The semantic representation of prejudice and stereotypes.

PubMed

Bhatia, Sudeep

2017-07-01

We use a theory of semantic representation to study prejudice and stereotyping. Particularly, we consider large datasets of newspaper articles published in the United States, and apply latent semantic analysis (LSA), a prominent model of human semantic memory, to these datasets to learn representations for common male and female, White, African American, and Latino names. LSA performs a singular value decomposition on word distribution statistics in order to recover word vector representations, and we find that our recovered representations display the types of biases observed in human participants using tasks such as the implicit association test. Importantly, these biases are strongest for vector representations with moderate dimensionality, and weaken or disappear for representations with very high or very low dimensionality. Moderate dimensional LSA models are also the best at learning race, ethnicity, and gender-based categories, suggesting that social category knowledge, acquired through dimensionality reduction on word distribution statistics, can facilitate prejudiced and stereotyped associations. Copyright © 2017 Elsevier B.V. All rights reserved.

Categorical clustering of the neural representation of color.

PubMed

Brouwer, Gijs Joost; Heeger, David J

2013-09-25

Cortical activity was measured with functional magnetic resonance imaging (fMRI) while human subjects viewed 12 stimulus colors and performed either a color-naming or diverted attention task. A forward model was used to extract lower dimensional neural color spaces from the high-dimensional fMRI responses. The neural color spaces in two visual areas, human ventral V4 (V4v) and VO1, exhibited clustering (greater similarity between activity patterns evoked by stimulus colors within a perceptual category, compared to between-category colors) for the color-naming task, but not for the diverted attention task. Response amplitudes and signal-to-noise ratios were higher in most visual cortical areas for color naming compared to diverted attention. But only in V4v and VO1 did the cortical representation of color change to a categorical color space. A model is presented that induces such a categorical representation by changing the response gains of subpopulations of color-selective neurons.

Categorical Clustering of the Neural Representation of Color

PubMed Central

Heeger, David J.

2013-01-01

Cortical activity was measured with functional magnetic resonance imaging (fMRI) while human subjects viewed 12 stimulus colors and performed either a color-naming or diverted attention task. A forward model was used to extract lower dimensional neural color spaces from the high-dimensional fMRI responses. The neural color spaces in two visual areas, human ventral V4 (V4v) and VO1, exhibited clustering (greater similarity between activity patterns evoked by stimulus colors within a perceptual category, compared to between-category colors) for the color-naming task, but not for the diverted attention task. Response amplitudes and signal-to-noise ratios were higher in most visual cortical areas for color naming compared to diverted attention. But only in V4v and VO1 did the cortical representation of color change to a categorical color space. A model is presented that induces such a categorical representation by changing the response gains of subpopulations of color-selective neurons. PMID:24068814

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

PubMed

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

2016-01-01

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

Quantum dynamics calculations using symmetrized, orthogonal Weyl-Heisenberg wavelets with a phase space truncation scheme. III. Representations and calculations.

PubMed

Poirier, Bill; Salam, A

2004-07-22

In a previous paper [J. Theo. Comput. Chem. 2, 65 (2003)], one of the authors (B.P.) presented a method for solving the multidimensional Schrodinger equation, using modified Wilson-Daubechies wavelets, and a simple phase space truncation scheme. Unprecedented numerical efficiency was achieved, enabling a ten-dimensional calculation of nearly 600 eigenvalues to be performed using direct matrix diagonalization techniques. In a second paper [J. Chem. Phys. 121, 1690 (2004)], and in this paper, we extend and elaborate upon the previous work in several important ways. The second paper focuses on construction and optimization of the wavelength functions, from theoretical and numerical viewpoints, and also examines their localization. This paper deals with their use in representations and eigenproblem calculations, which are extended to 15-dimensional systems. Even higher dimensionalities are possible using more sophisticated linear algebra techniques. This approach is ideally suited to rovibrational spectroscopy applications, but can be used in any context where differential equations are involved.

Maximally Informative Hierarchical Representations of High-Dimensional Data

DTIC Science & Technology

2015-05-11

will be considered dis- crete but the domain of the X i ’s is not restricted. Entropy is defined in the usual way as H(X) ⌘ E X [log 1/p(x)]. We use...natural logarithms so that the unit of information is nats. Higher-order entropies can be constructed in various ways from this standard definition. For...sense, not truly high-dimensional and can be charac- terized separately. On the other hand, the entropy of X, H(X), can naively be considered the

Consistent Alignment of World Embedding Models

DTIC Science & Technology

2017-03-02

propose a solution that aligns variations of the same model (or different models) in a joint low-dimensional la- tent space leveraging carefully...representations of linguistic enti- ties, most often referred to as embeddings. This includes techniques that rely on matrix factoriza- tion (Levy & Goldberg ...higher, the variation is much higher as well. As we increase the size of the neighborhood, or improve the quality of our sample by only picking the most

Low-dimensional representations of the three component loop braid group

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

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

2015-11-01

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

High dimensional model representation method for fuzzy structural dynamics

NASA Astrophysics Data System (ADS)

Adhikari, S.; Chowdhury, R.; Friswell, M. I.

2011-03-01

Uncertainty propagation in multi-parameter complex structures possess significant computational challenges. This paper investigates the possibility of using the High Dimensional Model Representation (HDMR) approach when uncertain system parameters are modeled using fuzzy variables. In particular, the application of HDMR is proposed for fuzzy finite element analysis of linear dynamical systems. The HDMR expansion is an efficient formulation for high-dimensional mapping in complex systems if the higher order variable correlations are weak, thereby permitting the input-output relationship behavior to be captured by the terms of low-order. The computational effort to determine the expansion functions using the α-cut method scales polynomically with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is first illustrated for multi-parameter nonlinear mathematical test functions with fuzzy variables. The method is then integrated with a commercial finite element software (ADINA). Modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations. It is shown that using the proposed HDMR approach, the number of finite element function calls can be reduced without significantly compromising the accuracy.

Combinatorial approach to the representation of the Schur-Weyl duality in one-dimensional spin systems

NASA Astrophysics Data System (ADS)

Jakubczyk, Dorota; Jakubczyk, Paweł

2018-02-01

We propose combinatorial approach to the representation of Schur-Weyl duality in physical systems on the example of one-dimensional spin chains. Exploiting the Robinson-Schensted-Knuth algorithm, we perform decomposition of the dual group representations into irreducible representations in a fully combinatorial way. As representation space, we choose the Hilbert space of the spin chains, but this approach can be easily generalized to an arbitrary physical system where the Schur-Weyl duality works.

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

NASA Technical Reports Server (NTRS)

Bhansali, Vineer

1993-01-01

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

Cortical dynamics of three-dimensional figure-ground perception of two-dimensional pictures.

PubMed

Grossberg, S

1997-07-01

This article develops the FACADE theory of 3-dimensional (3-D) vision and figure-ground separation to explain data concerning how 2-dimensional pictures give rise to 3-D percepts of occluding and occluded objects. The model describes how geometrical and contrastive properties of a picture can either cooperate or compete when forming the boundaries and surface representation that subserve conscious percepts. Spatially long-range cooperation and spatially short-range competition work together to separate the boundaries of occluding figures from their occluded neighbors. This boundary ownership process is sensitive to image T junctions at which occluded figures contact occluding figures. These boundaries control the filling-in of color within multiple depth-sensitive surface representations. Feedback between surface and boundary representations strengthens consistent boundaries while inhibiting inconsistent ones. Both the boundary and the surface representations of occluded objects may be amodally completed, while the surface representations of unoccluded objects become visible through modal completion. Functional roles for conscious modal and amodal representations in object recognition, spatial attention, and reaching behaviors are discussed. Model interactions are interpreted in terms of visual, temporal, and parietal cortices.

Deep neural networks for texture classification-A theoretical analysis.

PubMed

Basu, Saikat; Mukhopadhyay, Supratik; Karki, Manohar; DiBiano, Robert; Ganguly, Sangram; Nemani, Ramakrishna; Gayaka, Shreekant

2018-01-01

We investigate the use of Deep Neural Networks for the classification of image datasets where texture features are important for generating class-conditional discriminative representations. To this end, we first derive the size of the feature space for some standard textural features extracted from the input dataset and then use the theory of Vapnik-Chervonenkis dimension to show that hand-crafted feature extraction creates low-dimensional representations which help in reducing the overall excess error rate. As a corollary to this analysis, we derive for the first time upper bounds on the VC dimension of Convolutional Neural Network as well as Dropout and Dropconnect networks and the relation between excess error rate of Dropout and Dropconnect networks. The concept of intrinsic dimension is used to validate the intuition that texture-based datasets are inherently higher dimensional as compared to handwritten digits or other object recognition datasets and hence more difficult to be shattered by neural networks. We then derive the mean distance from the centroid to the nearest and farthest sampling points in an n-dimensional manifold and show that the Relative Contrast of the sample data vanishes as dimensionality of the underlying vector space tends to infinity. Copyright © 2017 Elsevier Ltd. All rights reserved.

Deep linear autoencoder and patch clustering-based unified one-dimensional coding of image and video

NASA Astrophysics Data System (ADS)

Li, Honggui

2017-09-01

This paper proposes a unified one-dimensional (1-D) coding framework of image and video, which depends on deep learning neural network and image patch clustering. First, an improved K-means clustering algorithm for image patches is employed to obtain the compact inputs of deep artificial neural network. Second, for the purpose of best reconstructing original image patches, deep linear autoencoder (DLA), a linear version of the classical deep nonlinear autoencoder, is introduced to achieve the 1-D representation of image blocks. Under the circumstances of 1-D representation, DLA is capable of attaining zero reconstruction error, which is impossible for the classical nonlinear dimensionality reduction methods. Third, a unified 1-D coding infrastructure for image, intraframe, interframe, multiview video, three-dimensional (3-D) video, and multiview 3-D video is built by incorporating different categories of videos into the inputs of patch clustering algorithm. Finally, it is shown in the results of simulation experiments that the proposed methods can simultaneously gain higher compression ratio and peak signal-to-noise ratio than those of the state-of-the-art methods in the situation of low bitrate transmission.

Factorial structure of the German version of the dimensional assessment of personality pathology-basic questionnaire in clinical and nonclinical samples.

PubMed

Pukrop, R; Gentil, I; Steinbring, I; Steinmeyer, E

2001-10-01

The Dimensional Assessment of Personality Pathology-Basic Questionnaire (DAPP-BQ) assesses 18 traits to provide a systematic representation of the overall domain of personality disorders. We tested the cross-cultural stability of the prediction that four higher-order factors (Emotional Dysregulation, Dissocial Behavior, Inhibitedness, and Compulsivity) underlie the 18 basic traits. A total of 81 patients who were primarily treated for an Axis II personality disorder and N = 166 healthy control patients completed the German version of the DAPP-BQ. Results clearly confirmed cross-cultural stability of the postulated four-factor structure in both samples, accounting for 74.7% (clinical sample), and 65.7% (nonclinical sample) of the total variance. All four higher-order factors showed specific correlational relationships with dimensional assessments of DSM-IV personality disorders.

Graphical Representations and Cluster Algorithms for Ice Rule Vertex Models.

NASA Astrophysics Data System (ADS)

Shtengel, Kirill; Chayes, L.

2002-03-01

We introduce a new class of polymer models which is closely related to loop models, recently a topic of intensive studies. These particular models arise as graphical representations for ice-rule vertex models. The associated cluster algorithms provide a unification and generalisation of most of the existing algorithms. For many lattices, percolation in the polymer models evidently indicates first order phase transitions in the vertex models. Critical phases can be understood as being susceptible to colour symmetry breaking in the polymer models. The analysis includes, but is certainly not limited to the square lattice six-vertex model. In particular, analytic criteria can be found for low temperature phases in other even coordinated 2D lattices such as the triangular lattice, or higher dimensional lattices such as the hyper-cubic lattices of arbitrary dimensionality. Finally, our approach can be generalised to the vertex models that do not obey the ice rule, such as the eight-vertex model.

Region based route planning - Multi-abstraction route planning based on intermediate level vision processing

NASA Technical Reports Server (NTRS)

Doshi, Rajkumar S.; Lam, Raymond; White, James E.

1989-01-01

Intermediate and high level processing operations are performed on vision data for the organization of images into more meaningful, higher-level topological representations by means of a region-based route planner (RBRP). The RBRP operates in terrain scenarios where some or most of the terrain is occluded, proceeding without a priori maps on the basis of two-dimensional representations and gradient-and-roughness information. Route planning is accomplished by three successive abstractions and yields a detailed point-by-point path by searching only within the boundaries of relatively small regions.

Supercomputer algorithms for efficient linear octree encoding of three-dimensional brain images.

PubMed

Berger, S B; Reis, D J

1995-02-01

We designed and implemented algorithms for three-dimensional (3-D) reconstruction of brain images from serial sections using two important supercomputer architectures, vector and parallel. These architectures were represented by the Cray YMP and Connection Machine CM-2, respectively. The programs operated on linear octree representations of the brain data sets, and achieved 500-800 times acceleration when compared with a conventional laboratory workstation. As the need for higher resolution data sets increases, supercomputer algorithms may offer a means of performing 3-D reconstruction well above current experimental limits.

Sparse representation of multi parametric DCE-MRI features using K-SVD for classifying gene expression based breast cancer recurrence risk

NASA Astrophysics Data System (ADS)

Mahrooghy, Majid; Ashraf, Ahmed B.; Daye, Dania; Mies, Carolyn; Rosen, Mark; Feldman, Michael; Kontos, Despina

2014-03-01

We evaluate the prognostic value of sparse representation-based features by applying the K-SVD algorithm on multiparametric kinetic, textural, and morphologic features in breast dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). K-SVD is an iterative dimensionality reduction method that optimally reduces the initial feature space by updating the dictionary columns jointly with the sparse representation coefficients. Therefore, by using K-SVD, we not only provide sparse representation of the features and condense the information in a few coefficients but also we reduce the dimensionality. The extracted K-SVD features are evaluated by a machine learning algorithm including a logistic regression classifier for the task of classifying high versus low breast cancer recurrence risk as determined by a validated gene expression assay. The features are evaluated using ROC curve analysis and leave one-out cross validation for different sparse representation and dimensionality reduction numbers. Optimal sparse representation is obtained when the number of dictionary elements is 4 (K=4) and maximum non-zero coefficients is 2 (L=2). We compare K-SVD with ANOVA based feature selection for the same prognostic features. The ROC results show that the AUC of the K-SVD based (K=4, L=2), the ANOVA based, and the original features (i.e., no dimensionality reduction) are 0.78, 0.71. and 0.68, respectively. From the results, it can be inferred that by using sparse representation of the originally extracted multi-parametric, high-dimensional data, we can condense the information on a few coefficients with the highest predictive value. In addition, the dimensionality reduction introduced by K-SVD can prevent models from over-fitting.

Partition function of free conformal fields in 3-plet representation

NASA Astrophysics Data System (ADS)

Beccaria, Matteo; Tseytlin, Arkady A.

2017-05-01

Simplest examples of AdS/CFT duality correspond to free CFTs in d dimensions with fields in vector or adjoint representation of an internal symmetry group dual in the large N limit to a theory of massless or massless plus massive higher spins in AdS d+1. One may also study generalizations when conformal fields belong to higher dimensional representations, i.e. carry more than two internal symmetry indices. Here we consider the case of the 3-fundamental ("3-plet") representation. One motivation is a conjectured connection to multiple M5-brane theory: heuristic arguments suggest that it may be related to an (interacting) CFT of 6d (2,0) tensor multiplets in 3-plet representation of large N symmetry group that has an AdS7 dual. We compute the singlet partition function Z on S 1 × S d-1 for a free field in 3-plet representation of U( N) and analyse its novel large N behaviour. The large N limit of the low temperature expansion of Z which is convergent in the vector and adjoint cases here is only asymptotic, reflecting the much faster growth of the number of singlet operators with dimension, indicating a phase transition at very low temperature. Indeed, while the critical temperatures in the vector ( T c ˜ N γ , γ > 0) and adjoint ( T c ˜ 1) cases are finite, we find that in the 3-plet case T c ˜ (log N)-1, i.e. it approaches zero at large N. We discuss some details of large N solution for the eigenvalue distribution. Similar conclusions apply to higher p-plet representations of U( N) or O( N) and also to the free p-tensor theories invariant under [U( N)] p or [ O( N)] p with p ≥ 3.

Finite-Dimensional Representations for Controlled Diffusions with Delay

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

Federico, Salvatore, E-mail: salvatore.federico@unimi.it; Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr

2015-02-15

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.

Ince-Gaussian series representation of the two-dimensional fractional Fourier transform.

PubMed

Bandres, Miguel A; Gutiérrez-Vega, Julio C

2005-03-01

We introduce the Ince-Gaussian series representation of the two-dimensional fractional Fourier transform in elliptical coordinates. A physical interpretation is provided in terms of field propagation in quadratic graded-index media whose eigenmodes in elliptical coordinates are derived for the first time to our knowledge. The kernel of the new series representation is expressed in terms of Ince-Gaussian functions. The equivalence among the Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian series representations is verified by establishing the relation among the three definitions.

Visualising elastic anisotropy: theoretical background and computational implementation

NASA Astrophysics Data System (ADS)

Nordmann, J.; Aßmus, M.; Altenbach, H.

2018-02-01

In this article, we present the technical realisation for visualisations of characteristic parameters of the fourth-order elasticity tensor, which is classified by three-dimensional symmetry groups. Hereby, expressions for spatial representations of uc(Young)'s modulus and bulk modulus as well as plane representations of shear modulus and uc(Poisson)'s ratio are derived and transferred into a comprehensible form to computer algebra systems. Additionally, we present approaches for spatial representations of both latter parameters. These three- and two-dimensional representations are implemented into the software MATrix LABoratory. Exemplary representations of characteristic materials complete the present treatise.

Partition functions with spin in AdS2 via quasinormal mode methods

DOE PAGES

Keeler, Cynthia; Lisbão, Pedro; Ng, Gim Seng

2016-10-12

We extend the results of [1], computing one loop partition functions for massive fields with spin half in AdS 2 using the quasinormal mode method proposed by Denef, Hartnoll, and Sachdev [2]. We find the finite representations of SO(2,1) for spin zero and spin half, consisting of a highest weight state |hi and descendants with non-unitary values of h. These finite representations capture the poles and zeroes of the one loop determinants. Together with the asymptotic behavior of the partition functions (which can be easily computed using a large mass heat kernel expansion), these are sufficient to determine the fullmore » answer for the one loop determinants. We also discuss extensions to higher dimensional AdS 2n and higher spins.« less

Three-Dimensional Messages for Interstellar Communication

NASA Astrophysics Data System (ADS)

Vakoch, Douglas A.

One of the challenges facing independently evolved civilizations separated by interstellar distances is to communicate information unique to one civilization. One commonly proposed solution is to begin with two-dimensional pictorial representations of mathematical concepts and physical objects, in the hope that this will provide a foundation for overcoming linguistic barriers. However, significant aspects of such representations are highly conventional, and may not be readily intelligible to a civilization with different conventions. The process of teaching conventions of representation may be facilitated by the use of three-dimensional representations redundantly encoded in multiple formats (e.g., as both vectors and as rasters). After having illustrated specific conventions for representing mathematical objects in a three-dimensional space, this method can be used to describe a physical environment shared by transmitter and receiver: a three-dimensional space defined by the transmitter--receiver axis, and containing stars within that space. This method can be extended to show three-dimensional representations varying over time. Having clarified conventions for representing objects potentially familiar to both sender and receiver, novel objects can subsequently be depicted. This is illustrated through sequences showing interactions between human beings, which provide information about human behavior and personality. Extensions of this method may allow the communication of such culture-specific features as aesthetic judgments and religious beliefs. Limitations of this approach will be noted, with specific reference to ETI who are not primarily visual.

The Effect of Two-dimensional and Stereoscopic Presentation on Middle School Students' Performance of Spatial Cognition Tasks

NASA Astrophysics Data System (ADS)

Price, Aaron; Lee, Hee-Sun

2010-02-01

We investigated whether and how student performance on three types of spatial cognition tasks differs when worked with two-dimensional or stereoscopic representations. We recruited nineteen middle school students visiting a planetarium in a large Midwestern American city and analyzed their performance on a series of spatial cognition tasks in terms of response accuracy and task completion time. Results show that response accuracy did not differ between the two types of representations while task completion time was significantly greater with the stereoscopic representations. The completion time increased as the number of mental manipulations of 3D objects increased in the tasks. Post-interviews provide evidence that some students continued to think of stereoscopic representations as two-dimensional. Based on cognitive load and cue theories, we interpret that, in the absence of pictorial depth cues, students may need more time to be familiar with stereoscopic representations for optimal performance. In light of these results, we discuss potential uses of stereoscopic representations for science learning.

