTRS)

Nealy, John E.; Chang, C. K.; Norman, Ryan B.; Blattnig, Steve R.; Badavi, Francis F.; Adamczyk, Anne M.

2010-01-01

A deterministic computational procedure has been developed to describe transport of space environment electrons in various shield media. This code is an upgrade and extension of an earlier electron code. Whereas the former code was formulated on the basis of parametric functions derived from limited laboratory data, the present code utilizes well established theoretical representations to describe the relevant interactions and transport processes. The shield material specification has been made more general, as have the pertinent cross sections. A combined mean free path and average trajectory approach has been used in the transport formalism. Comparisons with Monte Carlo calculations are presented.

Enhancing sparsity of Hermite polynomial expansions by iterative rotations

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

Yang, Xiu; Lei, Huan; Baker, Nathan A.

2016-02-01

Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more sparse with new basis functions associated with the new random variables. This sparsity increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. Specifically, we consider rotation- based linear mappings which are determined iteratively for Hermite polynomial expansions. We demonstrate the effectiveness of the new method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.

Neurosemantics, neurons and system theory.

PubMed

Breidbach, Olaf

2007-08-01

Following the concept of internal representations, signal processing in a neuronal system has to be evaluated exclusively based on internal system characteristics. Thus, this approach omits the external observer as a control function for sensory integration. Instead, the configuration of the system and its computational performance are the effects of endogenous factors. Such self-referential operation is due to a strictly local computation in a network and, thereby, computations follow a set of rules that constitute the emergent behaviour of the system. These rules can be shown to correspond to a "logic" that is intrinsic to the system, an idea which provides the basis for neurosemantics.

Utilization of group theory in studies of molecular clusters

NASA Astrophysics Data System (ADS)

Ocak, Mahir E.

The structure of the molecular symmetry group of molecular clusters was analyzed and it is shown that the molecular symmetry group of a molecular cluster can be written as direct products and semidirect products of its subgroups. Symmetry adaptation of basis functions in direct product groups and semidirect product groups was considered in general and the sequential symmetry adaptation procedure which is already known for direct product groups was extended to the case of semidirect product groups. By using the sequential symmetry adaptation procedure a new method for calculating the VRT spectra of molecular clusters which is named as Monomer Basis Representation (MBR) method is developed. In the MBR method, calculations starts with a single monomer with the purpose of obtaining an optimized basis for that monomer as a linear combination of some primitive basis functions. Then, an optimized basis for each identical monomer is generated from the optimized basis of this monomer. By using the optimized bases of the monomers, a basis is generated generated for the solution of the full problem, and the VRT spectra of the cluster is obtained by using this basis. Since an optimized basis is used for each monomer which has a much smaller size than the primitive basis from which the optimized bases are generated, the MBR method leads to an exponential optimization in the size of the basis that is required for the calculations. Application of the MBR method has been illustrated by calculating the VRT spectra of water dimer by using the SAPT-5st potential surface of Groenenboom et al. The rest of the calculations are in good agreement with both the original calculations of Groenenboom et al. and also with the experimental results. Comparing the size of the optimized basis with the size of the primitive basis, it can be said that the method works efficiently. Because of its efficiency, the MBR method can be used for studies of clusters bigger than dimers. Thus, MBR method can be used for studying the many-body terms and for deriving accurate potential surfaces.

The neural basis of human social values: evidence from functional MRI.

PubMed

Zahn, Roland; Moll, Jorge; Paiva, Mirella; Garrido, Griselda; Krueger, Frank; Huey, Edward D; Grafman, Jordan

2009-02-01

Social values are composed of social concepts (e.g., "generosity") and context-dependent moral sentiments (e.g., "pride"). The neural basis of this intricate cognitive architecture has not been investigated thus far. Here, we used functional magnetic resonance imaging while subjects imagined their own actions toward another person (self-agency) which either conformed or were counter to a social value and were associated with pride or guilt, respectively. Imagined actions of another person toward the subjects (other-agency) in accordance with or counter to a value were associated with gratitude or indignation/anger. As hypothesized, superior anterior temporal lobe (aTL) activity increased with conceptual detail in all conditions. During self-agency, activity in the anterior ventromedial prefrontal cortex correlated with pride and guilt, whereas activity in the subgenual cingulate solely correlated with guilt. In contrast, indignation/anger activated lateral orbitofrontal-insular cortices. Pride and gratitude additionally evoked mesolimbic and basal forebrain activations. Our results demonstrate that social values emerge from coactivation of stable abstract social conceptual representations in the superior aTL and context-dependent moral sentiments encoded in fronto-mesolimbic regions. This neural architecture may provide the basis of our ability to communicate about the meaning of social values across cultural contexts without limiting our flexibility to adapt their emotional interpretation.

A Distributed, Developmental Model of Word Recognition and Naming

DTIC Science & Technology

1989-07-14

reading and clues to their neurophysiological bases (Patterson, M. Coltheart & Marshall, 1986). Our model provides the basis for an account of some aspects...is that distributed representations provide a basis for making lexical decisions; moreover, the model provides an enlightening account of some

The Prosodic Basis of the Tiberian Hebrew System of Accents.

ERIC Educational Resources Information Center

Dresher, Bezalel Elan

1994-01-01

It is argued that the Tiberian system of accents that annotate the text of the Hebrew Bible has a prosodic basis. Tiberian representation can best be understood by integrating results of phonological, phonetic, and psycholinguistic research on prosodic structure. (93 references) (Author/LB)

Parental Socioeconomic Status and the Neural Basis of Arithmetic: Differential Relations to Verbal and Visuo-Spatial Representations

ERIC Educational Resources Information Center

Demir, Özlem Ece; Prado, Jérôme; Booth, James R.

2015-01-01

We examined the relation of parental socioeconomic status (SES) to the neural bases of subtraction in school-age children (9- to 12-year-olds). We independently localized brain regions subserving verbal versus visuo-spatial representations to determine whether the parental SES-related differences in children's reliance on these neural…

Representation and Analysis of Chemistry Core Ideas in Science Education Standards between China and the United States

ERIC Educational Resources Information Center

Wan, Yanlan; Bi, Hualin

2016-01-01

Chemistry core ideas play an important role in students' chemistry learning. On the basis of the representations of chemistry core ideas about "substances" and "processes" in the Chinese Chemistry Curriculum Standards (CCCS) and the U.S. Next Generation Science Standards (NGSS), we conduct a critical comparison of chemistry…

(Re)Presentations of Islam in Albanian History Textbooks from 1990 to 2013

ERIC Educational Resources Information Center

Sulstarova, Enis

2017-01-01

This article investigates the role of Islam in representations of the self and the other in the contemporary Albanian national discourse, on the basis of an analysis of history textbooks published in postcommunist Albania between 1990 and 2013, focusing specifcally on texts used in pre-university education. Even after the dissolution of the…

Red Onions, "Elodea," or Decalcified Chicken Eggs? Selecting & Sequencing Representations for Teaching Diffusion & Osmosis

ERIC Educational Resources Information Center

Lankford, Deanna; Friedrichsen, Patricia

2012-01-01

Diffusion and osmosis are important biological concepts that students often struggle to understand. These are important concepts because they are the basis for many complex biological processes, such as photosynthesis and cellular respiration. We examine a wide variety of representations used by experienced teachers to teach diffusion and osmosis.…

Application of Radial Basis Functional Link Networks to Exploration for Proterozoic Mineral Deposits in Central Iran

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

Behnia, Pouran

2007-06-15

The metallogeny of Central Iran is characterized mainly by the presence of several iron, apatite, and uranium deposits of Proterozoic age. Radial Basis Function Link Networks (RBFLN) were used as a data-driven method for GIS-based predictive mapping of Proterozoic mineralization in this area. To generate the input data for RBFLN, the evidential maps comprising stratigraphic, structural, geophysical, and geochemical data were used. Fifty-eight deposits and 58 'nondeposits' were used to train the network. The operations for the application of neural networks employed in this study involve both multiclass and binary representation of evidential maps. Running RBFLN on different input datamore » showed that an increase in the number of evidential maps and classes leads to a larger classification sum of squared error (SSE). As a whole, an increase in the number of iterations resulted in the improvement of training SSE. The results of applying RBFLN showed that a successful classification depends on the existence of spatially well distributed deposits and nondeposits throughout the study area.« less

Spatial Bayesian Latent Factor Regression Modeling of Coordinate-based Meta-analysis Data

PubMed Central

Montagna, Silvia; Wager, Tor; Barrett, Lisa Feldman; Johnson, Timothy D.; Nichols, Thomas E.

2017-01-01

Summary Now over 20 years old, functional MRI (fMRI) has a large and growing literature that is best synthesised with meta-analytic tools. As most authors do not share image data, only the peak activation coordinates (foci) reported in the paper are available for Coordinate-Based Meta-Analysis (CBMA). Neuroimaging meta-analysis is used to 1) identify areas of consistent activation; and 2) build a predictive model of task type or cognitive process for new studies (reverse inference). To simultaneously address these aims, we propose a Bayesian point process hierarchical model for CBMA. We model the foci from each study as a doubly stochastic Poisson process, where the study-specific log intensity function is characterised as a linear combination of a high-dimensional basis set. A sparse representation of the intensities is guaranteed through latent factor modeling of the basis coefficients. Within our framework, it is also possible to account for the effect of study-level covariates (meta-regression), significantly expanding the capabilities of the current neuroimaging meta-analysis methods available. We apply our methodology to synthetic data and neuroimaging meta-analysis datasets. PMID:28498564

Shared and Distinctive Origins and Correlates of Adult Attachment Representations: The Developmental Organization of Romantic Functioning

PubMed Central

Haydon, Katherine C.; Collins, W. Andrew; Salvatore, Jessica E.; Simpson, Jeffry A.; Roisman, Glenn I.

2012-01-01

To test proposals regarding the hierarchical organization of adult attachment, this study examined developmental origins of generalized and romantic attachment representations and their concurrent associations with romantic functioning. Participants (N = 112) in a 35-year prospective study completed the Adult Attachment Interview (AAI) and Current Relationship Interview (CRI). Two-way ANOVAs tested interactive associations of AAI and CRI security with infant attachment, early parenting quality, preschool ego resiliency, adolescent friendship quality, and adult romantic functioning. Both representations were associated with earlier parenting and core attachment-related romantic behavior, but romantic representations had distinctive links to ego resiliency and relationship-specific romantic behaviors. Attachment representations were independent and did not interactively predict romantic functioning, suggesting that they confer somewhat distinctive benefits for romantic functioning. PMID:22694197

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

Wavelet based free-form deformations for nonrigid registration

NASA Astrophysics Data System (ADS)

Sun, Wei; Niessen, Wiro J.; Klein, Stefan

2014-03-01

In nonrigid registration, deformations may take place on the coarse and fine scales. For the conventional B-splines based free-form deformation (FFD) registration, these coarse- and fine-scale deformations are all represented by basis functions of a single scale. Meanwhile, wavelets have been proposed as a signal representation suitable for multi-scale problems. Wavelet analysis leads to a unique decomposition of a signal into its coarse- and fine-scale components. Potentially, this could therefore be useful for image registration. In this work, we investigate whether a wavelet-based FFD model has advantages for nonrigid image registration. We use a B-splines based wavelet, as defined by Cai and Wang.1 This wavelet is expressed as a linear combination of B-spline basis functions. Derived from the original B-spline function, this wavelet is smooth, differentiable, and compactly supported. The basis functions of this wavelet are orthogonal across scales in Sobolev space. This wavelet was previously used for registration in computer vision, in 2D optical flow problems,2 but it was not compared with the conventional B-spline FFD in medical image registration problems. An advantage of choosing this B-splines based wavelet model is that the space of allowable deformation is exactly equivalent to that of the traditional B-spline. The wavelet transformation is essentially a (linear) reparameterization of the B-spline transformation model. Experiments on 10 CT lung and 18 T1-weighted MRI brain datasets show that wavelet based registration leads to smoother deformation fields than traditional B-splines based registration, while achieving better accuracy.

Potential energy function for CH3+CH3 ⇆ C2H6: Attributes of the minimum energy path

NASA Astrophysics Data System (ADS)

Robertson, S. H.; Wardlaw, D. M.; Hirst, D. M.

1993-11-01

The region of the potential energy surface for the title reaction in the vicinity of its minimum energy path has been predicted from the analysis of ab initio electronic energy calculations. The ab initio procedure employs a 6-31G** basis set and a configuration interaction calculation which uses the orbitals obtained in a generalized valence bond calculation. Calculated equilibrium properties of ethane and of isolated methyl radical are compared to existing theoretical and experimental results. The reaction coordinate is represented by the carbon-carbon interatomic distance. The following attributes are reported as a function of this distance and fit to functional forms which smoothly interpolate between reactant and product values of each attribute: the minimum energy path potential, the minimum energy path geometry, normal mode frequencies for vibrational motion orthogonal to the reaction coordinate, a torsional potential, and a fundamental anharmonic frequency for local mode, out-of-plane CH3 bending (umbrella motion). The best representation is provided by a three-parameter modified Morse function for the minimum energy path potential and a two-parameter hyperbolic tangent switching function for all other attributes. A poorer but simpler representation, which may be satisfactory for selected applications, is provided by a standard Morse function and a one-parameter exponential switching function. Previous applications of the exponential switching function to estimate the reaction coordinate dependence of the frequencies and geometry of this system have assumed the same value of the range parameter α for each property and have taken α to be less than or equal to the ``standard'' value of 1.0 Å-1. Based on the present analysis this is incorrect: The α values depend on the property and range from ˜1.2 to ˜1.8 Å-1.

DataView: a computational visualisation system for multidisciplinary design and analysis

NASA Astrophysics Data System (ADS)

Wang, Chengen

2016-01-01

Rapidly processing raw data and effectively extracting underlining information from huge volumes of multivariate data become essential to all decision-making processes in sectors like finance, government, medical care, climate analysis, industries, science, etc. Remarkably, visualisation is recognised as a fundamental technology that props up human comprehension, cognition and utilisation of burgeoning amounts of heterogeneous data. This paper presents a computational visualisation system, named DataView, which has been developed for graphically displaying and capturing outcomes of multiphysics problem-solvers widely used in engineering fields. The DataView is functionally composed of techniques for table/diagram representation, and graphical illustration of scalar, vector and tensor fields. The field visualisation techniques are implemented on the basis of a range of linear and non-linear meshes, which flexibly adapts to disparate data representation schemas adopted by a variety of disciplinary problem-solvers. The visualisation system has been successfully applied to a number of engineering problems, of which some illustrations are presented to demonstrate effectiveness of the visualisation techniques.

N-representability of the Jastrow wave function pair density of the lowest-order.

PubMed

Higuchi, Katsuhiko; Higuchi, Masahiko

2017-08-08

Conditions for the N-representability of the pair density (PD) are needed for the development of the PD functional theory. We derive sufficient conditions for the N-representability of the PD that is calculated from the Jastrow wave function within the lowest order. These conditions are used as the constraints on the correlation function of the Jastrow wave function. A concrete procedure to search the suitable correlation function is also presented.

Scattering by a groove in an impedance plane

NASA Technical Reports Server (NTRS)

Bindiganavale, Sunil; Volakis, John L.

1993-01-01

An analysis of two-dimensional scattering from a narrow groove in an impedance plane is presented. The groove is represented by a impedance surface and the problem reduces to that of scattering from an impedance strip in an otherwise uniform impedance plane. On the basis of this model, appropriate integral equations are constructed using a form of the impedance plane Green's functions involving rapidly convergent integrals. The integral equations are solved by introducing a single basis representation of the equivalent current on the narrow impedance insert. Both transverse electric (TE) and transverse magnetic (TM) polarizations are treated. The resulting solution is validated by comparison with results from the standard boundary integral method (BIM) and a high frequency solution. It is found that the presented solution for narrow impedance inserts can be used in conjunction with the high frequency solution for the characterization of impedance inserts of any given width.

DIY EOS: Experimentally Validated Equations of State for Planetary Fluids to GPa Pressures, Tools for Understanding Planetary Processes and Habitability

NASA Astrophysics Data System (ADS)

Vance, Steven; Brown, J. Michael; Bollengier, Olivier

2016-10-01

Sound speeds are fundamental to seismology, and provide a path allowing the accurate determination of thermodynamic potentials. Prior equations of state (EOS) for pure ammonia (Harr and Gallagher 1978, Tillner-Roth et al. 1993) are based primarily on measured densities and heat capacities. Sound speeds, not included in the fitting, are poorly predicted.We couple recent high pressure sound speed data with prior densities and heat capacities to generate a new equation of state. Our representation fits both the earlier lower pressure work as well as measured sound speeds to 4 GPa and 700 K and the Hugoniot to 70 GPa and 6000 K.In contrast to the damped polynomial representation previously used, our equation of state is based on local basis functions in the form of tensor b-splines. Regularization allows the thermodynamic surface to be continued into regimes poorly sampled by experiments. We discuss application of this framework for aqueous equations of state validated by experimental measurements. Preliminary equations of state have been prepared applying the local basis function methodology to aqueous NH3, Mg2SO4, NaCl, and Na2SO4. We describe its use for developing new equations of state, and provide some applications of the new thermodynamic data to the interior structures of gas giant planets and ocean worlds.References:L. Haar and J. S. Gallagher. Thermodynamic properties of ammonia. American Chemical Society and the American Institute of Physics for the National Bureau of Standards, 1978.R. Tillner-Roth, F. Harms-Watzenberg, and H. Baehr. Eine neue fundamentalgleichung fuer ammoniak. DKV TAGUNGSBERICHT, 20:67-67, 1993.

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.

The relationship between perceived discomfort of static posture holding and posture holding time.

PubMed

Ogutu, Jack; Park, Woojin

2015-01-01

Few studies have investigated mathematical characteristics of the discomfort-time relationship during prolonged static posture holding (SPH) on an individual basis. Consequently, the discomfort-time relationship is not clearly understood at individual trial level. The objective of this study was to examine discomfort-time sequence data obtained from a large number of maximum-duration SPH trials to understand the perceived discomfort-posture holding time relationship at the individual SPH trial level. Thirty subjects (15 male, 15 female) participated in this study as paid volunteers. The subjects performed maximum-duration SPH trials employing 12 different wholebody static postures. The hand-held load for all the task trials was a ``generic'' box weighing 2 kg. Three mathematical functions, that is, linear, logarithmic and power functions were examined as possible mathematical models for representing individual discomfort-time profiles of SPH trials. Three different time increase patterns (negatively accelerated, linear and positively accelerated) were observed in the discomfort-time sequences data. The power function model with an additive constant term was found to adequately fit most (96.4%) of the observed discomfort-time sequences, and thus, was recommended as a general mathematical representation of the perceived discomfort-posture holding time relationship in SPH. The new knowledge on the nature of the discomfort-time relationship in SPH and the power function representation found in this study will facilitate analyzing discomfort-time data of SPH and developing future posture analysis tools for work-related discomfort control.

48 CFR 315.204-5 - Part IV-Representations and instructions.

Code of Federal Regulations, 2013 CFR

2013-10-01

... as using too few.) (3) Examples of topics that form a basis for evaluation factors. Typical examples of topics that form a basis for the development of evaluation factors are listed in the following... special research, test, and other equipment or facilities. (vii) Managerial capability (ability to achieve...

48 CFR 315.204-5 - Part IV-Representations and instructions.

Code of Federal Regulations, 2014 CFR

2014-10-01

... as using too few.) (3) Examples of topics that form a basis for evaluation factors. Typical examples of topics that form a basis for the development of evaluation factors are listed in the following... special research, test, and other equipment or facilities. (vii) Managerial capability (ability to achieve...

48 CFR 315.204-5 - Part IV-Representations and instructions.

Code of Federal Regulations, 2012 CFR

2012-10-01

... as using too few.) (3) Examples of topics that form a basis for evaluation factors. Typical examples of topics that form a basis for the development of evaluation factors are listed in the following... special research, test, and other equipment or facilities. (vii) Managerial capability (ability to achieve...

The neural basis of precise visual short-term memory for complex recognisable objects.

PubMed

Veldsman, Michele; Mitchell, Daniel J; Cusack, Rhodri

2017-10-01

Recent evidence suggests that visual short-term memory (VSTM) capacity estimated using simple objects, such as colours and oriented bars, may not generalise well to more naturalistic stimuli. More visual detail can be stored in VSTM when complex, recognisable objects are maintained compared to simple objects. It is not yet known if it is recognisability that enhances memory precision, nor whether maintenance of recognisable objects is achieved with the same network of brain regions supporting maintenance of simple objects. We used a novel stimulus generation method to parametrically warp photographic images along a continuum, allowing separate estimation of the precision of memory representations and the number of items retained. The stimulus generation method was also designed to create unrecognisable, though perceptually matched, stimuli, to investigate the impact of recognisability on VSTM. We adapted the widely-used change detection and continuous report paradigms for use with complex, photographic images. Across three functional magnetic resonance imaging (fMRI) experiments, we demonstrated greater precision for recognisable objects in VSTM compared to unrecognisable objects. This clear behavioural advantage was not the result of recruitment of additional brain regions, or of stronger mean activity within the core network. Representational similarity analysis revealed greater variability across item repetitions in the representations of recognisable, compared to unrecognisable complex objects. We therefore propose that a richer range of neural representations support VSTM for complex recognisable objects. Copyright © 2017 Elsevier Inc. All rights reserved.

From needs to goals and representations: Foundations for a unified theory of motivation, personality, and development.

PubMed

Dweck, Carol S

2017-11-01

Drawing on both classic and current approaches, I propose a theory that integrates motivation, personality, and development within one framework, using a common set of principles and mechanisms. The theory begins by specifying basic needs and by suggesting how, as people pursue need-fulfilling goals, they build mental representations of their experiences (beliefs, representations of emotions, and representations of action tendencies). I then show how these needs, goals, and representations can serve as the basis of both motivation and personality, and can help to integrate disparate views of personality. The article builds on this framework to provide a new perspective on development, particularly on the forces that propel development and the roles of nature and nurture. I argue throughout that the focus on representations provides an important entry point for change and growth. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

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.

Comment on "Nonuniqueness of algebraic first-order density-matrix functionals"

NASA Astrophysics Data System (ADS)

Gritsenko, O. V.

2018-02-01

Wang and Knowles (WK) [Phys. Rev. A 92, 012520 (2015), 10.1103/PhysRevA.92.012520] have given a counterexample to the conventional in reduced density-matrix functional theory representation of the second-order reduced density matrix (2RDM) Γi j ,k l in the basis of the natural orbitals as a function Γi j ,k l(n ) of the orbital occupation numbers (ONs) ni. The observed nonuniqueness of Γi j ,k l for prototype systems of different symmetry has been interpreted as the inherent inability of ON functions to reproduce the 2RDM, due to the insufficient information contained in the 1RDM spectrum. In this Comment, it is argued that, rather than totally invalidating Γi j ,k l(n ) , the WK example exposes its symmetry dependence which, as well as the previously established analogous dependence in density functional theory, is demonstrated with a general formulation based on the Levy constrained search.

Excitation basis for (3+1)d topological phases

NASA Astrophysics Data System (ADS)

Delcamp, Clement

2017-12-01

We consider an exactly solvable model in 3+1 dimensions, based on a finite group, which is a natural generalization of Kitaev's quantum double model. The corresponding lattice Hamiltonian yields excitations located at torus-boundaries. By cutting open the three-torus, we obtain a manifold bounded by two tori which supports states satisfying a higher-dimensional version of Ocneanu's tube algebra. This defines an algebraic structure extending the Drinfel'd double. Its irreducible representations, labeled by two fluxes and one charge, characterize the torus-excitations. The tensor product of such representations is introduced in order to construct a basis for (3+1)d gauge models which relies upon the fusion of the defect excitations. This basis is defined on manifolds of the form Σ × S_1 , with Σ a two-dimensional Riemann surface. As such, our construction is closely related to dimensional reduction from (3+1)d to (2+1)d topological orders.

Spline methods for approximating quantile functions and generating random samples

NASA Technical Reports Server (NTRS)

Schiess, J. R.; Matthews, C. G.

1985-01-01

Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.

On push-forward representations in the standard gyrokinetic model

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

Miyato, N., E-mail: miyato.naoaki@jaea.go.jp; Yagi, M.; Scott, B. D.

2015-01-15

Two representations of fluid moments in terms of a gyro-center distribution function and gyro-center coordinates, which are called push-forward representations, are compared in the standard electrostatic gyrokinetic model. In the representation conventionally used to derive the gyrokinetic Poisson equation, the pull-back transformation of the gyro-center distribution function contains effects of the gyro-center transformation and therefore electrostatic potential fluctuations, which is described by the Poisson brackets between the distribution function and scalar functions generating the gyro-center transformation. Usually, only the lowest order solution of the generating function at first order is considered to explicitly derive the gyrokinetic Poisson equation. This ismore » true in explicitly deriving representations of scalar fluid moments with polarization terms. One also recovers the particle diamagnetic flux at this order because it is associated with the guiding-center transformation. However, higher-order solutions are needed to derive finite Larmor radius terms of particle flux including the polarization drift flux from the conventional representation. On the other hand, the lowest order solution is sufficient for the other representation, in which the gyro-center transformation part is combined with the guiding-center one and the pull-back transformation of the distribution function does not appear.« less

Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere

NASA Astrophysics Data System (ADS)

Miller, W., Jr.; Li, Q.

2015-04-01

The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L2 of H in terms of an eigenbasis of another symmetry operator L1, but the exact relationship appears not to have been made explicit. We work out the details of the expansion to show, explicitly, how the polynomials arise and how the principal properties of these functions: the measure, 3-term recurrence relation, 2nd order difference equation, duality of these relations, permutation symmetry, intertwining operators and an alternate derivation of Wilson functions - follow from the symmetry of this quantum system. This paper is an exercise to show that quantum mechancal concepts and recurrence relations for Gausian hypergeometrc functions alone suffice to explain these properties; we make no assumptions about the structure of Wilson polynomial/functions, but derive them from quantum principles. There is active interest in the relation between multivariable Wilson polynomials and the quantum superintegrable system on the n-sphere with generic potential, and these results should aid in the generalization. Contracting function space realizations of irreducible representations of this quadratic algebra to the other superintegrable systems one can obtain the full Askey scheme of orthogonal hypergeometric polynomials. All of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2,C). All of the polynomials produced are interpretable as quantum expansion coefficients. It is important to extend this process to higher dimensions.

Science, education and industry information resources complementarity as a basis for design of knowledge management systems

NASA Astrophysics Data System (ADS)

Maksimov, N. V.; Tikhomirov, G. V.; Golitsyna, O. L.

2017-01-01

The main problems and circumstances that influence the processes of creating effective knowledge management systems were described. These problems particularly include high species diversity of instruments for knowledge representation, lack of adequate lingware, including formal representation of semantic relationships. For semantic data descriptions development a conceptual model of the subject area and a conceptual-lexical system should be designed on proposals of ISO-15926 standard. It is proposed to conduct an information integration of educational and production processes on the basis of information systems technologies. Integrated knowledge management system information environment combines both traditional information resources and specific information resources of subject domain including task context and implicit/tacit knowledge.

Hierarchical representation and machine learning from faulty jet engine behavioral examples to detect real time abnormal conditions

NASA Technical Reports Server (NTRS)

Gupta, U. K.; Ali, M.

1988-01-01

The theoretical basis and operation of LEBEX, a machine-learning system for jet-engine performance monitoring, are described. The behavior of the engine is modeled in terms of four parameters (the rotational speeds of the high- and low-speed sections and the exhaust and combustion temperatures), and parameter variations indicating malfunction are transformed into structural representations involving instances and events. LEBEX extracts descriptors from a set of training data on normal and faulty engines, represents them hierarchically in a knowledge base, and uses them to diagnose and predict faults on a real-time basis. Diagrams of the system architecture and printouts of typical results are shown.

The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r(4)) scaling.

PubMed

Shenvi, Neil; van Aggelen, Helen; Yang, Yang; Yang, Weitao; Schwerdtfeger, Christine; Mazziotti, David

2013-08-07

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r(4)), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T).

Neurocognitive inefficacy of the strategy process.

PubMed

Klein, Harold E; D'Esposito, Mark

2007-11-01

The most widely used (and taught) protocols for strategic analysis-Strengths, Weaknesses, Opportunities, and Threats (SWOT) and Porter's (1980) Five Force Framework for industry analysis-have been found to be insufficient as stimuli for strategy creation or even as a basis for further strategy development. We approach this problem from a neurocognitive perspective. We see profound incompatibilities between the cognitive process-deductive reasoning-channeled into the collective mind of strategists within the formal planning process through its tools of strategic analysis (i.e., rational technologies) and the essentially inductive reasoning process actually needed to address ill-defined, complex strategic situations. Thus, strategic analysis protocols that may appear to be and, indeed, are entirely rational and logical are not interpretable as such at the neuronal substrate level where thinking takes place. The analytical structure (or propositional representation) of these tools results in a mental dead end, the phenomenon known in cognitive psychology as functional fixedness. The difficulty lies with the inability of the brain to make out meaningful (i.e., strategy-provoking) stimuli from the mental images (or depictive representations) generated by strategic analysis tools. We propose decreasing dependence on these tools and conducting further research employing brain imaging technology to explore complex data handling protocols with richer mental representation and greater potential for strategy creation.

Increasing the efficiency and accuracy of time-resolved electronic spectra calculations with on-the-fly ab initio quantum dynamics methods

NASA Astrophysics Data System (ADS)

Vanicek, Jiri

2014-03-01

Rigorous quantum-mechanical calculations of coherent ultrafast electronic spectra remain difficult. I will present several approaches developed in our group that increase the efficiency and accuracy of such calculations: First, we justified the feasibility of evaluating time-resolved spectra of large systems by proving that the number of trajectories needed for convergence of the semiclassical dephasing representation/phase averaging is independent of dimensionality. Recently, we further accelerated this approximation with a cellular scheme employing inverse Weierstrass transform and optimal scaling of the cell size. The accuracy of potential energy surfaces was increased by combining the dephasing representation with accurate on-the-fly ab initio electronic structure calculations, including nonadiabatic and spin-orbit couplings. Finally, the inherent semiclassical approximation was removed in the exact quantum Gaussian dephasing representation, in which semiclassical trajectories are replaced by communicating frozen Gaussian basis functions evolving classically with an average Hamiltonian. Among other examples I will present an on-the-fly ab initio semiclassical dynamics calculation of the dispersed time-resolved stimulated emission spectrum of the 54-dimensional azulene. This research was supported by EPFL and by the Swiss National Science Foundation NCCR MUST (Molecular Ultrafast Science and Technology) and Grant No. 200021124936/1.

Parental Socioeconomic Status and the Neural Basis of Arithmetic: Differential Relations to Verbal and Visuo-spatial Representations

PubMed Central

Demir, Özlem Ece; Prado, Jérôme; Booth, James R.

2015-01-01

We examined the relation of parental socioeconomic status (SES) to the neural bases of subtraction in school-age children (9- to 12-year-olds). We independently localized brain regions subserving verbal versus visuo-spatial representations to determine whether the parental SES-related differences in children’s reliance on these neural representations vary as a function of math skill. At higher SES levels, higher skill was associated with greater recruitment of the left temporal cortex, identified by the verbal localizer. At lower SES levels, higher skill was associated with greater recruitment of right parietal cortex, identified by the visuo-spatial localizer. This suggests that depending on parental SES, children engage different neural systems to solve subtraction problems. Furthermore, SES was related to the activation in the left temporal and frontal cortex during the independent verbal localizer task, but it was not related to activation during the independent visuo-spatial localizer task. Differences in activation during the verbal localizer task in turn were related to differences in activation during the subtraction task in right parietal cortex. The relation was stronger at lower SES levels. This result suggests that SES-related differences in the visuo-spatial regions during subtraction might be based in SES-related verbal differences. PMID:25664675

4D Hyperspherical Harmonic (HyperSPHARM) Representation of Surface Anatomy: A Holistic Treatment of Multiple Disconnected Anatomical Structures

PubMed Central

Hosseinbor, A. Pasha; Chung, Moo K.; Koay, Cheng Guan; Schaefer, Stacey M.; van Reekum, Carien M.; Schmitz, Lara Peschke; Sutterer, Matt; Alexander, Andrew L.; Davidson, Richard J.

2015-01-01

Image-based parcellation of the brain often leads to multiple disconnected anatomical structures, which pose significant challenges for analyses of morphological shapes. Existing shape models, such as the widely used spherical harmonic (SPHARM) representation, assume topological invariance, so are unable to simultaneously parameterize multiple disjoint structures. In such a situation, SPHARM has to be applied separately to each individual structure. We present a novel surface parameterization technique using 4D hyperspherical harmonics in representing multiple disjoint objects as a single analytic function, terming it HyperSPHARM. The underlying idea behind Hyper-SPHARM is to stereographically project an entire collection of disjoint 3D objects onto the 4D hypersphere and subsequently simultaneously parameterize them with the 4D hyperspherical harmonics. Hence, HyperSPHARM allows for a holistic treatment of multiple disjoint objects, unlike SPHARM. In an imaging dataset of healthy adult human brains, we apply HyperSPHARM to the hippocampi and amygdalae. The HyperSPHARM representations are employed as a data smoothing technique, while the HyperSPHARM coefficients are utilized in a support vector machine setting for object classification. HyperSPHARM yields nearly identical results as SPHARM, as will be shown in the paper. Its key advantage over SPHARM lies computationally; Hyper-SPHARM possess greater computational efficiency than SPHARM because it can parameterize multiple disjoint structures using much fewer basis functions and stereographic projection obviates SPHARM's burdensome surface flattening. In addition, HyperSPHARM can handle any type of topology, unlike SPHARM, whose analysis is confined to topologically invariant structures. PMID:25828650

The opponent channel population code of sound location is an efficient representation of natural binaural sounds.

PubMed

Młynarski, Wiktor

2015-05-01

In mammalian auditory cortex, sound source position is represented by a population of broadly tuned neurons whose firing is modulated by sounds located at all positions surrounding the animal. Peaks of their tuning curves are concentrated at lateral position, while their slopes are steepest at the interaural midline, allowing for the maximum localization accuracy in that area. These experimental observations contradict initial assumptions that the auditory space is represented as a topographic cortical map. It has been suggested that a "panoramic" code has evolved to match specific demands of the sound localization task. This work provides evidence suggesting that properties of spatial auditory neurons identified experimentally follow from a general design principle- learning a sparse, efficient representation of natural stimuli. Natural binaural sounds were recorded and served as input to a hierarchical sparse-coding model. In the first layer, left and right ear sounds were separately encoded by a population of complex-valued basis functions which separated phase and amplitude. Both parameters are known to carry information relevant for spatial hearing. Monaural input converged in the second layer, which learned a joint representation of amplitude and interaural phase difference. Spatial selectivity of each second-layer unit was measured by exposing the model to natural sound sources recorded at different positions. Obtained tuning curves match well tuning characteristics of neurons in the mammalian auditory cortex. This study connects neuronal coding of the auditory space with natural stimulus statistics and generates new experimental predictions. Moreover, results presented here suggest that cortical regions with seemingly different functions may implement the same computational strategy-efficient coding.

The Role of the Teaching Experiment: Students' Construction of Transformations in a Multiple Representational Environment.

ERIC Educational Resources Information Center

Borba, Marcelo; Confrey, Jere

Function Probe is a multi-representational software for Apple Macintosh computers. It was designed to allow students to approach problems in different ways and/or use different representations. This case study describes a 16-year-old student as he creates a path among a variety of representations of transformations of functions while using the…

Machine learning of neural representations of suicide and emotion concepts identifies suicidal youth

PubMed Central

Just, Marcel Adam; Pan, Lisa; Cherkassky, Vladimir L.; McMakin, Dana; Cha, Christine; Nock, Matthew K.; Brent, David

2017-01-01

The clinical assessment of suicidal risk would be significantly complemented by a biologically-based measure that assesses alterations in the neural representations of concepts related to death and life in people who engage in suicidal ideation. This study used machine-learning algorithms (Gaussian Naïve Bayes) to identify such individuals (17 suicidal ideators vs 17 controls) with high (91%) accuracy, based on their altered fMRI neural signatures of death and life-related concepts. The most discriminating concepts were death, cruelty, trouble, carefree, good, and praise. A similar classification accurately (94%) discriminated 9 suicidal ideators who had made a suicide attempt from 8 who had not. Moreover, a major facet of the concept alterations was the evoked emotion, whose neural signature served as an alternative basis for accurate (85%) group classification. The study establishes a biological, neurocognitive basis for altered concept representations in participants with suicidal ideation, which enables highly accurate group membership classification. PMID:29367952

Representation and visualization of variability in a 3D anatomical atlas using the kidney as an example

NASA Astrophysics Data System (ADS)

Hacker, Silke; Handels, Heinz

2006-03-01

Computer-based 3D atlases allow an interactive exploration of the human body. However, in most cases such 3D atlases are derived from one single individual, and therefore do not regard the variability of anatomical structures concerning their shape and size. Since the geometric variability across humans plays an important role in many medical applications, our goal is to develop a framework of an anatomical atlas for representation and visualization of the variability of selected anatomical structures. The basis of the project presented is the VOXEL-MAN atlas of inner organs that was created from the Visible Human data set. For modeling anatomical shapes and their variability we utilize "m-reps" which allow a compact representation of anatomical objects on the basis of their skeletons. As an example we used a statistical model of the kidney that is based on 48 different variants. With the integration of a shape description into the VOXEL-MAN atlas it is now possible to query and visualize different shape variations of an organ, e.g. by specifying a person's age or gender. In addition to the representation of individual shape variants, the average shape of a population can be displayed. Besides a surface representation, a volume-based representation of the kidney's shape variants is also possible. It results from the deformation of the reference kidney of the volume-based model using the m-rep shape description. In this way a realistic visualization of the shape variants becomes possible, as well as the visualization of the organ's internal structures.

System identification of an unmanned quadcopter system using MRAN neural

NASA Astrophysics Data System (ADS)

Pairan, M. F.; Shamsudin, S. S.

2017-12-01

This project presents the performance analysis of the radial basis function neural network (RBF) trained with Minimal Resource Allocating Network (MRAN) algorithm for real-time identification of quadcopter. MRAN’s performance is compared with the RBF with Constant Trace algorithm for 2500 input-output pair data sampling. MRAN utilizes adding and pruning hidden neuron strategy to obtain optimum RBF structure, increase prediction accuracy and reduce training time. The results indicate that MRAN algorithm produces fast training time and more accurate prediction compared with standard RBF. The model proposed in this paper is capable of identifying and modelling a nonlinear representation of the quadcopter flight dynamics.

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

Orbital dependent functionals: An atom projector augmented wave method implementation

NASA Astrophysics Data System (ADS)

Xu, Xiao

This thesis explores the formulation and numerical implementation of orbital dependent exchange-correlation functionals within electronic structure calculations. These orbital-dependent exchange-correlation functionals have recently received renewed attention as a means to improve the physical representation of electron interactions within electronic structure calculations. In particular, electron self-interaction terms can be avoided. In this thesis, an orbital-dependent functional is considered in the context of Hartree-Fock (HF) theory as well as the Optimized Effective Potential (OEP) method and the approximate OEP method developed by Krieger, Li, and Iafrate, known as the KLI approximation. In this thesis, the Fock exchange term is used as a simple well-defined example of an orbital-dependent functional. The Projected Augmented Wave (PAW) method developed by P. E. Blochl has proven to be accurate and efficient for electronic structure calculations for local and semi-local functions because of its accurate evaluation of interaction integrals by controlling multiple moments. We have extended the PAW method to treat orbital-dependent functionals in Hartree-Fock theory and the Optimized Effective Potential method, particularly in the KLI approximation. In the course of study we develop a frozen-core orbital approximation that accurately treats the core electron contributions for above three methods. The main part of the thesis focuses on the treatment of spherical atoms. We have investigated the behavior of PAW-Hartree Fock and PAW-KLI basis, projector, and pseudopotential functions for several elements throughout the periodic table. We have also extended the formalism to the treatment of solids in a plane wave basis and implemented PWPAW-KLI code, which will appear in future publications.

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

Executive function depletion in children and its impact on theory of mind.

PubMed

Powell, Lindsey J; Carey, Susan

2017-07-01

The current studies provide an experimental, rather than correlational, method for testing hypotheses about the role of executive function (EF) in conceptual development. Previous research has established that adults' tendency to deploy EF can be temporarily diminished by use. Exercising self-control in one context decreases adults' performance on other EF demanding tasks immediately thereafter. Using two different depletion methods, Experiments 1 and 3 extend this finding to preschool-aged children. Experiments 2 and 4 make use of these EF depletion methods to elucidate the role of EF in children's theory of mind reasoning. Experiment 2 shows that EF depletion affects 5-year-olds' ability to predict another's behavior on the basis of that person's false belief, and Experiment 4 shows that this negative effect of depletion extends to 4- and 5-year-olds' ability to explain others' behavior on the basis of their false beliefs. These findings provide direct evidence that EF is required for the expression of an understanding of others' false beliefs across a variety of task demands, even in children who clearly have the capacity to construct such representations. We suggest ways in which depletion may be used as a tool for further investigating the role of executive function in cognitive development. Copyright © 2017. Published by Elsevier B.V.

Shared orthographic neuronal representations for spelling and reading.

PubMed

Purcell, Jeremy J; Jiang, Xiong; Eden, Guinevere F

2017-02-15

A central question in the study of the neural basis of written language is whether reading and spelling utilize shared orthographic representations. While recent studies employing fMRI to test this question report that the left inferior frontal gyrus (IFG) and ventral occipitotemporal cortex (vOTC) are active during both spelling and reading in the same subjects (Purcell et al., 2011a; Rapp and Lipka, 2011), the spatial resolution of fMRI limits the interpretation of these findings. Specifically, it is unknown if the neurons which encode orthography for reading are also involved in spelling of the same words. Here we address this question by employing an event-related functional magnetic resonance imaging-adaptation (fMRI-A) paradigm designed to examine shared orthographic representations across spelling and reading. First, we identified areas that independently showed adaptation to reading, and adaptation to spelling. Then we identified spatial convergence for these two separate maps via a conjunction analysis. Consistent with previous studies (Purcell et al., 2011a; Rapp and Lipka, 2011), this analysis revealed the left dorsal IFG, vOTC and supplementary motor area. To further validate these observations, we then interrogated these regions using an across-task adaptation technique, and found adaptation across reading and spelling in the left dorsal IFG (BA 44/9). Our final analysis focused specifically on the Visual Word Form Area (VWFA) in the vOTC, whose variability in location among subjects requires the use of subject-specific identification mechanisms (Glezer and Riesenhuber, 2013). Using a functional localizer for reading, we defined the VWFA in each subject, and found adaptation effects for both within the spelling and reading conditions, respectively, as well as across spelling and reading. Because none of these effects were observed during a phonological/semantic control condition, we conclude that the left dorsal IFG and VWFA are involved in accessing the same orthography-specific representations for spelling and reading. Copyright © 2016 Elsevier Inc. All rights reserved.

Shared Orthographic Neuronal Representations for Spelling and Reading

PubMed Central

Purcell, Jeremy J.; Jiang, Xiong; Eden, Guinevere F.

2017-01-01

A central question in the study of the neural basis of written language is whether reading and spelling utilize shared orthographic representations. While recent studies employing fMRI to test this question report that the left inferior frontal gyrus (IFG) and ventral occipitotemporal cortex (vOTC) are active during both spelling and reading in the same subjects (Purcell et al., 2011a; Rapp and Lipka, 2011), the spatial resolution of fMRI limits the interpretation of these findings. Specifically, it is unknown if the neurons which encode orthography for reading are also involved in spelling of the same words. Here we address this question by employing an event-related functional magnetic resonance imaging-adaptation (fMRI-A) paradigm designed to examine shared orthographic representations across spelling and reading. First, we identified areas that independently showed adaptation to reading, and adaptation to spelling. Then we identified spatial convergence for these two separate maps via a conjunction analysis. Consistent with previous studies (Purcell et al., 2011a; Rapp and Lipka, 2011), this analysis revealed the left dorsal IFG, vOTC and supplementary motor area. To further validate these observations, we then interrogated these regions using an across-task adaptation technique, and found adaptation across reading and spelling in the left dorsal IFG (BA 44/9). Our final analysis focused specifically on the Visual Word Form Area (VWFA) in the vOTC, whose variability in location among subjects requires the use of subject-specific identification mechanisms (Glezer and Riesenhuber, 2013). Using a functional localizer for reading, we defined the VWFA in each subject, and found adaptation effects for both within the spelling and reading conditions, respectively, as well as across spelling and reading. Because none of these effects were observed during a phonological/semantic control condition, we conclude that the left dorsal IFG and VWFA are involved in accessing the same orthography-specific representations for spelling and reading. PMID:28011250

An essay on dreaming, psychical working out and working through.

PubMed

da Rocha Barros, Elias M

2002-10-01

In this paper the author attempts to expand the idea put forward by Freud who considered dreams as a special form of unconscious thinking. It is the author's contention that the psychical working-out function performed by dreams is a form of unconscious thinking, which transforms affects into memories and mental structures. He also attempts to clarify the way in which meaning is built and transformed in mental life. In that respect the unconscious internal world is seen as a form of unconscious thinking, a private theatre where meaning is generated and transformed. He focuses on what happens to feelings in dreams in connection with the meanings as a result of and an expression of the several stages of working through. The dream world is described as the setting where the mind gives expressive pictorial representation to the emotions involved in a conflict: a first step towards thinkability. The dreamwork also constitutes a process through which meaning is apprehended, built on and transformed at an expressive non-discursive level, based on representation through figurative/pictorial images. The author draws on Meltzer's formulation to conjecture that the working-through function of dreams, mainly in response to interpretations, is performed by a process of progression in formal qualities of the representations made available by dreaming in the form he has called affective pictograms. It is through progression in formal qualities of the representation that the thinking capabilities of the affective life develop and become part of the process of what is called metaphorically the metabolisation of emotional life. This process takes place through migration of meaning across various levels of mental process. In this perspective the analyst's interpretations of dreams effect what linguists call transmutation of the symbolic basis, a process that is necessary to help the mind to improve its capacity to think. Something expressed on the evocative plane and condensed into a pictographic image is then transformed into verbal language that expresses meaning. These conceptions are illustrated by a detailed clinical case.

Mental Representation and Mental Practice: Experimental Investigation on the Functional Links between Motor Memory and Motor Imagery

PubMed Central

Frank, Cornelia; Land, William M.; Popp, Carmen; Schack, Thomas

2014-01-01

Recent research on mental representation of complex action has revealed distinct differences in the structure of representational frameworks between experts and novices. More recently, research on the development of mental representation structure has elicited functional changes in novices' representations as a result of practice. However, research investigating if and how mental practice adds to this adaptation process is lacking. In the present study, we examined the influence of mental practice (i.e., motor imagery rehearsal) on both putting performance and the development of one's representation of the golf putt during early skill acquisition. Novice golfers (N = 52) practiced the task of golf putting under one of four different practice conditions: mental, physical, mental-physical combined, and no practice. Participants were tested prior to and after a practice phase, as well as after a three day retention interval. Mental representation structures of the putt were measured, using the structural dimensional analysis of mental representation. This method provides psychometric data on the distances and groupings of basic action concepts in long-term memory. Additionally, putting accuracy and putting consistency were measured using two-dimensional error scores of each putt. Findings revealed significant performance improvements over the course of practice together with functional adaptations in mental representation structure. Interestingly, after three days of practice, the mental representations of participants who incorporated mental practice into their practice regime displayed representation structures that were more similar to a functional structure than did participants who did not incorporate mental practice. The findings of the present study suggest that mental practice promotes the cognitive adaptation process during motor learning, leading to more elaborate representations than physical practice only. PMID:24743576

A Unified Approach to Model-Based Planning and Execution

NASA Technical Reports Server (NTRS)

Muscettola, Nicola; Dorais, Gregory A.; Fry, Chuck; Levinson, Richard; Plaunt, Christian; Norvig, Peter (Technical Monitor)

2000-01-01

Writing autonomous software is complex, requiring the coordination of functionally and technologically diverse software modules. System and mission engineers must rely on specialists familiar with the different software modules to translate requirements into application software. Also, each module often encodes the same requirement in different forms. The results are high costs and reduced reliability due to the difficulty of tracking discrepancies in these encodings. In this paper we describe a unified approach to planning and execution that we believe provides a unified representational and computational framework for an autonomous agent. We identify the four main components whose interplay provides the basis for the agent's autonomous behavior: the domain model, the plan database, the plan running module, and the planner modules. This representational and problem solving approach can be applied at all levels of the architecture of a complex agent, such as Remote Agent. In the rest of the paper we briefly describe the Remote Agent architecture. The new agent architecture proposed here aims at achieving the full Remote Agent functionality. We then give the fundamental ideas behind the new agent architecture and point out some implication of the structure of the architecture, mainly in the area of reactivity and interaction between reactive and deliberative decision making. We conclude with related work and current status.

Protein Structure Classification and Loop Modeling Using Multiple Ramachandran Distributions.

PubMed

Najibi, Seyed Morteza; Maadooliat, Mehdi; Zhou, Lan; Huang, Jianhua Z; Gao, Xin

2017-01-01

Recently, the study of protein structures using angular representations has attracted much attention among structural biologists. The main challenge is how to efficiently model the continuous conformational space of the protein structures based on the differences and similarities between different Ramachandran plots. Despite the presence of statistical methods for modeling angular data of proteins, there is still a substantial need for more sophisticated and faster statistical tools to model the large-scale circular datasets. To address this need, we have developed a nonparametric method for collective estimation of multiple bivariate density functions for a collection of populations of protein backbone angles. The proposed method takes into account the circular nature of the angular data using trigonometric spline which is more efficient compared to existing methods. This collective density estimation approach is widely applicable when there is a need to estimate multiple density functions from different populations with common features. Moreover, the coefficients of adaptive basis expansion for the fitted densities provide a low-dimensional representation that is useful for visualization, clustering, and classification of the densities. The proposed method provides a novel and unique perspective to two important and challenging problems in protein structure research: structure-based protein classification and angular-sampling-based protein loop structure prediction.

Health-related quality of life in patients with hepatocellular carcinoma: the mediation effects of illness perceptions and coping.

PubMed

Fan, Sheng-Yu; Eiser, Christine; Ho, Ming-Chih; Lin, Cheng-Yao

2013-06-01

The aims of this study were to explore health-related quality of life (HRQOL) in patients with hepatocellular carcinoma (HCC). We report the following: (1) differences in HRQOL between patients with HCC and the general population; (2) significant physical and psychological predictors of HRQOL; and (3) mediation effects of illness perceptions and coping on HRQOL. Patients with HCC (n = 286) from Taiwan completed standardized measures of HRQOL, illness perception (cognitive representations, emotional representations and illness comprehensibility) and coping (emotion-oriented and problem-orientation coping). Demographic and physical variables were also collected. Patients with HCC had worse global HRQOL, physical, role, cognitive and social functioning, but better emotional functioning than the general population. Physical variables and cognitive representation were significant predictors of global HRQOL, physical functioning and emotional functioning. Cognitive representation mediated the relationships between physical variables and global HRQOL, physical functioning and emotional functioning, but coping only mediated the relationship between cognitive representation and global HRQOL. The results suggest that physical variables have direct effects on global HRQOL and physical functioning, but there were also partial mediations through cognitive representation. The effect of physical variables on emotional functioning was mediated through cognitive and emotional representations. Patients with better performance status and positive illness perceptions tended to report better HRQOL, but those with negative illness perceptions and who used more emotion-oriented coping had worse HRQOL. Limitations of the work associated with use of theory and measures developed in Europe and the US are discussed, as are the clinical implications for patients with HCC. Copyright © 2012 John Wiley & Sons, Ltd.

Data Representation, Coding, and Communication Standards.

PubMed

Amin, Milon; Dhir, Rajiv

2015-06-01

The immense volume of cases signed out by surgical pathologists on a daily basis gives little time to think about exactly how data are stored. An understanding of the basics of data representation has implications that affect a pathologist's daily practice. This article covers the basics of data representation and its importance in the design of electronic medical record systems. Coding in surgical pathology is also discussed. Finally, a summary of communication standards in surgical pathology is presented, including suggested resources that establish standards for select aspects of pathology reporting. Copyright © 2015 Elsevier Inc. All rights reserved.

Noisy bases in Hilbert space: A new class of thermal coherent states and their properties

NASA Technical Reports Server (NTRS)

Vourdas, A.; Bishop, R. F.

1995-01-01

Coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at finite temperature, are introduced as a 'random' (or 'thermal' or 'noisy') basis in Hilbert space. A resolution of the identity for these states is proved and used to generalize the usual coherent state formalism for the finite temperature case. The Bargmann representation of an operator is introduced and its relation to the P and Q representations is studied. Generalized P and Q representations for the finite temperature case are also considered and several interesting relations among them are derived.

Triple representation of language, working memory, social and emotion processing in the cerebellum: convergent evidence from task and seed-based resting-state fMRI analyses in a single large cohort.

PubMed

Guell, Xavier; Gabrieli, John D E; Schmahmann, Jeremy D

2018-05-15

Delineation of functional topography is critical to the evolving understanding of the cerebellum's role in a wide range of nervous system functions. We used data from the Human Connectome Project (n = 787) to analyze cerebellar fMRI task activation (motor, working memory, language, social and emotion processing) and resting-state functional connectivity calculated from cerebral cortical seeds corresponding to the peak Cohen's d of each task contrast. The combination of exceptional statistical power, activation from both motor and multiple non-motor tasks in the same participants, and convergent resting-state networks in the same participants revealed novel aspects of the functional topography of the human cerebellum. Consistent with prior studies there were two distinct representations of motor activation. Newly revealed were three distinct representations each for working memory, language, social, and emotional task processing that were largely separate for these four cognitive and affective domains. In most cases, the task-based activations and the corresponding resting-network correlations were congruent in identifying the two motor representations and the three non-motor representations that were unique to working memory, language, social cognition, and emotion. The definitive localization and characterization of distinct triple representations for cognition and emotion task processing in the cerebellum opens up new basic science questions as to why there are triple representations (what different functions are enabled by the different representations?) and new clinical questions (what are the differing consequences of lesions to the different representations?). Copyright © 2018 Elsevier Inc. All rights reserved.