The Interaction between Semantic Representation and Episodic Memory.

PubMed

Fang, Jing; Rüther, Naima; Bellebaum, Christian; Wiskott, Laurenz; Cheng, Sen

2018-02-01

The experimental evidence on the interrelation between episodic memory and semantic memory is inconclusive. Are they independent systems, different aspects of a single system, or separate but strongly interacting systems? Here, we propose a computational role for the interaction between the semantic and episodic systems that might help resolve this debate. We hypothesize that episodic memories are represented as sequences of activation patterns. These patterns are the output of a semantic representational network that compresses the high-dimensional sensory input. We show quantitatively that the accuracy of episodic memory crucially depends on the quality of the semantic representation. We compare two types of semantic representations: appropriate representations, which means that the representation is used to store input sequences that are of the same type as those that it was trained on, and inappropriate representations, which means that stored inputs differ from the training data. Retrieval accuracy is higher for appropriate representations because the encoded sequences are less divergent than those encoded with inappropriate representations. Consistent with our model prediction, we found that human subjects remember some aspects of episodes significantly more accurately if they had previously been familiarized with the objects occurring in the episode, as compared to episodes involving unfamiliar objects. We thus conclude that the interaction with the semantic system plays an important role for episodic memory.

Fermionic minimal dark matter in 5D gauge-Higgs unification

NASA Astrophysics Data System (ADS)

Maru, Nobuhito; Okada, Nobuchika; Okada, Satomi

2017-12-01

We propose a minimal dark matter (MDM) scenario in the context of a simple gauge-Higgs unification (GHU) model based on the gauge group S U (3 )×U (1 )' in five-dimensional Minkowski space with a compactification of the fifth dimension on the 1S/Z2 orbifold. A pair of vectorlike S U (3 ) multiplet fermions in a higher-dimensional representation is introduced in the bulk, and the DM particle is identified with the lightest mass eigenstate among the components in the multiplets. In the original model description, the DM particle communicates with the Standard Model (SM) particles only through the bulk gauge interaction, and hence our model is the GHU version of the MDM scenario. There are two typical realizations of the DM particle in four-dimensional effective theory: (i) the DM particle is mostly composed of the SM S U (2 )L multiplets, or (ii) the DM is mostly composed of the SM S U (2 )L singlets. Since the case (i) is very similar to the original MDM scenario, we focus on the case (ii), which is a realization of the Higgs-portal DM scenario in the context of the GHU model. We identify an allowed parameter region to be consistent with the current experimental constraints, which will be fully covered by the direct dark matter detection experiments in the near future. In the presence of the bulk multiplet fermions in higher-dimensional S U (3 ) representations, we reproduce the 125 GeV Higgs boson mass through the renormalization group evolution of Higgs quartic coupling with the compactification scale of 10-100 TeV.

Compact Representation of High-Dimensional Feature Vectors for Large-Scale Image Recognition and Retrieval.

PubMed

Zhang, Yu; Wu, Jianxin; Cai, Jianfei

2016-05-01

In large-scale visual recognition and image retrieval tasks, feature vectors, such as Fisher vector (FV) or the vector of locally aggregated descriptors (VLAD), have achieved state-of-the-art results. However, the combination of the large numbers of examples and high-dimensional vectors necessitates dimensionality reduction, in order to reduce its storage and CPU costs to a reasonable range. In spite of the popularity of various feature compression methods, this paper shows that the feature (dimension) selection is a better choice for high-dimensional FV/VLAD than the feature (dimension) compression methods, e.g., product quantization. We show that strong correlation among the feature dimensions in the FV and the VLAD may not exist, which renders feature selection a natural choice. We also show that, many dimensions in FV/VLAD are noise. Throwing them away using feature selection is better than compressing them and useful dimensions altogether using feature compression methods. To choose features, we propose an efficient importance sorting algorithm considering both the supervised and unsupervised cases, for visual recognition and image retrieval, respectively. Combining with the 1-bit quantization, feature selection has achieved both higher accuracy and less computational cost than feature compression methods, such as product quantization, on the FV and the VLAD image representations.

Generative Representations for the Automated Design of Modular Physical Robots

NASA Technical Reports Server (NTRS)

Hornby, Gregory S.; Lipson, Hod; Pollack, Jordan B.

2003-01-01

We will begin with a brief background of evolutionary robotics and related work, and demonstrate the scaling problem with our own prior results. Next we propose the use of an evolved generative representation as opposed to a non-generative representation. We describe this representation in detail as well as the evolutionary process that uses it. We then compare progress of evolved robots with and without the use of the grammar, and quantify the obtained advantage. Working two- dimensional and three-dimensional physical robots produced by the system are shown.

Spline function approximation techniques for image geometric distortion representation. [for registration of multitemporal remote sensor imagery

NASA Technical Reports Server (NTRS)

Anuta, P. E.

1975-01-01

Least squares approximation techniques were developed for use in computer aided correction of spatial image distortions for registration of multitemporal remote sensor imagery. Polynomials were first used to define image distortion over the entire two dimensional image space. Spline functions were then investigated to determine if the combination of lower order polynomials could approximate a higher order distortion with less computational difficulty. Algorithms for generating approximating functions were developed and applied to the description of image distortion in aircraft multispectral scanner imagery. Other applications of the techniques were suggested for earth resources data processing areas other than geometric distortion representation.

On the n-symplectic structure of faithful irreducible representations

NASA Astrophysics Data System (ADS)

Norris, L. K.

2017-04-01

Each faithful irreducible representation of an N-dimensional vector space V1 on an n-dimensional vector space V2 is shown to define a unique irreducible n-symplectic structure on the product manifold V1×V2 . The basic details of the associated Poisson algebra are developed for the special case N = n2, and 2n-dimensional symplectic submanifolds are shown to exist.

Generating a 2D Representation of a Complex Data Structure

NASA Technical Reports Server (NTRS)

James, Mark

2006-01-01

A computer program, designed to assist in the development and debugging of other software, generates a two-dimensional (2D) representation of a possibly complex n-dimensional (where n is an integer >2) data structure or abstract rank-n object in that other software. The nature of the 2D representation is such that it can be displayed on a non-graphical output device and distributed by non-graphical means.

Out-of-Sample Extrapolation utilizing Semi-Supervised Manifold Learning (OSE-SSL): Content Based Image Retrieval for Histopathology Images

PubMed Central

Sparks, Rachel; Madabhushi, Anant

2016-01-01

Content-based image retrieval (CBIR) retrieves database images most similar to the query image by (1) extracting quantitative image descriptors and (2) calculating similarity between database and query image descriptors. Recently, manifold learning (ML) has been used to perform CBIR in a low dimensional representation of the high dimensional image descriptor space to avoid the curse of dimensionality. ML schemes are computationally expensive, requiring an eigenvalue decomposition (EVD) for every new query image to learn its low dimensional representation. We present out-of-sample extrapolation utilizing semi-supervised ML (OSE-SSL) to learn the low dimensional representation without recomputing the EVD for each query image. OSE-SSL incorporates semantic information, partial class label, into a ML scheme such that the low dimensional representation co-localizes semantically similar images. In the context of prostate histopathology, gland morphology is an integral component of the Gleason score which enables discrimination between prostate cancer aggressiveness. Images are represented by shape features extracted from the prostate gland. CBIR with OSE-SSL for prostate histology obtained from 58 patient studies, yielded an area under the precision recall curve (AUPRC) of 0.53 ± 0.03 comparatively a CBIR with Principal Component Analysis (PCA) to learn a low dimensional space yielded an AUPRC of 0.44 ± 0.01. PMID:27264985

Continuous family of finite-dimensional representations of a solvable Lie algebra arising from singularities

PubMed Central

Yau, Stephen S.-T.

1983-01-01

A natural mapping from the set of complex analytic isolated hypersurface singularities to the set of finite dimensional Lie algebras is first defined. It is proven that the image under this natural mapping is contained in the set of solvable Lie algebras. This approach gives rise to a continuous inequivalent family of finite dimensional representations of a solvable Lie algebra. PMID:16593401

A Method for Computing the Core Flow in Three-Dimensional Leading-Edge Vortices. Ph.D. Thesis - North Carolina State Univ.

NASA Technical Reports Server (NTRS)

Luckring, J. M.

1985-01-01

A theory is presented for calculating the flow in the core of a separation-induced leading-edge vortex. The method is based on matching inner and outer representations of the vortex. The inner model of the vortex is based on the quasicylindrical Navier-Stokes equations; the flow is assumed to be steady, axially symmetric, and incompressible and in addition, gradients in the radial direction are assumed to be much larger then gradients in the axial direction. The outer model is based on the three-dimensional free-vortex-sheet theory, a higher-order panel method which solves the Prandtl-Glauert equation including nonlinear boundary conditions pertinent to the concentrated vorticity representation of the leading edge vortex. The resultant flow is evaluated a posteriori for evidence of incipient vortex breakdown and the critical helix angle concept, in conjunction with an adverse longitudinal pressure gradient, is found to correlate well with the occurrence of vortex breakdown at the trailing edge of delta, arrow, and diamond wings.

On representations of U{sub q}osp(1{vert_bar}2) when q is a root of unity

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

Chung, W.; Suzuki, T.

1997-06-01

The infinite dimensional highest weight representations of U{sub q}osp(1{vert_bar}2) for the deformation parameter q being a root of unity are investigated. As in the cases of q-deformed nongraded Lie algebras, we find that every irreducible representation is isomorphic to the tensor product of a highest weight representation of sl{sub 2}(R) and a finite dimensional one of U{sub q}osp(1{vert_bar}2). The structure is investigated in detail. {copyright} {ital 1997 American Institute of Physics.}

The effects of mental representation on performance in a navigation task

NASA Technical Reports Server (NTRS)

Barshi, Immanuel; Healy, Alice F.

2002-01-01

In three experiments, we investigated the mental representations employed when instructions were followed that involved navigation in a space displayed as a grid on a computer screen. Performance was affected much more by the number of instructional units than by the number of words per unit. Performance in a three-dimensional space was independent of the number of dimensions along which participants navigated. However, memory for and accuracy in following the instructions were reduced when the task required mentally representing a three-dimensional space, as compared with representing a two-dimensional space, although the words used in the instructions were identical in the two cases. These results demonstrate the interdependence of verbal and spatial memory representations, because individuals' immediate memory for verbal navigation instructions is affected by their mental representation of the space referred to by the instructions.

Student Learning about Biomolecular Self-Assembly Using Two Different External Representations

ERIC Educational Resources Information Center

Host, Gunnar E.; Larsson, Caroline; Olson, Arthur; Tibell, Lena A. E.

2013-01-01

Self-assembly is the fundamental but counterintuitive principle that explains how ordered biomolecular complexes form spontaneously in the cell. This study investigated the impact of using two external representations of virus self-assembly, an interactive tangible three-dimensional model and a static two-dimensional image, on student learning…

Three-dimensional representation of curved nanowires.

PubMed

Huang, Z; Dikin, D A; Ding, W; Qiao, Y; Chen, X; Fridman, Y; Ruoff, R S

2004-12-01

Nanostructures, such as nanowires, nanotubes and nanocoils, can be described in many cases as quasi one-dimensional curved objects projecting in three-dimensional space. A parallax method to construct the correct three-dimensional geometry of such one-dimensional nanostructures is presented. A series of scanning electron microscope images was acquired at different view angles, thus providing a set of image pairs that were used to generate three-dimensional representations using a matlab program. An error analysis as a function of the view angle between the two images is presented and discussed. As an example application, the importance of knowing the true three-dimensional shape of boron nanowires is demonstrated; without the nanowire's correct length and diameter, mechanical resonance data cannot provide an accurate estimate of Young's modulus.

Spatial versus Tree Representations of Proximity Data.

ERIC Educational Resources Information Center

Pruzansky, Sandra; And Others

1982-01-01

Two-dimensional euclidean planes and additive trees are two of the most common representations of proximity data for multidimensional scaling. Guidelines for comparing these representations and discovering properties that could help identify which representation is more appropriate for a given data set are presented. (Author/JKS)

A 2.5-D Representation of the Human Hand

ERIC Educational Resources Information Center

Longo, Matthew R.; Haggard, Patrick

2012-01-01

Primary somatosensory maps in the brain represent the body as a discontinuous, fragmented set of two-dimensional (2-D) skin regions. We nevertheless experience our body as a coherent three-dimensional (3-D) volumetric object. The links between these different aspects of body representation, however, remain poorly understood. Perceiving the body's…

Expression-invariant representations of faces.

PubMed

Bronstein, Alexander M; Bronstein, Michael M; Kimmel, Ron

2007-01-01

Addressed here is the problem of constructing and analyzing expression-invariant representations of human faces. We demonstrate and justify experimentally a simple geometric model that allows to describe facial expressions as isometric deformations of the facial surface. The main step in the construction of expression-invariant representation of a face involves embedding of the facial intrinsic geometric structure into some low-dimensional space. We study the influence of the embedding space geometry and dimensionality choice on the representation accuracy and argue that compared to its Euclidean counterpart, spherical embedding leads to notably smaller metric distortions. We experimentally support our claim showing that a smaller embedding error leads to better recognition.

Magnetic dynamo action in two-dimensional turbulent magneto-hydrodynamics

NASA Technical Reports Server (NTRS)

Fyfe, D.; Joyce, G.; Montgomery, D.

1977-01-01

Two-dimensional magnetohydrodynamic turbulence is explored by means of numerical simulation. Previous analytical theory, based on non-dissipative constants of the motion in a truncated Fourier representation, is verified by following the evolution of highly non-equilibrium initial conditions numerically. Dynamo action (conversion of a significant fraction of turbulent kinetic energy into long-wavelength magnetic field energy) is observed. It is conjectured that in the presence of dissipation and external forcing, a dual cascade will be observed for zero-helicity situations. Energy will cascade to higher wavenumbers simultaneously with a cascade of mean square vector potential to lower wavenumbers, leading to an omni-directional magnetic energy spectrum.

Representation of Probability Density Functions from Orbit Determination using the Particle Filter

NASA Technical Reports Server (NTRS)

Mashiku, Alinda K.; Garrison, James; Carpenter, J. Russell

2012-01-01

Statistical orbit determination enables us to obtain estimates of the state and the statistical information of its region of uncertainty. In order to obtain an accurate representation of the probability density function (PDF) that incorporates higher order statistical information, we propose the use of nonlinear estimation methods such as the Particle Filter. The Particle Filter (PF) is capable of providing a PDF representation of the state estimates whose accuracy is dependent on the number of particles or samples used. For this method to be applicable to real case scenarios, we need a way of accurately representing the PDF in a compressed manner with little information loss. Hence we propose using the Independent Component Analysis (ICA) as a non-Gaussian dimensional reduction method that is capable of maintaining higher order statistical information obtained using the PF. Methods such as the Principal Component Analysis (PCA) are based on utilizing up to second order statistics, hence will not suffice in maintaining maximum information content. Both the PCA and the ICA are applied to two scenarios that involve a highly eccentric orbit with a lower apriori uncertainty covariance and a less eccentric orbit with a higher a priori uncertainty covariance, to illustrate the capability of the ICA in relation to the PCA.

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

PubMed

Wang, Shunfang; Liu, Shuhui

2015-12-19

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

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

PubMed Central

Wang, Shunfang; Liu, Shuhui

2015-01-01

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

The construction of tridimensional representation of body and external reality in man. The greatest achievement of evolution to date implications for virtual reality.

PubMed

Woodbury, M A; Woodbury, M F

1998-01-01

Our 3-D Body Representation constructed during development by our Central Nervous System under the direction of our DNA, consists of a holographic representation arising from sensory input in the cerebellum and projected extraneurally in the brain ventricular fluid which has the chemical structure of liquid crystal. The structure of 3-D holographic Body Representation is then extrapolated by such cognitive instruments as boundarization, geometrization and gestalt organization upon the external environment which is perceived consequently as three dimensional. When the Body Representation collapses as in psychotic panic states. patients become terrified as they suddenly lose the perception of themselves and the world around them as three dimensional, solid in a reliably solid environment but feel suddenly that they are no longer a person but a disorganized blob. In our clinical practice we found serendipitously that the structure of three dimensionality can be restored even without medication by techniques involving stimulation of the body sensory system in the presence of a benevolent psychotherapist. Implications for Virtual Reality will be discussed.

Rhotrix Vector Spaces

ERIC Educational Resources Information Center

Aminu, Abdulhadi

2010-01-01

By rhotrix we understand an object that lies in some way between (n x n)-dimensional matrices and (2n - 1) x (2n - 1)-dimensional matrices. Representation of vectors in rhotrices is different from the representation of vectors in matrices. A number of vector spaces in matrices and their properties are known. On the other hand, little seems to be…

A Conference on Three-Dimensional Representation held in University of Minnesota on 24-26 May 1989

NASA Astrophysics Data System (ADS)

Biederman, Irving

1989-06-01

This is the final report for a conference grant entitled: A conference on Three-Dimensional Representation. The two and one-half day conference was held at the University of Minn. on May 24 to 26, 1989 to evaluate the current status of problem associated with three-dimensional representations from current computational, psychological, development, and neurophysiological perspectives. Nineteen presentations were made spanning these approaches. One hundred sixty-six individuals attended the conference. Of 44 evaluations received, 75 percent rated the conference as excellent, 20 percent as good, and 5 percent as fair. None rated it poor. The report consists of the original and revised program, conference abstracts evaluation summary and the rooster of attendees.

Geometrical structure of Neural Networks: Geodesics, Jeffrey's Prior and Hyper-ribbons

NASA Astrophysics Data System (ADS)

Hayden, Lorien; Alemi, Alex; Sethna, James

2014-03-01

Neural networks are learning algorithms which are employed in a host of Machine Learning problems including speech recognition, object classification and data mining. In practice, neural networks learn a low dimensional representation of high dimensional data and define a model manifold which is an embedding of this low dimensional structure in the higher dimensional space. In this work, we explore the geometrical structure of a neural network model manifold. A Stacked Denoising Autoencoder and a Deep Belief Network are trained on handwritten digits from the MNIST database. Construction of geodesics along the surface and of slices taken from the high dimensional manifolds reveal a hierarchy of widths corresponding to a hyper-ribbon structure. This property indicates that neural networks fall into the class of sloppy models, in which certain parameter combinations dominate the behavior. Employing this information could prove valuable in designing both neural network architectures and training algorithms. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No . DGE-1144153.

Multilayered nonuniform sampling for three-dimensional scene representation

NASA Astrophysics Data System (ADS)

Lin, Huei-Yung; Xiao, Yu-Hua; Chen, Bo-Ren

2015-09-01

The representation of a three-dimensional (3-D) scene is essential in multiview imaging technologies. We present a unified geometry and texture representation based on global resampling of the scene. A layered data map representation with a distance-dependent nonuniform sampling strategy is proposed. It is capable of increasing the details of the 3-D structure locally and is compact in size. The 3-D point cloud obtained from the multilayered data map is used for view rendering. For any given viewpoint, image synthesis with different levels of detail is carried out using the quadtree-based nonuniformly sampled 3-D data points. Experimental results are presented using the 3-D models of reconstructed real objects.

Hydrological model parameter dimensionality is a weak measure of prediction uncertainty

NASA Astrophysics Data System (ADS)

Pande, S.; Arkesteijn, L.; Savenije, H.; Bastidas, L. A.

2015-04-01

This paper shows that instability of hydrological system representation in response to different pieces of information and associated prediction uncertainty is a function of model complexity. After demonstrating the connection between unstable model representation and model complexity, complexity is analyzed in a step by step manner. This is done measuring differences between simulations of a model under different realizations of input forcings. Algorithms are then suggested to estimate model complexity. Model complexities of the two model structures, SAC-SMA (Sacramento Soil Moisture Accounting) and its simplified version SIXPAR (Six Parameter Model), are computed on resampled input data sets from basins that span across the continental US. The model complexities for SIXPAR are estimated for various parameter ranges. It is shown that complexity of SIXPAR increases with lower storage capacity and/or higher recession coefficients. Thus it is argued that a conceptually simple model structure, such as SIXPAR, can be more complex than an intuitively more complex model structure, such as SAC-SMA for certain parameter ranges. We therefore contend that magnitudes of feasible model parameters influence the complexity of the model selection problem just as parameter dimensionality (number of parameters) does and that parameter dimensionality is an incomplete indicator of stability of hydrological model selection and prediction problems.

General tensor discriminant analysis and gabor features for gait recognition.