Neural representations of social status hierarchy in human inferior parietal cortex.

PubMed

Chiao, Joan Y; Harada, Tokiko; Oby, Emily R; Li, Zhang; Parrish, Todd; Bridge, Donna J

2009-01-01

Mental representations of social status hierarchy share properties with that of numbers. Previous neuroimaging studies have shown that the neural representation of numerical magnitude lies within a network of regions within inferior parietal cortex. However the neural basis of social status hierarchy remains unknown. Using fMRI, we studied subjects while they compared social status magnitude of people, objects and symbols, as well as numerical magnitude. Both social status and number comparisons recruited bilateral intraparietal sulci. We also observed a semantic distance effect whereby neural activity within bilateral intraparietal sulci increased for semantically close relative to far numerical and social status comparisons. These results demonstrate that social status and number comparisons recruit distinct and overlapping neuronal representations within human inferior parietal cortex.

Designing scalable product families by the radial basis function-high-dimensional model representation metamodelling technique

NASA Astrophysics Data System (ADS)

Pirmoradi, Zhila; Haji Hajikolaei, Kambiz; Wang, G. Gary

2015-10-01

Product family design is cost-efficient for achieving the best trade-off between commonalization and diversification. However, for computationally intensive design functions which are viewed as black boxes, the family design would be challenging. A two-stage platform configuration method with generalized commonality is proposed for a scale-based family with unknown platform configuration. Unconventional sensitivity analysis and information on variation in the individual variants' optimal design are used for platform configuration design. Metamodelling is employed to provide the sensitivity and variable correlation information, leading to significant savings in function calls. A family of universal electric motors is designed for product performance and the efficiency of this method is studied. The impact of the employed parameters is also analysed. Then, the proposed method is modified for obtaining higher commonality. The proposed method is shown to yield design solutions with better objective function values, allowable performance loss and higher commonality than the previously developed methods in the literature.

Robust Joint Graph Sparse Coding for Unsupervised Spectral Feature Selection.

PubMed

Zhu, Xiaofeng; Li, Xuelong; Zhang, Shichao; Ju, Chunhua; Wu, Xindong

2017-06-01

In this paper, we propose a new unsupervised spectral feature selection model by embedding a graph regularizer into the framework of joint sparse regression for preserving the local structures of data. To do this, we first extract the bases of training data by previous dictionary learning methods and, then, map original data into the basis space to generate their new representations, by proposing a novel joint graph sparse coding (JGSC) model. In JGSC, we first formulate its objective function by simultaneously taking subspace learning and joint sparse regression into account, then, design a new optimization solution to solve the resulting objective function, and further prove the convergence of the proposed solution. Furthermore, we extend JGSC to a robust JGSC (RJGSC) via replacing the least square loss function with a robust loss function, for achieving the same goals and also avoiding the impact of outliers. Finally, experimental results on real data sets showed that both JGSC and RJGSC outperformed the state-of-the-art algorithms in terms of k -nearest neighbor classification performance.

First-principles calculations on the four phases of BaTiO3.

PubMed

Evarestov, Robert A; Bandura, Andrei V

2012-04-30

The calculations based on linear combination of atomic orbitals basis functions as implemented in CRYSTAL09 computer code have been performed for cubic, tetragonal, orthorhombic, and rhombohedral modifications of BaTiO(3) crystal. Structural and electronic properties as well as phonon frequencies were obtained using local density approximation, generalized gradient approximation, and hybrid exchange-correlation density functional theory (DFT) functionals for four stable phases of BaTiO(3). A comparison was made between the results of different DFT techniques. It is concluded that the hybrid PBE0 [J. P. Perdew, K. Burke, M. Ernzerhof, J. Chem. Phys. 1996, 105, 9982.] functional is able to predict correctly the structural stability and phonon properties both for cubic and ferroelectric phases of BaTiO(3). The comparative phonon symmetry analysis in BaTiO(3) four phases has been made basing on the site symmetry and irreducible representation indexes for the first time. Copyright © 2012 Wiley Periodicals, Inc.

New Actions Upon Old Objects: A New Ontological Perspective on Functions.

ERIC Educational Resources Information Center

Schwarz, Baruch; Dreyfus, Tommy

1995-01-01

A computer microworld called Triple Representation Model uses graphical, tabular, and algebraic representations to influence conceptions of function. A majority of students were able to cope with partial data, recognize invariants while coordinating actions among representations, and recognize invariants while creating and comparing different…

Representations and uses of light distribution functions

NASA Astrophysics Data System (ADS)

Lalonde, Paul Albert

1998-11-01

At their lowest level, all rendering algorithms depend on models of local illumination to define the interplay of light with the surfaces being rendered. These models depend both on the representations of light scattering at a surface due to reflection and to an equal extent on the representation of light sources and light fields. Both emission and reflection have in common that they describe how light leaves a surface as a function of direction. Reflection also depends on an incident light direction. Emission can depend on the position on the light source We call the functions representing emission and reflection light distribution functions (LDF's). There are some difficulties to using measured light distribution functions. The data sets are very large-the size of the data grows with the fourth power of the sampling resolution. For example, a bidirectional reflectance distribution function (BRDF) sampled at five degrees angular resolution, which is arguably insufficient to capture highlights and other high frequency effects in the reflection, can easily require one and a half million samples. Once acquired this data requires some form of interpolation to use them. Any compression method used must be efficient, both in space and in the time required to evaluate the function at a point or over a range of points. This dissertation examines a wavelet representation of light distribution functions that addresses these issues. A data structure is presented that allows efficient reconstruction of LDFs for a given set of parameters, making the wavelet representation feasible for rendering tasks. Texture mapping methods that take advantage of our LDF representations are examined, as well as techniques for filtering LDFs, and methods for using wavelet compressed bidirection reflectance distribution functions (BRDFs) and light sources with Monte Carlo path tracing algorithms. The wavelet representation effectively compresses BRDF and emission data while inducing only a small error in the reconstructed signal. The representation can be used to evaluate efficiently some integrals that appear in shading computation which allows fast, accurate computation of local shading. The representation can be used to represent light fields and is used to reconstruct views of environments interactively from a precomputed set of views. The representation of the BRDF also allows the efficient generation of reflected directions for Monte Carlo array tracing applications. The method can be integrated into many different global illumination algorithms, including ray tracers and wavelet radiosity systems.

Feature-Selective Attentional Modulations in Human Frontoparietal Cortex.

PubMed

Ester, Edward F; Sutterer, David W; Serences, John T; Awh, Edward

2016-08-03

Control over visual selection has long been framed in terms of a dichotomy between "source" and "site," where top-down feedback signals originating in frontoparietal cortical areas modulate or bias sensory processing in posterior visual areas. This distinction is motivated in part by observations that frontoparietal cortical areas encode task-level variables (e.g., what stimulus is currently relevant or what motor outputs are appropriate), while posterior sensory areas encode continuous or analog feature representations. Here, we present evidence that challenges this distinction. We used fMRI, a roving searchlight analysis, and an inverted encoding model to examine representations of an elementary feature property (orientation) across the entire human cortical sheet while participants attended either the orientation or luminance of a peripheral grating. Orientation-selective representations were present in a multitude of visual, parietal, and prefrontal cortical areas, including portions of the medial occipital cortex, the lateral parietal cortex, and the superior precentral sulcus (thought to contain the human homolog of the macaque frontal eye fields). Additionally, representations in many-but not all-of these regions were stronger when participants were instructed to attend orientation relative to luminance. Collectively, these findings challenge models that posit a strict segregation between sources and sites of attentional control on the basis of representational properties by demonstrating that simple feature values are encoded by cortical regions throughout the visual processing hierarchy, and that representations in many of these areas are modulated by attention. Influential models of visual attention posit a distinction between top-down control and bottom-up sensory processing networks. These models are motivated in part by demonstrations showing that frontoparietal cortical areas associated with top-down control represent abstract or categorical stimulus information, while visual areas encode parametric feature information. Here, we show that multivariate activity in human visual, parietal, and frontal cortical areas encode representations of a simple feature property (orientation). Moreover, representations in several (though not all) of these areas were modulated by feature-based attention in a similar fashion. These results provide an important challenge to models that posit dissociable top-down control and sensory processing networks on the basis of representational properties. Copyright © 2016 the authors 0270-6474/16/368188-12$15.00/0.

An accurate, compact and computationally efficient representation of orbitals for quantum Monte Carlo calculations

NASA Astrophysics Data System (ADS)

Luo, Ye; Esler, Kenneth; Kent, Paul; Shulenburger, Luke

Quantum Monte Carlo (QMC) calculations of giant molecules, surface and defect properties of solids have been feasible recently due to drastically expanding computational resources. However, with the most computationally efficient basis set, B-splines, these calculations are severely restricted by the memory capacity of compute nodes. The B-spline coefficients are shared on a node but not distributed among nodes, to ensure fast evaluation. A hybrid representation which incorporates atomic orbitals near the ions and B-spline ones in the interstitial regions offers a more accurate and less memory demanding description of the orbitals because they are naturally more atomic like near ions and much smoother in between, thus allowing coarser B-spline grids. We will demonstrate the advantage of hybrid representation over pure B-spline and Gaussian basis sets and also show significant speed-up like computing the non-local pseudopotentials with our new scheme. Moreover, we discuss a new algorithm for atomic orbital initialization which used to require an extra workflow step taking a few days. With this work, the highly efficient hybrid representation paves the way to simulate large size even in-homogeneous systems using QMC. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Computational Materials Sciences Program.

Corrected confidence bands for functional data using principal components.

PubMed

Goldsmith, J; Greven, S; Crainiceanu, C

2013-03-01

Functional principal components (FPC) analysis is widely used to decompose and express functional observations. Curve estimates implicitly condition on basis functions and other quantities derived from FPC decompositions; however these objects are unknown in practice. In this article, we propose a method for obtaining correct curve estimates by accounting for uncertainty in FPC decompositions. Additionally, pointwise and simultaneous confidence intervals that account for both model- and decomposition-based variability are constructed. Standard mixed model representations of functional expansions are used to construct curve estimates and variances conditional on a specific decomposition. Iterated expectation and variance formulas combine model-based conditional estimates across the distribution of decompositions. A bootstrap procedure is implemented to understand the uncertainty in principal component decomposition quantities. Our method compares favorably to competing approaches in simulation studies that include both densely and sparsely observed functions. We apply our method to sparse observations of CD4 cell counts and to dense white-matter tract profiles. Code for the analyses and simulations is publicly available, and our method is implemented in the R package refund on CRAN. Copyright © 2013, The International Biometric Society.

Corrected Confidence Bands for Functional Data Using Principal Components

PubMed Central

Goldsmith, J.; Greven, S.; Crainiceanu, C.

2014-01-01

Functional principal components (FPC) analysis is widely used to decompose and express functional observations. Curve estimates implicitly condition on basis functions and other quantities derived from FPC decompositions; however these objects are unknown in practice. In this article, we propose a method for obtaining correct curve estimates by accounting for uncertainty in FPC decompositions. Additionally, pointwise and simultaneous confidence intervals that account for both model- and decomposition-based variability are constructed. Standard mixed model representations of functional expansions are used to construct curve estimates and variances conditional on a specific decomposition. Iterated expectation and variance formulas combine model-based conditional estimates across the distribution of decompositions. A bootstrap procedure is implemented to understand the uncertainty in principal component decomposition quantities. Our method compares favorably to competing approaches in simulation studies that include both densely and sparsely observed functions. We apply our method to sparse observations of CD4 cell counts and to dense white-matter tract profiles. Code for the analyses and simulations is publicly available, and our method is implemented in the R package refund on CRAN. PMID:23003003

A Review on Human Activity Recognition Using Vision-Based Method.

PubMed

Zhang, Shugang; Wei, Zhiqiang; Nie, Jie; Huang, Lei; Wang, Shuang; Li, Zhen

2017-01-01

Human activity recognition (HAR) aims to recognize activities from a series of observations on the actions of subjects and the environmental conditions. The vision-based HAR research is the basis of many applications including video surveillance, health care, and human-computer interaction (HCI). This review highlights the advances of state-of-the-art activity recognition approaches, especially for the activity representation and classification methods. For the representation methods, we sort out a chronological research trajectory from global representations to local representations, and recent depth-based representations. For the classification methods, we conform to the categorization of template-based methods, discriminative models, and generative models and review several prevalent methods. Next, representative and available datasets are introduced. Aiming to provide an overview of those methods and a convenient way of comparing them, we classify existing literatures with a detailed taxonomy including representation and classification methods, as well as the datasets they used. Finally, we investigate the directions for future research.

A Review on Human Activity Recognition Using Vision-Based Method

PubMed Central

Nie, Jie

2017-01-01

Human activity recognition (HAR) aims to recognize activities from a series of observations on the actions of subjects and the environmental conditions. The vision-based HAR research is the basis of many applications including video surveillance, health care, and human-computer interaction (HCI). This review highlights the advances of state-of-the-art activity recognition approaches, especially for the activity representation and classification methods. For the representation methods, we sort out a chronological research trajectory from global representations to local representations, and recent depth-based representations. For the classification methods, we conform to the categorization of template-based methods, discriminative models, and generative models and review several prevalent methods. Next, representative and available datasets are introduced. Aiming to provide an overview of those methods and a convenient way of comparing them, we classify existing literatures with a detailed taxonomy including representation and classification methods, as well as the datasets they used. Finally, we investigate the directions for future research. PMID:29065585

An RBF-based compression method for image-based relighting.

PubMed

Leung, Chi-Sing; Wong, Tien-Tsin; Lam, Ping-Man; Choy, Kwok-Hung

2006-04-01

In image-based relighting, a pixel is associated with a number of sampled radiance values. This paper presents a two-level compression method. In the first level, the plenoptic property of a pixel is approximated by a spherical radial basis function (SRBF) network. That means that the spherical plenoptic function of each pixel is represented by a number of SRBF weights. In the second level, we apply a wavelet-based method to compress these SRBF weights. To reduce the visual artifact due to quantization noise, we develop a constrained method for estimating the SRBF weights. Our proposed approach is superior to JPEG, JPEG2000, and MPEG. Compared with the spherical harmonics approach, our approach has a lower complexity, while the visual quality is comparable. The real-time rendering method for our SRBF representation is also discussed.

Two-spinor description of massive particles and relativistic spin projection operators

NASA Astrophysics Data System (ADS)

Isaev, A. P.; Podoinitsyn, M. A.

2018-04-01

On the basis of the Wigner unitary representations of the covering group ISL (2 , C) of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinor formalism we construct spin-vectors of polarizations and obtain conditions that fix the corresponding relativistic spin projection operators (Behrends-Fronsdal projection operators). With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends-Fronsdal projection operators) and then find relativistic spin projection operators for half integer spins. These projection operators determine the numerators in the propagators of fields of relativistic particles. We deduce generalizations of the Behrends-Fronsdal projection operators for arbitrary space-time dimensions D > 2.

A complete active space valence bond method with nonorthogonal orbitals

NASA Astrophysics Data System (ADS)

Hirao, Kimihiko; Nakano, Haruyuki; Nakayama, Kenichi

1997-12-01

A complete active space self-consistent field (SCF) wave function is transformed into a valence bond type representation built from nonorthogonal orbitals, each strongly localized on a single atom. Nonorthogonal complete active space SCF orbitals are constructed by Ruedenberg's projected localization procedure so that they have maximal overlaps with the corresponding minimum basis set of atomic orbitals of the free-atoms. The valence bond structures which are composed of such nonorthogonal quasiatomic orbitals constitute the wave function closest to the concept of the oldest and most simple valence bond method. The method is applied to benzene, butadiene, hydrogen, and methane molecules and compared to the previously proposed complete active space valence bond approach with orthogonal orbitals. The results demonstrate the validity of the method as a powerful tool for describing the electronic structure of various molecules.

Maximally Entangled States of a Two-Qubit System

NASA Astrophysics Data System (ADS)

Singh, Manu P.; Rajput, B. S.

2013-12-01

Entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin correlation functions has been established, correspondence between evolution of maximally entangled states (MES) of two-qubit system and representation of SU(2) group has been worked out and the evolution of MES under a rotating magnetic field has been investigated. Necessary and sufficient conditions for the general two-qubit state to be maximally entangled state (MES) have been obtained and a new set of MES constituting a very powerful and reliable eigen basis (different from magic bases) of two-qubit systems has been constructed. In terms of the MES constituting this basis, Bell’s States have been generated and all the qubits of two-qubit system have been obtained. It has shown that a MES corresponds to a point in the SO(3) sphere and an evolution of MES corresponds to a trajectory connecting two points on this sphere. Analysing the evolution of MES under a rotating magnetic field, it has been demonstrated that a rotating magnetic field is equivalent to a three dimensional rotation in real space leading to the evolution of a MES.

Robust mode space approach for atomistic modeling of realistically large nanowire transistors

NASA Astrophysics Data System (ADS)

Huang, Jun Z.; Ilatikhameneh, Hesameddin; Povolotskyi, Michael; Klimeck, Gerhard

2018-01-01

Nanoelectronic transistors have reached 3D length scales in which the number of atoms is countable. Truly atomistic device representations are needed to capture the essential functionalities of the devices. Atomistic quantum transport simulations of realistically extended devices are, however, computationally very demanding. The widely used mode space (MS) approach can significantly reduce the numerical cost, but a good MS basis is usually very hard to obtain for atomistic full-band models. In this work, a robust and parallel algorithm is developed to optimize the MS basis for atomistic nanowires. This enables engineering-level, reliable tight binding non-equilibrium Green's function simulation of nanowire metal-oxide-semiconductor field-effect transistor (MOSFET) with a realistic cross section of 10 nm × 10 nm using a small computer cluster. This approach is applied to compare the performance of InGaAs and Si nanowire n-type MOSFETs (nMOSFETs) with various channel lengths and cross sections. Simulation results with full-band accuracy indicate that InGaAs nanowire nMOSFETs have no drive current advantage over their Si counterparts for cross sections up to about 10 nm × 10 nm.

Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code. [predicting the response of a lightweight aircraft during a crash

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1980-01-01

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.

Spatial Bayesian latent factor regression modeling of coordinate-based meta-analysis data.

PubMed

Montagna, Silvia; Wager, Tor; Barrett, Lisa Feldman; Johnson, Timothy D; Nichols, Thomas E

2018-03-01

Now over 20 years old, functional MRI (fMRI) has a large and growing literature that is best synthesised with meta-analytic tools. As most authors do not share image data, only the peak activation coordinates (foci) reported in the article are available for Coordinate-Based Meta-Analysis (CBMA). Neuroimaging meta-analysis is used to (i) identify areas of consistent activation; and (ii) build a predictive model of task type or cognitive process for new studies (reverse inference). To simultaneously address these aims, we propose a Bayesian point process hierarchical model for CBMA. We model the foci from each study as a doubly stochastic Poisson process, where the study-specific log intensity function is characterized as a linear combination of a high-dimensional basis set. A sparse representation of the intensities is guaranteed through latent factor modeling of the basis coefficients. Within our framework, it is also possible to account for the effect of study-level covariates (meta-regression), significantly expanding the capabilities of the current neuroimaging meta-analysis methods available. We apply our methodology to synthetic data and neuroimaging meta-analysis datasets. © 2017, The International Biometric Society.

Master equations and the theory of stochastic path integrals.

PubMed

Weber, Markus F; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Using field observations to inform thermal hydrology models of permafrost dynamics with ATS (v0.83)

DOE PAGES

Atchley, A. L.; Painter, S. L.; Harp, D. R.; ...

2015-04-14

Climate change is profoundly transforming the carbon-rich Arctic tundra landscape, potentially moving it from a carbon sink to a carbon source by increasing the thickness of soil that thaws on a seasonal basis. However, the modeling capability and precise parameterizations of the physical characteristics needed to estimate projected active layer thickness (ALT) are limited in Earth System Models (ESMs). In particular, discrepancies in spatial scale between field measurements and Earth System Models challenge validation and parameterization of hydrothermal models. A recently developed surface/subsurface model for permafrost thermal hydrology, the Advanced Terrestrial Simulator (ATS), is used in combination with field measurementsmore » to calibrate and identify fine scale controls of ALT in ice wedge polygon tundra in Barrow, Alaska. An iterative model refinement procedure that cycles between borehole temperature and snow cover measurements and simulations functions to evaluate and parameterize different model processes necessary to simulate freeze/thaw processes and ALT formation. After model refinement and calibration, reasonable matches between simulated and measured soil temperatures are obtained, with the largest errors occurring during early summer above ice wedges (e.g. troughs). The results suggest that properly constructed and calibrated one-dimensional thermal hydrology models have the potential to provide reasonable representation of the subsurface thermal response and can be used to infer model input parameters and process representations. The models for soil thermal conductivity and snow distribution were found to be the most sensitive process representations. However, information on lateral flow and snowpack evolution might be needed to constrain model representations of surface hydrology and snow depth.« less

Facilitating the Genesis of Functional Working Spaces in Guided Explorations

ERIC Educational Resources Information Center

Miranda, Vicente Carrión; Pluvinage, François; Adjiage, Robert

2016-01-01

Approximating given real-valued functions by affine functions is among the most basic activities with functions. In this study we examine two contexts in which two such approximations are performed. The first involves a microscopic representation of functions for the study of tangents; the second a macroscopic representation of functions for the…

Semantics based approach for analyzing disease-target associations.

PubMed

Kaalia, Rama; Ghosh, Indira

2016-08-01

A complex disease is caused by heterogeneous biological interactions between genes and their products along with the influence of environmental factors. There have been many attempts for understanding the cause of these diseases using experimental, statistical and computational methods. In the present work the objective is to address the challenge of representation and integration of information from heterogeneous biomedical aspects of a complex disease using semantics based approach. Semantic web technology is used to design Disease Association Ontology (DAO-db) for representation and integration of disease associated information with diabetes as the case study. The functional associations of disease genes are integrated using RDF graphs of DAO-db. Three semantic web based scoring algorithms (PageRank, HITS (Hyperlink Induced Topic Search) and HITS with semantic weights) are used to score the gene nodes on the basis of their functional interactions in the graph. Disease Association Ontology for Diabetes (DAO-db) provides a standard ontology-driven platform for describing genes, proteins, pathways involved in diabetes and for integrating functional associations from various interaction levels (gene-disease, gene-pathway, gene-function, gene-cellular component and protein-protein interactions). An automatic instance loader module is also developed in present work that helps in adding instances to DAO-db on a large scale. Our ontology provides a framework for querying and analyzing the disease associated information in the form of RDF graphs. The above developed methodology is used to predict novel potential targets involved in diabetes disease from the long list of loose (statistically associated) gene-disease associations. Copyright © 2016 Elsevier Inc. All rights reserved.

Design of chemical space networks on the basis of Tversky similarity

NASA Astrophysics Data System (ADS)

Wu, Mengjun; Vogt, Martin; Maggiora, Gerald M.; Bajorath, Jürgen

2016-01-01

Chemical space networks (CSNs) have been introduced as a coordinate-free representation of chemical space. In CSNs, nodes represent compounds and edges pairwise similarity relationships. These network representations are mostly used to navigate sections of biologically relevant chemical space. Different types of CSNs have been designed on the basis of alternative similarity measures including continuous numerical similarity values or substructure-based similarity criteria. CSNs can be characterized and compared on the basis of statistical concepts from network science. Herein, a new CSN design is introduced that is based upon asymmetric similarity assessment using the Tversky coefficient and termed TV-CSN. Compared to other CSNs, TV-CSNs have unique features. While CSNs typically contain separate compound communities and exhibit small world character, many TV-CSNs are also scale-free in nature and contain hubs, i.e., extensively connected central compounds. Compared to other CSNs, these hubs are a characteristic of TV-CSN topology. Hub-containing compound communities are of particular interest for the exploration of structure-activity relationships.

Quaternion-based adaptive output feedback attitude control of spacecraft using Chebyshev neural networks.

PubMed

Zou, An-Min; Dev Kumar, Krishna; Hou, Zeng-Guang

2010-09-01

This paper investigates the problem of output feedback attitude control of an uncertain spacecraft. Two robust adaptive output feedback controllers based on Chebyshev neural networks (CNN) termed adaptive neural networks (NN) controller-I and adaptive NN controller-II are proposed for the attitude tracking control of spacecraft. The four-parameter representations (quaternion) are employed to describe the spacecraft attitude for global representation without singularities. The nonlinear reduced-order observer is used to estimate the derivative of the spacecraft output, and the CNN is introduced to further improve the control performance through approximating the spacecraft attitude motion. The implementation of the basis functions of the CNN used in the proposed controllers depends only on the desired signals, and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the CNN approximation errors and external disturbances. The adaptive NN controller-II can efficiently avoid the over-estimation problem (i.e., the bound of the CNNs output is much larger than that of the approximated unknown function, and hence, the control input may be very large) existing in the adaptive NN controller-I. Both adaptive output feedback controllers using CNN can guarantee that all signals in the resulting closed-loop system are uniformly ultimately bounded. For performance comparisons, the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed. Simulation studies are presented to show the advantages of the proposed CNN-based output feedback approach over the standard adaptive output feedback approach.

A Brain System for Auditory Working Memory.

PubMed

Kumar, Sukhbinder; Joseph, Sabine; Gander, Phillip E; Barascud, Nicolas; Halpern, Andrea R; Griffiths, Timothy D

2016-04-20

The brain basis for auditory working memory, the process of actively maintaining sounds in memory over short periods of time, is controversial. Using functional magnetic resonance imaging in human participants, we demonstrate that the maintenance of single tones in memory is associated with activation in auditory cortex. In addition, sustained activation was observed in hippocampus and inferior frontal gyrus. Multivoxel pattern analysis showed that patterns of activity in auditory cortex and left inferior frontal gyrus distinguished the tone that was maintained in memory. Functional connectivity during maintenance was demonstrated between auditory cortex and both the hippocampus and inferior frontal cortex. The data support a system for auditory working memory based on the maintenance of sound-specific representations in auditory cortex by projections from higher-order areas, including the hippocampus and frontal cortex. In this work, we demonstrate a system for maintaining sound in working memory based on activity in auditory cortex, hippocampus, and frontal cortex, and functional connectivity among them. Specifically, our work makes three advances from the previous work. First, we robustly demonstrate hippocampal involvement in all phases of auditory working memory (encoding, maintenance, and retrieval): the role of hippocampus in working memory is controversial. Second, using a pattern classification technique, we show that activity in the auditory cortex and inferior frontal gyrus is specific to the maintained tones in working memory. Third, we show long-range connectivity of auditory cortex to hippocampus and frontal cortex, which may be responsible for keeping such representations active during working memory maintenance. Copyright © 2016 Kumar et al.

A Riemannian framework for orientation distribution function computing.

PubMed

Cheng, Jian; Ghosh, Aurobrata; Jiang, Tianzi; Deriche, Rachid

2009-01-01

Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied for tensor computing in DTI. In this paper, we present a state of the art Riemannian framework for ODF computing based on Information Geometry and sparse representation of orthonormal bases. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms. And the weighted Frechet mean exists uniquely on this manifold. We also propose a novel scalar measurement, named Geometric Anisotropy (GA), which is the Riemannian geodesic distance between the ODF and the isotropic ODF. The Renyi entropy H1/2 of the ODF can be computed from the GA. Moreover, we present an Affine-Euclidean framework and a Log-Euclidean framework so that we can work in an Euclidean space. As an application, Lagrange interpolation on ODF field is proposed based on weighted Frechet mean. We validate our methods on synthetic and real data experiments. Compared with existing Riemannian frameworks on ODF, our framework is model-free. The estimation of the parameters, i.e. Riemannian coordinates, is robust and linear. Moreover it should be noted that our theoretical results can be used for any probability density function (PDF) under an orthonormal basis representation.

Why do we remember? The communicative function of episodic memory.

PubMed

Mahr, Johannes; Csibra, Gergely

2017-01-19

Episodic memory has been analyzed in a number of different ways in both philosophy and psychology, and most controversy has centered on its self-referential, 'autonoetic' character. Here, we offer a comprehensive characterization of episodic memory in representational terms, and propose a novel functional account on this basis. We argue that episodic memory should be understood as a distinctive epistemic attitude taken towards an event simulation. On this view, episodic memory has a metarepresentational format and should not be equated with beliefs about the past. Instead, empirical findings suggest that the contents of human episodic memory are often constructed in the service of the explicit justification of such beliefs. Existing accounts of episodic memory function that have focused on explaining its constructive character through its role in 'future-oriented mental time travel' neither do justice to its capacity to ground veridical beliefs about the past nor to its representational format. We provide an account of the metarepresentational structure of episodic memory in terms of its role in communicative interaction. The generative nature of recollection allows us to represent and communicate the reasons for why we hold certain beliefs about the past. In this process, autonoesis corresponds to the capacity to determine when and how to assert epistemic authority in making claims about the past. A domain where such claims are indispensable are human social engagements. Such engagements commonly require the justification of entitlements and obligations, which is often possible only by explicit reference to specific past events.

A single-sided homogeneous Green's function representation for holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval

NASA Astrophysics Data System (ADS)

Wapenaar, Kees; Thorbecke, Jan; van der Neut, Joost

2016-04-01

Green's theorem plays a fundamental role in a diverse range of wavefield imaging applications, such as holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval. In many of those applications, the homogeneous Green's function (i.e. the Green's function of the wave equation without a singularity on the right-hand side) is represented by a closed boundary integral. In practical applications, sources and/or receivers are usually present only on an open surface, which implies that a significant part of the closed boundary integral is by necessity ignored. Here we derive a homogeneous Green's function representation for the common situation that sources and/or receivers are present on an open surface only. We modify the integrand in such a way that it vanishes on the part of the boundary where no sources and receivers are present. As a consequence, the remaining integral along the open surface is an accurate single-sided representation of the homogeneous Green's function. This single-sided representation accounts for all orders of multiple scattering. The new representation significantly improves the aforementioned wavefield imaging applications, particularly in situations where the first-order scattering approximation breaks down.

Beyond the word and image: characteristics of a common meaning system for language and vision revealed by functional and structural imaging.

PubMed

Jouen, A L; Ellmore, T M; Madden, C J; Pallier, C; Dominey, P F; Ventre-Dominey, J

2015-02-01

This research tests the hypothesis that comprehension of human events will engage an extended semantic representation system, independent of the input modality (sentence vs. picture). To investigate this, we examined brain activation and connectivity in 19 subjects who read sentences and viewed pictures depicting everyday events, in a combined fMRI and DTI study. Conjunction of activity in understanding sentences and pictures revealed a common fronto-temporo-parietal network that included the middle and inferior frontal gyri, the parahippocampal-retrosplenial complex, the anterior and middle temporal gyri, the inferior parietal lobe in particular the temporo-parietal cortex. DTI tractography seeded from this temporo-parietal cortex hub revealed a multi-component network reaching into the temporal pole, the ventral frontal pole and premotor cortex. A significant correlation was found between the relative pathway density issued from the temporo-parietal cortex and the imageability of sentences for individual subjects, suggesting a potential functional link between comprehension and the temporo-parietal connectivity strength. These data help to define a "meaning" network that includes components of recently characterized systems for semantic memory, embodied simulation, and visuo-spatial scene representation. The network substantially overlaps with the "default mode" network implicated as part of a core network of semantic representation, along with brain systems related to the formation of mental models, and reasoning. These data are consistent with a model of real-world situational understanding that is highly embodied. Crucially, the neural basis of this embodied understanding is not limited to sensorimotor systems, but extends to the highest levels of cognition, including autobiographical memory, scene analysis, mental model formation, reasoning and theory of mind. Copyright © 2014 Elsevier Inc. All rights reserved.

The Opponent Channel Population Code of Sound Location Is an Efficient Representation of Natural Binaural Sounds

PubMed Central

Młynarski, Wiktor

2015-01-01

In mammalian auditory cortex, sound source position is represented by a population of broadly tuned neurons whose firing is modulated by sounds located at all positions surrounding the animal. Peaks of their tuning curves are concentrated at lateral position, while their slopes are steepest at the interaural midline, allowing for the maximum localization accuracy in that area. These experimental observations contradict initial assumptions that the auditory space is represented as a topographic cortical map. It has been suggested that a “panoramic” code has evolved to match specific demands of the sound localization task. This work provides evidence suggesting that properties of spatial auditory neurons identified experimentally follow from a general design principle- learning a sparse, efficient representation of natural stimuli. Natural binaural sounds were recorded and served as input to a hierarchical sparse-coding model. In the first layer, left and right ear sounds were separately encoded by a population of complex-valued basis functions which separated phase and amplitude. Both parameters are known to carry information relevant for spatial hearing. Monaural input converged in the second layer, which learned a joint representation of amplitude and interaural phase difference. Spatial selectivity of each second-layer unit was measured by exposing the model to natural sound sources recorded at different positions. Obtained tuning curves match well tuning characteristics of neurons in the mammalian auditory cortex. This study connects neuronal coding of the auditory space with natural stimulus statistics and generates new experimental predictions. Moreover, results presented here suggest that cortical regions with seemingly different functions may implement the same computational strategy-efficient coding. PMID:25996373

Mean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure.

PubMed

Özarslan, Evren; Koay, Cheng Guan; Shepherd, Timothy M; Komlosh, Michal E; İrfanoğlu, M Okan; Pierpaoli, Carlo; Basser, Peter J

2013-09-01

Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in "q-space," and the corresponding "mean apparent propagator (MAP)" describing molecular displacements in "r-space." We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit "displacement" sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions-the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue. Copyright © 2013 Elsevier Inc. All rights reserved.

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.

Visual adaptation and face perception

PubMed Central

Webster, Michael A.; MacLeod, Donald I. A.

2011-01-01

The appearance of faces can be strongly affected by the characteristics of faces viewed previously. These perceptual after-effects reflect processes of sensory adaptation that are found throughout the visual system, but which have been considered only relatively recently in the context of higher level perceptual judgements. In this review, we explore the consequences of adaptation for human face perception, and the implications of adaptation for understanding the neural-coding schemes underlying the visual representation of faces. The properties of face after-effects suggest that they, in part, reflect response changes at high and possibly face-specific levels of visual processing. Yet, the form of the after-effects and the norm-based codes that they point to show many parallels with the adaptations and functional organization that are thought to underlie the encoding of perceptual attributes like colour. The nature and basis for human colour vision have been studied extensively, and we draw on ideas and principles that have been developed to account for norms and normalization in colour vision to consider potential similarities and differences in the representation and adaptation of faces. PMID:21536555

Gait recognition based on Gabor wavelets and modified gait energy image for human identification

NASA Astrophysics Data System (ADS)

Huang, Deng-Yuan; Lin, Ta-Wei; Hu, Wu-Chih; Cheng, Chih-Hsiang

2013-10-01

This paper proposes a method for recognizing human identity using gait features based on Gabor wavelets and modified gait energy images (GEIs). Identity recognition by gait generally involves gait representation, extraction, and classification. In this work, a modified GEI convolved with an ensemble of Gabor wavelets is proposed as a gait feature. Principal component analysis is then used to project the Gabor-wavelet-based gait features into a lower-dimension feature space for subsequent classification. Finally, support vector machine classifiers based on a radial basis function kernel are trained and utilized to recognize human identity. The major contributions of this paper are as follows: (1) the consideration of the shadow effect to yield a more complete segmentation of gait silhouettes; (2) the utilization of motion estimation to track people when walkers overlap; and (3) the derivation of modified GEIs to extract more useful gait information. Extensive performance evaluation shows a great improvement of recognition accuracy due to the use of shadow removal, motion estimation, and gait representation using the modified GEIs and Gabor wavelets.

Visual adaptation and face perception.

PubMed

Webster, Michael A; MacLeod, Donald I A

2011-06-12

The appearance of faces can be strongly affected by the characteristics of faces viewed previously. These perceptual after-effects reflect processes of sensory adaptation that are found throughout the visual system, but which have been considered only relatively recently in the context of higher level perceptual judgements. In this review, we explore the consequences of adaptation for human face perception, and the implications of adaptation for understanding the neural-coding schemes underlying the visual representation of faces. The properties of face after-effects suggest that they, in part, reflect response changes at high and possibly face-specific levels of visual processing. Yet, the form of the after-effects and the norm-based codes that they point to show many parallels with the adaptations and functional organization that are thought to underlie the encoding of perceptual attributes like colour. The nature and basis for human colour vision have been studied extensively, and we draw on ideas and principles that have been developed to account for norms and normalization in colour vision to consider potential similarities and differences in the representation and adaptation of faces.

Face aging effect simulation model based on multilayer representation and shearlet transform

NASA Astrophysics Data System (ADS)

Li, Yuancheng; Li, Yan

2017-09-01

In order to extract detailed facial features, we build a face aging effect simulation model based on multilayer representation and shearlet transform. The face is divided into three layers: the global layer of the face, the local features layer, and texture layer, which separately establishes the aging model. First, the training samples are classified according to different age groups, and we use active appearance model (AAM) at the global level to obtain facial features. The regression equations of shape and texture with age are obtained by fitting the support vector machine regression, which is based on the radial basis function. We use AAM to simulate the aging of facial organs. Then, for the texture detail layer, we acquire the significant high-frequency characteristic components of the face by using the multiscale shearlet transform. Finally, we get the last simulated aging images of the human face by the fusion algorithm. Experiments are carried out on the FG-NET dataset, and the experimental results show that the simulated face images have less differences from the original image and have a good face aging simulation effect.

Estimation of the Thermal Process in the Honeycomb Panel by a Monte Carlo Method

NASA Astrophysics Data System (ADS)

Gusev, S. A.; Nikolaev, V. N.

2018-01-01

A new Monte Carlo method for estimating the thermal state of the heat insulation containing honeycomb panels is proposed in the paper. The heat transfer in the honeycomb panel is described by a boundary value problem for a parabolic equation with discontinuous diffusion coefficient and boundary conditions of the third kind. To obtain an approximate solution, it is proposed to use the smoothing of the diffusion coefficient. After that, the obtained problem is solved on the basis of the probability representation. The probability representation is the expectation of the functional of the diffusion process corresponding to the boundary value problem. The process of solving the problem is reduced to numerical statistical modelling of a large number of trajectories of the diffusion process corresponding to the parabolic problem. It was used earlier the Euler method for this object, but that requires a large computational effort. In this paper the method is modified by using combination of the Euler and the random walk on moving spheres methods. The new approach allows us to significantly reduce the computation costs.

Dynamic cultural influences on neural representations of the self.

PubMed

Chiao, Joan Y; Harada, Tokiko; Komeda, Hidetsugu; Li, Zhang; Mano, Yoko; Saito, Daisuke; Parrish, Todd B; Sadato, Norihiro; Iidaka, Tetsuya

2010-01-01

People living in multicultural environments often encounter situations which require them to acquire different cultural schemas and to switch between these cultural schemas depending on their immediate sociocultural context. Prior behavioral studies show that priming cultural schemas reliably impacts mental processes and behavior underlying self-concept. However, less well understood is whether or not cultural priming affects neurobiological mechanisms underlying the self. Here we examined whether priming cultural values of individualism and collectivism in bicultural individuals affects neural activity in cortical midline structures underlying self-relevant processes using functional magnetic resonance imaging. Biculturals primed with individualistic values showed increased activation within medial prefrontal cortex (MPFC) and posterior cingulate cortex (PCC) during general relative to contextual self-judgments, whereas biculturals primed with collectivistic values showed increased response within MPFC and PCC during contextual relative to general self-judgments. Moreover, degree of cultural priming was positively correlated with degree of MPFC and PCC activity during culturally congruent self-judgments. These findings illustrate the dynamic influence of culture on neural representations underlying the self and, more broadly, suggest a neurobiological basis by which people acculturate to novel environments.

Optimization of digital designs

NASA Technical Reports Server (NTRS)

Miles, Lowell H. (Inventor); Whitaker, Sterling R. (Inventor)

2009-01-01

An application specific integrated circuit is optimized by translating a first representation of its digital design to a second representation. The second representation includes multiple syntactic expressions that admit a representation of a higher-order function of base Boolean values. The syntactic expressions are manipulated to form a third representation of the digital design.

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.

Verifying the equivalence of representations of the knee joint moment vector from a drop vertical jump task.

PubMed

Nichols, Julia K; O'Reilly, Oliver M

2017-03-01

Biomechanics software programs, such as Visual3D, Nexus, Cortex, and OpenSim, have the capability of generating several distinct component representations for joint moments and forces from motion capture data. These representations include those for orthonormal proximal and distal coordinate systems and a non-orthogonal joint coordinate system. In this article, a method is presented to address the challenging problem of evaluating and verifying the equivalence of these representations. The method accommodates the difficulty that there are two possible sets of non-orthogonal basis vectors that can be used to express a vector in the joint coordinate system and is illuminated using motion capture data from a drop vertical jump task. Copyright © 2016 Elsevier B.V. All rights reserved.

Rational Solutions of the Painlevé-II Equation Revisited

NASA Astrophysics Data System (ADS)

Miller, Peter D.; Sheng, Yue

2017-08-01

The rational solutions of the Painlevé-II equation appear in several applications and are known to have many remarkable algebraic and analytic properties. They also have several different representations, useful in different ways for establishing these properties. In particular, Riemann-Hilbert representations have proven to be useful for extracting the asymptotic behavior of the rational solutions in the limit of large degree (equivalently the large-parameter limit). We review the elementary properties of the rational Painlevé-II functions, and then we describe three different Riemann-Hilbert representations of them that have appeared in the literature: a representation by means of the isomonodromy theory of the Flaschka-Newell Lax pair, a second representation by means of the isomonodromy theory of the Jimbo-Miwa Lax pair, and a third representation found by Bertola and Bothner related to pseudo-orthogonal polynomials. We prove that the Flaschka-Newell and Bertola-Bothner Riemann-Hilbert representations of the rational Painlevé-II functions are explicitly connected to each other. Finally, we review recent results describing the asymptotic behavior of the rational Painlevé-II functions obtained from these Riemann-Hilbert representations by means of the steepest descent method.

A representational basis for the development of a distributed expert system for Space Shuttle flight control

NASA Technical Reports Server (NTRS)

Helly, J. J., Jr.; Bates, W. V.; Cutler, M.; Kelem, S.

1984-01-01

A new representation of malfunction procedure logic which permits the automation of these procedures using Boolean normal forms is presented. This representation is discussed in the context of the development of an expert system for space shuttle flight control including software and hardware implementation modes, and a distributed architecture. The roles and responsibility of the flight control team as well as previous work toward the development of expert systems for flight control support at Johnson Space Center are discussed. The notion of malfunction procedures as graphs is introduced as well as the concept of hardware-equivalence.

Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children.

PubMed

Lourenco, Stella F; Bonny, Justin W

2017-07-01

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises questions about whether the non-symbolic basis of mathematical thinking is unique to numerical magnitude. Here we examined this issue in 5- and 6-year-old children using comparison tasks of non-symbolic number arrays and cumulative area as well as standardized tests of math competence. One set of findings revealed that scores on both magnitude comparison tasks were modulated by ratio, consistent with shared analog format. Moreover, scores on these tasks were moderately correlated, suggesting overlap in the precision of numerical and non-numerical magnitudes, as expected under a general magnitude system. Another set of findings revealed that the precision of both types of magnitude contributed shared and unique variance to the same math measures (e.g. calculation and geometry), after accounting for age and verbal competence. These findings argue against an exclusive role for non-symbolic number in supporting early mathematical understanding. Moreover, they suggest that mathematical understanding may be rooted in a general system of magnitude representation that is not specific to numerical magnitude but that also encompasses non-numerical magnitude. © 2016 John Wiley & Sons Ltd.

Body representation in patients after vascular brain injuries.

PubMed

Razmus, Magdalena

2017-11-01

Neuropsychological literature suggests that body representation is a multidimensional concept consisting of various types of representations. Previous studies have demonstrated dissociations between three types of body representation specified by the kind of data and processes, i.e. body schema, body structural description, and body semantics. The aim of the study was to describe the state of body representation in patients after vascular brain injuries and to provide evidence for the different types of body representation. The question about correlations between body representation deficits and neuropsychological dysfunctions was also investigated. Fifty patients after strokes and 50 control individuals participated in the study. They were examined with tasks referring to dynamic representation of body parts positions, topological body map, and lexical and semantic knowledge about the body. Data analysis showed that vascular brain injuries result in deficits of body representation, which may co-occur with cognitive dysfunctions, but the latter are a possible risk factor for body representation deficits rather than sufficient or imperative requisites for them. The study suggests that types of body representation may be separated on the basis not only of their content, but also of their relation with self. Principal component analysis revealed three factors, which explained over 66% of results variance. The factors, which may be interpreted as types or dimensions of mental model of a body, represent different degrees of connection with self. The results indicate another possibility of body representation types classification, which should be verified in future research.

Demonstration of Detection and Ranging Using Solvable Chaos

NASA Technical Reports Server (NTRS)

Corron, Ned J.; Stahl, Mark T.; Blakely, Jonathan N.

2013-01-01

Acoustic experiments demonstrate a novel approach to ranging and detection that exploits the properties of a solvable chaotic oscillator. This nonlinear oscillator includes an ordinary differential equation and a discrete switching condition. The chaotic waveform generated by this hybrid system is used as the transmitted waveform. The oscillator admits an exact analytic solution that can be written as the linear convolution of binary symbols and a single basis function. This linear representation enables coherent reception using a simple analog matched filter and without need for digital sampling or signal processing. An audio frequency implementation of the transmitter and receiver is described. Successful acoustic ranging measurements are presented to demonstrate the viability of the approach.

Unified double- and single-sided homogeneous Green’s function representations

PubMed Central

van der Neut, Joost; Slob, Evert

2016-01-01

In wave theory, the homogeneous Green’s function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green’s function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green’s function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green’s function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green’s function retrieval. PMID:27436983

Unified double- and single-sided homogeneous Green's function representations

NASA Astrophysics Data System (ADS)

Wapenaar, Kees; van der Neut, Joost; Slob, Evert

2016-06-01

In wave theory, the homogeneous Green's function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green's function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green's function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green's function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green's function retrieval.

The Analytic Structure of Scattering Amplitudes in N = 4 Super-Yang-Mills Theory

NASA Astrophysics Data System (ADS)

Litsey, Sean Christopher

We begin the dissertation in Chapter 1 with a discussion of tree-level amplitudes in Yang-. Mills theories. The DDM and BCJ decompositions of the amplitudes are described and. related to one another by the introduction of a transformation matrix. This is related to the. Kleiss-Kuijf and BCJ amplitude identities, and we conjecture a connection to the existence. of a BCJ representation via a condition on the generalized inverse of that matrix. Under. two widely-believed assumptions, this relationship is proved. Switching gears somewhat, we introduce the RSVW formulation of the amplitude, and the extension of BCJ-like features to residues of the RSVW integrand is proposed. Using the previously proven connection of BCJ representations to the generalized inverse condition, this extension is validated, including a version of gravitational double copy. The remainder of the dissertation involves an analysis of the analytic properties of loop. amplitudes in N = 4 super-Yang-Mills theory. Chapter 2 contains a review of the planar case, including an exposition of dual variables and momentum twistors, dual conformal symmetry, and their implications for the amplitude. After defining the integrand and on-shell diagrams, we explain the crucial properties that the amplitude has no poles at infinite momentum and that its leading singularities are dual-conformally-invariant cross ratios, and can therefore be normalized to unity. We define the concept of a dlog form, and show that it is a feature of the planar integrand as well. This leads to the definition of a pure integrand basis. The proceeding setup is connected to the amplituhedron formulation, and we put forward the hypothesis that the amplitude is determined by zero conditions. Chapter 3 contains the primary computations of the dissertation. This chapter treats. amplitudes in fully nonplanar N = 4 super-Yang-Mills, analyzing the conjecture that they. follow the pattern of having no poles at infinity, can be written in dlog form, and can. be decomposed into a pure integrand basis, with each basis element having unit leading. singularity. Through explicit calculation, we show that this is true for the two-loop fourpoint, three-loop four-point, and two-loop five-point amplitudes, and discuss the features of. each case. We then discuss the zero condition hypothesis, showing explicitly that it holds for the two-loop four-particle amplitude, and showing the set of conditions that fix the amplitude in the three-loop four-particle and two-loop five-particle cases without explicitly performing the fixing. This concludes the body of the dissertation. Two appendices complete the dissertation. Appendix B includes an in-depth discussion of. dlog forms, including purely mathematical examples and a discussion of their appearance in one-loop amplitudes. Finally, Appendix C redoes portions of the analysis of Chapter 3 for the two- and three-loop four-particle amplitudes, but gives representations that are not in a pure integrand basis. Instead diagram symmetry is imposed on the basis elements, and diagrams that lack maximal cuts are pushed into maximal-cut diagrams. This gives representations closer in spirit to the previously-constructed representations of these amplitudes, such as the BCJ representations. It also highlights the role of color Jacobi identities and the freedom in the amplitude representation they can generate, and contains an explicit discussion of these features that is unpublished elsewhere.

Generalised Transfer Functions of Neural Networks

NASA Astrophysics Data System (ADS)

Fung, C. F.; Billings, S. A.; Zhang, H.

1997-11-01

When artificial neural networks are used to model non-linear dynamical systems, the system structure which can be extremely useful for analysis and design, is buried within the network architecture. In this paper, explicit expressions for the frequency response or generalised transfer functions of both feedforward and recurrent neural networks are derived in terms of the network weights. The derivation of the algorithm is established on the basis of the Taylor series expansion of the activation functions used in a particular neural network. This leads to a representation which is equivalent to the non-linear recursive polynomial model and enables the derivation of the transfer functions to be based on the harmonic expansion method. By mapping the neural network into the frequency domain information about the structure of the underlying non-linear system can be recovered. Numerical examples are included to demonstrate the application of the new algorithm. These examples show that the frequency response functions appear to be highly sensitive to the network topology and training, and that the time domain properties fail to reveal deficiencies in the trained network structure.

Estimating and Identifying Unspecified Correlation Structure for Longitudinal Data

PubMed Central

Hu, Jianhua; Wang, Peng; Qu, Annie

2014-01-01

Identifying correlation structure is important to achieving estimation efficiency in analyzing longitudinal data, and is also crucial for drawing valid statistical inference for large size clustered data. In this paper, we propose a nonparametric method to estimate the correlation structure, which is applicable for discrete longitudinal data. We utilize eigenvector-based basis matrices to approximate the inverse of the empirical correlation matrix and determine the number of basis matrices via model selection. A penalized objective function based on the difference between the empirical and model approximation of the correlation matrices is adopted to select an informative structure for the correlation matrix. The eigenvector representation of the correlation estimation is capable of reducing the risk of model misspecification, and also provides useful information on the specific within-cluster correlation pattern of the data. We show that the proposed method possesses the oracle property and selects the true correlation structure consistently. The proposed method is illustrated through simulations and two data examples on air pollution and sonar signal studies. PMID:26361433

Disparity channels in early vision

PubMed Central

Roe, AW; Parker, AJ; Born, RT; DeAngelis, GC

2008-01-01

The last decade has seen a dramatic increase in our knowledge of the neural basis of stereopsis. New cortical areas have been found to represent binocular disparities, new representations of disparity information (e.g., relative disparity signals) have been uncovered, the first topographic maps of disparity have been measured, and the first causal links between neural activity and depth perception have been established. Equally exciting is the finding that training and experience affects how signals are channeled through different brain areas, a flexibility that may be crucial for learning, plasticity, and recovery of function. The collective efforts of several laboratories have established stereo vision as one of the most productive model systems for elucidating the neural basis of perception. Much remains to be learned about how the disparity signals that are initially encoded in primary visual cortex are routed to and processed by extrastriate areas to mediate the diverse capacities of 3D vision that enhance our daily experience of the world. PMID:17978018

Specificity of Emotion Inferences as a Function of Emotional Contextual Support

ERIC Educational Resources Information Center

Gillioz, Christelle; Gygax, Pascal M.

2017-01-01

Research on emotion inferences has shown that readers include a representation of the main character's emotional state in their mental representations of the text. We examined the specificity of emotion representations as a function of the emotion content of short narratives, in terms of the quantity and quality of emotion components included in…

VLSI architectures for computing multiplications and inverses in GF(2m)

NASA Technical Reports Server (NTRS)

Wang, C. C.; Truong, T. K.; Shao, H. M.; Deutsch, L. J.; Omura, J. K.

1985-01-01

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that are easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. A pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal-basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.

VLSI architectures for computing multiplications and inverses in GF(2-m)

NASA Technical Reports Server (NTRS)

Wang, C. C.; Truong, T. K.; Shao, H. M.; Deutsch, L. J.; Omura, J. K.; Reed, I. S.

1983-01-01

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that are easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. A pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal-basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.

VLSI architectures for computing multiplications and inverses in GF(2m).

PubMed

Wang, C C; Truong, T K; Shao, H M; Deutsch, L J; Omura, J K; Reed, I S

1985-08-01

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that can be easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. In this paper, a pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal basis representation used together with this multiplier, a pipeline architecture is developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable, and therefore, naturally suitable for VLSI implementation.