PubMed

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

2007-10-01

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

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

PubMed

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

2016-10-01

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

Three-Dimensionality as an Effective Mode of Representation for Expressing Sequential Time Perception

ERIC Educational Resources Information Center

Eden, Sigal; Passig, David

2007-01-01

The process of developing concepts of time continues from age 5 to 11 years (Zakay, 1998). This study sought the representation mode in which children could best express time concepts, especially the proper arrangement of events in a logical and temporal order. Usually, temporal order is examined and taught by 2D (2-dimensional) pictorial scripts.…

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

PubMed Central

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

2013-01-01

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

Low-rank separated representation surrogates of high-dimensional stochastic functions: Application in Bayesian inference

NASA Astrophysics Data System (ADS)

Validi, AbdoulAhad

2014-03-01

This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov Chain Monte Carlo simulations in Bayesian inference. The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities. The model approximates a vector of a continuous solution at discrete values of a physical variable. The required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality. The computational cost of the model construction is quadratic in the number of random inputs, which potentially tackles the curse of dimensionality in high-dimensional stochastic functions. Furthermore, this vector-valued separated representation-based model, in comparison to the available scalar-valued case, leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size. The performance of the method is studied through its application to three numerical examples including a 41-dimensional elliptic PDE and a 21-dimensional cavity flow.

Upon Generating (2+1)-dimensional Dynamical Systems

NASA Astrophysics Data System (ADS)

Zhang, Yufeng; Bai, Yang; Wu, Lixin

2016-06-01

Under the framework of the Adler-Gel'fand-Dikii(AGD) scheme, we first propose two Hamiltonian operator pairs over a noncommutative ring so that we construct a new dynamical system in 2+1 dimensions, then we get a generalized special Novikov-Veselov (NV) equation via the Manakov triple. Then with the aid of a special symmetric Lie algebra of a reductive homogeneous group G, we adopt the Tu-Andrushkiw-Huang (TAH) scheme to generate a new integrable (2+1)-dimensional dynamical system and its Hamiltonian structure, which can reduce to the well-known (2+1)-dimensional Davey-Stewartson (DS) hierarchy. Finally, we extend the binormial residue representation (briefly BRR) scheme to the super higher dimensional integrable hierarchies with the help of a super subalgebra of the super Lie algebra sl(2/1), which is also a kind of symmetric Lie algebra of the reductive homogeneous group G. As applications, we obtain a super 2+1 dimensional MKdV hierarchy which can be reduced to a super 2+1 dimensional generalized AKNS equation. Finally, we compare the advantages and the shortcomings for the three schemes to generate integrable dynamical systems.

A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems

NASA Astrophysics Data System (ADS)

Dölz, Jürgen; Harbrecht, Helmut; Kurz, Stefan; Schöps, Sebastian; Wolf, Felix

2018-03-01

We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract the problems arising due to the dense matrices produced by boundary element methods. By solving Laplace and Helmholtz problems via a single layer approach we show, through a series of numerical examples suitable for easy comparison with other numerical schemes, that one can indeed achieve extremely high rates of convergence of the pointwise potential through the utilisation of higher order B-spline-based ansatz functions.

Linear canonical transformations of coherent and squeezed states in the Wigner phase space. III - Two-mode states

NASA Technical Reports Server (NTRS)

Han, D.; Kim, Y. S.; Noz, Marilyn E.

1990-01-01

It is shown that the basic symmetry of two-mode squeezed states is governed by the group SP(4) in the Wigner phase space which is locally isomorphic to the (3 + 2)-dimensional Lorentz group. This symmetry, in the Schroedinger picture, appears as Dirac's two-oscillator representation of O(3,2). It is shown that the SU(2) and SU(1,1) interferometers exhibit the symmetry of this higher-dimensional Lorentz group. The mathematics of two-mode squeezed states is shown to be applicable to other branches of physics including thermally excited states in statistical mechanics and relativistic extended hadrons in the quark model.

Geometric Representations for Discrete Fourier Transforms

NASA Technical Reports Server (NTRS)

Cambell, C. W.

1986-01-01

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

Affine.m—Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

NASA Astrophysics Data System (ADS)

Nazarov, Anton

2012-11-01

In this paper we present Affine.m-a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most important problems for us. These problems have numerous applications in physics and we provide some examples of these applications. The program is implemented in the popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras. Catalogue identifier: AENA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENB_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 844 No. of bytes in distributed program, including test data, etc.: 1 045 908 Distribution format: tar.gz Programming language: Mathematica. Computer: i386-i686, x86_64. Operating system: Linux, Windows, Mac OS, Solaris. RAM: 5-500 Mb Classification: 4.2, 5. Nature of problem: Representation theory of finite-dimensional Lie algebras has many applications in different branches of physics, including elementary particle physics, molecular physics, nuclear physics. Representations of affine Lie algebras appear in string theories and two-dimensional conformal field theory used for the description of critical phenomena in two-dimensional systems. Also Lie symmetries play a major role in a study of quantum integrable systems. Solution method: We work with weights and roots of finite-dimensional and affine Lie algebras and use Weyl symmetry extensively. Central problems which are the computations of weight multiplicities, branching and fusion coefficients are solved using one general recurrent algorithm based on generalization of Weyl character formula. We also offer alternative implementation based on the Freudenthal multiplicity formula which can be faster in some cases. Restrictions: Computational complexity grows fast with the rank of an algebra, so computations for algebras of ranks greater than 8 are not practical. Unusual features: We offer the possibility of using a traditional mathematical notation for the objects in representation theory of Lie algebras in computations if Affine.m is used in the Mathematica notebook interface. Running time: From seconds to days depending on the rank of the algebra and the complexity of the representation.

Evaluating the Effectiveness of Organic Chemistry Textbooks in Promoting Representational Fluency and Understanding of 2D-3D Diagrammatic Relationships

ERIC Educational Resources Information Center

Kumi, Bryna C.; Olimpo, Jeffrey T.; Bartlett, Felicia; Dixon, Bonnie L.

2013-01-01

The use of two-dimensional (2D) representations to communicate and reason about micromolecular phenomena is common practice in chemistry. While experts are adept at using such representations, research suggests that novices often exhibit great difficulty in understanding, manipulating, and translating between various representational forms. When…

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.

Population Coding of Visual Space: Comparison of Spatial Representations in Dorsal and Ventral Pathways

PubMed Central

Sereno, Anne B.; Lehky, Sidney R.

2011-01-01

Although the representation of space is as fundamental to visual processing as the representation of shape, it has received relatively little attention from neurophysiological investigations. In this study we characterize representations of space within visual cortex, and examine how they differ in a first direct comparison between dorsal and ventral subdivisions of the visual pathways. Neural activities were recorded in anterior inferotemporal cortex (AIT) and lateral intraparietal cortex (LIP) of awake behaving monkeys, structures associated with the ventral and dorsal visual pathways respectively, as a stimulus was presented at different locations within the visual field. In spatially selective cells, we find greater modulation of cell responses in LIP with changes in stimulus position. Further, using a novel population-based statistical approach (namely, multidimensional scaling), we recover the spatial map implicit within activities of neural populations, allowing us to quantitatively compare the geometry of neural space with physical space. We show that a population of spatially selective LIP neurons, despite having large receptive fields, is able to almost perfectly reconstruct stimulus locations within a low-dimensional representation. In contrast, a population of AIT neurons, despite each cell being spatially selective, provide less accurate low-dimensional reconstructions of stimulus locations. They produce instead only a topologically (categorically) correct rendition of space, which nevertheless might be critical for object and scene recognition. Furthermore, we found that the spatial representation recovered from population activity shows greater translation invariance in LIP than in AIT. We suggest that LIP spatial representations may be dimensionally isomorphic with 3D physical space, while in AIT spatial representations may reflect a more categorical representation of space (e.g., “next to” or “above”). PMID:21344010

Surface representations of two- and three-dimensional fluid flow topology

NASA Technical Reports Server (NTRS)

Helman, James L.; Hesselink, Lambertus

1990-01-01

We discuss our work using critical point analysis to generate representations of the vector field topology of numerical flow data sets. Critical points are located and characterized in a two-dimensional domain, which may be either a two-dimensional flow field or the tangential velocity field near a three-dimensional body. Tangent curves are then integrated out along the principal directions of certain classes of critical points. The points and curves are linked to form a skeleton representing the two-dimensional vector field topology. When generated from the tangential velocity field near a body in a three-dimensional flow, the skeleton includes the critical points and curves which provide a basis for analyzing the three-dimensional structure of the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations to generate surfaces representing the topology of the associated flow separations.

Evaluation of molecular dynamics simulation methods for ionic liquid electric double layers.

PubMed

Haskins, Justin B; Lawson, John W

2016-05-14

We investigate how systematically increasing the accuracy of various molecular dynamics modeling techniques influences the structure and capacitance of ionic liquid electric double layers (EDLs). The techniques probed concern long-range electrostatic interactions, electrode charging (constant charge versus constant potential conditions), and electrolyte polarizability. Our simulations are performed on a quasi-two-dimensional, or slab-like, model capacitor, which is composed of a polarizable ionic liquid electrolyte, [EMIM][BF4], interfaced between two graphite electrodes. To ensure an accurate representation of EDL differential capacitance, we derive new fluctuation formulas that resolve the differential capacitance as a function of electrode charge or electrode potential. The magnitude of differential capacitance shows sensitivity to different long-range electrostatic summation techniques, while the shape of differential capacitance is affected by charging technique and the polarizability of the electrolyte. For long-range summation techniques, errors in magnitude can be mitigated by employing two-dimensional or corrected three dimensional electrostatic summations, which led to electric fields that conform to those of a classical electrostatic parallel plate capacitor. With respect to charging, the changes in shape are a result of ions in the Stern layer (i.e., ions at the electrode surface) having a higher electrostatic affinity to constant potential electrodes than to constant charge electrodes. For electrolyte polarizability, shape changes originate from induced dipoles that soften the interaction of Stern layer ions with the electrode. The softening is traced to ion correlations vertical to the electrode surface that induce dipoles that oppose double layer formation. In general, our analysis indicates an accuracy dependent differential capacitance profile that transitions from the characteristic camel shape with coarser representations to a more diffuse profile with finer representations.

Irreducible representations of finitely generated nilpotent groups

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

Beloshapka, I V; Gorchinskiy, S O

2016-01-31

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

The art of seeing and painting.

PubMed

Grossberg, Stephen

2008-01-01

The human urge to represent the three-dimensional world using two-dimensional pictorial representations dates back at least to Paleolithic times. Artists from ancient to modern times have struggled to understand how a few contours or color patches on a flat surface can induce mental representations of a three-dimensional scene. This article summarizes some of the recent breakthroughs in scientifically understanding how the brain sees that shed light on these struggles. These breakthroughs illustrate how various artists have intuitively understood paradoxical properties about how the brain sees, and have used that understanding to create great art. These paradoxical properties arise from how the brain forms the units of conscious visual perception; namely, representations of three-dimensional boundaries and surfaces. Boundaries and surfaces are computed in parallel cortical processing streams that obey computationally complementary properties. These streams interact at multiple levels to overcome their complementary weaknesses and to transform their complementary properties into consistent percepts. The article describes how properties of complementary consistency have guided the creation of many great works of art.

Analysis of students’ spatial thinking in geometry: 3D object into 2D representation

NASA Astrophysics Data System (ADS)

Fiantika, F. R.; Maknun, C. L.; Budayasa, I. K.; Lukito, A.

2018-05-01

The aim of this study is to find out the spatial thinking process of students in transforming 3-dimensional (3D) object to 2-dimensional (2D) representation. Spatial thinking is helpful in using maps, planning routes, designing floor plans, and creating art. The student can engage geometric ideas by using concrete models and drawing. Spatial thinking in this study is identified through geometrical problems of transforming a 3-dimensional object into a 2-dimensional object image. The problem was resolved by the subject and analyzed by reference to predetermined spatial thinking indicators. Two representative subjects of elementary school were chosen based on mathematical ability and visual learning style. Explorative description through qualitative approach was used in this study. The result of this study are: 1) there are different representations of spatial thinking between a boy and a girl object, 2) the subjects has their own way to invent the fastest way to draw cube net.

Husimi function and phase-space analysis of bilayer quantum Hall systems at ν = 2/λ

NASA Astrophysics Data System (ADS)

Calixto, M.; Peón-Nieto, C.

2018-05-01

We propose localization measures in phase space of the ground state of bilayer quantum Hall systems at fractional filling factors , to characterize the three quantum phases (shortly denoted by spin, canted and ppin) for arbitrary -isospin λ. We use a coherent state (Bargmann) representation of quantum states, as holomorphic functions in the 8-dimensional Grassmannian phase-space (a higher-dimensional generalization of the Haldane’s 2-dimensional sphere ). We quantify the localization (inverse volume) of the ground state wave function in phase-space throughout the phase diagram (i.e. as a function of Zeeman, tunneling, layer distance, etc, control parameters) with the Husimi function second moment, a kind of inverse participation ratio that behaves as an order parameter. Then we visualize the different ground state structure in phase space of the three quantum phases, the canted phase displaying a much higher delocalization (a Schrödinger cat structure) than the spin and ppin phases, where the ground state is highly coherent. We find a good agreement between analytic (variational) and numeric diagonalization results.

Gauging hidden symmetries in two dimensions

NASA Astrophysics Data System (ADS)

Samtleben, Henning; Weidner, Martin

2007-08-01

We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with minimal couplings and a particular topological term. The gauge groups typically include hidden symmetries that are not among the target-space isometries of the ungauged theory. The gaugings constructed in this paper are described group-theoretically in terms of a constant embedding tensor subject to a number of constraints which parametrizes the different theories and entirely encodes the gauged Lagrangian. The prime example is the bosonic sector of the maximally supersymmetric theory whose ungauged version admits an affine fraktur e9 global symmetry algebra. The various parameters (related to higher-dimensional p-form fluxes, geometric and non-geometric fluxes, etc.) which characterize the possible gaugings, combine into an embedding tensor transforming in the basic representation of fraktur e9. This yields an infinite-dimensional class of maximally supersymmetric theories in two dimensions. We work out and discuss several examples of higher-dimensional origin which can be systematically analyzed using the different gradings of fraktur e9.

Lax representations for matrix short pulse equations

NASA Astrophysics Data System (ADS)

Popowicz, Z.

2017-10-01

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

Peridynamic Theory as a New Paradigm for Multiscale Modeling of Sintering

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

Silling, Stewart A.; Abdeljawad, Fadi; Ford, Kurtis Ross

2017-09-01

Sintering is a component fabrication process in which powder is compacted by pressing or some other means and then held at elevated temperature for a period of hours. The powder grains bond with each other, leading to the formation of a solid component with much lower porosity, and therefore higher density and higher strength, than the original powder compact. In this project, we investigated a new way of computationally modeling sintering at the length scale of grains. The model uses a high-fidelity, three-dimensional representation with a few hundred nodes per grain. The numerical model solves the peridynamic equations, in whichmore » nonlocal forces allow representation of the attraction, adhesion, and mass diffusion between grains. The deformation of the grains is represented through a viscoelastic material model. The project successfully demonstrated the use of this method to reproduce experimentally observed features of material behavior in sintering, including densification, the evolution of microstructure, and the occurrence of random defects in the sintered solid.« less

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

NASA Technical Reports Server (NTRS)

Olson, Erik D.

2015-01-01

Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

The effects of mental representation on performance in a navigation task

NASA Astrophysics Data System (ADS)

Barshi, Immanuel

Most aviation accidents and incidents are attributed to human error. Among the various kinds of human errors found in aviation, problems in communication constitute a large majority. The purpose of this study is to understand some of the cognitive factors influencing these misunderstandings so they can be prevented. Five experiments tested individuals' ability to follow verbal instructions pertaining to navigating in space. The experiments simulated the kinds of instructions pilots receive from air traffic controllers. All five experiments show the importance of the mental representation of the task over and above the short-term memory demands. The results of Experiment 1 show that the number of instructional units is a critical factor, rather than the number of words per unit. The results of Experiment 2 show that when moving in a three dimensional space, it does not matter whether movement is required along all three dimensions or along only two of the three dimensions. The results of Experiment 3 show that individuals perform much better when they have to maintain a two-dimensional mental representation than when they have to maintain a three-dimensional mental representation. What is more, it shows that even immediate verbatim recall is affected by the representation of the situation to which the language input applies. The results of Experiments 4 and 5 show that the two-dimensional advantage found in Experiment 3 is indeed an aspect of the mental representation, rather than a result of translating a visual display into a mental representation. These results also suggest that three units is the capacity limit of short-term memory. Thus, to minimize misunderstandings due to message length, air traffic controllers are advised to limit their messages to no more than three instructions at a time. In addition to ATC procedures, this research has practical implications for computer/visual displays, and for training environments.

Interleaved Practice in Multi-Dimensional Learning Tasks: Which Dimension Should We Interleave?

ERIC Educational Resources Information Center

Rau, Martina A.; Aleven, Vincent; Rummel, Nikol

2013-01-01

Research shows that multiple representations can enhance student learning. Many curricula use multiple representations across multiple task types. The temporal sequence of representations and task types is likely to impact student learning. Research on contextual interference shows that interleaving learning tasks leads to better learning results…

Low-Dimensional Statistics of Anatomical Variability via Compact Representation of Image Deformations.

PubMed

Zhang, Miaomiao; Wells, William M; Golland, Polina

2016-10-01

Using image-based descriptors to investigate clinical hypotheses and therapeutic implications is challenging due to the notorious "curse of dimensionality" coupled with a small sample size. In this paper, we present a low-dimensional analysis of anatomical shape variability in the space of diffeomorphisms and demonstrate its benefits for clinical studies. To combat the high dimensionality of the deformation descriptors, we develop a probabilistic model of principal geodesic analysis in a bandlimited low-dimensional space that still captures the underlying variability of image data. We demonstrate the performance of our model on a set of 3D brain MRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our model yields a more compact representation of group variation at substantially lower computational cost than models based on the high-dimensional state-of-the-art approaches such as tangent space PCA (TPCA) and probabilistic principal geodesic analysis (PPGA).

Compressive sensing for sparse time-frequency representation of nonstationary signals in the presence of impulsive noise

NASA Astrophysics Data System (ADS)

Orović, Irena; Stanković, Srdjan; Amin, Moeness

2013-05-01

A modified robust two-dimensional compressive sensing algorithm for reconstruction of sparse time-frequency representation (TFR) is proposed. The ambiguity function domain is assumed to be the domain of observations. The two-dimensional Fourier bases are used to linearly relate the observations to the sparse TFR, in lieu of the Wigner distribution. We assume that a set of available samples in the ambiguity domain is heavily corrupted by an impulsive type of noise. Consequently, the problem of sparse TFR reconstruction cannot be tackled using standard compressive sensing optimization algorithms. We introduce a two-dimensional L-statistics based modification into the transform domain representation. It provides suitable initial conditions that will produce efficient convergence of the reconstruction algorithm. This approach applies sorting and weighting operations to discard an expected amount of samples corrupted by noise. The remaining samples serve as observations used in sparse reconstruction of the time-frequency signal representation. The efficiency of the proposed approach is demonstrated on numerical examples that comprise both cases of monocomponent and multicomponent signals.

A scalable method to improve gray matter segmentation at ultra high field MRI.

PubMed

Gulban, Omer Faruk; Schneider, Marian; Marquardt, Ingo; Haast, Roy A M; De Martino, Federico

2018-01-01

High-resolution (functional) magnetic resonance imaging (MRI) at ultra high magnetic fields (7 Tesla and above) enables researchers to study how anatomical and functional properties change within the cortical ribbon, along surfaces and across cortical depths. These studies require an accurate delineation of the gray matter ribbon, which often suffers from inclusion of blood vessels, dura mater and other non-brain tissue. Residual segmentation errors are commonly corrected by browsing the data slice-by-slice and manually changing labels. This task becomes increasingly laborious and prone to error at higher resolutions since both work and error scale with the number of voxels. Here we show that many mislabeled, non-brain voxels can be corrected more efficiently and semi-automatically by representing three-dimensional anatomical images using two-dimensional histograms. We propose both a uni-modal (based on first spatial derivative) and multi-modal (based on compositional data analysis) approach to this representation and quantify the benefits in 7 Tesla MRI data of nine volunteers. We present an openly accessible Python implementation of these approaches and demonstrate that editing cortical segmentations using two-dimensional histogram representations as an additional post-processing step aids existing algorithms and yields improved gray matter borders. By making our data and corresponding expert (ground truth) segmentations openly available, we facilitate future efforts to develop and test segmentation algorithms on this challenging type of data.