ABJM Wilson loops in arbitrary representations

NASA Astrophysics Data System (ADS)

Hatsuda, Yasuyuki; Honda, Masazumi; Moriyama, Sanefumi; Okuyama, Kazumi

2013-10-01

We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.

Representational Issues in Systemic Functional Grammar and Systemic Grammar and Functional Unification Grammar. ISI Reprint Series.

ERIC Educational Resources Information Center

Matthiessen, Christian; Kasper, Robert

Consisting of two separate papers, "Representational Issues in Systemic Functional Grammar," by Christian Matthiessen and "Systemic Grammar and Functional Unification Grammar," by Robert Kasper, this document deals with systemic aspects of natural language processing and linguistic theory and with computational applications of…

Representations of self and other in the narratives of neglected, physically abused, and sexually abused preschoolers.

PubMed

Toth, S L; Cicchetti, D; Macfie, J; Emde, R N

1997-01-01

The MacArthur Story Stem Battery was used to examine maternal and self-representations in neglected, physically abused, sexually abused, and nonmaltreated comparison preschool children. The narratives of maltreated children contained more negative maternal representations and more negative self-representations than did the narratives of nonmaltreated children. Maltreated children also were more controlling with and less responsive to the examiner. In examining the differential impact of maltreatment subtype differences on maternal and self-representations, physically abused children evidenced the most negative maternal representations; they also had more negative self-representations than nonmaltreated children. Sexually abused children manifested more positive self-representations than neglected children. Despite these differences in the nature of maternal and self-representations, physically and sexually abused children both were more controlling and less responsive to the examiner. The investigation adds to the corpus of knowledge regarding disturbances in the self-system functioning of maltreated children and provides support for relations between representational models of self and other and the self-organizing function that these models exert on children's lives.

Lexical is as lexical does: computational approaches to lexical representation

PubMed Central

Woollams, Anna M.

2015-01-01

In much of neuroimaging and neuropsychology, regions of the brain have been associated with ‘lexical representation’, with little consideration as to what this cognitive construct actually denotes. Within current computational models of word recognition, there are a number of different approaches to the representation of lexical knowledge. Structural lexical representations, found in original theories of word recognition, have been instantiated in modern localist models. However, such a representational scheme lacks neural plausibility in terms of economy and flexibility. Connectionist models have therefore adopted distributed representations of form and meaning. Semantic representations in connectionist models necessarily encode lexical knowledge. Yet when equipped with recurrent connections, connectionist models can also develop attractors for familiar forms that function as lexical representations. Current behavioural, neuropsychological and neuroimaging evidence shows a clear role for semantic information, but also suggests some modality- and task-specific lexical representations. A variety of connectionist architectures could implement these distributed functional representations, and further experimental and simulation work is required to discriminate between these alternatives. Future conceptualisations of lexical representations will therefore emerge from a synergy between modelling and neuroscience. PMID:25893204

7 CFR 924.26 - Vacancies.

Code of Federal Regulations, 2010 CFR

2010-01-01

... an alternate member of the committee to qualify, or in the event of the death, removal, resignation... vacancy without regard to nominations, which selection shall be made on the basis of representation...

7 CFR 929.26 - Vacancies.

Code of Federal Regulations, 2010 CFR

2010-01-01

... member of the committee to qualify, or in the event of the death, removal, resignation, or... regard to nominations, which selection shall be made on the basis of representation provided for in...

On the nature of hand-action representations evoked during written sentence comprehension.

PubMed

Bub, Daniel N; Masson, Michael E J

2010-09-01

We examine the nature of motor representations evoked during comprehension of written sentences describing hand actions. We distinguish between two kinds of hand actions: a functional action, applied when using the object for its intended purpose, and a volumetric action, applied when picking up or holding the object. In Experiment 1, initial activation of both action representations was followed by selection of the functional action, regardless of sentence context. Experiment 2 showed that when the sentence was followed by a picture of the object, clear context-specific effects on evoked action representations were obtained. Experiment 3 established that when a picture of an object was presented alone, the time course of both functional and volumetric actions was the same. These results provide evidence that representations of object-related hand actions are evoked as part of sentence processing. In addition, we discuss the conditions that elicit context-specific evocation of motor representations. 2010 Elsevier B.V. All rights reserved.

A new transform for the analysis of complex fractionated atrial electrograms

PubMed Central

2011-01-01

Background Representation of independent biophysical sources using Fourier analysis can be inefficient because the basis is sinusoidal and general. When complex fractionated atrial electrograms (CFAE) are acquired during atrial fibrillation (AF), the electrogram morphology depends on the mix of distinct nonsinusoidal generators. Identification of these generators using efficient methods of representation and comparison would be useful for targeting catheter ablation sites to prevent arrhythmia reinduction. Method A data-driven basis and transform is described which utilizes the ensemble average of signal segments to identify and distinguish CFAE morphologic components and frequencies. Calculation of the dominant frequency (DF) of actual CFAE, and identification of simulated independent generator frequencies and morphologies embedded in CFAE, is done using a total of 216 recordings from 10 paroxysmal and 10 persistent AF patients. The transform is tested versus Fourier analysis to detect spectral components in the presence of phase noise and interference. Correspondence is shown between ensemble basis vectors of highest power and corresponding synthetic drivers embedded in CFAE. Results The ensemble basis is orthogonal, and efficient for representation of CFAE components as compared with Fourier analysis (p ≤ 0.002). When three synthetic drivers with additive phase noise and interference were decomposed, the top three peaks in the ensemble power spectrum corresponded to the driver frequencies more closely as compared with top Fourier power spectrum peaks (p ≤ 0.005). The synthesized drivers with phase noise and interference were extractable from their corresponding ensemble basis with a mean error of less than 10%. Conclusions The new transform is able to efficiently identify CFAE features using DF calculation and by discerning morphologic differences. Unlike the Fourier transform method, it does not distort CFAE signals prior to analysis, and is relatively robust to jitter in periodic events. Thus the ensemble method can provide a useful alternative for quantitative characterization of CFAE during clinical study. PMID:21569421

Organization and evolution of parieto-frontal processing streams in macaque monkeys and humans.

PubMed

Caminiti, Roberto; Innocenti, Giorgio M; Battaglia-Mayer, Alexandra

2015-09-01

The functional organization of the parieto-frontal system is crucial for understanding cognitive-motor behavior and provides the basis for interpreting the consequences of parietal lesions in humans from a neurobiological perspective. The parieto-frontal connectivity defines some main information streams that, rather than being devoted to restricted functions, underlie a rich behavioral repertoire. Surprisingly, from macaque to humans, evolution has added only a few, new functional streams, increasing however their complexity and encoding power. In fact, the characterization of the conduction times of parietal and frontal areas to different target structures has recently opened a new window on cortical dynamics, suggesting that evolution has amplified the probability of dynamic interactions between the nodes of the network, thanks to communication patterns based on temporally-dispersed conduction delays. This might allow the representation of sensory-motor signals within multiple neural assemblies and reference frames, as to optimize sensory-motor remapping within an action space characterized by different and more complex demands across evolution. Copyright © 2015 Elsevier Ltd. All rights reserved.

GABA Neurons and the Mechanisms of Network Oscillations: Implications for Understanding Cortical Dysfunction in Schizophrenia

PubMed Central

Gonzalez-Burgos, Guillermo; Lewis, David A.

2008-01-01

Synchronization of neuronal activity in the neocortex may underlie the coordination of neural representations and thus is critical for optimal cognitive function. Because cognitive deficits are the major determinant of functional outcome in schizophrenia, identifying their neural basis is important for the development of new therapeutic interventions. Here we review the data suggesting that phasic synaptic inhibition mediated by specific subtypes of cortical γ-aminobutyric acid (GABA) neurons is essential for the production of synchronized network oscillations. We also discuss evidence indicating that GABA neurotransmission is altered in schizophrenia and propose mechanisms by which such alterations can decrease the strength of inhibitory connections in a cell-type–specific manner. We suggest that some alterations observed in the neocortex of schizophrenia subjects may be compensatory responses that partially restore inhibitory synaptic efficacy. The findings of altered neural synchrony and impaired cognitive function in schizophrenia suggest that such compensatory responses are insufficient and that interventions aimed at augmenting the efficacy of GABA neurotransmission might be of therapeutic value. PMID:18586694

GABA neurons and the mechanisms of network oscillations: implications for understanding cortical dysfunction in schizophrenia.

PubMed

Gonzalez-Burgos, Guillermo; Lewis, David A

2008-09-01

Synchronization of neuronal activity in the neocortex may underlie the coordination of neural representations and thus is critical for optimal cognitive function. Because cognitive deficits are the major determinant of functional outcome in schizophrenia, identifying their neural basis is important for the development of new therapeutic interventions. Here we review the data suggesting that phasic synaptic inhibition mediated by specific subtypes of cortical gamma-aminobutyric acid (GABA) neurons is essential for the production of synchronized network oscillations. We also discuss evidence indicating that GABA neurotransmission is altered in schizophrenia and propose mechanisms by which such alterations can decrease the strength of inhibitory connections in a cell-type-specific manner. We suggest that some alterations observed in the neocortex of schizophrenia subjects may be compensatory responses that partially restore inhibitory synaptic efficacy. The findings of altered neural synchrony and impaired cognitive function in schizophrenia suggest that such compensatory responses are insufficient and that interventions aimed at augmenting the efficacy of GABA neurotransmission might be of therapeutic value.

Luminosity function and cosmological evolution of X-ray selected quasars

NASA Technical Reports Server (NTRS)

Maccacaro, T.; Gioia, I. M.

1983-01-01

The preliminary analysis of a complete sample of 55 X-ray sources is presented as part of the Medium Sensitivity Survey of the Einstein Observatory. A pure luminosity evolutionary law is derived in order to determine the uniform distribution of the sources and the rates of evolution for Active Galactic Nuclei (AGNs) observed by X-ray and optical techniques are compared. A nonparametric representation of the luminosity function is fitted to the observational data. On the basis of the reduced data, it is determined that: (1) AGNs evolve cosmologically; (2) less evolution is required to explain the X-ray data than the optical data; (3) the high-luminosity portion of the X-ray luminosity can be described by a power-law with a slope of gamma = 3.6; and (4) the X-ray luminosity function flattens at low luminosities. Some of the implications of the results for conventional theoretical models of the evolution of quasars and Seyfert galaxies are discussed.

The sentient self.

PubMed

Craig, A D Bud

2010-06-01

This article addresses the neuroanatomical evidence for a progression of integrative representations of affective feelings from the body that lead to an ultimate representation of all feelings in the bilateral anterior insulae, or "the sentient self." Evidence for somatotopy in the primary interoceptive sensory cortex is presented, and the organization of the mid-insula and the anterior insula is discussed. Issues that need to be addressed are highlighted. A possible basis for subjectivity in a cinemascopic model of awareness is presented.

7 CFR 958.30 - Vacancies.

Code of Federal Regulations, 2010 CFR

2010-01-01

... alternate, to qualify, or in the event of the death, removal, resignation, or disqualification of any... shall be made on the basis of the representation provided for in this subpart. Expenses and Assessments ...

7 CFR 923.26 - Vacancies.

Code of Federal Regulations, 2010 CFR

2010-01-01

... committee to qualify, or in the event of the death, removal, resignation, or disqualification of any member..., which selection shall be made on the basis of representation provided for in § 923.20. ...

Magneto-optical spectra and electron structure of Nd0.5Gd0.5Fe3(BO3)4 single crystal

NASA Astrophysics Data System (ADS)

Malakhovskii, A. V.; Gnatchenko, S. L.; Kachur, I. S.; Piryatinskaya, V. G.; Sukhachev, A. L.; Temerov, V. L.

2016-03-01

Polarized absorption spectra and magnetic circular dichroism (MCD) spectra of Nd0.5Gd0.5Fe3(BO3)4 single crystal were measured in the range of 10000-21000 cm-1 and at temperatures 2-300 K. On the basis of these data, in the paramagnetic state of the crystal, the 4f states of the Nd3+ ion were identified in terms of the irreducible representations and in terms of | J , ±MJ 〉 wave functions of the free atom. The changes of the Landé factor during f-f transitions were found theoretically in the | J , ±MJ 〉 wave functions approximation and were determined experimentally with the help of the measured MCD spectra. In the majority of cases the experimentally found values are close to the theoretically predicted ones.

The neural basis of episodic memory: evidence from functional neuroimaging.

PubMed Central

Rugg, Michael D; Otten, Leun J; Henson, Richard N A

2002-01-01

We review some of our recent research using functional neuroimaging to investigate neural activity supporting the encoding and retrieval of episodic memories, that is, memories for unique events. Findings from studies of encoding indicate that, at the cortical level, the regions responsible for the effective encoding of a stimulus event as an episodic memory include some of the regions that are also engaged to process the event 'online'. Thus, it appears that there is no single cortical site or circuit responsible for episodic encoding. The results of retrieval studies indicate that successful recollection of episodic information is associated with activation of lateral parietal cortex, along with more variable patterns of activity in dorsolateral and anterior prefrontal cortex. Whereas parietal regions may play a part in the representation of retrieved information, prefrontal areas appear to support processes that act on the products of retrieval to align behaviour with the demands of the retrieval task. PMID:12217177

Human brain networks function in connectome-specific harmonic waves.

PubMed

Atasoy, Selen; Donnelly, Isaac; Pearson, Joel

2016-01-21

A key characteristic of human brain activity is coherent, spatially distributed oscillations forming behaviour-dependent brain networks. However, a fundamental principle underlying these networks remains unknown. Here we report that functional networks of the human brain are predicted by harmonic patterns, ubiquitous throughout nature, steered by the anatomy of the human cerebral cortex, the human connectome. We introduce a new technique extending the Fourier basis to the human connectome. In this new frequency-specific representation of cortical activity, that we call 'connectome harmonics', oscillatory networks of the human brain at rest match harmonic wave patterns of certain frequencies. We demonstrate a neural mechanism behind the self-organization of connectome harmonics with a continuous neural field model of excitatory-inhibitory interactions on the connectome. Remarkably, the critical relation between the neural field patterns and the delicate excitation-inhibition balance fits the neurophysiological changes observed during the loss and recovery of consciousness.

Concepts and Categories: A Cognitive Neuropsychological Perspective

PubMed Central

Mahon, Bradford Z.; Caramazza, Alfonso

2010-01-01

One of the most provocative and exciting issues in cognitive science is how neural specificity for semantic categories of common objects arises in the functional architecture of the brain. More than two decades of research on the neuropsychological phenomenon of category-specific semantic deficits has generated detailed claims about the organization and representation of conceptual knowledge. More recently, researchers have sought to test hypotheses developed on the basis of neuropsychological evidence with functional imaging. From those two fields, the empirical generalization emerges that object domain and sensory modality jointly constrain the organization of knowledge in the brain. At the same time, research within the embodied cognition framework has highlighted the need to articulate how information is communicated between the sensory and motor systems, and processes that represent and generalize abstract information. Those developments point toward a new approach for understanding category specificity in terms of the coordinated influences of diverse regions and cognitive systems. PMID:18767921

Uniform quantized electron gas

NASA Astrophysics Data System (ADS)

Høye, Johan S.; Lomba, Enrique

2016-10-01

In this work we study the correlation energy of the quantized electron gas of uniform density at temperature T  =  0. To do so we utilize methods from classical statistical mechanics. The basis for this is the Feynman path integral for the partition function of quantized systems. With this representation the quantum mechanical problem can be interpreted as, and is equivalent to, a classical polymer problem in four dimensions where the fourth dimension is imaginary time. Thus methods, results, and properties obtained in the statistical mechanics of classical fluids can be utilized. From this viewpoint we recover the well known RPA (random phase approximation). Then to improve it we modify the RPA by requiring the corresponding correlation function to be such that electrons with equal spins can not be on the same position. Numerical evaluations are compared with well known results of a standard parameterization of Monte Carlo correlation energies.

Growth Points in Linking Representations of Function: A Research-Based Framework

ERIC Educational Resources Information Center

Ronda, Erlina

2015-01-01

This paper describes five growth points in linking representations of function developed from a study of secondary school learners. Framed within the cognitivist perspective and process-object conception of function, the growth points were identified and described based on linear and quadratic function tasks learners can do and their strategies…

A potential energy surface for the process H2 + H2O yielding H + H + H2O - Ab initio calculations and analytical representation

NASA Technical Reports Server (NTRS)

Schwenke, David W.; Walch, Stephen P.; Taylor, Peter R.

1991-01-01

Extensive ab initio calculations on the ground state potential energy surface of H2 + H2O were performed using a large contracted Gaussian basis set and a high level of correlation treatment. An analytical representation of the potential energy surface was then obtained which reproduces the calculated energies with an overall root-mean-square error of only 0.64 mEh. The analytic representation explicitly includes all nine internal degrees of freedom and is also well behaved as the H2 dissociates; it thus can be used to study collision-induced dissociation or recombination of H2. The strategy used to minimize the number of energy calculations is discussed, as well as other advantages of the present method for determining the analytical representation.

Mapping the Multiple Graded Contributions of the Anterior Temporal Lobe Representational Hub to Abstract and Social Concepts: Evidence from Distortion-corrected fMRI.

PubMed

Binney, Richard J; Hoffman, Paul; Lambon Ralph, Matthew A

2016-09-06

A growing body of recent convergent evidence indicates that the anterior temporal lobe (ATL) has connectivity-derived graded differences in semantic function: the ventrolateral region appears to be the transmodal, omni-category center-point of the hub whilst secondary contributions come from the peripheries of the hub in a manner that reflects their differential connectivity to different input/output modalities. One of the key challenges for this neurocognitive theory is how different types of concept, especially those with less reliance upon external sensory experience (such as abstract and social concepts), are coded across the graded ATL hub. We were able to answer this key question by using distortion-corrected fMRI to detect functional activations across the entire ATL region and thus to map the neural basis of social and psycholinguistically-matched abstract concepts. Both types of concept engaged a core left-hemisphere semantic network, including the ventrolateral ATL, prefrontal regions and posterior MTG. Additionally, we replicated previous findings of weaker differential activation of the superior and polar ATL for the processing of social stimuli, in addition to the stronger, omni-category activation observed in the vATL. These results are compatible with the view of the ATL as a graded transmodal substrate for the representation of coherent concepts. © The Author 2016. Published by Oxford University Press.

Mapping the Multiple Graded Contributions of the Anterior Temporal Lobe Representational Hub to Abstract and Social Concepts: Evidence from Distortion-corrected fMRI

PubMed Central

Binney, Richard J.; Hoffman, Paul; Lambon Ralph, Matthew A.

2016-01-01

A growing body of recent convergent evidence indicates that the anterior temporal lobe (ATL) has connectivity-derived graded differences in semantic function: the ventrolateral region appears to be the transmodal, omni-category center-point of the hub whilst secondary contributions come from the peripheries of the hub in a manner that reflects their differential connectivity to different input/output modalities. One of the key challenges for this neurocognitive theory is how different types of concept, especially those with less reliance upon external sensory experience (such as abstract and social concepts), are coded across the graded ATL hub. We were able to answer this key question by using distortion-corrected fMRI to detect functional activations across the entire ATL region and thus to map the neural basis of social and psycholinguistically-matched abstract concepts. Both types of concept engaged a core left-hemisphere semantic network, including the ventrolateral ATL, prefrontal regions and posterior MTG. Additionally, we replicated previous findings of weaker differential activation of the superior and polar ATL for the processing of social stimuli, in addition to the stronger, omni-category activation observed in the vATL. These results are compatible with the view of the ATL as a graded transmodal substrate for the representation of coherent concepts. PMID:27600844

Action Priority: Early Neurophysiological Interaction of Conceptual and Motor Representations

PubMed Central

Koester, Dirk; Schack, Thomas

2016-01-01

Handling our everyday life, we often react manually to verbal requests or instruction, but the functional interrelations of motor control and language are not fully understood yet, especially their neurophysiological basis. Here, we investigated whether specific motor representations for grip types interact neurophysiologically with conceptual information, that is, when reading nouns. Participants performed lexical decisions and, for words, executed a grasp-and-lift task on objects of different sizes involving precision or power grips while the electroencephalogram was recorded. Nouns could denote objects that require either a precision or a power grip and could, thus, be (in)congruent with the performed grasp. In a control block, participants pointed at the objects instead of grasping them. The main result revealed an event-related potential (ERP) interaction of grip type and conceptual information which was not present for pointing. Incongruent compared to congruent conditions elicited an increased positivity (100–200 ms after noun onset). Grip type effects were obtained in response-locked analyses of the grasping ERPs (100–300 ms at left anterior electrodes). These findings attest that grip type and conceptual information are functionally related when planning a grasping action but such an interaction could not be detected for pointing. Generally, the results suggest that control of behaviour can be modulated by task demands; conceptual noun information (i.e., associated action knowledge) may gain processing priority if the task requires a complex motor response. PMID:27973539

The Feeling of Action Tendencies: On the Emotional Regulation of Goal-Directed Behavior

PubMed Central

Lowe, Robert; Ziemke, Tom

2011-01-01

In this article, we review the nature of the functional and causal relationship between neurophysiologically/psychologically generated states of emotional feeling and action tendencies and extrapolate a novel perspective. Emotion theory, over the past century and beyond, has tended to regard feeling and action tendency as independent phenomena: attempts to outline the functional and causal relationship that exists between them have been framed therein. Classically, such relationships have been viewed as unidirectional, but an argument for bidirectionality rooted in a dynamic systems perspective has gained strength in recent years whereby the feeling–action tendency relationship is viewed as a composite whole. On the basis of our review of somatic–visceral theories of feelings, we argue that feelings are grounded upon neural-dynamic representations (elevated and stable activation patterns) of action tendency. Such representations amount to predictions updated by cognitive and bodily feedback. Specifically, we view emotional feelings as minimalist predictions of the action tendency (what the agent is physiologically and cognitively primed to do) in a given situation. The essence of this point is captured by our exposition of action tendency prediction–feedback loops which we consider, above all, in the context of emotion regulation, and in particular, of emotional regulation of goal-directed behavior. The perspective outlined may be of use to emotion theorists, computational modelers, and roboticists. PMID:22207854

On the efficiency of treating singularities in triatomic variational vibrational computations. The vibrational states of H(+)3 up to dissociation.

PubMed

Szidarovszky, Tamás; Császár, Attila G; Czakó, Gábor

2010-08-01

Several techniques of varying efficiency are investigated, which treat all singularities present in the triatomic vibrational kinetic energy operator given in orthogonal internal coordinates of the two distances-one angle type. The strategies are based on the use of a direct-product basis built from one-dimensional discrete variable representation (DVR) bases corresponding to the two distances and orthogonal Legendre polynomials, or the corresponding Legendre-DVR basis, corresponding to the angle. The use of Legendre functions ensures the efficient treatment of the angular singularity. Matrix elements of the singular radial operators are calculated employing DVRs using the quadrature approximation as well as special DVRs satisfying the boundary conditions and thus allowing for the use of exact DVR expressions. Potential optimized (PO) radial DVRs, based on one-dimensional Hamiltonians with potentials obtained by fixing or relaxing the two non-active coordinates, are also studied. The numerical calculations employed Hermite-DVR, spherical-oscillator-DVR, and Bessel-DVR bases as the primitive radial functions. A new analytical formula is given for the determination of the matrix elements of the singular radial operator using the Bessel-DVR basis. The usually claimed failure of the quadrature approximation in certain singular integrals is revisited in one and three dimensions. It is shown that as long as no potential optimization is carried out the quadrature approximation works almost as well as the exact DVR expressions. If wave functions with finite amplitude at the boundary are to be computed, the basis sets need to meet the required boundary conditions. The present numerical results also confirm that PO-DVRs should be constructed employing relaxed potentials and PO-DVRs can be useful for optimizing quadrature points for calculations applying large coordinate intervals and describing large-amplitude motions. The utility and efficiency of the different algorithms is demonstrated by the computation of converged near-dissociation vibrational energy levels for the H molecular ion.

Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

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

Konakli, Katerina, E-mail: konakli@ibk.baug.ethz.ch; Sudret, Bruno

2016-09-15

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely themore » exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor–product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input dimension, a situation that is often encountered in real-life problems. By introducing the conditional generalization error, we further demonstrate that canonical LRA tend to outperform sparse PCE in the prediction of extreme model responses, which is critical in reliability analysis.« less

Efficient Approaches for Evaluating the Planar Microstrip Green's Function and its Applications to the Analysis of Microstrip Antennas.

NASA Astrophysics Data System (ADS)

Barkeshli, Sina

A relatively simple and efficient closed form asymptotic representation of the microstrip dyadic surface Green's function is developed. The large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the planar microstrip configuration. Surprisingly, this asymptotic solution remains accurate even for very small (almost two tenths of a wavelength) lateral separation of the source and field points. The present asymptotic Green's function will thus allow a very efficient calculation of the currents excited on microstrip antenna patches/feed lines and monolithic millimeter and microwave integrated circuit (MIMIC) elements based on a moment method (MM) solution of an integral equation for these currents. The kernal of the latter integral equation is the present asymptotic form of the microstrip Green's function. It is noted that the conventional Sommerfeld integral representation of the microstrip surface Green's function is very poorly convergent when used in this MM formulation. In addition, an efficient exact steepest descent path integral form employing a radially propagating representation of the microstrip dyadic Green's function is also derived which exhibits a relatively faster convergence when compared to the conventional Sommerfeld integral representation. The same steepest descent form could also be obtained by deforming the integration contour of the conventional Sommerfeld representation; however, the radially propagating integral representation exhibits better convergence properties for laterally separated source and field points even before the steepest descent path of integration is used. Numerical results based on the efficient closed form asymptotic solution for the microstrip surface Green's function developed in this work are presented for the mutual coupling between a pair of dipoles on a single layer grounded dielectric slab. The accuracy of the latter calculations is confirmed by comparison with results based on an exact integral representation for that Green's function.

The association of personal semantic memory to identity representations: insight into higher-order networks of autobiographical contents.

PubMed

Grilli, Matthew D

2017-11-01

Identity representations are higher-order knowledge structures that organise autobiographical memories on the basis of personality and role-based themes of one's self-concept. In two experiments, the extent to which different types of personal semantic content are reflected in these higher-order networks of memories was investigated. Healthy, young adult participants generated identity representations that varied in remoteness of formation and verbally reflected on these themes in an open-ended narrative task. The narrative responses were scored for retrieval of episodic, experience-near personal semantic and experience-far (i.e., abstract) personal semantic contents. Results revealed that to reflect on remotely formed identity representations, experience-far personal semantic contents were retrieved more than experience-near personal semantic contents. In contrast, to reflect on recently formed identity representations, experience-near personal semantic contents were retrieved more than experience-far personal semantic contents. Although episodic memory contents were retrieved less than both personal semantic content types to reflect on remotely formed identity representations, this content type was retrieved at a similar frequency as experience-far personal semantic content to reflect on recently formed identity representations. These findings indicate that the association of personal semantic content to identity representations is robust and related to time since acquisition of these knowledge structures.

7 CFR 947.34 - Vacancies.

Code of Federal Regulations, 2010 CFR

2010-01-01

... as a committee member or as an alternate to qualify, or in the event of the death, removal... without regard to nominations, which selection shall be made on the basis of the representation provided...

7 CFR 987.26 - Vacancies.

Code of Federal Regulations, 2010 CFR

2010-01-01

..., resignation, disqualification, or death of any person nominated to serve on the Committee, or any member or... without regard to nominations, and the selection shall be made on the basis of representation provided in...

7 CFR 920.26 - Vacancies.

Code of Federal Regulations, 2010 CFR

2010-01-01

... member or as an alternate member of the committee to qualify, or in the event of the death, removal... vacancy without regard to nominations, which selection shall be made on the basis of representation...

Students' Ability to Connect Function Properties to Different Types of Elementary Functions: An Empirical Study on the Role of External Representations

ERIC Educational Resources Information Center

De Bock, Dirk; Neyens, Deborah; Van Dooren, Wim

2017-01-01

Recent research on the phenomenon of improper proportional reasoning focused on students' understanding of elementary functions and their external representations. So far, the role of basic function properties in students' concept images of functions remained unclear. We add to this research line by investigating how accurate students are in…

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 Novel Cylindrical Representation for Characterizing Intrinsic Properties of Protein Sequences.

PubMed

Yu, Jia-Feng; Dou, Xiang-Hua; Wang, Hong-Bo; Sun, Xiao; Zhao, Hui-Ying; Wang, Ji-Hua

2015-06-22

The composition and sequence order of amino acid residues are the two most important characteristics to describe a protein sequence. Graphical representations facilitate visualization of biological sequences and produce biologically useful numerical descriptors. In this paper, we propose a novel cylindrical representation by placing the 20 amino acid residue types in a circle and sequence positions along the z axis. This representation allows visualization of the composition and sequence order of amino acids at the same time. Ten numerical descriptors and one weighted numerical descriptor have been developed to quantitatively describe intrinsic properties of protein sequences on the basis of the cylindrical model. Their applications to similarity/dissimilarity analysis of nine ND5 proteins indicated that these numerical descriptors are more effective than several classical numerical matrices. Thus, the cylindrical representation obtained here provides a new useful tool for visualizing and charactering protein sequences. An online server is available at http://biophy.dzu.edu.cn:8080/CNumD/input.jsp .

Genetic determinants of time perception mediated by the serotonergic system.

PubMed

Sysoeva, Olga V; Tonevitsky, Alexander G; Wackermann, Jirí

2010-09-17

The present study investigates neurobiological underpinnings of individual differences in time perception. Forty-four right-handed Russian Caucasian males (18-35 years old) participated in the experiment. The polymorphism of the genes related to the activity of serotonin (5-HT) and dopamine (DA)-systems (such as 5-HTT, 5HT2a, MAOA, DAT, DRD2, COMT) was determined upon the basis of DNA analysis according to a standard procedure. Time perception in the supra-second range (mean duration 4.8 s) was studied, using the duration discrimination task and parametric fitting of psychometric functions, resulting in individual determination of the point of subjective equality (PSE). Assuming the 'dual klepsydra model' of internal duration representation, the PSE values were transformed into equivalent values of the parameter κ (kappa), which is a measure of the 'loss rate' of the duration representation. An association between time representation parameters (PSE and κ, respectively) and 5-HT-related genes was found, but not with DA-related genes. Higher 'loss rate' (κ) of the cumulative duration representation were found for the carriers of genotypes characterized by higher 5-HT transmission, i.e., 1) lower 5-HT reuptake, known for the 5-HTTLPR SS polymorphism compared with LL, 2) lower 5-HT degradation, described for the 'low expression' variant of MAOA VNTR gene compared with 'high expression' variant, and 3) higher 5-HT2a receptor density, proposed for the TT polymorphism of 5-HT2a T102C gene compared with CC. Convergent findings of the present study and previous psychopharmacological studies suggest an action path from 5-HT-activity-related genes, via activity of 5-HT in the brain, to time perception. An involvement of the DA-system in the encoding of durations in the supra-second range is questioned.

Neo: an object model for handling electrophysiology data in multiple formats

PubMed Central

Garcia, Samuel; Guarino, Domenico; Jaillet, Florent; Jennings, Todd; Pröpper, Robert; Rautenberg, Philipp L.; Rodgers, Chris C.; Sobolev, Andrey; Wachtler, Thomas; Yger, Pierre; Davison, Andrew P.

2014-01-01

Neuroscientists use many different software tools to acquire, analyze and visualize electrophysiological signals. However, incompatible data models and file formats make it difficult to exchange data between these tools. This reduces scientific productivity, renders potentially useful analysis methods inaccessible and impedes collaboration between labs. A common representation of the core data would improve interoperability and facilitate data-sharing. To that end, we propose here a language-independent object model, named “Neo,” suitable for representing data acquired from electroencephalographic, intracellular, or extracellular recordings, or generated from simulations. As a concrete instantiation of this object model we have developed an open source implementation in the Python programming language. In addition to representing electrophysiology data in memory for the purposes of analysis and visualization, the Python implementation provides a set of input/output (IO) modules for reading/writing the data from/to a variety of commonly used file formats. Support is included for formats produced by most of the major manufacturers of electrophysiology recording equipment and also for more generic formats such as MATLAB. Data representation and data analysis are conceptually separate: it is easier to write robust analysis code if it is focused on analysis and relies on an underlying package to handle data representation. For that reason, and also to be as lightweight as possible, the Neo object model and the associated Python package are deliberately limited to representation of data, with no functions for data analysis or visualization. Software for neurophysiology data analysis and visualization built on top of Neo automatically gains the benefits of interoperability, easier data sharing and automatic format conversion; there is already a burgeoning ecosystem of such tools. We intend that Neo should become the standard basis for Python tools in neurophysiology. PMID:24600386

Neo: an object model for handling electrophysiology data in multiple formats.

PubMed

Garcia, Samuel; Guarino, Domenico; Jaillet, Florent; Jennings, Todd; Pröpper, Robert; Rautenberg, Philipp L; Rodgers, Chris C; Sobolev, Andrey; Wachtler, Thomas; Yger, Pierre; Davison, Andrew P

2014-01-01

Neuroscientists use many different software tools to acquire, analyze and visualize electrophysiological signals. However, incompatible data models and file formats make it difficult to exchange data between these tools. This reduces scientific productivity, renders potentially useful analysis methods inaccessible and impedes collaboration between labs. A common representation of the core data would improve interoperability and facilitate data-sharing. To that end, we propose here a language-independent object model, named "Neo," suitable for representing data acquired from electroencephalographic, intracellular, or extracellular recordings, or generated from simulations. As a concrete instantiation of this object model we have developed an open source implementation in the Python programming language. In addition to representing electrophysiology data in memory for the purposes of analysis and visualization, the Python implementation provides a set of input/output (IO) modules for reading/writing the data from/to a variety of commonly used file formats. Support is included for formats produced by most of the major manufacturers of electrophysiology recording equipment and also for more generic formats such as MATLAB. Data representation and data analysis are conceptually separate: it is easier to write robust analysis code if it is focused on analysis and relies on an underlying package to handle data representation. For that reason, and also to be as lightweight as possible, the Neo object model and the associated Python package are deliberately limited to representation of data, with no functions for data analysis or visualization. Software for neurophysiology data analysis and visualization built on top of Neo automatically gains the benefits of interoperability, easier data sharing and automatic format conversion; there is already a burgeoning ecosystem of such tools. We intend that Neo should become the standard basis for Python tools in neurophysiology.

Using field observations to inform thermal hydrology models of permafrost dynamics with ATS (v0.83)

DOE PAGES

Atchley, Adam L.; Painter, Scott L.; Harp, Dylan R.; ...

2015-09-01

Climate change is profoundly transforming the carbon-rich Arctic tundra landscape, potentially moving it from a carbon sink to a carbon source by increasing the thickness of soil that thaws on a seasonal basis. Thus, the modeling capability and precise parameterizations of the physical characteristics needed to estimate projected active layer thickness (ALT) are limited in Earth system models (ESMs). In particular, discrepancies in spatial scale between field measurements and Earth system models challenge validation and parameterization of hydrothermal models. A recently developed surface–subsurface model for permafrost thermal hydrology, the Advanced Terrestrial Simulator (ATS), is used in combination with field measurementsmore » to achieve the goals of constructing a process-rich model based on plausible parameters and to identify fine-scale controls of ALT in ice-wedge polygon tundra in Barrow, Alaska. An iterative model refinement procedure that cycles between borehole temperature and snow cover measurements and simulations functions to evaluate and parameterize different model processes necessary to simulate freeze–thaw processes and ALT formation. After model refinement and calibration, reasonable matches between simulated and measured soil temperatures are obtained, with the largest errors occurring during early summer above ice wedges (e.g., troughs). The results suggest that properly constructed and calibrated one-dimensional thermal hydrology models have the potential to provide reasonable representation of the subsurface thermal response and can be used to infer model input parameters and process representations. The models for soil thermal conductivity and snow distribution were found to be the most sensitive process representations. However, information on lateral flow and snowpack evolution might be needed to constrain model representations of surface hydrology and snow depth.« less

Testing a dynamic-field account of interactions between spatial attention and spatial working memory.

PubMed

Johnson, Jeffrey S; Spencer, John P

2016-05-01

Studies examining the relationship between spatial attention and spatial working memory (SWM) have shown that discrimination responses are faster for targets appearing at locations that are being maintained in SWM, and that location memory is impaired when attention is withdrawn during the delay. These observations support the proposal that sustained attention is required for successful retention in SWM: If attention is withdrawn, memory representations are likely to fail, increasing errors. In the present study, this proposal was reexamined in light of a neural-process model of SWM. On the basis of the model's functioning, we propose an alternative explanation for the observed decline in SWM performance when a secondary task is performed during retention: SWM representations drift systematically toward the location of targets appearing during the delay. To test this explanation, participants completed a color discrimination task during the delay interval of a spatial-recall task. In the critical shifting-attention condition, the color stimulus could appear either toward or away from the midline reference axis, relative to the memorized location. We hypothesized that if shifting attention during the delay leads to the failure of SWM representations, there should be an increase in the variance of recall errors, but no change in directional errors, regardless of the direction of the shift. Conversely, if shifting attention induces drift of SWM representations-as predicted by the model-systematic changes in the patterns of spatial-recall errors should occur that would depend on the direction of the shift. The results were consistent with the latter possibility-recall errors were biased toward the locations of discrimination targets appearing during the delay.

Orienting numbers in mental space: horizontal organization trumps vertical.

PubMed

Holmes, Kevin J; Lourenco, Stella F

2012-01-01

While research on the spatial representation of number has provided substantial evidence for a horizontally oriented mental number line, recent studies suggest vertical organization as well. Directly comparing the relative strength of horizontal and vertical organization, however, we found no evidence of spontaneous vertical orientation (upward or downward), and horizontal trumped vertical when pitted against each other (Experiment 1). Only when numbers were conceptualized as magnitudes (as opposed to nonmagnitude ordinal sequences) did reliable vertical organization emerge, with upward orientation preferred (Experiment 2). Altogether, these findings suggest that horizontal representations predominate, and that vertical representations, when elicited, may be relatively inflexible. Implications for spatial organization beyond number, and its ontogenetic basis, are discussed.

Social representations and themata: the construction and functioning of social knowledge about donation and transplantation.

PubMed

Moloney, Gail; Hall, Rob; Walker, Iain

2005-09-01

This study extends previous research investigating the social representation of organ donation and transplantation (Moloney & Walker, 2000, 2002) by exploring the accommodation of contradiction (Wagner, Duveen, Verma, & Thelmel, 2000) within consensual reality (Rose et al., 1995), and the role of themata (Markova, 2000) in a representation. The study employed a mail-out questionnaire embedded with eight experimental conditions, which manipulated two tasks, scenario rating scale and word association. WMDS (INDSCAL) analyses demonstrated that the dialectical concepts of life and death are generative of a contradictory representational field that is maintained through the differential elicitation of the normative and functional dimensions (Guimelli, 1998) of the representation in accordance with social context.

Technology Focus: Multi-Representational Approaches to Equation Solving

ERIC Educational Resources Information Center

Garofalo, Joe; Trinter, Christine

2009-01-01

Most mathematical functions can be represented in numerous ways. The main representations typically addressed in school, often referred to as "the big three," are graphical, algebraic, and numerical representations, but there are others as well (e.g., diagrams, words, simulations). These different types of representations "often illuminate…

Impact of action primes on implicit processing of thematic and functional similarity relations: evidence from eye-tracking.

PubMed

Pluciennicka, Ewa; Wamain, Yannick; Coello, Yann; Kalénine, Solène

2016-07-01

The aim of this study was to specify the role of action representations in thematic and functional similarity relations between manipulable artifact objects. Recent behavioral and neurophysiological evidence indicates that while they are all relevant for manipulable artifact concepts, semantic relations based on thematic (e.g., saw-wood), specific function similarity (e.g., saw-axe), and general function similarity (e.g., saw-knife) are differently processed, and may relate to different levels of action representation. Point-light displays of object-related actions previously encoded at the gesture level (e.g., "sawing") or at the higher level of action representation (e.g., "cutting") were used as primes before participants identified target objects (e.g., saw) among semantically related and unrelated distractors (e.g., wood, feather, piano). Analysis of eye movements on the different objects during target identification informed about the amplitude and the timing of implicit activation of the different semantic relations. Results showed that action prime encoding impacted the processing of thematic relations, but not that of functional similarity relations. Semantic competition with thematic distractors was greater and earlier following action primes encoded at the gesture level compared to action primes encoded at higher level. As a whole, these findings highlight the direct influence of action representations on thematic relation processing, and suggest that thematic relations involve gesture-level representations rather than intention-level representations.

19 CFR 181.11 - Certificate of Origin.

Code of Federal Regulations, 2012 CFR

2012-04-01

... Certificate on the basis of: (1) Its knowledge of whether the good qualifies as an originating good; (2) Its reasonable reliance on the producer's written representation that the good qualifies as an originating good...

19 CFR 181.11 - Certificate of Origin.

Code of Federal Regulations, 2010 CFR

2010-04-01

... Certificate on the basis of: (1) Its knowledge of whether the good qualifies as an originating good; (2) Its reasonable reliance on the producer's written representation that the good qualifies as an originating good...

7 CFR 932.33 - Vacancies.

Code of Federal Regulations, 2010 CFR

2010-01-01

... the event of the removal, resignation, disqualification, or death of any member or alternate member, a... nominations, but on the basis of the applicable representations and qualifications set forth in §§ 932.25, 932...

7 CFR 945.28 - Vacancies.

Code of Federal Regulations, 2010 CFR

2010-01-01

... member or as an alternate to qualify, or in the event of the death, removal, resignation, or... nominations, which selection shall be made on the basis of the representation provided for in § 945.24. ...

A wavelet-based intermittency detection technique from PIV investigations in transitional boundary layers

NASA Astrophysics Data System (ADS)

Simoni, Daniele; Lengani, Davide; Guida, Roberto

2016-09-01

The transition process of the boundary layer growing over a flat plate with pressure gradient simulating the suction side of a low-pressure turbine blade and elevated free-stream turbulence intensity level has been analyzed by means of PIV and hot-wire measurements. A detailed view of the instantaneous flow field in the wall-normal plane highlights the physics characterizing the complex process leading to the formation of large-scale coherent structures during breaking down of the ordered motion of the flow, thus generating randomized oscillations (i.e., turbulent spots). This analysis gives the basis for the development of a new procedure aimed at determining the intermittency function describing (statistically) the transition process. To this end, a wavelet-based method has been employed for the identification of the large-scale structures created during the transition process. Successively, a probability density function of these events has been defined so that an intermittency function is deduced. This latter strictly corresponds to the intermittency function of the transitional flow computed trough a classic procedure based on hot-wire data. The agreement between the two procedures in the intermittency shape and spot production rate proves the capability of the method in providing the statistical representation of the transition process. The main advantages of the procedure here proposed concern with its applicability to PIV data; it does not require a threshold level to discriminate first- and/or second-order time-derivative of hot-wire time traces (that makes the method not influenced by the operator); and it provides a clear evidence of the connection between the flow physics and the statistical representation of transition based on theory of turbulent spot propagation.

Explicit correlation treatment of the six-dimensional potential energy surface and predicted infrared spectra for OCS-H2

NASA Astrophysics Data System (ADS)

Liu, Jing-Min; Zhai, Yu; Li, Hui

2017-07-01

An effective six-dimensional ab initio potential energy surface (PES) for H2-OCS which explicitly includes the intramolecular stretch normal modes of carbonyl sulfide (OCS) is presented. The electronic structure computations are carried out using the explicitly correlated coupled cluster [CCSD(T)-F12] method with the augmented correlation-consistent aug-cc-pVTZ basis set, and the accuracy is critically tested by performing a series of benchmark calculations. Analytic four-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies to the Morse/long-range potential model. These fits to 13 485 points have a root-mean-square deviation (RMSD) of 0.16 cm-1. The combined radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to evaluate the rovibrational energy levels for five isotopic species of the OCS-hydrogen complexes. The predicted transition frequencies and intensities based on the resulting vibrationally averaged PESs are in good agreement with the available experimental values, whose RMSDs are smaller than 0.004 cm-1 for five different species of OCS-hydrogen complexes. The calculated infrared band origin shifts for all five species of OCS-hydrogen complexes are only 0.03 cm-1 smaller than the corresponding experimental values. These validate the high quality of our PESs which can be used for modeling OCS doped in hydrogen clusters to further study quantum solution and microscopic superfluidity. In addition, the analytic coordinate transformation functions between isotopologues are also derived due to the center of mass shifting of different isotope substitutes.

Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection

DOE PAGES

Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max; ...

2016-08-04

This work proposes a hyperspherical sparse approximation framework for detecting jump discontinuities in functions in high-dimensional spaces. The need for a novel approach results from the theoretical and computational inefficiencies of well-known approaches, such as adaptive sparse grids, for discontinuity detection. Our approach constructs the hyperspherical coordinate representation of the discontinuity surface of a function. Then sparse approximations of the transformed function are built in the hyperspherical coordinate system, with values at each point estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computationalmore » cost, compared to existing methods. Several approaches are used to approximate the transformed discontinuity surface in the hyperspherical system, including adaptive sparse grid and radial basis function interpolation, discrete least squares projection, and compressed sensing approximation. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. In conclusion, rigorous complexity analyses of the new methods are provided, as are several numerical examples that illustrate the effectiveness of our approach.« less

A critical evaluation of validity and utility of translational imaging in pain and analgesia: Utilizing functional imaging to enhance the process.

PubMed

Upadhyay, Jaymin; Geber, Christian; Hargreaves, Richard; Birklein, Frank; Borsook, David

2018-01-01

Assessing clinical pain and metrics related to function or quality of life predominantly relies on patient reported subjective measures. These outcome measures are generally not applicable to the preclinical setting where early signs pointing to analgesic value of a therapy are sought, thus introducing difficulties in animal to human translation in pain research. Evaluating brain function in patients and respective animal model(s) has the potential to characterize mechanisms associated with pain or pain-related phenotypes and thereby provide a means of laboratory to clinic translation. This review summarizes the progress made towards understanding of brain function in clinical and preclinical pain states elucidated using an imaging approach as well as the current level of validity of translational pain imaging. We hypothesize that neuroimaging can describe the central representation of pain or pain phenotypes and yields a basis for the development and selection of clinically relevant animal assays. This approach may increase the probability of finding meaningful new analgesics that can help satisfy the significant unmet medical needs of patients. Copyright © 2017 Elsevier Ltd. All rights reserved.

Reconstruction of 2D PET data with Monte Carlo generated system matrix for generalized natural pixels

NASA Astrophysics Data System (ADS)

Vandenberghe, Stefaan; Staelens, Steven; Byrne, Charles L.; Soares, Edward J.; Lemahieu, Ignace; Glick, Stephen J.

2006-06-01

In discrete detector PET, natural pixels are image basis functions calculated from the response of detector pairs. By using reconstruction with natural pixel basis functions, the discretization of the object into a predefined grid can be avoided. Here, we propose to use generalized natural pixel reconstruction. Using this approach, the basis functions are not the detector sensitivity functions as in the natural pixel case but uniform parallel strips. The backprojection of the strip coefficients results in the reconstructed image. This paper proposes an easy and efficient way to generate the matrix M directly by Monte Carlo simulation. Elements of the generalized natural pixel system matrix are formed by calculating the intersection of a parallel strip with the detector sensitivity function. These generalized natural pixels are easier to use than conventional natural pixels because the final step from solution to a square pixel representation is done by simple backprojection. Due to rotational symmetry in the PET scanner, the matrix M is block circulant and only the first blockrow needs to be stored. Data were generated using a fast Monte Carlo simulator using ray tracing. The proposed method was compared to a listmode MLEM algorithm, which used ray tracing for doing forward and backprojection. Comparison of the algorithms with different phantoms showed that an improved resolution can be obtained using generalized natural pixel reconstruction with accurate system modelling. In addition, it was noted that for the same resolution a lower noise level is present in this reconstruction. A numerical observer study showed the proposed method exhibited increased performance as compared to a standard listmode EM algorithm. In another study, more realistic data were generated using the GATE Monte Carlo simulator. For these data, a more uniform contrast recovery and a better contrast-to-noise performance were observed. It was observed that major improvements in contrast recovery were obtained with MLEM when the correct system matrix was used instead of simple ray tracing. The correct modelling was the major cause of improved contrast for the same background noise. Less important factors were the choice of the algorithm (MLEM performed better than ART) and the basis functions (generalized natural pixels gave better results than pixels).

Characterizing optical chirality

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

Bliokh, Konstantin Y.; Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198; Nori, Franco

We examine the recently introduced measure of chirality of a monochromatic optical field [Y. Tang and A. E. Cohen, Phys. Rev. Lett. 104, 163901 (2010)] using the momentum (plane-wave) representation and helicity basis. Our analysis clarifies the physical meaning of the measure of chirality and unveils its close relation to the polarization helicity, spin angular momentum, energy density, and Poynting energy flow. We derive the operators of the optical chirality and of the corresponding chiral momentum, which acquire remarkably simple forms in the helicity representation.

University Students' Unions: Changing Functions, a UK and Comparative Perspective

ERIC Educational Resources Information Center

Guan, Lu; Cole, Michael; Worthington, Frank

2016-01-01

In this article, we consider the functions of students' unions (SUs) through a UK case study. First, a functional classification of educational representation; wider representation; delivery of commercial services and faciliating a student community is outlined. Second, we specify a theoretical framework in terms of neo-liberalism and therapeutic…

Using Multiple Representations to Teach Composition of Functions

ERIC Educational Resources Information Center

Steketee, Scott; Scher, Daniel

2012-01-01

Composition of functions is one of the five big ideas identified in NCTM's "Developing Essential Understanding of Functions, Grades 9-12" (Cooney, Beckmann, and Lloyd 2010). Through multiple representations (another big idea) and the use of The Geometer's Sketchpad[R] (GSP), students can directly manipulate variables and thus see dynamic visual…

Helping Students-Connect Functions and Their Representations

ERIC Educational Resources Information Center

Moore-Russo, Deborah; Golzy, John B.

2005-01-01

The description about the changed instruction to encourage student exploration of the graphical and then the algebraic representations of functions is presented, which enables the students to understand how the graph, equation, and table of a function are related. The activity addresses both the Learning Principle and the Connection standard and…

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.

Neural basis of attributional style in schizophrenia.

PubMed

Park, Kyung-Min; Kim, Jae-Jin; Ku, Jeonghun; Kim, So Young; Lee, Hyeong Rae; Kim, Sun I; Yoon, Kang-Jun

2009-07-31

Attributional style means how people typically infer the causes of emotional behaviors. No study has shown neural basis of attributional style in schizophrenia, although it was suggested as a major area of social cognition research of schizophrenia. Fifteen patients with schizophrenia and 16 healthy controls underwent functional magnetic resonance imaging while performing three (happy, angry, and neutral) conditions of attribution task. Each condition included inferring situational causes of an avatar' (virtual character) emotional or neutral behavior. In the between-groups contrast maps of the happy conditions, the patient group compared to the control group showed decreased activations in the inferior frontal (BA 44) and the ventral premotor cortex (BA 6), in which the % signal changes were associated with negative symptoms. In the angry conditions, the patient group compared to the control group exhibited increased activations in the precuneus/posterior cingulate cortex (Pcu/PCC) (BA 7/31), in which the % signal changes were related to positive symptoms. In conclusion, patients with schizophrenia may have functional deficits in mirror neuron system when attributing positive behaviors, which may be related to a lack of inner simulation and empathy and negative symptoms. In contrast, patients may have increased activation in the Pcu/PCC related to self-representations while attributing negative behaviors, which may be related to failures in self- and source-monitoring and positive symptoms.

On the homogenization of the acoustic wave propagation in perforated ducts of finite length for an inviscid and a viscous model.

PubMed

Semin, Adrien; Schmidt, Kersten

2018-02-01

The direct numerical simulation of the acoustic wave propagation in multiperforated absorbers with hundreds or thousands of tiny openings would result in a huge number of basis functions to resolve the microstructure. One is, however, primarily interested in effective and so homogenized transmission and absorption properties and how they are influenced by microstructure and its endpoints. For this, we introduce the surface homogenization that asymptotically decomposes the solution in a macroscopic part, a boundary layer corrector close to the interface and a near-field part close to its ends. The effective transmission and absorption properties are expressed by transmission conditions for the macroscopic solution on an infinitely thin interface and corner conditions at its endpoints to ensure the correct singular behaviour, which are intrinsic to the microstructure. We study and give details on the computation of the effective parameters for an inviscid and a viscous model and show their dependence on geometrical properties of the microstructure for the example of Helmholtz equation. Numerical experiments indicate that with the obtained macroscopic solution representation one can achieve an high accuracy for low and high porosities as well as for viscous boundary conditions while using only a small number of basis functions.

Place Cell Networks in Pre-weanling Rats Show Associative Memory Properties from the Onset of Exploratory Behavior.

PubMed

Muessig, L; Hauser, J; Wills, T J; Cacucci, F

2016-08-01

Place cells are hippocampal pyramidal cells that are active when an animal visits a restricted area of the environment, and collectively their activity constitutes a neural representation of space. Place cell populations in the adult rat hippocampus display fundamental properties consistent with an associative memory network: the ability to 1) generate new and distinct spatial firing patterns when encountering novel spatial contexts or changes in sensory input ("remapping") and 2) reinstate previously stored firing patterns when encountering a familiar context, including on the basis of an incomplete/degraded set of sensory cues ("pattern completion"). To date, it is unknown when these spatial memory responses emerge during brain development. Here, we show that, from the age of first exploration (postnatal day 16) onwards, place cell populations already exhibit these key features: they generate new representations upon exposure to a novel context and can reactivate familiar representations on the basis of an incomplete set of sensory cues. These results demonstrate that, as early as exploratory behaviors emerge, and despite the absence of an adult-like grid cell network, the developing hippocampus processes incoming sensory information as an associative memory network. © The Author 2016. Published by Oxford University Press.