A scalable method to improve gray matter segmentation at ultra high field MRI

PubMed Central

De Martino, Federico

2018-01-01

High-resolution (functional) magnetic resonance imaging (MRI) at ultra high magnetic fields (7 Tesla and above) enables researchers to study how anatomical and functional properties change within the cortical ribbon, along surfaces and across cortical depths. These studies require an accurate delineation of the gray matter ribbon, which often suffers from inclusion of blood vessels, dura mater and other non-brain tissue. Residual segmentation errors are commonly corrected by browsing the data slice-by-slice and manually changing labels. This task becomes increasingly laborious and prone to error at higher resolutions since both work and error scale with the number of voxels. Here we show that many mislabeled, non-brain voxels can be corrected more efficiently and semi-automatically by representing three-dimensional anatomical images using two-dimensional histograms. We propose both a uni-modal (based on first spatial derivative) and multi-modal (based on compositional data analysis) approach to this representation and quantify the benefits in 7 Tesla MRI data of nine volunteers. We present an openly accessible Python implementation of these approaches and demonstrate that editing cortical segmentations using two-dimensional histogram representations as an additional post-processing step aids existing algorithms and yields improved gray matter borders. By making our data and corresponding expert (ground truth) segmentations openly available, we facilitate future efforts to develop and test segmentation algorithms on this challenging type of data. PMID:29874295

Quantum autoencoders for efficient compression of quantum data

NASA Astrophysics Data System (ADS)

Romero, Jonathan; Olson, Jonathan P.; Aspuru-Guzik, Alan

2017-12-01

Classical autoencoders are neural networks that can learn efficient low-dimensional representations of data in higher-dimensional space. The task of an autoencoder is, given an input x, to map x to a lower dimensional point y such that x can likely be recovered from y. The structure of the underlying autoencoder network can be chosen to represent the data on a smaller dimension, effectively compressing the input. Inspired by this idea, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a particular data set of quantum states, where a classical compression algorithm cannot be employed. The parameters of the quantum autoencoder are trained using classical optimization algorithms. We show an example of a simple programmable circuit that can be trained as an efficient autoencoder. We apply our model in the context of quantum simulation to compress ground states of the Hubbard model and molecular Hamiltonians.

Time-varying higher order spectra

NASA Astrophysics Data System (ADS)

Boashash, Boualem; O'Shea, Peter

1991-12-01

A general solution for the problem of time-frequency signal representation of nonlinear FM signals is provided, based on a generalization of the Wigner-Ville distribution. The Wigner- Ville distribution (WVD) is a second order time-frequency representation. That is, it is able to give ideal energy concentration for quadratic phase signals and its ensemble average is a second order time-varying spectrum. The same holds for Cohen's class of time-frequency distributions, which are smoothed versions of the WVD. The WVD may be extended so as to achieve ideal energy concentration for higher order phase laws, and such that the expectation is a time-varying higher order spectrum. The usefulness of these generalized Wigner-Ville distributions (GWVD) is twofold. Firstly, because they achieve ideal energy concentration for polynomial phase signals, they may be used for optimal instantaneous frequency estimation. Second, they are useful for discriminating between nonstationary processes of differing higher order moments. In the same way that the WVD is generalized, we generalize Cohen's class of TFDs by defining a class of generalized time-frequency distributions (GTFDs) obtained by a two dimensional smoothing of the GWVD. Another results derived from this approach is a method based on higher order spectra which allows the separation of cross-terms and auto- terms in the WVD.

Attitude Error Representations for Kalman Filtering

NASA Technical Reports Server (NTRS)

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

2002-01-01

The quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation. The quaternion must obey a unit norm constraint, though, which has led to the development of an extended Kalman filter using a quaternion for the global attitude estimate and a three-component representation for attitude errors. We consider various attitude error representations for this Multiplicative Extended Kalman Filter and its second-order extension.

Scaling effects in direct shear tests

USGS Publications Warehouse

Orlando, A.D.; Hanes, D.M.; Shen, H.H.

2009-01-01

Laboratory experiments of the direct shear test were performed on spherical particles of different materials and diameters. Results of the bulk friction vs. non-dimensional shear displacement are presented as a function of the non-dimensional particle diameter. Simulations of the direct shear test were performed using the Discrete Element Method (DEM). The simulation results show Considerable differences with the physical experiments. Particle level material properties, such as the coefficients of static friction, restitution and rolling friction need to be known a priori in order to guarantee that the simulation results are an accurate representation of the physical phenomenon. Furthermore, laboratory results show a clear size dependency on the results, with smaller particles having a higher bulk friction than larger ones. ?? 2009 American Institute of Physics.

Three-Dimensional Dispaly Of Document Set

DOEpatents

Lantrip, David B.; Pennock, Kelly A.; Pottier, Marc C.; Schur, Anne; Thomas, James J.; Wise, James A.

2003-06-24

A method for spatializing text content for enhanced visual browsing and analysis. The invention is applied to large text document corpora such as digital libraries, regulations and procedures, archived reports, and the like. The text content from these sources may be transformed to a spatial representation that preserves informational characteristics from the documents. The three-dimensional representation may then be visually browsed and analyzed in ways that avoid language processing and that reduce the analysts' effort.

Three-dimensional display of document set

DOEpatents

Lantrip, David B [Oxnard, CA; Pennock, Kelly A [Richland, WA; Pottier, Marc C [Richland, WA; Schur, Anne [Richland, WA; Thomas, James J [Richland, WA; Wise, James A [Richland, WA

2006-09-26

A method for spatializing text content for enhanced visual browsing and analysis. The invention is applied to large text document corpora such as digital libraries, regulations and procedures, archived reports, and the like. The text content from these sources may e transformed to a spatial representation that preserves informational characteristics from the documents. The three-dimensional representation may then be visually browsed and analyzed in ways that avoid language processing and that reduce the analysts' effort.

Three-dimensional display of document set

DOEpatents

Lantrip, David B [Oxnard, CA; Pennock, Kelly A [Richland, WA; Pottier, Marc C [Richland, WA; Schur, Anne [Richland, WA; Thomas, James J [Richland, WA; Wise, James A [Richland, WA

2001-10-02

A method for spatializing text content for enhanced visual browsing and analysis. The invention is applied to large text document corpora such as digital libraries, regulations and procedures, archived reports, and the like. The text content from these sources may be transformed to a spatial representation that preserves informational characteristics from the documents. The three-dimensional representation may then be visually browsed and analyzed in ways that avoid language processing and that reduce the analysts' effort.

Three-dimensional display of document set

DOEpatents

Lantrip, David B [Oxnard, CA; Pennock, Kelly A [Richland, WA; Pottier, Marc C [Richland, WA; Schur, Anne [Richland, WA; Thomas, James J [Richland, WA; Wise, James A [Richland, WA; York, Jeremy [Bothell, WA

2009-06-30

A method for spatializing text content for enhanced visual browsing and analysis. The invention is applied to large text document corpora such as digital libraries, regulations and procedures, archived reports, and the like. The text content from these sources may be transformed to a spatial representation that preserves informational characteristics from the documents. The three-dimensional representation may then be visually browsed and analyzed in ways that avoid language processing and that reduce the analysts' effort.

Fractional representation theory - Robustness results with applications to finite dimensional control of a class of linear distributed systems

NASA Technical Reports Server (NTRS)

Nett, C. N.; Jacobson, C. A.; Balas, M. J.

1983-01-01

This paper reviews and extends the fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. The design is for stability in an input-output sense, but particular attention is paid to internal stability as well.

Interrogation of an object for dimensional and topographical information

DOEpatents

McMakin, Douglas L.; Severtsen, Ronald H.; Hall, Thomas E.; Sheen, David M.; Kennedy, Mike O.

2004-03-09

Disclosed are systems, methods, devices, and apparatus to interrogate a clothed individual with electromagnetic radiation to determine one or more body measurements at least partially covered by the individual's clothing. The invention further includes techniques to interrogate an object with electromagnetic radiation in the millimeter and/or microwave range to provide a volumetric representation of the object. This representation can be used to display images and/or determine dimensional information concerning the object.

Interrogation of an object for dimensional and topographical information

DOEpatents

McMakin, Doug L [Richland, WA; Severtsen, Ronald H [Richland, WA; Hall, Thomas E [Richland, WA; Sheen, David M [Richland, WA

2003-01-14

Disclosed are systems, methods, devices, and apparatus to interrogate a clothed individual with electromagnetic radiation to determine one or more body measurements at least partially covered by the individual's clothing. The invention further includes techniques to interrogate an object with electromagnetic radiation in the millimeter and/or microwave range to provide a volumetric representation of the object. This representation can be used to display images and/or determine dimensional information concerning the object.

Leak detection utilizing analog binaural (VLSI) techniques

NASA Technical Reports Server (NTRS)

Hartley, Frank T. (Inventor)

1995-01-01

A detection method and system utilizing silicon models of the traveling wave structure of the human cochlea to spatially and temporally locate a specific sound source in the presence of high noise pandemonium. The detection system combines two-dimensional stereausis representations, which are output by at least three VLSI binaural hearing chips, to generate a three-dimensional stereausis representation including both binaural and spectral information which is then used to locate the sound source.

A rudimentary database for three-dimensional objects using structural representation

NASA Technical Reports Server (NTRS)

Sowers, James P.

1987-01-01

A database which enables users to store and share the description of three-dimensional objects in a research environment is presented. The main objective of the design is to make it a compact structure that holds sufficient information to reconstruct the object. The database design is based on an object representation scheme which is information preserving, reasonably efficient, and yet economical in terms of the storage requirement. The determination of the needed data for the reconstruction process is guided by the belief that it is faster to do simple computations to generate needed data/information for construction than to retrieve everything from memory. Some recent techniques of three-dimensional representation that influenced the design of the database are discussed. The schema for the database and the structural definition used to define an object are given. The user manual for the software developed to create and maintain the contents of the database is included.

A New Perspective on Surface Weather Maps

ERIC Educational Resources Information Center

Meyer, Steve

2006-01-01

A two-dimensional weather map is actually a physical representation of three-dimensional atmospheric conditions at a specific point in time. Abstract thinking is required to visualize this two-dimensional image in three-dimensional form. But once that visualization is accomplished, many of the meteorological concepts and processes conveyed by the…

Non-AdS holography in 3-dimensional higher spin gravity — General recipe and example

NASA Astrophysics Data System (ADS)

Afshar, H.; Gary, M.; Grumiller, D.; Rashkov, R.; Riegler, M.

2012-11-01

We present the general algorithm to establish the classical and quantum asymptotic symmetry algebra for non-AdS higher spin gravity and implement it for the specific example of spin-3 gravity in the non-principal embedding with Lobachevsky ( {{{{H}}^2}× {R}} ) boundary conditions. The asymptotic symmetry algebra for this example consists of a quantum W_3^{(2) } (Polyakov-Bershadsky) and an affine û(1) algebra. We show that unitary representations of the quantum W_3^{(2) } algebra exist only for two values of its central charge, the trivial c = 0 "theory" and the simple c = 1 theory.

Neural Integration of Information Specifying Human Structure from Form, Motion, and Depth

PubMed Central

Jackson, Stuart; Blake, Randolph

2010-01-01

Recent computational models of biological motion perception operate on ambiguous two-dimensional representations of the body (e.g., snapshots, posture templates) and contain no explicit means for disambiguating the three-dimensional orientation of a perceived human figure. Are there neural mechanisms in the visual system that represent a moving human figure’s orientation in three dimensions? To isolate and characterize the neural mechanisms mediating perception of biological motion, we used an adaptation paradigm together with bistable point-light (PL) animations whose perceived direction of heading fluctuates over time. After exposure to a PL walker with a particular stereoscopically defined heading direction, observers experienced a consistent aftereffect: a bistable PL walker, which could be perceived in the adapted orientation or reversed in depth, was perceived predominantly reversed in depth. A phase-scrambled adaptor produced no aftereffect, yet when adapting and test walkers differed in size or appeared on opposite sides of fixation aftereffects did occur. Thus, this heading direction aftereffect cannot be explained by local, disparity-specific motion adaptation, and the properties of scale and position invariance imply higher-level origins of neural adaptation. Nor is disparity essential for producing adaptation: when suspended on top of a stereoscopically defined, rotating globe, a context-disambiguated “globetrotter” was sufficient to bias the bistable walker’s direction, as were full-body adaptors. In sum, these results imply that the neural signals supporting biomotion perception integrate information on the form, motion, and three-dimensional depth orientation of the moving human figure. Models of biomotion perception should incorporate mechanisms to disambiguate depth ambiguities in two-dimensional body representations. PMID:20089892

Phenotypic and genetic structure of traits delineating personality disorder.

PubMed

Livesley, W J; Jang, K L; Vernon, P A

1998-10-01

The evidence suggests that personality traits are hierarchically organized with more specific or lower-order traits combining to form more generalized higher-order traits. Agreement exists across studies regarding the lower-order traits that delineate personality disorder but not the higher-order traits. This study seeks to identify the higher-order structure of personality disorder by examining the phenotypic and genetic structures underlying lower-order traits. Eighteen lower-order traits were assessed using the Dimensional Assessment of Personality Disorder-Basic Questionnaire in samples of 656 personality disordered patients, 939 general population subjects, and a volunteer sample of 686 twin pairs. Principal components analysis yielded 4 components, labeled Emotional Dysregulation, Dissocial Behavior, Inhibitedness, and Compulsivity, that were similar across the 3 samples. Multivariate genetic analyses also yielded 4 genetic and environmental factors that were remarkably similar to the phenotypic factors. Analysis of the residual heritability of the lower-order traits when the effects of the higher-order factors were removed revealed a substantial residual heritable component for 12 of the 18 traits. The results support the following conclusions. First, the stable structure of traits across clinical and nonclinical samples is consistent with dimensional representations of personality disorders. Second, the higher-order traits of personality disorder strongly resemble dimensions of normal personality. This implies that a dimensional classification should be compatible with normative personality. Third, the residual heritability of the lower-order traits suggests that the personality phenotypes are based on a large number of specific genetic components.

The conformal characters

NASA Astrophysics Data System (ADS)

Bourget, Antoine; Troost, Jan

2018-04-01

We revisit the study of the multiplets of the conformal algebra in any dimension. The theory of highest weight representations is reviewed in the context of the Bernstein-Gelfand-Gelfand category of modules. The Kazhdan-Lusztig polynomials code the relation between the Verma modules and the irreducible modules in the category and are the key to the characters of the conformal multiplets (whether finite dimensional, infinite dimensional, unitary or non-unitary). We discuss the representation theory and review in full generality which representations are unitarizable. The mathematical theory that allows for both the general treatment of characters and the full analysis of unitarity is made accessible. A good understanding of the mathematics of conformal multiplets renders the treatment of all highest weight representations in any dimension uniform, and provides an overarching comprehension of case-by-case results. Unitary highest weight representations and their characters are classified and computed in terms of data associated to cosets of the Weyl group of the conformal algebra. An executive summary is provided, as well as look-up tables up to and including rank four.

Supermultiplet of β-deformations from twistors

NASA Astrophysics Data System (ADS)

Milián, Segundo P.

2017-09-01

We consider the supermultiplet of linearized beta-deformation of 𝒩 = 4 super-Yang-Mills (SYM). It was previously studied on the gravitational side. We study the supermultiplet of beta-deformations on the field theory side and we compare two finite-dimensional representations of psl(4|4,R) algebra. We show that they are related by an intertwining operator. We develop a twistor-based approach which could be useful for studying other finite-dimensional and nonunitary representations in AdS/CFT correspondence.

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.

One-dimensional representation of Earth to show SRTM coverage

NASA Image and Video Library

2000-02-04

JSC2000E01555 (January 2000) --- A one-dimensional representation of Earth indicates only a portion of the total anticipated coverage area for the Shuttle Radar Topography Mission (SRTM). The primary objective of SRTM is to acquire a high-resolution topographic map of the Earth's land mass (between 60 degrees north and 56 degrees south latitude) and to test new technologies for deployment of large rigid structures and measurement of their distortions to extremely high precision.

Towards building a team of intelligent robots

NASA Technical Reports Server (NTRS)

Varanasi, Murali R.; Mehrotra, R.

1987-01-01

Topics addressed include: collision-free motion planning of multiple robot arms; two-dimensional object recognition; and pictorial databases (storage and sharing of the representations of three-dimensional objects).

Length-Two Representations of Quantum Affine Superalgebras and Baxter Operators

NASA Astrophysics Data System (ADS)

Zhang, Huafeng

2018-03-01

Associated to quantum affine general linear Lie superalgebras are two families of short exact sequences of representations whose first and third terms are irreducible: the Baxter TQ relations involving infinite-dimensional representations; the extended T-systems of Kirillov-Reshetikhin modules. We make use of these representations over the full quantum affine superalgebra to define Baxter operators as transfer matrices for the quantum integrable model and to deduce Bethe Ansatz Equations, under genericity conditions.

Simplifying the representation of complex free-energy landscapes using sketch-map

PubMed Central

Ceriotti, Michele; Tribello, Gareth A.; Parrinello, Michele

2011-01-01

A new scheme, sketch-map, for obtaining a low-dimensional representation of the region of phase space explored during an enhanced dynamics simulation is proposed. We show evidence, from an examination of the distribution of pairwise distances between frames, that some features of the free-energy surface are inherently high-dimensional. This makes dimensionality reduction problematic because the data does not satisfy the assumptions made in conventional manifold learning algorithms We therefore propose that when dimensionality reduction is performed on trajectory data one should think of the resultant embedding as a quickly sketched set of directions rather than a road map. In other words, the embedding tells one about the connectivity between states but does not provide the vectors that correspond to the slow degrees of freedom. This realization informs the development of sketch-map, which endeavors to reproduce the proximity information from the high-dimensionality description in a space of lower dimensionality even when a faithful embedding is not possible. PMID:21730167

The Mental Representation of Social Connections: Generalizability Extended to Beijing Adults

PubMed Central

Hawkley, Louise C.; Gu, Yuanyuan; Luo, Yue-Jia; Cacioppo, John T.

2012-01-01

Social connections are essential for the survival of a social species like humans. People differ in the degree to which they are sensitive to perceived deficits in their social connections, but evidence suggests that they nevertheless construe the nature of their social connections similarly. This construal can be thought of as a mental representation of a multi-faceted social experience. A three-dimensional mental representation has been identified with the UCLA Loneliness Scale and consists of Intimate, Relational, and Collective Connectedness reflecting beliefs about one's individual, dyadic, and collective (group) social value, respectively. Moreover, this mental representation has been replicated with other scales and validated across age, gender, and racial/ethnic lines in U.S. samples. The purpose of this study is to evaluate the extent to which this three-dimensional representation applies to people whose social lives are experienced in a collectivistic rather than individualistic culture. To that end, we used confirmatory factor analyses to assess the fit of the three-dimensional mental structure to data collected from Chinese people living in China. Two hundred sixty-seven young adults (16–25 yrs) and 250 older adults (50–65 yrs) in Beijing completed the revised UCLA Loneliness Scale and demographic and social activity questionnaires. Results revealed adequate fit of the structure to data from young and older Chinese adults. Moreover, the structure exhibited equivalent fit in young and older Chinese adults despite changes in the Chinese culture that exposed these two generations to different cultural experiences. Social activity variables that discriminated among the three dimensions in the Chinese samples corresponded well with variables that discriminated among the three dimensions in the U.S.-based samples, indicating cultural commonalities in the factors predicting dimensions of people's representations of their social connections. Equivalence of the three-dimensional structure is relevant for an understanding of cultural differences in the sources of loneliness and social connectedness. PMID:23028486

The mental representation of social connections: generalizability extended to Beijing adults.

PubMed

Hawkley, Louise C; Gu, Yuanyuan; Luo, Yue-Jia; Cacioppo, John T

2012-01-01

Social connections are essential for the survival of a social species like humans. People differ in the degree to which they are sensitive to perceived deficits in their social connections, but evidence suggests that they nevertheless construe the nature of their social connections similarly. This construal can be thought of as a mental representation of a multi-faceted social experience. A three-dimensional mental representation has been identified with the UCLA Loneliness Scale and consists of Intimate, Relational, and Collective Connectedness reflecting beliefs about one's individual, dyadic, and collective (group) social value, respectively. Moreover, this mental representation has been replicated with other scales and validated across age, gender, and racial/ethnic lines in U.S. samples. The purpose of this study is to evaluate the extent to which this three-dimensional representation applies to people whose social lives are experienced in a collectivistic rather than individualistic culture. To that end, we used confirmatory factor analyses to assess the fit of the three-dimensional mental structure to data collected from Chinese people living in China. Two hundred sixty-seven young adults (16-25 yrs) and 250 older adults (50-65 yrs) in Beijing completed the revised UCLA Loneliness Scale and demographic and social activity questionnaires. Results revealed adequate fit of the structure to data from young and older Chinese adults. Moreover, the structure exhibited equivalent fit in young and older Chinese adults despite changes in the Chinese culture that exposed these two generations to different cultural experiences. Social activity variables that discriminated among the three dimensions in the Chinese samples corresponded well with variables that discriminated among the three dimensions in the U.S.-based samples, indicating cultural commonalities in the factors predicting dimensions of people's representations of their social connections. Equivalence of the three-dimensional structure is relevant for an understanding of cultural differences in the sources of loneliness and social connectedness.