Where Should the Nuclei Be Located?

ERIC Educational Resources Information Center

Ying Liu; Yue Liu; Drew, Michael G. B.

2005-01-01

The approach of determining the nature of the electron wave function via orbital representations qualitatively and via numerical calculations quantitatively is demonstrated. The angular part of the wave function provides suitable representation of the positions of the nuclei.

Visual perception from the perspective of a representational, non-reductionistic, level-dependent account of perception and conscious awareness

PubMed Central

Overgaard, Morten; Mogensen, Jesper

2014-01-01

This article proposes a new model to interpret seemingly conflicting evidence concerning the correlation of consciousness and neural processes. Based on an analysis of research of blindsight and subliminal perception, the reorganization of elementary functions and consciousness framework suggests that mental representations consist of functions at several different levels of analysis, including truly localized perceptual elementary functions and perceptual algorithmic modules, which are interconnections of the elementary functions. We suggest that conscious content relates to the ‘top level’ of analysis in a ‘situational algorithmic strategy’ that reflects the general state of an individual. We argue that conscious experience is intrinsically related to representations that are available to guide behaviour. From this perspective, we find that blindsight and subliminal perception can be explained partly by too coarse-grained methodology, and partly by top-down enhancing of representations that normally would not be relevant to action. PMID:24639581

Linear-scaling explicitly correlated treatment of solids: periodic local MP2-F12 method.

PubMed

Usvyat, Denis

2013-11-21

Theory and implementation of the periodic local MP2-F12 method in the 3*A fixed-amplitude ansatz is presented. The method is formulated in the direct space, employing local representation for the occupied, virtual, and auxiliary orbitals in the form of Wannier functions (WFs), projected atomic orbitals (PAOs), and atom-centered Gaussian-type orbitals, respectively. Local approximations are introduced, restricting the list of the explicitly correlated pairs, as well as occupied, virtual, and auxiliary spaces in the strong orthogonality projector to the pair-specific domains on the basis of spatial proximity of respective orbitals. The 4-index two-electron integrals appearing in the formalism are approximated via the direct-space density fitting technique. In this procedure, the fitting orbital spaces are also restricted to local fit-domains surrounding the fitted densities. The formulation of the method and its implementation exploits the translational symmetry and the site-group symmetries of the WFs. Test calculations are performed on LiH crystal. The results show that the periodic LMP2-F12 method substantially accelerates basis set convergence of the total correlation energy, and even more so the correlation energy differences. The resulting energies are quite insensitive to the resolution-of-the-identity domain sizes and the quality of the auxiliary basis sets. The convergence with the orbital domain size is somewhat slower, but still acceptable. Moreover, inclusion of slightly more diffuse functions, than those usually used in the periodic calculations, improves the convergence of the LMP2-F12 correlation energy with respect to both the size of the PAO-domains and the quality of the orbital basis set. At the same time, the essentially diffuse atomic orbitals from standard molecular basis sets, commonly utilized in molecular MP2-F12 calculations, but problematic in the periodic context, are not necessary for LMP2-F12 treatment of crystals.

A Description of Exotic Nuclei by the Aid of Virtual States

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

Vertse, T.; University of Debrecen, Faculty of Information Science, H-4010 Debrecen, Pf. 12; Id Betan, R.

2005-11-21

A new unified shell model scheme is introduced in which the single particle basis is a generalization of the Berggren representation. This repesentation includes virtual i.e. antibound basis states as well. We apply the new scheme to the ground state of the exotic nucleus 11Li. Here the antibound pole and the complex continuum both have large contributions and neither of them can be neglected.

Tick, Tock, Tick, Tock...

NASA Astrophysics Data System (ADS)

Evans, N. W.; Molloy, M.

2014-07-01

The Gaia dataset will require a huge leap forward in terms of modelling of the Milky Way. Two problems are highlighted here. First, models of the Galactic Bar remain primitive as compared to the Galactic Disk and Stellar Halo. Although Schwarzschild and N-body methods are useful, the future belongs to Made-to-Measure (M2M) models which have significant advantages in terms of storage and flexibility. Second, the Milky Way potential will need much better representation than hitherto. Most models still use very simple building blocks (Miyamoto-Nagai disks or Hernquist bulges) and these will not be fit for purpose in the Gaia Era. Expansions in terms of basis functions offer the possibility of incorporating cosmological information as priors, as well as mych greater adaptability.

Get the picture? The effects of iconicity on toddlers' reenactment from picture books.

PubMed

Simcock, Gabrielle; DeLoache, Judy

2006-11-01

What do toddlers learn from everyday picture-book reading interactions? To date, there has been scant research exploring this question. In this study, the authors adapted a standard imitation procedure to examine 18- to 30-month-olds' ability to learn how to reenact a novel action sequence from a picture book. The results provide evidence that toddlers can imitate specific target actions on novel real-world objects on the basis of a picture-book interaction. Children's imitative performance after the reading interaction varied both as a function of age and the level of iconicity of the pictures in the book. These findings are discussed in terms of children's emerging symbolic capacity and the flexibility of the cognitive representation.

Towards a neural basis of music perception.

PubMed

Koelsch, Stefan; Siebel, Walter A

2005-12-01

Music perception involves complex brain functions underlying acoustic analysis, auditory memory, auditory scene analysis, and processing of musical syntax and semantics. Moreover, music perception potentially affects emotion, influences the autonomic nervous system, the hormonal and immune systems, and activates (pre)motor representations. During the past few years, research activities on different aspects of music processing and their neural correlates have rapidly progressed. This article provides an overview of recent developments and a framework for the perceptual side of music processing. This framework lays out a model of the cognitive modules involved in music perception, and incorporates information about the time course of activity of some of these modules, as well as research findings about where in the brain these modules might be located.

40 CFR 1620.3 - Administrative claim; who may file.

Code of Federal Regulations, 2010 CFR

2010-07-01

...) A claim based on death may be presented by the executor or administrator of the decedent's estate... that the basis for the representation is documented in writing. (d) A claim for loss totally...

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.

Cognitive and artificial representations in handwriting recognition

NASA Astrophysics Data System (ADS)

Lenaghan, Andrew P.; Malyan, Ron

1996-03-01

Both cognitive processes and artificial recognition systems may be characterized by the forms of representation they build and manipulate. This paper looks at how handwriting is represented in current recognition systems and the psychological evidence for its representation in the cognitive processes responsible for reading. Empirical psychological work on feature extraction in early visual processing is surveyed to show that a sound psychological basis for feature extraction exists and to describe the features this approach leads to. The first stage of the development of an architecture for a handwriting recognition system which has been strongly influenced by the psychological evidence for the cognitive processes and representations used in early visual processing, is reported. This architecture builds a number of parallel low level feature maps from raw data. These feature maps are thresholded and a region labeling algorithm is used to generate sets of features. Fuzzy logic is used to quantify the uncertainty in the presence of individual features.

Representational constraints on children's suggestibility.

PubMed

Ceci, Stephen J; Papierno, Paul B; Kulkofsky, Sarah

2007-06-01

In a multistage experiment, twelve 4- and 9-year-old children participated in a triad rating task. Their ratings were mapped with multidimensional scaling, from which euclidean distances were computed to operationalize semantic distance between items in target pairs. These children and age-mates then participated in an experiment that employed these target pairs in a story, which was followed by a misinformation manipulation. Analyses linked individual and developmental differences in suggestibility to children's representations of the target items. Semantic proximity was a strong predictor of differences in suggestibility: The closer a suggested distractor was to the original item's representation, the greater was the distractor's suggestive influence. The triad participants' semantic proximity subsequently served as the basis for correctly predicting memory performance in the larger group. Semantic proximity enabled a priori counterintuitive predictions of reverse age-related trends to be confirmed whenever the distance between representations of items in a target pair was greater for younger than for older children.

Is the asymmetry in young infants' categorization of humans versus nonhuman animals based on head, body, or global gestalt information?

PubMed

Quinn, Paul C

2004-02-01

Quinn and Eimas (1998) reported an asymmetry in the exclusivity of the category representations that young infants form for humans and nonhuman animals: category representations for nonhuman animal species were found to exclude humans, whereas a category representation for humans was found to include nonhuman animal species (i.e., cats, horses). The present experiment utilized the familiarization/novelty-preference procedure with 3- and 4-month-olds to determine the perceptual cues (i.e., whole stimulus, head alone, body alone) that provided the basis for this asymmetry. The data revealed the asymmetry to be observable only with the whole animal stimuli and not when infants were provided with information from just the head or the body of the exemplars. The results indicate that the incorporation of nonhuman animal species into a category representation for humans is based on holistic information.

The Koslowski-Sahlmann representation: quantum configuration space

NASA Astrophysics Data System (ADS)

Campiglia, Miguel; Varadarajan, Madhavan

2014-09-01

The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of loop quantum gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the KS representation supports, in addition to the action of the holonomy and flux operators, the action of operators which are the quantum counterparts of certain connection dependent functions known as ‘background exponentials’. Here we show that the KS representation displays the following properties which are the exact counterparts of LQG ones: (i) the abelian * algebra of SU(2) holonomies and ‘U(1)’ background exponentials can be completed to a C* algebra, (ii) the space of semianalytic SU(2) connections is topologically dense in the spectrum of this algebra, (iii) there exists a measure on this spectrum for which the KS Hilbert space is realized as the space of square integrable functions on the spectrum, (iv) the spectrum admits a characterization as a projective limit of finite numbers of copies of SU(2) and U(1), (v) the algebra underlying the KS representation is constructed from cylindrical functions and their derivations in exactly the same way as the LQG (holonomy-flux) algebra except that the KS cylindrical functions depend on the holonomies and the background exponentials, this extra dependence being responsible for the differences between the KS and LQG algebras. While these results are obtained for compact spaces, they are expected to be of use for the construction of the KS representation in the asymptotically flat case.

Potential role of monkey inferior parietal neurons coding action semantic equivalences as precursors of parts of speech.

PubMed

Yamazaki, Yumiko; Yokochi, Hiroko; Tanaka, Michio; Okanoya, Kazuo; Iriki, Atsushi

2010-01-01

The anterior portion of the inferior parietal cortex possesses comprehensive representations of actions embedded in behavioural contexts. Mirror neurons, which respond to both self-executed and observed actions, exist in this brain region in addition to those originally found in the premotor cortex. We found that parietal mirror neurons responded differentially to identical actions embedded in different contexts. Another type of parietal mirror neuron represents an inverse and complementary property of responding equally to dissimilar actions made by itself and others for an identical purpose. Here, we propose a hypothesis that these sets of inferior parietal neurons constitute a neural basis for encoding the semantic equivalence of various actions across different agents and contexts. The neurons have mirror neuron properties, and they encoded generalization of agents, differentiation of outcomes, and categorization of actions that led to common functions. By integrating the activities of these mirror neurons with various codings, we further suggest that in the ancestral primates' brains, these various representations of meaningful action led to the gradual establishment of equivalence relations among the different types of actions, by sharing common action semantics. Such differential codings of the components of actions might represent precursors to the parts of protolanguage, such as gestural communication, which are shared among various members of a society. Finally, we suggest that the inferior parietal cortex serves as an interface between this action semantics system and other higher semantic systems, through common structures of action representation that mimic language syntax.

Potential role of monkey inferior parietal neurons coding action semantic equivalences as precursors of parts of speech

PubMed Central

Yamazaki, Yumiko; Yokochi, Hiroko; Tanaka, Michio; Okanoya, Kazuo; Iriki, Atsushi

2010-01-01

The anterior portion of the inferior parietal cortex possesses comprehensive representations of actions embedded in behavioural contexts. Mirror neurons, which respond to both self-executed and observed actions, exist in this brain region in addition to those originally found in the premotor cortex. We found that parietal mirror neurons responded differentially to identical actions embedded in different contexts. Another type of parietal mirror neuron represents an inverse and complementary property of responding equally to dissimilar actions made by itself and others for an identical purpose. Here, we propose a hypothesis that these sets of inferior parietal neurons constitute a neural basis for encoding the semantic equivalence of various actions across different agents and contexts. The neurons have mirror neuron properties, and they encoded generalization of agents, differentiation of outcomes, and categorization of actions that led to common functions. By integrating the activities of these mirror neurons with various codings, we further suggest that in the ancestral primates' brains, these various representations of meaningful action led to the gradual establishment of equivalence relations among the different types of actions, by sharing common action semantics. Such differential codings of the components of actions might represent precursors to the parts of protolanguage, such as gestural communication, which are shared among various members of a society. Finally, we suggest that the inferior parietal cortex serves as an interface between this action semantics system and other higher semantic systems, through common structures of action representation that mimic language syntax. PMID:20119879

Students' Understanding of External Representations of the Potassium Ion Channel Protein Part II: Structure-Function Relationships and Fragmented Knowledge

ERIC Educational Resources Information Center

Harle, Marissa; Towns, Marcy H.

2012-01-01

Research that has focused on external representations in biochemistry has uncovered student difficulties in comprehending and interpreting external representations. This study focuses on students' understanding of three external representations (ribbon diagram, wireframe, and hydrophobic/hydrophilic) of the potassium ion channel protein. Analysis…

OBJECT REPRESENTATION, IDENTITY, AND THE PARADOX OF EARLY PERMANENCE: Steps Toward a New Framework.

PubMed

Meltzoff, Andrew N; Moore, M Keith

1998-01-01

The sensorimotor theory of infancy has been overthrown, but there is little consensus on a replacement. We hypothesize that a capacity for representation is the starting point for infant development, not its culmination. Logical distinctions are drawn between object representation, identity, and permanence. Modern experiments on early object permanence and deferred imitation suggest: (a) even for young infants, representations persist over breaks in sensory contact, (b) numerical identity of objects ( O s) is initially specified by spatiotemporal criteria (place and trajectory), (c) featural and functional identity criteria develop, (d) events are analyzed by comparing representations to current perception, and (e) representation operates both prospectively, anticipating future contacts with an O , and retrospectively, reidentifying an O as the "same one again." A model of the architecture and functioning of the early representational system is proposed. It accounts for young infants' behavior toward absent people and things in terms of their efforts to determine the identity of objects. Our proposal is developmental without denying innate structure and elevates the power of perception and representation while being cautious about attributing complex concepts to young infants.

OBJECT REPRESENTATION, IDENTITY, AND THE PARADOX OF EARLY PERMANENCE: Steps Toward a New Framework

PubMed Central

Meltzoff, Andrew N.; Moore, M. Keith

2013-01-01

The sensorimotor theory of infancy has been overthrown, but there is little consensus on a replacement. We hypothesize that a capacity for representation is the starting point for infant development, not its culmination. Logical distinctions are drawn between object representation, identity, and permanence. Modern experiments on early object permanence and deferred imitation suggest: (a) even for young infants, representations persist over breaks in sensory contact, (b) numerical identity of objects (Os) is initially specified by spatiotemporal criteria (place and trajectory), (c) featural and functional identity criteria develop, (d) events are analyzed by comparing representations to current perception, and (e) representation operates both prospectively, anticipating future contacts with an O, and retrospectively, reidentifying an O as the “same one again.” A model of the architecture and functioning of the early representational system is proposed. It accounts for young infants’ behavior toward absent people and things in terms of their efforts to determine the identity of objects. Our proposal is developmental without denying innate structure and elevates the power of perception and representation while being cautious about attributing complex concepts to young infants. PMID:25147418

Understanding Linear Functions and Their Representations

ERIC Educational Resources Information Center

Wells, Pamela J.

2015-01-01

Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…

Students' Recognition of Function Transformations' Themes Associated with the Algebraic Representation

ERIC Educational Resources Information Center

Daher, Wajeeh M.; Anabousi, Anlam A.

2015-01-01

The topic of function transformations is a difficult mathematical topic for school and college students. This article examines how students conceive function transformations after working with GeoGebra, when this conceiving relates to the algebraic representation. The research participants were 19 ninth grade high achieving students who learned,…

A Complex Prime Numerical Representation of Amino Acids for Protein Function Comparison.

PubMed

Chen, Duo; Wang, Jiasong; Yan, Ming; Bao, Forrest Sheng

2016-08-01

Computationally assessing the functional similarity between proteins is an important task of bioinformatics research. It can help molecular biologists transfer knowledge on certain proteins to others and hence reduce the amount of tedious and costly benchwork. Representation of amino acids, the building blocks of proteins, plays an important role in achieving this goal. Compared with symbolic representation, representing amino acids numerically can expand our ability to analyze proteins, including comparing the functional similarity of them. Among the state-of-the-art methods, electro-ion interaction pseudopotential (EIIP) is widely adopted for the numerical representation of amino acids. However, it could suffer from degeneracy that two different amino acid sequences have the same numerical representation, due to the design of EIIP. In light of this challenge, we propose a complex prime numerical representation (CPNR) of amino acids, inspired by the similarity between a pattern among prime numbers and the number of codons of amino acids. To empirically assess the effectiveness of the proposed method, we compare CPNR against EIIP. Experimental results demonstrate that the proposed method CPNR always achieves better performance than EIIP. We also develop a framework to combine the advantages of CPNR and EIIP, which enables us to improve the performance and study the unique characteristics of different representations.

Does Mother's Rather than Father's Attachment Representation Contribute to the Adolescent's Attachment Representation? Commentary on: "Maternal Adult Attachment Interview (AAI) Collected During Pregnancy Predicts Reflective Functioning in AAIs from their First-Born Children 17 Years Later"

ERIC Educational Resources Information Center

Spangler, Gottfried

2016-01-01

In this commentary, Spangler evaluates the Steele, Perez, Segal, and Steele report that arguede that reflective functioning in adolescence could not be predicted by quality of early infant attachment, but was associated with maternal (but not paternal) attachment representation, assessed before the adolescents' birth. Assuming that parental…

Navigation based on a sensorimotor representation: a virtual reality study

NASA Astrophysics Data System (ADS)

Zetzsche, Christoph; Galbraith, Christopher; Wolter, Johannes; Schill, Kerstin

2007-02-01

We investigate the hypothesis that the basic representation of space which underlies human navigation does not resemble an image-like map and is not restricted by the laws of Euclidean geometry. For this we developed a new experimental technique in which we use the properties of a virtual environment (VE) to directly influence the development of the representation. We compared the navigation performance of human observers under two conditions. Either the VE is consistent with the geometrical properties of physical space and could hence be represented in a map-like fashion, or it contains severe violations of Euclidean metric and planar topology, and would thus pose difficulties for the correct development of such a representation. Performance is not influenced by this difference, suggesting that a map-like representation is not the major basis of human navigation. Rather, the results are consistent with a representation which is similar to a non-planar graph augmented with path length information, or with a sensorimotor representation which combines sensory properties and motor actions. The latter may be seen as part of a revised view of perceptual processes due to recent results in psychology and neurobiology, which indicate that the traditional strict separation of sensory and motor systems is no longer tenable.

Illuminating the conceptual structure of the space of moral violations with searchlight representational similarity analysis.

PubMed

Wasserman, E A; Chakroff, A; Saxe, R; Young, L

2017-10-01

Characterizing how representations of moral violations are organized, cognitively and neurally, is central to understanding how people conceive and judge them. Past work has identified brain regions that represent morally relevant features and distinguish moral domains, but has not yet advanced a broader account of where and on what basis neural representations of moral violations are organized. With searchlight representational similarity analysis, we investigate where category membership drives similarity in neural patterns during moral judgment of violations from two key moral domains: Harm and Purity. Representations converge across domains in a network of regions resembling the mentalizing network. However, Harm and Purity violation representations respectively converge in different regions: precuneus (PC) and left inferior frontal gyrus (LIFG). Examining substructure within moral domains, Harm violations converge in PC regardless of subdomain (physical harms, psychological harms), while Purity subdomains (pathogen-related violations, sex-related violations) converge in distinct sets of regions - mirroring a dissociation observed in principal-component analysis of behavioral data. Further, we find initial evidence for representation of morally relevant features within these two domain-encoding regions. The present analyses offer a case study for understanding how organization within the complex conceptual space of moral violations is reflected in the organization of neural patterns across the cortex. Copyright © 2017 Elsevier Inc. All rights reserved.

Fusion basis for lattice gauge theory and loop quantum gravity

NASA Astrophysics Data System (ADS)

Delcamp, Clement; Dittrich, Bianca; Riello, Aldo

2017-02-01

We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2 + 1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel'd double of the gauge group, and can be readily "fused" together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi-local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse-graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin-network basis, in which it is much more complicated to account for electric excitations, i.e. for Gauß constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi-scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2 + 1) gravity coupled to point particles. In a follow-up work, we have exploited this notion to provide a new definition of entanglement entropy for these theories.

Shared neural circuits for mentalizing about the self and others.

PubMed

Lombardo, Michael V; Chakrabarti, Bhismadev; Bullmore, Edward T; Wheelwright, Sally J; Sadek, Susan A; Suckling, John; Baron-Cohen, Simon

2010-07-01

Although many examples exist for shared neural representations of self and other, it is unknown how such shared representations interact with the rest of the brain. Furthermore, do high-level inference-based shared mentalizing representations interact with lower level embodied/simulation-based shared representations? We used functional neuroimaging (fMRI) and a functional connectivity approach to assess these questions during high-level inference-based mentalizing. Shared mentalizing representations in ventromedial prefrontal cortex, posterior cingulate/precuneus, and temporo-parietal junction (TPJ) all exhibited identical functional connectivity patterns during mentalizing of both self and other. Connectivity patterns were distributed across low-level embodied neural systems such as the frontal operculum/ventral premotor cortex, the anterior insula, the primary sensorimotor cortex, and the presupplementary motor area. These results demonstrate that identical neural circuits are implementing processes involved in mentalizing of both self and other and that the nature of such processes may be the integration of low-level embodied processes within higher level inference-based mentalizing.

Modeling shape and topology of low-resolution density maps of biological macromolecules.

PubMed Central

De-Alarcón, Pedro A; Pascual-Montano, Alberto; Gupta, Amarnath; Carazo, Jose M

2002-01-01

In the present work we develop an efficient way of representing the geometry and topology of volumetric datasets of biological structures from medium to low resolution, aiming at storing and querying them in a database framework. We make use of a new vector quantization algorithm to select the points within the macromolecule that best approximate the probability density function of the original volume data. Connectivity among points is obtained with the use of the alpha shapes theory. This novel data representation has a number of interesting characteristics, such as 1) it allows us to automatically segment and quantify a number of important structural features from low-resolution maps, such as cavities and channels, opening the possibility of querying large collections of maps on the basis of these quantitative structural features; 2) it provides a compact representation in terms of size; 3) it contains a subset of three-dimensional points that optimally quantify the densities of medium resolution data; and 4) a general model of the geometry and topology of the macromolecule (as opposite to a spatially unrelated bunch of voxels) is easily obtained by the use of the alpha shapes theory. PMID:12124252

Basic Information Processing Abilities at 11 years Account for Deficits in IQ Associated with Preterm Birth.

PubMed

Rose, Susan A; Feldman, Judith F; Jankowski, Jeffery J; Van Rossem, Ronan

2011-07-01

Although it is well established that preterms as a group do poorly relative to their full-term peers on tests of global cognitive functioning, the basis for this relative deficiency is less understood. The present paper examines preterm deficits in core cognitive abilities and determines their role in mediating preterm/full-term differences in IQ. The performance of 11-year-old children born preterm (birth weight <1750g) and their full-term controls were compared on a large battery of 15 tasks, covering four basic cognitive domains -- memory, attention, speed of processing and representational competence. The validity of these four domains was established using latent variables and confirmatory factor analysis (CFA). Preterms showed pervasive deficits within and across domains. Additionally, preterm deficits in IQ were completely mediated by these four cognitive domains in a structural equation model involving a cascade from elementary abilities (attention and speed), to more complex abilities (memory and representational competence), to IQ. The similarity of findings to those obtained with this cohort in infancy and toddlerhood suggest that preterm deficits persist - across time, across task, and from the non-verbal to the verbal period.

Global Neural Pattern Similarity as a Common Basis for Categorization and Recognition Memory

PubMed Central

Xue, Gui; Love, Bradley C.; Preston, Alison R.; Poldrack, Russell A.

2014-01-01

Familiarity, or memory strength, is a central construct in models of cognition. In previous categorization and long-term memory research, correlations have been found between psychological measures of memory strength and activation in the medial temporal lobes (MTLs), which suggests a common neural locus for memory strength. However, activation alone is insufficient for determining whether the same mechanisms underlie neural function across domains. Guided by mathematical models of categorization and long-term memory, we develop a theory and a method to test whether memory strength arises from the global similarity among neural representations. In human subjects, we find significant correlations between global similarity among activation patterns in the MTLs and both subsequent memory confidence in a recognition memory task and model-based measures of memory strength in a category learning task. Our work bridges formal cognitive theories and neuroscientific models by illustrating that the same global similarity computations underlie processing in multiple cognitive domains. Moreover, by establishing a link between neural similarity and psychological memory strength, our findings suggest that there may be an isomorphism between psychological and neural representational spaces that can be exploited to test cognitive theories at both the neural and behavioral levels. PMID:24872552

Refining Collective Coordinates and Improving Free Energy Representation in Variational Enhanced Sampling.

PubMed

Yang, Yi Isaac; Parrinello, Michele

2018-06-12

Collective variables are used often in many enhanced sampling methods, and their choice is a crucial factor in determining sampling efficiency. However, at times, searching for good collective variables can be challenging. In a recent paper, we combined time-lagged independent component analysis with well-tempered metadynamics in order to obtain improved collective variables from metadynamics runs that use lower quality collective variables [ McCarty, J.; Parrinello, M. J. Chem. Phys. 2017 , 147 , 204109 ]. In this work, we extend these ideas to variationally enhanced sampling. This leads to an efficient scheme that is able to make use of the many advantages of the variational scheme. We apply the method to alanine-3 in water. From an alanine-3 variationally enhanced sampling trajectory in which all the six dihedral angles are biased, we extract much better collective variables able to describe in exquisite detail the protein complex free energy surface in a low dimensional representation. The success of this investigation is helped by a more accurate way of calculating the correlation functions needed in the time-lagged independent component analysis and from the introduction of a new basis set to describe the dihedral angles arrangement.

Is the desire for amputation related to disturbed emotion processing? A multiple case study analysis in BIID.

PubMed

Bottini, Gabriella; Brugger, Peter; Sedda, Anna

2015-01-01

Body integrity identity disorder (BIID) is characterized by the overwhelming desire to amputate one or more healthy limbs or to be paraplegic. Recently, a neurological explanation of this condition has been proposed, in part on the basis of findings that the insular cortex might present structural anomalies in these individuals. While these studies focused on body representation, much less is known about emotional processing. Importantly, emotional impairments have been found in psychiatric disorders, and a psychiatric etiology is still a valid alternative to purely neurological accounts of BIID. In this study, we explored, by means of a computerized experiment, facial emotion recognition and emotional responses to disgusting images in seven individuals with BIID, taking into account their clinical features and investigating in detail disgust processing, strongly linked to insular functioning. We demonstrate that BIID is not characterized by a general emotional impairment; rather, there is a selectively reduced disgust response to violations of the body envelope. Taken together, our results support the need to explore this condition under an interdisciplinary perspective, taking into account also emotional connotations and the social modulation of body representation.