Structural Properties and Estimation of Delay Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kwong, R. H. S.

1975-01-01

Two areas in the theory of delay systems were studied: structural properties and their applications to feedback control, and optimal linear and nonlinear estimation. The concepts of controllability, stabilizability, observability, and detectability were investigated. The property of pointwise degeneracy of linear time-invariant delay systems is considered. Necessary and sufficient conditions for three dimensional linear systems to be made pointwise degenerate by delay feedback were obtained, while sufficient conditions for this to be possible are given for higher dimensional linear systems. These results were applied to obtain solvability conditions for the minimum time output zeroing control problem by delay feedback. A representation theorem is given for conditional moment functionals of general nonlinear stochastic delay systems, and stochastic differential equations are derived for conditional moment functionals satisfying certain smoothness properties.

Identification of DNA-Binding Proteins Using Mixed Feature Representation Methods.

PubMed

Qu, Kaiyang; Han, Ke; Wu, Song; Wang, Guohua; Wei, Leyi

2017-09-22

DNA-binding proteins play vital roles in cellular processes, such as DNA packaging, replication, transcription, regulation, and other DNA-associated activities. The current main prediction method is based on machine learning, and its accuracy mainly depends on the features extraction method. Therefore, using an efficient feature representation method is important to enhance the classification accuracy. However, existing feature representation methods cannot efficiently distinguish DNA-binding proteins from non-DNA-binding proteins. In this paper, a multi-feature representation method, which combines three feature representation methods, namely, K-Skip-N-Grams, Information theory, and Sequential and structural features (SSF), is used to represent the protein sequences and improve feature representation ability. In addition, the classifier is a support vector machine. The mixed-feature representation method is evaluated using 10-fold cross-validation and a test set. Feature vectors, which are obtained from a combination of three feature extractions, show the best performance in 10-fold cross-validation both under non-dimensional reduction and dimensional reduction by max-relevance-max-distance. Moreover, the reduced mixed feature method performs better than the non-reduced mixed feature technique. The feature vectors, which are a combination of SSF and K-Skip-N-Grams, show the best performance in the test set. Among these methods, mixed features exhibit superiority over the single features.

[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.

Assessment of Ice Shape Roughness Using a Self-Orgainizing Map Approach

NASA Technical Reports Server (NTRS)

Mcclain, Stephen T.; Kreeger, Richard E.

2013-01-01

Self-organizing maps are neural-network techniques for representing noisy, multidimensional data aligned along a lower-dimensional and nonlinear manifold. For a large set of noisy data, each element of a finite set of codebook vectors is iteratively moved in the direction of the data closest to the winner codebook vector. Through successive iterations, the codebook vectors begin to align with the trends of the higher-dimensional data. Prior investigations of ice shapes have focused on using self-organizing maps to characterize mean ice forms. The Icing Research Branch has recently acquired a high resolution three dimensional scanner system capable of resolving ice shape surface roughness. A method is presented for the evaluation of surface roughness variations using high-resolution surface scans based on a self-organizing map representation of the mean ice shape. The new method is demonstrated for 1) an 18-in. NACA 23012 airfoil 2 AOA just after the initial ice coverage of the leading 5 of the suction surface of the airfoil, 2) a 21-in. NACA 0012 at 0AOA following coverage of the leading 10 of the airfoil surface, and 3) a cold-soaked 21-in.NACA 0012 airfoil without ice. The SOM method resulted in descriptions of the statistical coverage limits and a quantitative representation of early stages of ice roughness formation on the airfoils. Limitations of the SOM method are explored, and the uncertainty limits of the method are investigated using the non-iced NACA 0012 airfoil measurements.

Highest weight representation for Sklyanin algebra sl(3)(u) with application to the Gaudin model

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

Burdik, C., E-mail: burdik@kmlinux.fjfi.cvut.cz; Navratil, O.

2011-06-15

We study the infinite-dimensional Sklyanin algebra sl(3)(u). Specifically we construct the highest weight representation for this algebra in an explicit form. Its application to the Gaudin model is mentioned.

Kernel-PCA data integration with enhanced interpretability

PubMed Central

2014-01-01

Background Nowadays, combining the different sources of information to improve the biological knowledge available is a challenge in bioinformatics. One of the most powerful methods for integrating heterogeneous data types are kernel-based methods. Kernel-based data integration approaches consist of two basic steps: firstly the right kernel is chosen for each data set; secondly the kernels from the different data sources are combined to give a complete representation of the available data for a given statistical task. Results We analyze the integration of data from several sources of information using kernel PCA, from the point of view of reducing dimensionality. Moreover, we improve the interpretability of kernel PCA by adding to the plot the representation of the input variables that belong to any dataset. In particular, for each input variable or linear combination of input variables, we can represent the direction of maximum growth locally, which allows us to identify those samples with higher/lower values of the variables analyzed. Conclusions The integration of different datasets and the simultaneous representation of samples and variables together give us a better understanding of biological knowledge. PMID:25032747

A 4-Dimensional Representation of Antennal Lobe Output Based on an Ensemble of Characterized Projection Neurons

PubMed Central

Staudacher, Erich M.; Huetteroth, Wolf; Schachtner, Joachim; Daly, Kevin C.

2009-01-01

A central problem facing studies of neural encoding in sensory systems is how to accurately quantify the extent of spatial and temporal responses. In this study, we take advantage of the relatively simple and stereotypic neural architecture found in invertebrates. We combine standard electrophysiological techniques, recently developed population analysis techniques, and novel anatomical methods to form an innovative 4-dimensional view of odor output representations in the antennal lobe of the moth Manduca sexta. This novel approach allows quantification of olfactory responses of characterized neurons with spike time resolution. Additionally, arbitrary integration windows can be used for comparisons with other methods such as imaging. By assigning statistical significance to changes in neuronal firing, this method can visualize activity across the entire antennal lobe. The resulting 4-dimensional representation of antennal lobe output complements imaging and multi-unit experiments yet provides a more comprehensive and accurate view of glomerular activation patterns in spike time resolution. PMID:19464513

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.

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

Low-Dimensional Feature Representation for Instrument Identification

NASA Astrophysics Data System (ADS)

Ihara, Mizuki; Maeda, Shin-Ichi; Ikeda, Kazushi; Ishii, Shin

For monophonic music instrument identification, various feature extraction and selection methods have been proposed. One of the issues toward instrument identification is that the same spectrum is not always observed even in the same instrument due to the difference of the recording condition. Therefore, it is important to find non-redundant instrument-specific features that maintain information essential for high-quality instrument identification to apply them to various instrumental music analyses. For such a dimensionality reduction method, the authors propose the utilization of linear projection methods: local Fisher discriminant analysis (LFDA) and LFDA combined with principal component analysis (PCA). After experimentally clarifying that raw power spectra are actually good for instrument classification, the authors reduced the feature dimensionality by LFDA or by PCA followed by LFDA (PCA-LFDA). The reduced features achieved reasonably high identification performance that was comparable or higher than those by the power spectra and those achieved by other existing studies. These results demonstrated that our LFDA and PCA-LFDA can successfully extract low-dimensional instrument features that maintain the characteristic information of the instruments.

Radiation from a D-dimensional collision of shock waves: Two-dimensional reduction and Carter-Penrose diagram

NASA Astrophysics Data System (ADS)

Coelho, Flávio S.; Sampaio, Marco O. P.

2016-05-01

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg-Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter-Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

NASA Astrophysics Data System (ADS)

Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet

2017-11-01

In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.

Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation

NASA Astrophysics Data System (ADS)

Tang, Kunkun; Congedo, Pietro M.; Abgrall, Rémi

2016-06-01

The Polynomial Dimensional Decomposition (PDD) is employed in this work for the global sensitivity analysis and uncertainty quantification (UQ) of stochastic systems subject to a moderate to large number of input random variables. Due to the intimate connection between the PDD and the Analysis of Variance (ANOVA) approaches, PDD is able to provide a simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to the Polynomial Chaos expansion (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of standard methods unaffordable for real engineering applications. In order to address the problem of the curse of dimensionality, this work proposes essentially variance-based adaptive strategies aiming to build a cheap meta-model (i.e. surrogate model) by employing the sparse PDD approach with its coefficients computed by regression. Three levels of adaptivity are carried out in this paper: 1) the truncated dimensionality for ANOVA component functions, 2) the active dimension technique especially for second- and higher-order parameter interactions, and 3) the stepwise regression approach designed to retain only the most influential polynomials in the PDD expansion. During this adaptive procedure featuring stepwise regressions, the surrogate model representation keeps containing few terms, so that the cost to resolve repeatedly the linear systems of the least-squares regression problem is negligible. The size of the finally obtained sparse PDD representation is much smaller than the one of the full expansion, since only significant terms are eventually retained. Consequently, a much smaller number of calls to the deterministic model is required to compute the final PDD coefficients.

A random-sampling high dimensional model representation neural network for building potential energy surfaces

NASA Astrophysics Data System (ADS)

Manzhos, Sergei; Carrington, Tucker

2006-08-01

We combine the high dimensional model representation (HDMR) idea of Rabitz and co-workers [J. Phys. Chem. 110, 2474 (2006)] with neural network (NN) fits to obtain an effective means of building multidimensional potentials. We verify that it is possible to determine an accurate many-dimensional potential by doing low dimensional fits. The final potential is a sum of terms each of which depends on a subset of the coordinates. This form facilitates quantum dynamics calculations. We use NNs to represent HDMR component functions that minimize error mode term by mode term. This NN procedure makes it possible to construct high-order component functions which in turn enable us to determine a good potential. It is shown that the number of available potential points determines the order of the HDMR which should be used.

A random-sampling high dimensional model representation neural network for building potential energy surfaces.

PubMed

Manzhos, Sergei; Carrington, Tucker

2006-08-28

We combine the high dimensional model representation (HDMR) idea of Rabitz and co-workers [J. Phys. Chem. 110, 2474 (2006)] with neural network (NN) fits to obtain an effective means of building multidimensional potentials. We verify that it is possible to determine an accurate many-dimensional potential by doing low dimensional fits. The final potential is a sum of terms each of which depends on a subset of the coordinates. This form facilitates quantum dynamics calculations. We use NNs to represent HDMR component functions that minimize error mode term by mode term. This NN procedure makes it possible to construct high-order component functions which in turn enable us to determine a good potential. It is shown that the number of available potential points determines the order of the HDMR which should be used.

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.

Three-dimensional reconstruction of frozen and thawed plant tissues from microscopic images

USDA-ARS?s Scientific Manuscript database

Histological analysis of frozen and thawed plants has been conducted for many years but the observation of individual sections only provides a 2 dimensional representation of a 3 dimensional phenomenon. Most techniques for viewing internal plant structure in 3 dimensions is either low in resolution...

Temporal fluctuations of tremor signals from inertial sensor: a preliminary study in differentiating Parkinson's disease from essential tremor.

PubMed

Thanawattano, Chusak; Pongthornseri, Ronachai; Anan, Chanawat; Dumnin, Songphon; Bhidayasiri, Roongroj

2015-11-04

Parkinson's disease (PD) and essential tremor (ET) are the two most common movement disorders but the rate of misdiagnosis rate in these disorders is high due to similar characteristics of tremor. The purpose of the study is to present: (a) a solution to identify PD and ET patients by using the novel measurement of tremor signal variations while performing the resting task, (b) the improvement of the differentiation of PD from ET patients can be obtained by using the ratio of the novel measurement while performing two specific tasks. 35 PD and 22 ET patients were asked to participate in the study. They were asked to wear a 6-axis inertial sensor on his/her index finger of the tremor dominant hand and perform three tasks including kinetic, postural and resting tasks. Each task required 10 s to complete. The angular rate signal measured during the performance of these tasks was band-pass filtered and transformed into a two-dimensional representation. The ratio of the ellipse area covering 95 % of this two-dimensional representation of different tasks was investigated and the two best tasks were selected for the purpose of differentiation. The ellipse area of two-dimensional representation of the resting task of PD and ET subjects are statistically significantly different (p < 0.05). Furthermore, the fluctuation ratio, defined as a ratio of the ellipse area of two-dimensional representation of resting to kinetic tremor, of PD subjects were statistically significantly higher than ET subjects in all axes (p = 0.0014, 0.0011 and 0.0001 for x, y and z-axis, respectively). The validation shows that the proposed method provides 100 % sensitivity, specificity and accuracy of the discrimination in the 5 subjects in the validation group. While the method would have to be validated with a larger number of subjects, these preliminary results show the feasibility of the approach. This study provides the novel measurement of tremor variation in time domain termed 'temporal fluctuation'. The temporal fluctuation of the resting task can be used to discriminate PD from ET subjects. The ratio of the temporal fluctuation of the resting task to the kinetic task improves the reliability of the discrimination. While the method is powerful, it is also simple so it could be applied on low resource platforms such as smart phones and watches which are commonly equipped with inertial sensors.

bioWeb3D: an online webGL 3D data visualisation tool.

PubMed

Pettit, Jean-Baptiste; Marioni, John C

2013-06-07

Data visualization is critical for interpreting biological data. However, in practice it can prove to be a bottleneck for non trained researchers; this is especially true for three dimensional (3D) data representation. Whilst existing software can provide all necessary functionalities to represent and manipulate biological 3D datasets, very few are easily accessible (browser based), cross platform and accessible to non-expert users. An online HTML5/WebGL based 3D visualisation tool has been developed to allow biologists to quickly and easily view interactive and customizable three dimensional representations of their data along with multiple layers of information. Using the WebGL library Three.js written in Javascript, bioWeb3D allows the simultaneous visualisation of multiple large datasets inputted via a simple JSON, XML or CSV file, which can be read and analysed locally thanks to HTML5 capabilities. Using basic 3D representation techniques in a technologically innovative context, we provide a program that is not intended to compete with professional 3D representation software, but that instead enables a quick and intuitive representation of reasonably large 3D datasets.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low-dimensional input stochastic models to represent thermal diffusivity in two-phase microstructures. This model is used in analyzing the effect of topological variations of two-phase microstructures on the evolution of temperature in heat conduction processes.

Compressed digital holography: from micro towards macro

NASA Astrophysics Data System (ADS)

Schretter, Colas; Bettens, Stijn; Blinder, David; Pesquet-Popescu, Béatrice; Cagnazzo, Marco; Dufaux, Frédéric; Schelkens, Peter

2016-09-01

signal processing methods from software-driven computer engineering and applied mathematics. The compressed sensing theory in particular established a practical framework for reconstructing the scene content using few linear combinations of complex measurements and a sparse prior for regularizing the solution. Compressed sensing found direct applications in digital holography for microscopy. Indeed, the wave propagation phenomenon in free space mixes in a natural way the spatial distribution of point sources from the 3-dimensional scene. As the 3-dimensional scene is mapped to a 2-dimensional hologram, the hologram samples form a compressed representation of the scene as well. This overview paper discusses contributions in the field of compressed digital holography at the micro scale. Then, an outreach on future extensions towards the real-size macro scale is discussed. Thanks to advances in sensor technologies, increasing computing power and the recent improvements in sparse digital signal processing, holographic modalities are on the verge of practical high-quality visualization at a macroscopic scale where much higher resolution holograms must be acquired and processed on the computer.

The Representation of Three-Dimensional Space in Fish

PubMed Central

Burt de Perera, Theresa; Holbrook, Robert I.; Davis, Victoria

2016-01-01

In mammals, the so-called “seat of the cognitive map” is located in place cells within the hippocampus. Recent work suggests that the shape of place cell fields might be defined by the animals’ natural movement; in rats the fields appear to be laterally compressed (meaning that the spatial map of the animal is more highly resolved in the horizontal dimensions than in the vertical), whereas the place cell fields of bats are statistically spherical (which should result in a spatial map that is equally resolved in all three dimensions). It follows that navigational error should be equal in the horizontal and vertical dimensions in animals that travel freely through volumes, whereas in surface-bound animals would demonstrate greater vertical error. Here, we describe behavioral experiments on pelagic fish in which we investigated the way that fish encode three-dimensional space and we make inferences about the underlying processing. Our work suggests that fish, like mammals, have a higher order representation of space that assembles incoming sensory information into a neural unit that can be used to determine position and heading in three-dimensions. Further, our results are consistent with this representation being encoded isotropically, as would be expected for animals that move freely through volumes. Definitive evidence for spherical place fields in fish will not only reveal the neural correlates of space to be a deep seated vertebrate trait, but will also help address the questions of the degree to which environment spatial ecology has shaped cognitive processes and their underlying neural mechanisms. PMID:27014002

Images of Animals: Interpreting Three-Dimensional, Life-Sized 'Representations' of Animals--Zoo, Museum and Robotic Animals.

ERIC Educational Resources Information Center

Tunnicliffe, Sue Dale

A visit to the natural history museum is part of many pupils' educational program. One way of investigating what children learn about animals is to examine the mental models they reveal through their talk when they come face to face with animal representations. In this study, representations were provided by: (1) robotic models in a museum; (2)…

Difficulties that Students Face with Two-Dimensional Motion

ERIC Educational Resources Information Center

Mihas, P.; Gemousakakis, T.

2007-01-01

Some difficulties that students face with two-dimensional motion are addressed. The difficulties addressed are the vectorial representation of velocity, acceleration and force, the force-energy theorem and the understanding of the radius of curvature.

Interpretable dimensionality reduction of single cell transcriptome data with deep generative models.

PubMed

Ding, Jiarui; Condon, Anne; Shah, Sohrab P

2018-05-21

Single-cell RNA-sequencing has great potential to discover cell types, identify cell states, trace development lineages, and reconstruct the spatial organization of cells. However, dimension reduction to interpret structure in single-cell sequencing data remains a challenge. Existing algorithms are either not able to uncover the clustering structures in the data or lose global information such as groups of clusters that are close to each other. We present a robust statistical model, scvis, to capture and visualize the low-dimensional structures in single-cell gene expression data. Simulation results demonstrate that low-dimensional representations learned by scvis preserve both the local and global neighbor structures in the data. In addition, scvis is robust to the number of data points and learns a probabilistic parametric mapping function to add new data points to an existing embedding. We then use scvis to analyze four single-cell RNA-sequencing datasets, exemplifying interpretable two-dimensional representations of the high-dimensional single-cell RNA-sequencing data.

Solutions of evolution equations associated to infinite-dimensional Laplacian

NASA Astrophysics Data System (ADS)

Ouerdiane, Habib

2016-05-01

We study an evolution equation associated with the integer power of the Gross Laplacian ΔGp and a potential function V on an infinite-dimensional space. The initial condition is a generalized function. The main technique we use is the representation of the Gross Laplacian as a convolution operator. This representation enables us to apply the convolution calculus on a suitable distribution space to obtain the explicit solution of the perturbed evolution equation. Our results generalize those previously obtained by Hochberg [K. J. Hochberg, Ann. Probab. 6 (1978) 433.] in the one-dimensional case with V=0, as well as by Barhoumi-Kuo-Ouerdiane for the case p=1 (See Ref. [A. Barhoumi, H. H. Kuo and H. Ouerdiane, Soochow J. Math. 32 (2006) 113.]).

Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions

NASA Astrophysics Data System (ADS)

Ziegler, Benjamin; Rauhut, Guntram

2016-03-01

The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.

Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions.

PubMed

Ziegler, Benjamin; Rauhut, Guntram

2016-03-21

The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.

An intermediate-scale model for thermal hydrology in low-relief permafrost-affected landscapes

DOE PAGES

Jan, Ahmad; Coon, Ethan T.; Painter, Scott L.; ...

2017-07-10

Integrated surface/subsurface models for simulating the thermal hydrology of permafrost-affected regions in a warming climate have recently become available, but computational demands of those new process-rich simu- lation tools have thus far limited their applications to one-dimensional or small two-dimensional simulations. We present a mixed-dimensional model structure for efficiently simulating surface/subsurface thermal hydrology in low-relief permafrost regions at watershed scales. The approach replaces a full three-dimensional system with a two-dimensional overland thermal hydrology system and a family of one-dimensional vertical columns, where each column represents a fully coupled surface/subsurface thermal hydrology system without lateral flow. The system is then operatormore » split, sequentially updating the overland flow system without sources and the one-dimensional columns without lateral flows. We show that the app- roach is highly scalable, supports subcycling of different processes, and compares well with the corresponding fully three-dimensional representation at significantly less computational cost. Those advances enable recently developed representations of freezing soil physics to be coupled with thermal overland flow and surface energy balance at scales of 100s of meters. Furthermore developed and demonstrated for permafrost thermal hydrology, the mixed-dimensional model structure is applicable to integrated surface/subsurface thermal hydrology in general.« less

Vertex Space Analysis for Model-Based Target Recognition.

DTIC Science & Technology

1996-08-01

performed in our unique invariant representation, Vertex Space, that reduces both the dimensionality and size of the required search space. Vertex Space ... mapping results in a reduced representation that serves as a characteristic target signature which is invariant to four of the six viewing geometry

Highly effective action from large N gauge fields

NASA Astrophysics Data System (ADS)

Yang, Hyun Seok

2014-10-01

Recently Schwarz put forward a conjecture that the world-volume action of a probe D3-brane in an AdS5×S5 background of type IIB superstring theory can be reinterpreted as the highly effective action (HEA) of four-dimensional N =4 superconformal field theory on the Coulomb branch. We argue that the HEA can be derived from the noncommutative (NC) field theory representation of the AdS/CFT correspondence and the Seiberg-Witten (SW) map defining a spacetime field redefinition between ordinary and NC gauge fields. It is based only on the well-known facts that the master fields of large N matrices are higher-dimensional NC U(1) gauge fields and the SW map is a local coordinate transformation eliminating U(1) gauge fields known as the Darboux theorem in symplectic geometry.

Highest-weight representations of Brocherd`s algebras

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

Slansky, R.

1997-01-01

General features of highest-weight representations of Borcherd`s algebras are described. to show their typical features, several representations of Borcherd`s extensions of finite-dimensional algebras are analyzed. Then the example of the extension of affine- su(2) to a Borcherd`s algebra is examined. These algebras provide a natural way to extend a Kac-Moody algebra to include the hamiltonian and number-changing operators in a generalized symmetry structure.

Baxter operators and Hamiltonians for "nearly all" integrable closed gl(n) spin chains

NASA Astrophysics Data System (ADS)

Frassek, Rouven; Łukowski, Tomasz; Meneghelli, Carlo; Staudacher, Matthias

2013-09-01

We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to generic finite-dimensional representations in quantum space. The results equally apply to non-compact representations of highest or lowest weight type. We furthermore fill an apparent gap in the literature, and provide the nearest-neighbor Hamiltonians of the spin chains in question for all cases where the gl(n) representations are described by rectangular Young diagrams, as well as for their infinite-dimensional generalizations. They take the form of digamma functions depending on operator-valued shifted weights. We believe that this condition follows from [R0,I,Jba]=0, [R0,I,Jb˙a˙]=0, [R0,I,Jbc˙Jc˙a]=0, which are specializations, respectively, of the last equation in (2.14), (2.16) and (2.19) in the case of minimal representations. Clearly R0,I can be considered as a function of the Casimir operators of gl(n) as well. These are just constants in a given irreducible representation and will not enter the discussion regarding the determination of R0,I.

Modeling late rectal toxicities based on a parameterized representation of the 3D dose distribution

NASA Astrophysics Data System (ADS)

Buettner, Florian; Gulliford, Sarah L.; Webb, Steve; Partridge, Mike

2011-04-01

Many models exist for predicting toxicities based on dose-volume histograms (DVHs) or dose-surface histograms (DSHs). This approach has several drawbacks as firstly the reduction of the dose distribution to a histogram results in the loss of spatial information and secondly the bins of the histograms are highly correlated with each other. Furthermore, some of the complex nonlinear models proposed in the past lack a direct physical interpretation and the ability to predict probabilities rather than binary outcomes. We propose a parameterized representation of the 3D distribution of the dose to the rectal wall which explicitly includes geometrical information in the form of the eccentricity of the dose distribution as well as its lateral and longitudinal extent. We use a nonlinear kernel-based probabilistic model to predict late rectal toxicity based on the parameterized dose distribution and assessed its predictive power using data from the MRC RT01 trial (ISCTRN 47772397). The endpoints under consideration were rectal bleeding, loose stools, and a global toxicity score. We extract simple rules identifying 3D dose patterns related to a specifically low risk of complication. Normal tissue complication probability (NTCP) models based on parameterized representations of geometrical and volumetric measures resulted in areas under the curve (AUCs) of 0.66, 0.63 and 0.67 for predicting rectal bleeding, loose stools and global toxicity, respectively. In comparison, NTCP models based on standard DVHs performed worse and resulted in AUCs of 0.59 for all three endpoints. In conclusion, we have presented low-dimensional, interpretable and nonlinear NTCP models based on the parameterized representation of the dose to the rectal wall. These models had a higher predictive power than models based on standard DVHs and their low dimensionality allowed for the identification of 3D dose patterns related to a low risk of complication.

Development of a global aerosol model using a two-dimensional sectional method: 1. Model design

NASA Astrophysics Data System (ADS)

Matsui, H.

2017-08-01

This study develops an aerosol module, the Aerosol Two-dimensional bin module for foRmation and Aging Simulation version 2 (ATRAS2), and implements the module into a global climate model, Community Atmosphere Model. The ATRAS2 module uses a two-dimensional (2-D) sectional representation with 12 size bins for particles from 1 nm to 10 μm in dry diameter and 8 black carbon (BC) mixing state bins. The module can explicitly calculate the enhancement of absorption and cloud condensation nuclei activity of BC-containing particles by aging processes. The ATRAS2 module is an extension of a 2-D sectional aerosol module ATRAS used in our previous studies within a framework of a regional three-dimensional model. Compared with ATRAS, the computational cost of the aerosol module is reduced by more than a factor of 10 by simplifying the treatment of aerosol processes and 2-D sectional representation, while maintaining good accuracy of aerosol parameters in the simulations. Aerosol processes are simplified for condensation of sulfate, ammonium, and nitrate, organic aerosol formation, coagulation, and new particle formation processes, and box model simulations show that these simplifications do not substantially change the predicted aerosol number and mass concentrations and their mixing states. The 2-D sectional representation is simplified (the number of advected species is reduced) primarily by the treatment of chemical compositions using two interactive bin representations. The simplifications do not change the accuracy of global aerosol simulations. In part 2, comparisons with measurements and the results focused on aerosol processes such as BC aging processes are shown.

Motion representation of the long fingers: a proposal for the definitions of new anatomical frames.

PubMed

Coupier, Jérôme; Moiseev, Fédor; Feipel, Véronique; Rooze, Marcel; Van Sint Jan, Serge

2014-04-11

Despite the availability of the International Society of Biomechanics (ISB) recommendations for the orientation of anatomical frames, no consensus exists about motion representations related to finger kinematics. This paper proposes novel anatomical frames for motion representation of the phalangeal segments of the long fingers. A three-dimensional model of a human forefinger was acquired from a non-pathological fresh-frozen hand. Medical imaging was used to collect phalangeal discrete positions. Data processing was performed using a customized software interface ("lhpFusionBox") to create a specimen-specific model and to reconstruct the discrete motion path. Five examiners virtually palpated two sets of landmarks. These markers were then used to build anatomical frames following two methods: a reference method following ISB recommendations and a newly-developed method based on the mean helical axis (HA). Motion representations were obtained and compared between examiners. Virtual palpation precision was around 1mm, which is comparable to results from the literature. The comparison of the two methods showed that the helical axis method seemed more reproducible between examiners especially for secondary, or accessory, motions. Computed Root Mean Square distances comparing methods showed that the ISB method displayed a variability 10 times higher than the HA method. The HA method seems to be suitable for finger motion representation using discrete positions from medical imaging. Further investigations are required before being able to use the methodology with continuous tracking of markers set on the subject's hand. Copyright © 2014 Elsevier Ltd. All rights reserved.

The continuous spin representations of the Poincare and super-Poincare groups and their construction by the Inonu-Wigner group contraction

NASA Astrophysics Data System (ADS)

Khan, Abu M. A. S.

We study the continuous spin representation (CSR) of the Poincare group in arbitrary dimensions. In d dimensions, the CSRs are characterized by the length of the light-cone vector and the Dynkin labels of the SO(d-3) short little group which leaves the light-cone vector invariant. In addition to these, a solid angle Od-3 which specifies the direction of the light-cone vector is also required to label the states. We also find supersymmetric generalizations of the CSRs. In four dimensions, the supermultiplet contains one bosonic and one fermionic CSRs which transform into each other under the action of the supercharges. In a five dimensional case, the supermultiplet contains two bosonic and two fermionic CSRs which is like N = 2 supersymmetry in four dimensions. When constructed using Grassmann parameters, the light-cone vector becomes nilpotent. This makes the representation finite dimensional, but at the expense of introducing central charges even though the representation is massless. This leads to zero or negative norm states. The nilpotent constructions are valid only for even dimensions. We also show how the CSRs in four dimensions can be obtained from five dimensions by the combinations of Kaluza-Klein (KK) dimensional reduction and the Inonu-Wigner group contraction. The group contraction is a singular transformation. We show that the group contraction is equivalent to imposing periodic boundary condition along one direction and taking a double singular limit. In this form the contraction parameter is interpreted as the inverse KK radius. We apply this technique to both five dimensional regular massless and massive representations. For the regular massless case, we find that the contraction gives the CSR in four dimensions under a double singular limit and the representation wavefunction is the Bessel function. For the massive case, we use Majorana's infinite component theory as a model for the SO(4) little group. In this case, a triple singular limit is required to yield any CSR in four dimensions. The representation wavefunction is the Bessel function, as expected, but the scale factor is not the length of the light-cone vector. The amplitude and the scale factor are implicit functions of the parameter y which is a ratio of the internal and external coordinates. We also state under what conditions our solutions become identical to Wigner's solution.

30 CFR 250.105 - Definitions.

Code of Federal Regulations, 2010 CFR

2010-07-01

..., identification of lithologic and fossil content, core analysis, laboratory analyses of physical and chemical... form of schematic cross sections, 3-dimensional representations, and maps, developed by determining the... means geophysical knowledge, often in the form of schematic cross sections, 3-dimensional...

30 CFR 251.1 - Definitions.

Code of Federal Regulations, 2014 CFR

2014-07-01

... fossil content, core analyses, laboratory analyses of physical and chemical properties, well logs or... geological information means knowledge, often in the form of schematic cross sections, 3-dimensional... form of seismic cross sections, 3-dimensional representations, and maps, developed by determining the...

30 CFR 550.105 - Definitions.

Code of Federal Regulations, 2014 CFR

2014-07-01

..., identification of lithologic and fossil content, core analysis, laboratory analyses of physical and chemical... form of schematic cross sections, 3-dimensional representations, and maps, developed by determining the... means geophysical knowledge, often in the form of schematic cross sections, 3-dimensional...

30 CFR 251.1 - Definitions.

Code of Federal Regulations, 2012 CFR

2012-07-01

... fossil content, core analyses, laboratory analyses of physical and chemical properties, well logs or... geological information means knowledge, often in the form of schematic cross sections, 3-dimensional... form of seismic cross sections, 3-dimensional representations, and maps, developed by determining the...

30 CFR 550.105 - Definitions.

Code of Federal Regulations, 2013 CFR

2013-07-01

..., identification of lithologic and fossil content, core analysis, laboratory analyses of physical and chemical... form of schematic cross sections, 3-dimensional representations, and maps, developed by determining the... means geophysical knowledge, often in the form of schematic cross sections, 3-dimensional...

30 CFR 550.105 - Definitions.

Code of Federal Regulations, 2012 CFR

2012-07-01

..., identification of lithologic and fossil content, core analysis, laboratory analyses of physical and chemical... form of schematic cross sections, 3-dimensional representations, and maps, developed by determining the... means geophysical knowledge, often in the form of schematic cross sections, 3-dimensional...

30 CFR 251.1 - Definitions.

Code of Federal Regulations, 2013 CFR

2013-07-01

... fossil content, core analyses, laboratory analyses of physical and chemical properties, well logs or... geological information means knowledge, often in the form of schematic cross sections, 3-dimensional... form of seismic cross sections, 3-dimensional representations, and maps, developed by determining the...

30 CFR 250.105 - Definitions.

Code of Federal Regulations, 2011 CFR

2011-07-01

... include, but is not limited to, identification of lithologic and fossil content, core analysis, laboratory... form of schematic cross sections, 3-dimensional representations, and maps, developed by determining the... means geophysical knowledge, often in the form of schematic cross sections, 3-dimensional...

Wavepacket dynamics and the multi-configurational time-dependent Hartree approach

NASA Astrophysics Data System (ADS)

Manthe, Uwe

2017-06-01

Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.

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

Tang, Kunkun, E-mail: ktg@illinois.edu; Inria Bordeaux – Sud-Ouest, Team Cardamom, 200 avenue de la Vieille Tour, 33405 Talence; Congedo, Pietro M.

The Polynomial Dimensional Decomposition (PDD) is employed in this work for the global sensitivity analysis and uncertainty quantification (UQ) of stochastic systems subject to a moderate to large number of input random variables. Due to the intimate connection between the PDD and the Analysis of Variance (ANOVA) approaches, PDD is able to provide a simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to the Polynomial Chaos expansion (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of standard methods unaffordable formore » real engineering applications. In order to address the problem of the curse of dimensionality, this work proposes essentially variance-based adaptive strategies aiming to build a cheap meta-model (i.e. surrogate model) by employing the sparse PDD approach with its coefficients computed by regression. Three levels of adaptivity are carried out in this paper: 1) the truncated dimensionality for ANOVA component functions, 2) the active dimension technique especially for second- and higher-order parameter interactions, and 3) the stepwise regression approach designed to retain only the most influential polynomials in the PDD expansion. During this adaptive procedure featuring stepwise regressions, the surrogate model representation keeps containing few terms, so that the cost to resolve repeatedly the linear systems of the least-squares regression problem is negligible. The size of the finally obtained sparse PDD representation is much smaller than the one of the full expansion, since only significant terms are eventually retained. Consequently, a much smaller number of calls to the deterministic model is required to compute the final PDD coefficients.« less

bioWeb3D: an online webGL 3D data visualisation tool

PubMed Central

2013-01-01

Background Data visualization is critical for interpreting biological data. However, in practice it can prove to be a bottleneck for non trained researchers; this is especially true for three dimensional (3D) data representation. Whilst existing software can provide all necessary functionalities to represent and manipulate biological 3D datasets, very few are easily accessible (browser based), cross platform and accessible to non-expert users. Results An online HTML5/WebGL based 3D visualisation tool has been developed to allow biologists to quickly and easily view interactive and customizable three dimensional representations of their data along with multiple layers of information. Using the WebGL library Three.js written in Javascript, bioWeb3D allows the simultaneous visualisation of multiple large datasets inputted via a simple JSON, XML or CSV file, which can be read and analysed locally thanks to HTML5 capabilities. Conclusions Using basic 3D representation techniques in a technologically innovative context, we provide a program that is not intended to compete with professional 3D representation software, but that instead enables a quick and intuitive representation of reasonably large 3D datasets. PMID:23758781

Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Morozov, Oleg I.

2018-06-01

The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The exotic cohomology of the symmetry algebras opens a way to formulate such conditions in internal terms of the PDE s under the study. In this paper we consider certain examples of infinite-dimensional Lie algebras with nontrivial second exotic cohomology groups and show that the Maurer-Cartan forms of the associated extensions of these Lie algebras generate Lax representations for integrable systems, both known and new ones.

Spinors in Hilbert Space

NASA Astrophysics Data System (ADS)

Plymen, Roger; Robinson, Paul

1995-01-01

Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book, the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject.

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

Koenig, Robert; Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125; Mitchison, Graeme

In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's 'exponential' approximation by 'almost-product' states, a theorem which deals with certain triples of representations of the unitary group, and the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choicemore » of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states and leads to some new results, including an exponential theorem for infinite-dimensional systems.« less

The Coupling of Finite Element and Integral Equation Representations for Efficient Three-Dimensional Modeling of Electromagnetic Scattering and Radiation

NASA Technical Reports Server (NTRS)

Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz

1996-01-01

Finite element modeling has proven useful for accurtely simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength.

Plot Scale Factor Models for Standard Orthographic Views

ERIC Educational Resources Information Center

Osakue, Edward E.

2007-01-01

Geometric modeling provides graphic representations of real or abstract objects. Realistic representation requires three dimensional (3D) attributes since natural objects have three principal dimensions. CAD software gives the user the ability to construct realistic 3D models of objects, but often prints of these models must be generated on two…

Increasing the Coverage of Medicinal Chemistry-Relevant Space in Commercial Fragments Screening

PubMed Central

2014-01-01

Analyzing the chemical space coverage in commercial fragment screening collections revealed the overlap between bioactive medicinal chemistry substructures and rule-of-three compliant fragments is only ∼25%. We recommend including these fragments in fragment screening libraries to maximize confidence in discovering hit matter within known bioactive chemical space, while incorporation of nonoverlapping substructures could offer novel hits in screening libraries. Using principal component analysis, polar and three-dimensional substructures display a higher-than-average enrichment of bioactive compounds, indicating increasing representation of these substructures may be beneficial in fragment screening. PMID:24405118

From Rational Numbers to Dirac's Bra and Ket: Symbolic Representation of Physical Laws

NASA Astrophysics Data System (ADS)

D'Agostino, Salvo

2002-05-01

Beginning at least in the nineteenth century, symbols used by physicists in their equations interacted with their physical concepts. In the 1850s, Wilhelm Eduard Weber introduced a more rational order into symbolization by adopting an absolute system of units, and thus expressing electrodynamic laws in the form of algebraic equations instead of proportionality relationships, the formerly accepted representation of physical laws. In the 1860s, James Clerk Maxwell made a further advance by using dimensional quantities, and more complex symbolic forms such as gradient, convergence, rotor, and the like, in his electromagnetic and kinetic theories. In the twentieth century, Werner Heisenberg, Max Born, Erwin Schrödinger, and others introduced new symbols for complex numbers, operators, and matrices, thus passing from the representation of metrical properties of physical systems to higher-level mathematical objects. This process was enhanced in modern theoretical physics through the introduction of matrices, creation and destruction operators, Paul A. M. Dirac's q and c numbers, and so on. In the 1930s, Dirac radicalized this transformation of symbols, being aware of the profound modification in the method and scope of the mathematical-physical relationship it entailed.

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.

2d affine XY-spin model/4d gauge theory duality and deconfinement

NASA Astrophysics Data System (ADS)

Anber, Mohamed M.; Poppitz, Erich; Ünsal, Mithat

2012-04-01

We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2)/ {{Z}_2} gauge theories, compactified on a small spatial circle {{R}^{{^{{{1},{2}}}}}} × {{S}^{{^{{1}}}}} , and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on {{R}^{{^{{2}}}}} × {{T}^{{^{{2}}}}} . Similarly, thermal gauge theories of higher rank are dual to new families of "affine" XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU( N c ) gauge theories with n f ≥1 adjoint Weyl fermions.

Building Bridges to Spatial Reasoning

ERIC Educational Resources Information Center

Shumway, Jessica F.

2013-01-01

Spatial reasoning, which involves "building and manipulating mental representations of two-and three-dimensional objects and perceiving an object from different perspectives" is a critical aspect of geometric thinking and reasoning. Through building, drawing, and analyzing two-and three-dimensional shapes, students develop a foundation…

A non-linear dimension reduction methodology for generating data-driven stochastic input models

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

Ganapathysubramanian, Baskar; Zabaras, Nicholas

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem ofmore » manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R{sup n}. An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R{sup d}(d<

A moving observer in a three-dimensional world

PubMed Central

2016-01-01

For many tasks such as retrieving a previously viewed object, an observer must form a representation of the world at one location and use it at another. A world-based three-dimensional reconstruction of the scene built up from visual information would fulfil this requirement, something computer vision now achieves with great speed and accuracy. However, I argue that it is neither easy nor necessary for the brain to do this. I discuss biologically plausible alternatives, including the possibility of avoiding three-dimensional coordinate frames such as ego-centric and world-based representations. For example, the distance, slant and local shape of surfaces dictate the propensity of visual features to move in the image with respect to one another as the observer's perspective changes (through movement or binocular viewing). Such propensities can be stored without the need for three-dimensional reference frames. The problem of representing a stable scene in the face of continual head and eye movements is an appropriate starting place for understanding the goal of three-dimensional vision, more so, I argue, than the case of a static binocular observer. This article is part of the themed issue ‘Vision in our three-dimensional world’. PMID:27269608

Unitary Transformations in the Quantum Model for Conceptual Conjunctions and Its Application to Data Representation

PubMed Central

Veloz, Tomas; Desjardins, Sylvie

2015-01-01

Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked. In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations. PMID:26617556

Unitary Transformations in the Quantum Model for Conceptual Conjunctions and Its Application to Data Representation.

PubMed

Veloz, Tomas; Desjardins, Sylvie

2015-01-01

Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked. In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations.