A web-based system architecture for ontology-based data integration in the domain of IT benchmarking

NASA Astrophysics Data System (ADS)

Pfaff, Matthias; Krcmar, Helmut

2018-03-01

In the domain of IT benchmarking (ITBM), a variety of data and information are collected. Although these data serve as the basis for business analyses, no unified semantic representation of such data yet exists. Consequently, data analysis across different distributed data sets and different benchmarks is almost impossible. This paper presents a system architecture and prototypical implementation for an integrated data management of distributed databases based on a domain-specific ontology. To preserve the semantic meaning of the data, the ITBM ontology is linked to data sources and functions as the central concept for database access. Thus, additional databases can be integrated by linking them to this domain-specific ontology and are directly available for further business analyses. Moreover, the web-based system supports the process of mapping ontology concepts to external databases by introducing a semi-automatic mapping recommender and by visualizing possible mapping candidates. The system also provides a natural language interface to easily query linked databases. The expected result of this ontology-based approach of knowledge representation and data access is an increase in knowledge and data sharing in this domain, which will enhance existing business analysis methods.

Basic Information Processing Abilities at 11 years Account for Deficits in IQ Associated with Preterm Birth

PubMed Central

Rose, Susan A.; Feldman, Judith F.; Jankowski, Jeffery J.; Van Rossem, Ronan

2011-01-01

Although it is well established that preterms as a group do poorly relative to their full-term peers on tests of global cognitive functioning, the basis for this relative deficiency is less understood. The present paper examines preterm deficits in core cognitive abilities and determines their role in mediating preterm/full-term differences in IQ. The performance of 11-year-old children born preterm (birth weight <1750g) and their full-term controls were compared on a large battery of 15 tasks, covering four basic cognitive domains -- memory, attention, speed of processing and representational competence. The validity of these four domains was established using latent variables and confirmatory factor analysis (CFA). Preterms showed pervasive deficits within and across domains. Additionally, preterm deficits in IQ were completely mediated by these four cognitive domains in a structural equation model involving a cascade from elementary abilities (attention and speed), to more complex abilities (memory and representational competence), to IQ. The similarity of findings to those obtained with this cohort in infancy and toddlerhood suggest that preterm deficits persist – across time, across task, and from the non-verbal to the verbal period. PMID:21643482

[Sociophysiology: basic processes of empathy].

PubMed

Haker, Helene; Schimansky, Jenny; Rössler, Wulf

2010-01-01

The aim of this review is to describe sociophysiological and social cognitive processes that underlie the complex phenomenon of human empathy. Automatic reflexive processes such as physiological contagion and action mirroring are mediated by the mirror neuron system. They are a basis for further processing of social signals and a physiological link between two individuals. This link comprises simultaneous activation of shared motor representations. Shared representations lead implicitly via individual associations in the limbic and vegetative system to a shared affective state. These processes are called sociophysiology. Further controlled- reflective, self-referential processing of those social signals leads to explicit, conscious representations of others' minds. Those higher-order processes are called social cognition. The interaction of physiological and cognitive social processes lets arise the phenomenon of human empathy.

Students' meaning making in science: solving energy resource problems in virtual worlds combined with spreadsheets to develop graphs

NASA Astrophysics Data System (ADS)

Krange, Ingeborg; Arnseth, Hans Christian

2012-09-01

The aim of this study is to scrutinize the characteristics of conceptual meaning making when students engage with virtual worlds in combination with a spreadsheet with the aim to develop graphs. We study how these tools and the representations they contain or enable students to construct serve to influence their understanding of energy resource consumption. The data were gathered in 1st grade upper-secondary science classes and they constitute the basis for the interaction analysis of students' meaning making with representations. Our analyses demonstrate the difficulties involved in developing students' orientation toward more conceptual orientations to representations of the knowledge domain. Virtual worlds do not in themselves represent a solution to this problem.

Importance of perceptual representation in the visual control of action

NASA Astrophysics Data System (ADS)

Loomis, Jack M.; Beall, Andrew C.; Kelly, Jonathan W.; Macuga, Kristen L.

2005-03-01

In recent years, many experiments have demonstrated that optic flow is sufficient for visually controlled action, with the suggestion that perceptual representations of 3-D space are superfluous. In contrast, recent research in our lab indicates that some visually controlled actions, including some thought to be based on optic flow, are indeed mediated by perceptual representations. For example, we have demonstrated that people are able to perform complex spatial behaviors, like walking, driving, and object interception, in virtual environments which are rendered visible solely by cyclopean stimulation (random-dot cinematograms). In such situations, the absence of any retinal optic flow that is correlated with the objects and surfaces within the virtual environment means that people are using stereo-based perceptual representations to perform the behavior. The fact that people can perform such behaviors without training suggests that the perceptual representations are likely the same as those used when retinal optic flow is present. Other research indicates that optic flow, whether retinal or a more abstract property of the perceptual representation, is not the basis for postural control, because postural instability is related to perceived relative motion between self and the visual surroundings rather than to optic flow, even in the abstract sense.

On squares of representations of compact Lie algebras

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

Zeier, Robert, E-mail: robert.zeier@ch.tum.de; Zimborás, Zoltán, E-mail: zimboras@gmail.com

We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We show in a classification-free manner that the sum of multiplicities and the sum of squares of multiplicities in the corresponding decomposition of a tensor square into irreducible representations has to strictly grow when restricted from a compact semisimple Lie algebra to a proper subalgebra. For this purpose, relevant details on tensor products of representations are compiled from the literature. Since the summore » of squares of multiplicities is equal to the dimension of the commutant of the tensor-square representation, it can be determined by linear-algebra computations in a scenario where an a priori unknown Lie algebra is given by a set of generators which might not be a linear basis. Hence, our results offer a test to decide if a subalgebra of a compact semisimple Lie algebra is a proper one without calculating the relevant Lie closures, which can be naturally applied in the field of controlled quantum systems.« less

Rapid tuning shifts in human auditory cortex enhance speech intelligibility

PubMed Central

Holdgraf, Christopher R.; de Heer, Wendy; Pasley, Brian; Rieger, Jochem; Crone, Nathan; Lin, Jack J.; Knight, Robert T.; Theunissen, Frédéric E.

2016-01-01

Experience shapes our perception of the world on a moment-to-moment basis. This robust perceptual effect of experience parallels a change in the neural representation of stimulus features, though the nature of this representation and its plasticity are not well-understood. Spectrotemporal receptive field (STRF) mapping describes the neural response to acoustic features, and has been used to study contextual effects on auditory receptive fields in animal models. We performed a STRF plasticity analysis on electrophysiological data from recordings obtained directly from the human auditory cortex. Here, we report rapid, automatic plasticity of the spectrotemporal response of recorded neural ensembles, driven by previous experience with acoustic and linguistic information, and with a neurophysiological effect in the sub-second range. This plasticity reflects increased sensitivity to spectrotemporal features, enhancing the extraction of more speech-like features from a degraded stimulus and providing the physiological basis for the observed ‘perceptual enhancement' in understanding speech. PMID:27996965

Adaptive Sparse Representation for Source Localization with Gain/Phase Errors

PubMed Central

Sun, Ke; Liu, Yimin; Meng, Huadong; Wang, Xiqin

2011-01-01

Sparse representation (SR) algorithms can be implemented for high-resolution direction of arrival (DOA) estimation. Additionally, SR can effectively separate the coherent signal sources because the spectrum estimation is based on the optimization technique, such as the L1 norm minimization, but not on subspace orthogonality. However, in the actual source localization scenario, an unknown gain/phase error between the array sensors is inevitable. Due to this nonideal factor, the predefined overcomplete basis mismatches the actual array manifold so that the estimation performance is degraded in SR. In this paper, an adaptive SR algorithm is proposed to improve the robustness with respect to the gain/phase error, where the overcomplete basis is dynamically adjusted using multiple snapshots and the sparse solution is adaptively acquired to match with the actual scenario. The simulation results demonstrate the estimation robustness to the gain/phase error using the proposed method. PMID:22163875

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

Kinetic damping in the spectra of the spherical impedance probe

NASA Astrophysics Data System (ADS)

Oberrath, J.

2018-04-01

The impedance probe is a measurement device to measure plasma parameters, such as electron density. It consists of one electrode connected to a network analyzer via a coaxial cable and is immersed into a plasma. A bias potential superposed with an alternating potential is applied to the electrode and the response of the plasma is measured. Its dynamical interaction with the plasma in an electrostatic, kinetic description can be modeled in an abstract notation based on functional analytic methods. These methods provide the opportunity to derive a general solution, which is given as the response function of the probe–plasma system. It is defined by the matrix elements of the resolvent of an appropriate dynamical operator. Based on the general solution, a residual damping for vanishing pressure can be predicted and can only be explained by kinetic effects. In this paper, an explicit response function of the spherical impedance probe is derived. Therefore, the resolvent is determined by its algebraic representation based on an expansion in orthogonal basis functions. This allows one to compute an approximated response function and its corresponding spectra. These spectra show additional damping due to kinetic effects and are in good agreement with former kinetically determined spectra.

Overset grid implementation of the complex Kohn variational method for electron-polyatomic molecule scattering

NASA Astrophysics Data System (ADS)

McCurdy, C. William; Lucchese, Robert L.; Greenman, Loren

2017-04-01

The complex Kohn variational method, which represents the continuum wave function in each channel using a combination of Gaussians and Bessel or Coulomb functions, has been successful in numerous applications to electron-polyatomic molecule scattering and molecular photoionization. The hybrid basis representation limits it to relatively low energies (< 50 eV) , requires an approximation to exchange matrix elements involving continuum functions, and hampers its coupling to modern electronic structure codes for the description of correlated target states. We describe a successful implementation of the method using completely adaptive overset grids to describe continuum functions, in which spherical subgrids are placed on every atomic center to complement a spherical master grid that describes the behavior at large distances. An accurate method for applying the free-particle Green's function on the grid eliminates the need to operate explicitly with the kinetic energy, enabling a rapidly convergent Arnoldi algorithm for solving linear equations on the grid, and no approximations to exchange operators are made. Results for electron scattering from several polyatomic molecules will be presented. Army Research Office, MURI, WN911NF-14-1-0383 and U. S. DOE DE-SC0012198 (at Texas A&M).

Composite Structural Motifs of Binding Sites for Delineating Biological Functions of Proteins

PubMed Central

Kinjo, Akira R.; Nakamura, Haruki

2012-01-01

Most biological processes are described as a series of interactions between proteins and other molecules, and interactions are in turn described in terms of atomic structures. To annotate protein functions as sets of interaction states at atomic resolution, and thereby to better understand the relation between protein interactions and biological functions, we conducted exhaustive all-against-all atomic structure comparisons of all known binding sites for ligands including small molecules, proteins and nucleic acids, and identified recurring elementary motifs. By integrating the elementary motifs associated with each subunit, we defined composite motifs that represent context-dependent combinations of elementary motifs. It is demonstrated that function similarity can be better inferred from composite motif similarity compared to the similarity of protein sequences or of individual binding sites. By integrating the composite motifs associated with each protein function, we define meta-composite motifs each of which is regarded as a time-independent diagrammatic representation of a biological process. It is shown that meta-composite motifs provide richer annotations of biological processes than sequence clusters. The present results serve as a basis for bridging atomic structures to higher-order biological phenomena by classification and integration of binding site structures. PMID:22347478

Protective Measurement and Quantum Reality

NASA Astrophysics Data System (ADS)

Gao, Shan

2015-01-01

1. Protective measurements: an introduction Shan Gao; Part I. Fundamentals and Applications: 2. Protective measurements of the wave function of a single system Lev Vaidman; 3. Protective measurement, postselection and the Heisenberg representation Yakir Aharonov and Eliahu Cohen; 4. Protective and state measurement: a review Gennaro Auletta; 5. Determination of the stationary basis from protective measurement on a single system Lajos Diósi; 6. Weak measurements, the energy-momentum tensor and the Bohm approach Robert Flack and Basil J. Hiley; Part II. Meanings and Implications: 7. Measurement and metaphysics Peter J. Lewis; 8. Protective measurements and the explanatory gambit Michael Dickson; 9. Realism and instrumentalism about the wave function: how should we choose? Mauro Dorato and Frederico Laudisa; 10. Protective measurements and the PBR theorem Guy Hetzroni and Daniel Rohrlich; 11. The roads not taken: empty waves, waveform collapse and protective measurement in quantum theory Peter Holland; 12. Implications of protective measurements on de Broglie-Bohm trajectories Aurelien Drezet; 13. Entanglement, scaling, and the meaning of the wave function in protective measurement Maximilian Schlosshauer and Tangereen V. B. Claringbold; 14. Protective measurements and the nature of the wave function within the primitive ontology approach Vincent Lam; 15. Reality and meaning of the wave function Shan Gao; Index.

Self-Taught Learning Based on Sparse Autoencoder for E-Nose in Wound Infection Detection

PubMed Central

He, Peilin; Jia, Pengfei; Qiao, Siqi; Duan, Shukai

2017-01-01

For an electronic nose (E-nose) in wound infection distinguishing, traditional learning methods have always needed large quantities of labeled wound infection samples, which are both limited and expensive; thus, we introduce self-taught learning combined with sparse autoencoder and radial basis function (RBF) into the field. Self-taught learning is a kind of transfer learning that can transfer knowledge from other fields to target fields, can solve such problems that labeled data (target fields) and unlabeled data (other fields) do not share the same class labels, even if they are from entirely different distribution. In our paper, we obtain numerous cheap unlabeled pollutant gas samples (benzene, formaldehyde, acetone and ethylalcohol); however, labeled wound infection samples are hard to gain. Thus, we pose self-taught learning to utilize these gas samples, obtaining a basis vector θ. Then, using the basis vector θ, we reconstruct the new representation of wound infection samples under sparsity constraint, which is the input of classifiers. We compare RBF with partial least squares discriminant analysis (PLSDA), and reach a conclusion that the performance of RBF is superior to others. We also change the dimension of our data set and the quantity of unlabeled data to search the input matrix that produces the highest accuracy. PMID:28991154

Tests of the Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

NASA Technical Reports Server (NTRS)

Koshak, William; Solakiewicz, Richard; Attele, Rohan

2011-01-01

Satellite lightning imagers such as the NASA Tropical Rainfall Measuring Mission Lightning Imaging Sensor (TRMM/LIS) and the future GOES-R Geostationary Lightning Mapper (GLM) are designed to detect total lightning (ground flashes + cloud flashes). However, there is a desire to discriminate ground flashes from cloud flashes from the vantage point of space since this would enhance the overall information content of the satellite lightning data and likely improve its operational and scientific applications (e.g., in severe weather warning, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters (one of which is the ground flash fraction), a scalar function was minimized by a numerical method. In order to improve this optimization, a Grobner basis solution was introduced to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. In this study, we test the efficacy of the Grobner basis initialization using actual lightning imager measurements and ground flash truth derived from the national lightning network.

Improved hybrid algorithm with Gaussian basis sets and plane waves: First-principles calculations of ethylene adsorption on β-SiC(001)-(3×2)

NASA Astrophysics Data System (ADS)

Wieferink, Jürgen; Krüger, Peter; Pollmann, Johannes

2006-11-01

We present an algorithm for DFT calculations employing Gaussian basis sets for the wave function and a Fourier basis for the potential representation. In particular, a numerically very efficient calculation of the local potential matrix elements and the charge density is described. Special emphasis is placed on the consequences of periodicity and explicit k -vector dependence. The algorithm is tested by comparison with more straightforward ones for the case of adsorption of ethylene on the silicon-rich SiC(001)-(3×2) surface clearly revealing its substantial advantages. A complete self-consistency cycle is speeded up by roughly one order of magnitude since the calculation of matrix elements and of the charge density are accelerated by factors of 10 and 80, respectively, as compared to their straightforward calculation. Our results for C2H4:SiC(001)-(3×2) show that ethylene molecules preferentially adsorb in on-top positions above Si dimers on the substrate surface saturating both dimer dangling bonds per unit cell. In addition, a twist of the molecules around a surface-perpendicular axis is slightly favored energetically similar to the case of a complete monolayer of ethylene adsorbed on the Si(001)-(2×1) surface.

Age Differences in Symbolic Representation: Fluidity in Representational Construction.

ERIC Educational Resources Information Center

Reifel, Stuart

This paper reports a cross-sectional, developmental study of the fluidity of children's mental functioning (representational skills) in contexts involving the representational use of blocks. Data were collected from a sample of 40 children from a laboratory school: 20 four-year-olds and 20 seven-year-olds, with an equal number of boys and girls in…

A Galerkin Approach to Define Measured Terrain Surfaces with Analytic Basis Vectors to Produce a Compact Representation

DTIC Science & Technology

2010-11-01

defined herein as terrain whose surface deformation due to a single vehicle traversing the surface is negligible, such as paved roads (both asphalt ...ground vehicle reliability predictions. Current application of this work is limited to the analysis of U.S. Highways, comprised of both asphalt and...Highways that are consistent between asphalt and concrete roads b. The principle terrain characteristics are defined with analytic basis vectors

Design Features for Linguistically-Mediated Meaning Construction: The Relative Roles of the Linguistic and Conceptual Systems in Subserving the Ideational Function of Language.

PubMed

Evans, Vyvyan

2016-01-01

Recent research in language and cognitive science proposes that the linguistic system evolved to provide an "executive" control system on the evolutionarily more ancient conceptual system (e.g., Barsalou et al., 2008; Evans, 2009, 2015a,b; Bergen, 2012). In short, the claim is that embodied representations in the linguistic system interface with non-linguistic representations in the conceptual system, facilitating rich meanings, or simulations, enabling linguistically mediated communication. In this paper I build on these proposals by examining the nature of what I identify as design features for this control system. In particular, I address how the ideational function of language-our ability to deploy linguistic symbols to convey meanings of great complexity-is facilitated. The central proposal of this paper is as follows. The linguistic system of any given language user, of any given linguistic system-spoken or signed-facilitates access to knowledge representation-concepts-in the conceptual system, which subserves this ideational function. In the most general terms, the human meaning-making capacity is underpinned by two distinct, although tightly coupled representational systems: the conceptual system and the linguistic system. Each system contributes to meaning construction in qualitatively distinct ways. This leads to the first design feature: given that the two systems are representational-they are populated by semantic representations-the nature and function of the representations are qualitatively different. This proposed design feature I term the bifurcation in semantic representation. After all, it stands to reason that if a linguistic system has a different function, vis-à-vis the conceptual system, which is of far greater evolutionary antiquity, then the semantic representations will be complementary, and as such, qualitatively different, reflecting the functional distinctions of the two systems, in collectively giving rise to meaning. I consider the nature of these qualitatively distinct representations. And second, language itself is adapted to the conceptual system-the semantic potential-that it marshals in the meaning construction process. Hence, a linguistic system itself exhibits a bifurcation, in terms of the symbolic resources at its disposal. This design feature I dub the birfucation in linguistic organization. As I shall argue, this relates to two distinct reference strategies available for symbolic encoding in language: what I dub words-to-world reference and words-to-words reference. In slightly different terms, this design feature of language amounts to a distinction between a lexical subsystem, and a grammatical subsystem.

Students' Competencies in Working with Functions in Secondary Mathematics Education-Empirical Examination of a Competence Structure Model

ERIC Educational Resources Information Center

Nitsch, Renate; Fredebohm, Anneke; Bruder, Regina; Kelava, Augustin; Naccarella, Dominik; Leuders, Timo; Wirtz, Markus

2015-01-01

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…

Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment☆

PubMed Central

Szucs, Denes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2013-01-01

Developmental dyscalculia is thought to be a specific impairment of mathematics ability. Currently dominant cognitive neuroscience theories of developmental dyscalculia suggest that it originates from the impairment of the magnitude representation of the human brain, residing in the intraparietal sulcus, or from impaired connections between number symbols and the magnitude representation. However, behavioral research offers several alternative theories for developmental dyscalculia and neuro-imaging also suggests that impairments in developmental dyscalculia may be linked to disruptions of other functions of the intraparietal sulcus than the magnitude representation. Strikingly, the magnitude representation theory has never been explicitly contrasted with a range of alternatives in a systematic fashion. Here we have filled this gap by directly contrasting five alternative theories (magnitude representation, working memory, inhibition, attention and spatial processing) of developmental dyscalculia in 9–10-year-old primary school children. Participants were selected from a pool of 1004 children and took part in 16 tests and nine experiments. The dominant features of developmental dyscalculia are visuo-spatial working memory, visuo-spatial short-term memory and inhibitory function (interference suppression) impairment. We hypothesize that inhibition impairment is related to the disruption of central executive memory function. Potential problems of visuo-spatial processing and attentional function in developmental dyscalculia probably depend on short-term memory/working memory and inhibition impairments. The magnitude representation theory of developmental dyscalculia was not supported. PMID:23890692

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

NASA Astrophysics Data System (ADS)

Yu, Hua-Gen

2016-08-01

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using a multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH4 and H2CO are given, together with a comparison with previous results.

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

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

Yu, Hua-Gen, E-mail: hgy@bnl.gov

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using amore » multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH{sub 4} and H{sub 2}CO are given, together with a comparison with previous results.« less

Chronic non-communicable diseases, risk and health promotion: social construction of VIGITEL participants.

PubMed

Mássimo, Erika de Azevedo Leitão; de Souza, Hercília Najara Ferreira; Freitas, Maria Imaculada de Fátima

2015-03-01

The dimension of choice and adherence to healthy lifestyles is in the area of social constructions made in representations of individuals and had not yet been included in the Surveillance of Risk and Protective Factors for Chronic Diseases by Telephone Survey (VIGITEL) analysis systems. This article aims to understand, in individual narratives, representations contained in the trajectories of people's lives selected from the 2010 VIGITEL sample, in Belo Horizonte, Minas Gerais. It is a qualitative study based on Social Representation Theory. Thirty in-depth and open interviews with subjects selected from the 2010 VIGITEL sample were conducted in Belo Horizonte in the State of Minas Gerais. The Structural Analysis of Narrative technique was used to reveal the content of speeches. Age and heredity representations related to NCDs are part of the spectrum of current scientific information. Learning from childhood onwards is the basis of care. The lack of comprehension of the pathophysiology of NCDs, and the depth of representations of illness and death related to communicable diseases, is partly responsible for the difficulty of preventing NCDs.

fMRI-based Multivariate Pattern Analyses Reveal Imagery Modality and Imagery Content Specific Representations in Primary Somatosensory, Motor and Auditory Cortices.

PubMed

de Borst, Aline W; de Gelder, Beatrice

2017-08-01

Previous studies have shown that the early visual cortex contains content-specific representations of stimuli during visual imagery, and that these representational patterns of imagery content have a perceptual basis. To date, there is little evidence for the presence of a similar organization in the auditory and tactile domains. Using fMRI-based multivariate pattern analyses we showed that primary somatosensory, auditory, motor, and visual cortices are discriminative for imagery of touch versus sound. In the somatosensory, motor and visual cortices the imagery modality discriminative patterns were similar to perception modality discriminative patterns, suggesting that top-down modulations in these regions rely on similar neural representations as bottom-up perceptual processes. Moreover, we found evidence for content-specific representations of the stimuli during auditory imagery in the primary somatosensory and primary motor cortices. Both the imagined emotions and the imagined identities of the auditory stimuli could be successfully classified in these regions. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

A group matrix representation relevant to scales of measurement of clinical disease states via stratified vectors.

PubMed

Sawamura, Jitsuki; Morishita, Shigeru; Ishigooka, Jun

2016-02-09

Previously, we applied basic group theory and related concepts to scales of measurement of clinical disease states and clinical findings (including laboratory data). To gain a more concrete comprehension, we here apply the concept of matrix representation, which was not explicitly exploited in our previous work. Starting with a set of orthonormal vectors, called the basis, an operator Rj (an N-tuple patient disease state at the j-th session) was expressed as a set of stratified vectors representing plural operations on individual components, so as to satisfy the group matrix representation. The stratified vectors containing individual unit operations were combined into one-dimensional square matrices [Rj]s. The [Rj]s meet the matrix representation of a group (ring) as a K-algebra. Using the same-sized matrix of stratified vectors, we can also express changes in the plural set of [Rj]s. The method is demonstrated on simple examples. Despite the incompleteness of our model, the group matrix representation of stratified vectors offers a formal mathematical approach to clinical medicine, aligning it with other branches of natural science.

The neural basis for category-specific knowledge: an fMRI study.

PubMed

Grossman, Murray; Koenig, Phyllis; DeVita, Chris; Glosser, Guila; Alsop, David; Detre, John; Gee, James

2002-04-01

Functional neuroimaging studies of healthy adults have associated different categories of knowledge with distinct activation patterns. The basis for these recruitment patterns has been controversial, due in part to the limited range of categories that has been studied. We used fMRI to monitor regional cortical recruitment patterns while subjects were exposed to printed names of Animals, Implements, and Abstract nouns. Both Implements and Abstract nouns were related to recruitment of left posterolateral temporal cortex and left prefrontal cortex, and Abstract nouns additionally recruited posterolateral temporal and prefrontal regions of the right hemisphere. Animals were associated with activation of ventral-medial occipital cortex in the left hemisphere at a level that approaches significance. These findings are not consistent with the "sensory-motor" model proposed to explain the neural representation of word knowledge. We suggest instead a neural model of semantic memory that reflects the processes common to understanding Implements and Abstract nouns and a selective sensitivity, possibly evolving from adaptive pressures, to the overlapping, intercorrelated visual characteristics of Animals. (C)2002 Elsevier Science (USA).

21 CFR 1316.50 - Appearance; representation; authorization.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 21 Food and Drugs 9 2010-04-01 2010-04-01 false Appearance; representation; authorization. 1316.50 Section 1316.50 Food and Drugs DRUG ENFORCEMENT ADMINISTRATION, DEPARTMENT OF JUSTICE ADMINISTRATIVE FUNCTIONS, PRACTICES, AND PROCEDURES Administrative Hearings § 1316.50 Appearance; representation...

Local unitary representation of braids and N-qubit entanglements

NASA Astrophysics Data System (ADS)

Yu, Li-Wei

2018-03-01

In this paper, by utilizing the idea of stabilizer codes, we give some relationships between one local unitary representation of braid group in N-qubit tensor space and the corresponding entanglement properties of the N-qubit pure state |Ψ >, where the N-qubit state |Ψ > is obtained by applying the braiding operation on the natural basis. Specifically, we show that the separability of |Ψ > =B|0> ^{⊗ N} is closely related to the diagrammatic version of the braid operator B. This may provide us more insights about the topological entanglement and quantum entanglement.