Homological Order in Three and Four dimensions: Wilson Algebra, Entanglement Entropy and Twist Defects

NASA Astrophysics Data System (ADS)

Roy, Abhishek; Chen, Xiao; Teo, Jeffrey

2013-03-01

We investigate homological orders in two, three and four dimensions by studying Zk toric code models on simplicial, cellular or in general differential complexes. The ground state degeneracy is obtained from Wilson loop and surface operators, and the homological intersection form. We compute these for a series of closed 3 and 4 dimensional manifolds and study the projective representations of mapping class groups (modular transformations). Braiding statistics between point and string excitations in (3+1)-dimensions or between dual string excitations in (4+1)-dimensions are topologically determined by the higher dimensional linking number, and can be understood by an effective topological field theory. An algorithm for calculating entanglemnent entropy of any bipartition of closed manifolds is presented, and its topological signature is completely characterized homologically. Extrinsic twist defects (or disclinations) are studied in 2,3 and 4 dimensions and are shown to carry exotic fusion and braiding properties. Simons Fellowship

Quantitative three-dimensional ice roughness from scanning electron microscopy

NASA Astrophysics Data System (ADS)

Butterfield, Nicholas; Rowe, Penny M.; Stewart, Emily; Roesel, David; Neshyba, Steven

2017-03-01

We present a method for inferring surface morphology of ice from scanning electron microscope images. We first develop a novel functional form for the backscattered electron intensity as a function of ice facet orientation; this form is parameterized using smooth ice facets of known orientation. Three-dimensional representations of rough surfaces are retrieved at approximately micrometer resolution using Gauss-Newton inversion within a Bayesian framework. Statistical analysis of the resulting data sets permits characterization of ice surface roughness with a much higher statistical confidence than previously possible. A survey of results in the range -39°C to -29°C shows that characteristics of the roughness (e.g., Weibull parameters) are sensitive not only to the degree of roughening but also to the symmetry of the roughening. These results suggest that roughening characteristics obtained by remote sensing and in situ measurements of atmospheric ice clouds can potentially provide more facet-specific information than has previously been appreciated.

Magnetic dynamo action in two-dimensional turbulent magneto-hydrodynamics

NASA Technical Reports Server (NTRS)

Fyfe, D.; Joyce, G.; Montgomery, D.

1976-01-01

Two-dimensional magnetohydrodynamic turbulence is explored by means of numerical simulation. Previous analytical theory, based on non-dissipative constants of the motion in a truncated Fourier representation, is verified by following the evolution of highly non-equilibrium initial conditions numerically. Dynamo action (conversion of a significant fraction of turbulent kinetic energy into long-wavelength magnetic field energy) is observed. It is conjectured that in the presence of dissipation and external forcing, a dual cascade will be observed for zero-helicity situations. Energy will cascade to higher wave numbers simultaneously with a cascade of mean square vector potential to lower wave numbers, leading to an omni-directional magnetic energy spectrum which varies as 1/k 3 at lower wave numbers, simultaneously with a buildup of magnetic excitation at the lowest wave number of the system. Equipartition of kinetic and magnetic energies is expected at the highest wave numbers in the system.

Attitude Representations for Kalman Filtering

NASA Technical Reports Server (NTRS)

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

2001-01-01

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

High-Dimensional Semantic Space Accounts of Priming

ERIC Educational Resources Information Center

Jones, Michael N.; Kintsch, Walter; Mewhort, Douglas J. K.

2006-01-01

A broad range of priming data has been used to explore the structure of semantic memory and to test between models of word representation. In this paper, we examine the computational mechanisms required to learn distributed semantic representations for words directly from unsupervised experience with language. To best account for the variety of…

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.

Neural dynamics of 3-D surface perception: figure-ground separation and lightness perception.

PubMed

Kelly, F; Grossberg, S

2000-11-01

This article develops the FACADE theory of three-dimensional (3-D) vision to simulate data concerning how two-dimensional pictures give rise to 3-D percepts of occluded and occluding surfaces. The theory suggests how geometrical and contrastive properties of an image can either cooperate or compete when forming the boundary and surface representations that subserve conscious visual percepts. Spatially long-range cooperation and short-range competition work together to separate boundaries of occluding figures from their occluded neighbors, thereby providing sensitivity to T-junctions without the need to assume that T-junction "detectors" exist. Both boundary and surface representations of occluded objects may be amodally completed, whereas the surface representations of unoccluded objects become visible through modal processes. Computer simulations include Bregman-Kanizsa figure-ground separation, Kanizsa stratification, and various lightness percepts, including the Münker-White, Benary cross, and checkerboard percepts.

Physics of the Lorentz Group

NASA Astrophysics Data System (ADS)

Başkal, Sibel

2015-11-01

This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincaré sphere on polarization optics.

Picture This... Developing Standards for Electronic Images at the National Library of Medicine

PubMed Central

Masys, Daniel R.

1990-01-01

New computer technologies have made it feasible to represent, store, and communicate high resolution biomedical images via electronic means. Traditional two dimensional medical images such as those on printed pages have been supplemented by three dimensional images which can be rendered, rotated, and “dissected” from any point of view. The library of the future will provide electronic access not only to words and numbers, but to pictures, sounds, and other nontextual information. There currently exist few widely-accepted standards for the representation and communication of complex images, yet such standards will be critical to the feasibility and usefulness of digital image collections in the life sciences. The National Library of Medicine is embarked on a project to develop a complete digital volumetric representation of an adult human male and female. This “Visible Human Project” will address the issue of standards for computer representation of biological structure.

Quantum teleportation and Birman-Murakami-Wenzl algebra

NASA Astrophysics Data System (ADS)

Zhang, Kun; Zhang, Yong

2017-02-01

In this paper, we investigate the relationship of quantum teleportation in quantum information science and the Birman-Murakami-Wenzl (BMW) algebra in low-dimensional topology. For simplicity, we focus on the two spin-1/2 representation of the BMW algebra, which is generated by both the Temperley-Lieb projector and the Yang-Baxter gate. We describe quantum teleportation using the Temperley-Lieb projector and the Yang-Baxter gate, respectively, and study teleportation-based quantum computation using the Yang-Baxter gate. On the other hand, we exploit the extended Temperley-Lieb diagrammatical approach to clearly show that the tangle relations of the BMW algebra have a natural interpretation of quantum teleportation. Inspired by this interpretation, we construct a general representation of the tangle relations of the BMW algebra and obtain interesting representations of the BMW algebra. Therefore, our research sheds a light on a link between quantum information science and low-dimensional topology.

ImgLib2--generic image processing in Java.

PubMed

Pietzsch, Tobias; Preibisch, Stephan; Tomancák, Pavel; Saalfeld, Stephan

2012-11-15

ImgLib2 is an open-source Java library for n-dimensional data representation and manipulation with focus on image processing. It aims at minimizing code duplication by cleanly separating pixel-algebra, data access and data representation in memory. Algorithms can be implemented for classes of pixel types and generic access patterns by which they become independent of the specific dimensionality, pixel type and data representation. ImgLib2 illustrates that an elegant high-level programming interface can be achieved without sacrificing performance. It provides efficient implementations of common data types, storage layouts and algorithms. It is the data model underlying ImageJ2, the KNIME Image Processing toolbox and an increasing number of Fiji-Plugins. ImgLib2 is licensed under BSD. Documentation and source code are available at http://imglib2.net and in a public repository at https://github.com/imagej/imglib. Supplementary data are available at Bioinformatics Online. saalfeld@mpi-cbg.de

Cognitive mechanisms of insight: the role of heuristics and representational change in solving the eight-coin problem.

PubMed

Öllinger, Michael; Jones, Gary; Faber, Amory H; Knoblich, Günther

2013-05-01

The 8-coin insight problem requires the problem solver to move 2 coins so that each coin touches exactly 3 others. Ormerod, MacGregor, and Chronicle (2002) explained differences in task performance across different versions of the 8-coin problem using the availability of particular moves in a 2-dimensional search space. We explored 2 further explanations by developing 6 new versions of the 8-coin problem in order to investigate the influence of grouping and self-imposed constraints on solutions. The results identified 2 sources of problem difficulty: first, the necessity to overcome the constraint that a solution can be found in 2-dimensional space and, second, the necessity to decompose perceptual groupings. A detailed move analysis suggested that the selection of moves was driven by the established representation rather than the application of the appropriate heuristics. Both results support the assumptions of representational change theory (Ohlsson, 1992).

Microstructure representations for sound absorbing fibrous media: 3D and 2D multiscale modelling and experiments

NASA Astrophysics Data System (ADS)

Zieliński, Tomasz G.

2017-11-01

The paper proposes and investigates computationally-efficient microstructure representations for sound absorbing fibrous media. Three-dimensional volume elements involving non-trivial periodic arrangements of straight fibres are examined as well as simple two-dimensional cells. It has been found that a simple 2D quasi-representative cell can provide similar predictions as a volume element which is in general much more geometrically accurate for typical fibrous materials. The multiscale modelling allowed to determine the effective speeds and damping of acoustic waves propagating in such media, which brings up a discussion on the correlation between the speed, penetration range and attenuation of sound waves. Original experiments on manufactured copper-wire samples are presented and the microstructure-based calculations of acoustic absorption are compared with the corresponding experimental results. In fact, the comparison suggested the microstructure modifications leading to representations with non-uniformly distributed fibres.

Visualizing the ground motions of the 1906 San Francisco earthquake

USGS Publications Warehouse

Chourasia, A.; Cutchin, S.; Aagaard, Brad T.

2008-01-01

With advances in computational capabilities and refinement of seismic wave-propagation models in the past decade large three-dimensional simulations of earthquake ground motion have become possible. The resulting datasets from these simulations are multivariate, temporal and multi-terabyte in size. Past visual representations of results from seismic studies have been largely confined to static two-dimensional maps. New visual representations provide scientists with alternate ways of viewing and interacting with these results potentially leading to new and significant insight into the physical phenomena. Visualizations can also be used for pedagogic and general dissemination purposes. We present a workflow for visual representation of the data from a ground motion simulation of the great 1906 San Francisco earthquake. We have employed state of the art animation tools for visualization of the ground motions with a high degree of accuracy and visual realism. ?? 2008 Elsevier Ltd.

DD-HDS: A method for visualization and exploration of high-dimensional data.

PubMed

Lespinats, Sylvain; Verleysen, Michel; Giron, Alain; Fertil, Bernard

2007-09-01

Mapping high-dimensional data in a low-dimensional space, for example, for visualization, is a problem of increasingly major concern in data analysis. This paper presents data-driven high-dimensional scaling (DD-HDS), a nonlinear mapping method that follows the line of multidimensional scaling (MDS) approach, based on the preservation of distances between pairs of data. It improves the performance of existing competitors with respect to the representation of high-dimensional data, in two ways. It introduces (1) a specific weighting of distances between data taking into account the concentration of measure phenomenon and (2) a symmetric handling of short distances in the original and output spaces, avoiding false neighbor representations while still allowing some necessary tears in the original distribution. More precisely, the weighting is set according to the effective distribution of distances in the data set, with the exception of a single user-defined parameter setting the tradeoff between local neighborhood preservation and global mapping. The optimization of the stress criterion designed for the mapping is realized by "force-directed placement" (FDP). The mappings of low- and high-dimensional data sets are presented as illustrations of the features and advantages of the proposed algorithm. The weighting function specific to high-dimensional data and the symmetric handling of short distances can be easily incorporated in most distance preservation-based nonlinear dimensionality reduction methods.

Estimating the functional dimensionality of neural representations.

PubMed

Ahlheim, Christiane; Love, Bradley C

2018-06-07

Recent advances in multivariate fMRI analysis stress the importance of information inherent to voxel patterns. Key to interpreting these patterns is estimating the underlying dimensionality of neural representations. Dimensions may correspond to psychological dimensions, such as length and orientation, or involve other coding schemes. Unfortunately, the noise structure of fMRI data inflates dimensionality estimates and thus makes it difficult to assess the true underlying dimensionality of a pattern. To address this challenge, we developed a novel approach to identify brain regions that carry reliable task-modulated signal and to derive an estimate of the signal's functional dimensionality. We combined singular value decomposition with cross-validation to find the best low-dimensional projection of a pattern of voxel-responses at a single-subject level. Goodness of the low-dimensional reconstruction is measured as Pearson correlation with a test set, which allows to test for significance of the low-dimensional reconstruction across participants. Using hierarchical Bayesian modeling, we derive the best estimate and associated uncertainty of underlying dimensionality across participants. We validated our method on simulated data of varying underlying dimensionality, showing that recovered dimensionalities match closely true dimensionalities. We then applied our method to three published fMRI data sets all involving processing of visual stimuli. The results highlight three possible applications of estimating the functional dimensionality of neural data. Firstly, it can aid evaluation of model-based analyses by revealing which areas express reliable, task-modulated signal that could be missed by specific models. Secondly, it can reveal functional differences across brain regions. Thirdly, knowing the functional dimensionality allows assessing task-related differences in the complexity of neural patterns. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

Visual three-dimensional representation of beat-to-beat electrocardiogram traces during hemodiafiltration.

PubMed

Rodriguez-Fernandez, Rodrigo; Infante, Oscar; Perez-Grovas, Héctor; Hernandez, Erika; Ruiz-Palacios, Patricia; Franco, Martha; Lerma, Claudia

2012-06-01

This study evaluated the usefulness of the three-dimensional representation of electrocardiogram traces (3DECG) to reveal acute and gradual changes during a full session of hemodiafiltration (HDF) in end-stage renal disease (ESRD) patients. Fifteen ESRD patients were included (six men, nine women, age 46 ± 19 years old). Serum electrolytes, blood pressure, heart rate, and blood urea nitrogen (BUN) were measured before and after HDF. Continuous electrocardiograms (ECGs) obtained by Holter monitoring during HDF were used to produce the 3DECG. Several major disturbances were identified by 3DECG images: increase in QRS amplitude (47%), decrease in T-wave amplitude (33%), increase in heart rate (33%), and occurrence of arrhythmia (53%). Different arrhythmia types were often concurrent and included isolated supraventricular premature beats (N = 5), atrial fibrillation or atrial bigeminy (N = 2), and isolated premature ventricular beats (N = 6). Patients with decrease in T-wave amplitude had higher potassium and BUN (both before HDF and total removal) than those without decrease in T-wave amplitude (P < 0.05). Concurrent acute and gradual ECG changes during HDF are identified by the 3DECG, which could be useful as a preventive and prognostic method. © 2011, Copyright the Authors. Artificial Organs © 2011, International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.

Protein sequence comparison based on K-string dictionary.

PubMed

Yu, Chenglong; He, Rong L; Yau, Stephen S-T

2013-10-25

The current K-string-based protein sequence comparisons require large amounts of computer memory because the dimension of the protein vector representation grows exponentially with K. In this paper, we propose a novel concept, the "K-string dictionary", to solve this high-dimensional problem. It allows us to use a much lower dimensional K-string-based frequency or probability vector to represent a protein, and thus significantly reduce the computer memory requirements for their implementation. Furthermore, based on this new concept, we use Singular Value Decomposition to analyze real protein datasets, and the improved protein vector representation allows us to obtain accurate gene trees. © 2013.

Conformal Nets II: Conformal Blocks

NASA Astrophysics Data System (ADS)

Bartels, Arthur; Douglas, Christopher L.; Henriques, André

2017-08-01

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.

Constrained Low-Rank Learning Using Least Squares-Based Regularization.

PubMed

Li, Ping; Yu, Jun; Wang, Meng; Zhang, Luming; Cai, Deng; Li, Xuelong

2017-12-01

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional subspace for supervised learning tasks, e.g., classification and regression. This paper aims to learn both the discriminant low-rank representation (LRR) and the robust projecting subspace in a supervised manner. To achieve this goal, we cast the problem into a constrained rank minimization framework by adopting the least squares regularization. Naturally, the data label structure tends to resemble that of the corresponding low-dimensional representation, which is derived from the robust subspace projection of clean data by low-rank learning. Moreover, the low-dimensional representation of original data can be paired with some informative structure by imposing an appropriate constraint, e.g., Laplacian regularizer. Therefore, we propose a novel constrained LRR method. The objective function is formulated as a constrained nuclear norm minimization problem, which can be solved by the inexact augmented Lagrange multiplier algorithm. Extensive experiments on image classification, human pose estimation, and robust face recovery have confirmed the superiority of our method.

Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory

NASA Astrophysics Data System (ADS)

Hohm, Olaf; Wang, Yi-Nan

2015-04-01

We construct exceptional field theory for the duality group SL(3) × SL(2). The theory is defined on a space with 8 `external' coordinates and 6 `internal' coordinates in the (3, 2) fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invariance can be made manifest by introducing higher form gauge fields and a so-called tensor hierarchy, which we systematically develop to much higher degree than in previous studies. To this end we introduce a novel Cartan-like tensor calculus based on a covariant nil-potent differential, generalizing the exterior derivative of conventional differential geometry. The theory encodes the full D = 11 or type IIB supergravity, respectively.

Efficient High Order Central Schemes for Multi-Dimensional Hamilton-Jacobi Equations: Talk Slides

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Brian R. (Technical Monitor)

2002-01-01

This viewgraph presentation presents information on the attempt to produce high-order, efficient, central methods that scale well to high dimension. The central philosophy is that the equations should evolve to the point where the data is smooth. This is accomplished by a cyclic pattern of reconstruction, evolution, and re-projection. One dimensional and two dimensional representational methods are detailed, as well.

Minimal unitary representation of SO∗(8)=SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions

NASA Astrophysics Data System (ADS)

Fernando, Sudarshan; Günaydin, Murat

2010-12-01

We study the minimal unitary representation (minrep) of SO(6,2) over an Hilbert space of functions of five variables, obtained by quantizing its quasiconformal realization. The minrep of SO(6,2), which coincides with the minrep of SO(8) similarly constructed, corresponds to a massless conformal scalar field in six spacetime dimensions. There exists a family of "deformations" of the minrep of SO(8) labeled by the spin t of an SU(2 subgroup of the little group SO(4) of lightlike vectors. These deformations labeled by t are positive energy unitary irreducible representations of SO(8) that describe massless conformal fields in six dimensions. The SU(2 spin t is the six-dimensional counterpart of U(1) deformations of the minrep of 4D conformal group SU(2,2) labeled by helicity. We also construct the supersymmetric extensions of the minimal unitary representation of SO(8) to minimal unitary representations of OSp(8|2N) that describe massless six-dimensional conformal supermultiplets. The minimal unitary supermultiplet of OSp(8|4) is the massless supermultiplet of (2,0) conformal field theory that is believed to be dual to M-theory on AdS×S.

Mapping higher-order relations between brain structure and function with embedded vector representations of connectomes.

PubMed

Rosenthal, Gideon; Váša, František; Griffa, Alessandra; Hagmann, Patric; Amico, Enrico; Goñi, Joaquín; Avidan, Galia; Sporns, Olaf

2018-06-05

Connectomics generates comprehensive maps of brain networks, represented as nodes and their pairwise connections. The functional roles of nodes are defined by their direct and indirect connectivity with the rest of the network. However, the network context is not directly accessible at the level of individual nodes. Similar problems in language processing have been addressed with algorithms such as word2vec that create embeddings of words and their relations in a meaningful low-dimensional vector space. Here we apply this approach to create embedded vector representations of brain networks or connectome embeddings (CE). CE can characterize correspondence relations among brain regions, and can be used to infer links that are lacking from the original structural diffusion imaging, e.g., inter-hemispheric homotopic connections. Moreover, we construct predictive deep models of functional and structural connectivity, and simulate network-wide lesion effects using the face processing system as our application domain. We suggest that CE offers a novel approach to revealing relations between connectome structure and function.

Interactions as intertwiners in 4D QFT

NASA Astrophysics Data System (ADS)

de Mello Koch, Robert; Ramgoolam, Sanjaye

2016-03-01

In a recent paper we showed that the correlators of free scalar field theory in four dimensions can be constructed from a two dimensional topological field theory based on so(4 , 2) equivariant maps (intertwiners). The free field result, along with recent results of Frenkel and Libine on equivariance properties of Feynman integrals, are developed further in this paper. We show that the coefficient of the log term in the 1-loop 4-point conformal integral is a projector in the tensor product of so(4 , 2) representations. We also show that the 1-loop 4-point integral can be written as a sum of four terms, each associated with the quantum equation of motion for one of the four external legs. The quantum equation of motion is shown to be related to equivariant maps involving indecomposable representations of so(4 , 2), a phenomenon which illuminates multiplet recombination. The harmonic expansion method for Feynman integrals is a powerful tool for arriving at these results. The generalization to other interactions and higher loops is discussed.

A consensus embedding approach for segmentation of high resolution in vivo prostate magnetic resonance imagery

NASA Astrophysics Data System (ADS)

Viswanath, Satish; Rosen, Mark; Madabhushi, Anant

2008-03-01

Current techniques for localization of prostatic adenocarcinoma (CaP) via blinded trans-rectal ultrasound biopsy are associated with a high false negative detection rate. While high resolution endorectal in vivo Magnetic Resonance (MR) prostate imaging has been shown to have improved contrast and resolution for CaP detection over ultrasound, similarity in intensity characteristics between benign and cancerous regions on MR images contribute to a high false positive detection rate. In this paper, we present a novel unsupervised segmentation method that employs manifold learning via consensus schemes for detection of cancerous regions from high resolution 1.5 Tesla (T) endorectal in vivo prostate MRI. A significant contribution of this paper is a method to combine multiple weak, lower-dimensional representations of high dimensional feature data in a way analogous to classifier ensemble schemes, and hence create a stable and accurate reduced dimensional representation. After correcting for MR image intensity artifacts, such as bias field inhomogeneity and intensity non-standardness, our algorithm extracts over 350 3D texture features at every spatial location in the MR scene at multiple scales and orientations. Non-linear dimensionality reduction schemes such as Locally Linear Embedding (LLE) and Graph Embedding (GE) are employed to create multiple low dimensional data representations of this high dimensional texture feature space. Our novel consensus embedding method is used to average object adjacencies from within the multiple low dimensional projections so that class relationships are preserved. Unsupervised consensus clustering is then used to partition the objects in this consensus embedding space into distinct classes. Quantitative evaluation on 18 1.5 T prostate MR data against corresponding histology obtained from the multi-site ACRIN trials show a sensitivity of 92.65% and a specificity of 82.06%, which suggests that our method is successfully able to detect suspicious regions in the prostate.

The conventionality of pictorial representation in interstellar messages

NASA Astrophysics Data System (ADS)

Vakoch, D. A.

2000-06-01

Pictorial messages have previously been advocated for interstellar communication because such messages are presumed to be capable of presenting information in a non-arbitrary and easily intelligible manner. In contrast to this view, pictorial messages actually represent information in a partially conventional way. This point is demonstrated by examining pictorial representations of human beings from a range of cultures. While such representations may be understood quite readily by individuals familiar with the conventions of a particular culture, to the uninitiated outsider, such representations can be unintelligible. In spite of the partially arbitrary nature of pictorial representation, we may be able to construct messages that would teach extraterrestrial intelligence (ETI) some of the conventions by which we view pictures. One such approach is to pair numerical information about geometrical objects with pictorial representations of the same objects. Problems of conventionality can also be addressed in part through use of (1) multiple representations of the same object, (2) contextual cues, (3) three- and four-dimensional representations and (4) non-visual representations.

Examining the Relationship between 2D Diagrammatic Conventions and Students' Success on Representational Translation Tasks in Organic Chemistry

ERIC Educational Resources Information Center

Olimpo, Jeffrey T.; Kumi, Bryna C.; Wroblewski, Richard; Dixon, Bonnie L.

2015-01-01

Two-dimensional (2D) diagrams are essential in chemistry for conveying and communicating key knowledge about disciplinary phenomena. While experts are adept at identifying, interpreting, and manipulating these representations, novices often are not. Ongoing research efforts in the field suggest that students' effective use of concrete and virtual…

Classification Objects, Ideal Observers & Generative Models

ERIC Educational Resources Information Center

Olman, Cheryl; Kersten, Daniel

2004-01-01

A successful vision system must solve the problem of deriving geometrical information about three-dimensional objects from two-dimensional photometric input. The human visual system solves this problem with remarkable efficiency, and one challenge in vision research is to understand how neural representations of objects are formed and what visual…

Creating 3D Physical Models to Probe Student Understanding of Macromolecular Structure

ERIC Educational Resources Information Center

Cooper, A. Kat; Oliver-Hoyo, M. T.

2017-01-01

The high degree of complexity of macromolecular structure is extremely difficult for students to process. Students struggle to translate the simplified two-dimensional representations commonly used in biochemistry instruction to three-dimensional aspects crucial in understanding structure-property relationships. We designed four different physical…

Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)

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

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

The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible gl(m|n) modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations which include the contravariant tensor representations and an additional class of essentially typical representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.

Path-integral approach to the Wigner-Kirkwood expansion.

PubMed

Jizba, Petr; Zatloukal, Václav

2014-01-01

We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones, we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation, are discussed.

Invariant resolutions for several Fueter operators

NASA Astrophysics Data System (ADS)

Colombo, Fabrizio; Souček, Vladimir; Struppa, Daniele C.

2006-07-01

A proper generalization of complex function theory to higher dimension is Clifford analysis and an analogue of holomorphic functions of several complex variables were recently described as the space of solutions of several Dirac equations. The four-dimensional case has special features and is closely connected to functions of quaternionic variables. In this paper we present an approach to the Dolbeault sequence for several quaternionic variables based on symmetries and representation theory. In particular we prove that the resolution of the Cauchy-Fueter system obtained algebraically, via Gröbner bases techniques, is equivalent to the one obtained by R.J. Baston (J. Geom. Phys. 1992).

Modified GMDH-NN algorithm and its application for global sensitivity analysis

NASA Astrophysics Data System (ADS)

Song, Shufang; Wang, Lu

2017-11-01

Global sensitivity analysis (GSA) is a very useful tool to evaluate the influence of input variables in the whole distribution range. Sobol' method is the most commonly used among variance-based methods, which are efficient and popular GSA techniques. High dimensional model representation (HDMR) is a popular way to compute Sobol' indices, however, its drawbacks cannot be ignored. We show that modified GMDH-NN algorithm can calculate coefficients of metamodel efficiently, so this paper aims at combining it with HDMR and proposes GMDH-HDMR method. The new method shows higher precision and faster convergent rate. Several numerical and engineering examples are used to confirm its advantages.

Cyclic Mario worlds — color-decomposition for one-loop QCD

NASA Astrophysics Data System (ADS)

Kälin, Gregor

2018-04-01

We present a new color decomposition for QCD amplitudes at one-loop level as a generalization of the Del Duca-Dixon-Maltoni and Johansson-Ochirov decomposition at tree level. Starting from a minimal basis of planar primitive amplitudes we write down a color decomposition that is free of linear dependencies among appearing primitive amplitudes or color factors. The conjectured decomposition applies to any number of quark flavors and is independent of the choice of gauge group and matter representation. The results also hold for higher-dimensional or supersymmetric extensions of QCD. We provide expressions for any number of external quark-antiquark pairs and gluons. [Figure not available: see fulltext.

Quantum mechanics and hidden superconformal symmetry

NASA Astrophysics Data System (ADS)

Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.

2017-12-01

Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp (1 |2 ) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp (1 |2 ) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models—both oscillator and particlelike—realize all possible unitary irreducible representations of osp (1 |2 ).

Locality-preserving sparse representation-based classification in hyperspectral imagery

NASA Astrophysics Data System (ADS)

Gao, Lianru; Yu, Haoyang; Zhang, Bing; Li, Qingting

2016-10-01

This paper proposes to combine locality-preserving projections (LPP) and sparse representation (SR) for hyperspectral image classification. The LPP is first used to reduce the dimensionality of all the training and testing data by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold, where the high-dimensional data lies. Then, SR codes the projected testing pixels as sparse linear combinations of all the training samples to classify the testing pixels by evaluating which class leads to the minimum approximation error. The integration of LPP and SR represents an innovative contribution to the literature. The proposed approach, called locality-preserving SR-based classification, addresses the imbalance between high dimensionality of hyperspectral data and the limited number of training samples. Experimental results on three real hyperspectral data sets demonstrate that the proposed approach outperforms the original counterpart, i.e., SR-based classification.

Limited Rank Matrix Learning, discriminative dimension reduction and visualization.

PubMed

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

2012-02-01

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

The onset of layer undulations in smectic A liquid crystals due to a strong magnetic field

NASA Astrophysics Data System (ADS)

Contreras, A.; Garcia-Azpeitia, C.; García-Cervera, C. J.; Joo, S.

2016-08-01

We investigate the effect of a strong magnetic field on a three dimensional smectic A liquid crystal. We identify a critical field above which the uniform layered state loses stability; this is associated to the onset of layer undulations. In a previous work García-Cervera and Joo (2012 Arch. Ration. Mech. Anal. 203 1-43), García-Cervera and Joo considered the two dimensional case and analyzed the transition to the undulated state via a simple bifurcation. In dimension n  =  3 the situation is more delicate because the first eigenvalue of the corresponding linearized problem is not simple. We overcome the difficulties inherent to this higher dimensional setting by identifying the irreducible representations for natural actions on the functional that take into account the invariances of the problem thus allowing for reducing the bifurcation analysis to a subspace with symmetries. We are able to describe at least two bifurcation branches, highlighting the richer landscape of energy critical states in the three dimensional setting. Finally, we analyze a reduced two dimensional problem, assuming the magnetic field is very strong, and are able to relate this to a model in micromagnetics studied in Alouges et al (2002 ESAIM Control Optim. Calc. Var. 8 31-68), from where we deduce the periodicity property of minimizers.

Public Higher Education Performance Accountability Framework Report: Goal--Access and Affordability. Measure: Percentage of Racial Representation in Systems of Higher Education Compared to Racial Representation in the State. Commission Report 07-20

ERIC Educational Resources Information Center

California Postsecondary Education Commission, 2007

2007-01-01

Despite segmental efforts to increase diversity in higher education, African American and Latino students are not achieving levels of representation in California public universities that are equivalent to their levels of representation in the overall State population. Using data for the years 1997 through 2006, the California Postsecondary…

From Quantification to Visualization: A Taxonomy of Uncertainty Visualization Approaches

PubMed Central

Potter, Kristin; Rosen, Paul; Johnson, Chris R.

2014-01-01

Quantifying uncertainty is an increasingly important topic across many domains. The uncertainties present in data come with many diverse representations having originated from a wide variety of disciplines. Communicating these uncertainties is a task often left to visualization without clear connection between the quantification and visualization. In this paper, we first identify frequently occurring types of uncertainty. Second, we connect those uncertainty representations to ones commonly used in visualization. We then look at various approaches to visualizing this uncertainty by partitioning the work based on the dimensionality of the data and the dimensionality of the uncertainty. We also discuss noteworthy exceptions to our taxonomy along with future research directions for the uncertainty visualization community. PMID:25663949

Target recognition for ladar range image using slice image

NASA Astrophysics Data System (ADS)

Xia, Wenze; Han, Shaokun; Wang, Liang

2015-12-01

A shape descriptor and a complete shape-based recognition system using slice images as geometric feature descriptor for ladar range images are introduced. A slice image is a two-dimensional image generated by three-dimensional Hough transform and the corresponding mathematical transformation. The system consists of two processes, the model library construction and recognition. In the model library construction process, a series of range images are obtained after the model object is sampled at preset attitude angles. Then, all the range images are converted into slice images. The number of slice images is reduced by clustering analysis and finding a representation to reduce the size of the model library. In the recognition process, the slice image of the scene is compared with the slice image in the model library. The recognition results depend on the comparison. Simulated ladar range images are used to analyze the recognition and misjudgment rates, and comparison between the slice image representation method and moment invariants representation method is performed. The experimental results show that whether in conditions without noise or with ladar noise, the system has a high recognition rate and low misjudgment rate. The comparison experiment demonstrates that the slice image has better representation ability than moment invariants.

Confinement in F4 Exceptional Gauge Group Using Domain Structures

NASA Astrophysics Data System (ADS)

Rafibakhsh, Shahnoosh; Shahlaei, Amir

2017-03-01

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

De Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography.

PubMed

Renner, R; Cirac, J I

2009-03-20

We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks.

Stereoscopic Projection in Organic Chemistry: Bridging the Gap between Two and Three Dimensions.

ERIC Educational Resources Information Center

Rozzelle, Arlene A.; Rosenfeld, Stuart M.

1985-01-01

Shows how to make stereo slides of three-dimensional molecular models. The slides have been used to teach chirality, conformational isomerism, how models and two-dimensional representations embody selected aspects of structure, and fundamentals of using the specific model set required in a particular organic chemistry course. (JN)

Understanding Insecure Attachment: A Study Using Children's Bird Nest Imagery

ERIC Educational Resources Information Center

Sheller, Sandy

2007-01-01

This article describes a phenomenological study of the artistic creations of bird nests by four school-aged children to illuminate their internal experiences of attachment. The author analyzed qualitative data from in-depth interviews pertaining to two-dimensional and three-dimensional artistic representations of a bird's nest and a family of…

Design of a Three-Dimensional Cognitive Mapping Approach to Support Inquiry Learning

ERIC Educational Resources Information Center

Chen, Juanjuan; Wang, Minhong; Dede, Chris; Grotzer, Tina A.

2017-01-01

The use of external representations has the potential to facilitate inquiry learning, especially hypothesis generation and reasoning, which typically present difficulties for students. This study describes a novel three-dimensional cognitive mapping (3DCM) approach that supports inquiry learning by allowing learners to combine the information on a…

Two-Dimensional Motions of Rockets

ERIC Educational Resources Information Center

Kang, Yoonhwan; Bae, Saebyok

2007-01-01

We analyse the two-dimensional motions of the rockets for various types of rocket thrusts, the air friction and the gravitation by using a suitable representation of the rocket equation and the numerical calculation. The slope shapes of the rocket trajectories are discussed for the three types of rocket engines. Unlike the projectile motions, the…

Generalization of one-dimensional solute transport: A stochastic-convective flow conceptualization

NASA Astrophysics Data System (ADS)

Simmons, C. S.

1986-04-01

A stochastic-convective representation of one-dimensional solute transport is derived. It is shown to conceptually encompass solutions of the conventional convection-dispersion equation. This stochastic approach, however, does not rely on the assumption that dispersive flux satisfies Fick's diffusion law. Observable values of solute concentration and flux, which together satisfy a conservation equation, are expressed as expectations over a flow velocity ensemble, representing the inherent random processess that govern dispersion. Solute concentration is determined by a Lagrangian pdf for random spatial displacements, while flux is determined by an equivalent Eulerian pdf for random travel times. A condition for such equivalence is derived for steady nonuniform flow, and it is proven that both Lagrangian and Eulerian pdfs are required to account for specified initial and boundary conditions on a global scale. Furthermore, simplified modeling of transport is justified by proving that an ensemble of effectively constant velocities always exists that constitutes an equivalent representation. An example of how a two-dimensional transport problem can be reduced to a single-dimensional stochastic viewpoint is also presented to further clarify concepts.

Computer aided photographic engineering

NASA Technical Reports Server (NTRS)

Hixson, Jeffrey A.; Rieckhoff, Tom

1988-01-01

High speed photography is an excellent source of engineering data but only provides a two-dimensional representation of a three-dimensional event. Multiple cameras can be used to provide data for the third dimension but camera locations are not always available. A solution to this problem is to overlay three-dimensional CAD/CAM models of the hardware being tested onto a film or photographic image, allowing the engineer to measure surface distances, relative motions between components, and surface variations.

Quantum Superalgebras at Roots of Unity and Topological Invariants of Three-manifolds

NASA Astrophysics Data System (ADS)

Blumen, Sacha C.

2006-01-01

The general method of Reshetikhin and Turaev is followed to develop topological invariants of closed, connected, orientable 3-manifolds from a new class of algebras called pseudo-modular Hopf algebras. Pseudo-modular Hopf algebras are a class of Z_2-graded ribbon Hopf algebras that generalise the concept of a modular Hopf algebra. The quantum superalgebra U_q(osp(1|2n)) over C is considered with q a primitive N^th root of unity for all integers N >= 3. For such a q, a certain left ideal I of U_q(osp(1|2n)) is also a two-sided Hopf ideal, and the quotient algebra U_q^(N)(osp(1|2n)) = U_q(osp(1|2n)) / I is a Z_2-graded ribbon Hopf algebra. For all n and all N >= 3, a finite collection of finite dimensional representations of U_q^(N)(osp(1|2n)) is defined. Each such representation of U_q^(N)(osp(1|2n)) is labelled by an integral dominant weight belonging to the truncated dominant Weyl chamber. Properties of these representations are considered: the quantum superdimension of each representation is calculated, each representation is shown to be self-dual, and more importantly, the decomposition of the tensor product of an arbitrary number of such representations is obtained for even N. It is proved that the quotient algebra U_q^(N)(osp(1|2n)), together with the set of finite dimensional representations discussed above, form a pseudo-modular Hopf algebra when N >= 6 is twice an odd number. Using this pseudo-modular Hopf algebra, we construct a topological invariant of 3-manifolds. This invariant is shown to be different to the topological invariants of 3-manifolds arising from quantum so(2n+1) at roots of unity.

Modular invariant representations of infinite-dimensional Lie algebras and superalgebras

PubMed Central

Kac, Victor G.; Wakimoto, Minoru

1988-01-01

In this paper, we launch a program to describe and classify modular invariant representations of infinite-dimensional Lie algebras and superalgebras. We prove a character formula for a large class of highest weight representations L(λ) of a Kac-Moody algebra [unk] with a symmetrizable Cartan matrix, generalizing the Weyl-Kac character formula [Kac, V. G. (1974) Funct. Anal. Appl. 8, 68-70]. In the case of an affine [unk], this class includes modular invariant representations of arbitrary rational level m = t/u, where t [unk] Z and u [unk] N are relatively prime and m + g ≥ g/u (g is the dual Coxeter number). We write the characters of these representations in terms of theta functions and calculate their asymptotics, generalizing the results of Kac and Peterson [Kac, V. G. & Peterson, D. H. (1984) Adv. Math. 53, 125-264] and of Kac and Wakimoto [Kac, V. G. & Wakimoto, M. (1988) Adv. Math. 70, 156-234] for the u = 1 (integrable) case. We work out in detail the case [unk] = A1(1), in particular classifying all its modular invariant representations. Furthermore, we show that the modular invariant representations of the Virasoro algebra Vir are precisely the “minimal series” of Belavin et al. [Belavin, A. A., Polyakov, A. M. & Zamolodchikov, A. B. (1984) Nucl. Phys. B 241, 333-380] using the character formulas of Feigin and Fuchs [Feigin, B. L. & Fuchs, D. B. (1984) Lect. Notes Math. 1060, 230-245]. We show that tensoring the basic representation and modular invariant representations of A1(1) produces all modular invariant representations of Vir generalizing the results of Goddard et al. [Goddard P., Kent, A. & Olive, D. (1986) Commun. Math. Phys. 103, 105-119] and of Kac and Wakimoto [Kac, V. G. & Wakimoto, M. (1986) Lect. Notes Phys. 261, 345-371] in the unitary case. We study the general branching functions as well. All these results are generalized to the Kac-Moody superalgebras introduced by Kac [Kac, V. G. (1978) Adv. Math. 30, 85-136] and to N = 1 super Virasoro algebras. We work out in detail the case of the superalgebra B(0, 1)(1), showing, in particular, that restricting to its even part produces again all modular invariant representations of Vir. These results lead to general conjectures about asymptotic behavior of positive energy representations and classification of modular invariant representations. PMID:16593954

Ontology Sparse Vector Learning Algorithm for Ontology Similarity Measuring and Ontology Mapping via ADAL Technology

NASA Astrophysics Data System (ADS)

Gao, Wei; Zhu, Linli; Wang, Kaiyun

2015-12-01

Ontology, a model of knowledge representation and storage, has had extensive applications in pharmaceutics, social science, chemistry and biology. In the age of “big data”, the constructed concepts are often represented as higher-dimensional data by scholars, and thus the sparse learning techniques are introduced into ontology algorithms. In this paper, based on the alternating direction augmented Lagrangian method, we present an ontology optimization algorithm for ontological sparse vector learning, and a fast version of such ontology technologies. The optimal sparse vector is obtained by an iterative procedure, and the ontology function is then obtained from the sparse vector. Four simulation experiments show that our ontological sparse vector learning model has a higher precision ratio on plant ontology, humanoid robotics ontology, biology ontology and physics education ontology data for similarity measuring and ontology mapping applications.

Hierarchical feature representation and multimodal fusion with deep learning for AD/MCI diagnosis.

PubMed

Suk, Heung-Il; Lee, Seong-Whan; Shen, Dinggang

2014-11-01

For the last decade, it has been shown that neuroimaging can be a potential tool for the diagnosis of Alzheimer's Disease (AD) and its prodromal stage, Mild Cognitive Impairment (MCI), and also fusion of different modalities can further provide the complementary information to enhance diagnostic accuracy. Here, we focus on the problems of both feature representation and fusion of multimodal information from Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET). To our best knowledge, the previous methods in the literature mostly used hand-crafted features such as cortical thickness, gray matter densities from MRI, or voxel intensities from PET, and then combined these multimodal features by simply concatenating into a long vector or transforming into a higher-dimensional kernel space. In this paper, we propose a novel method for a high-level latent and shared feature representation from neuroimaging modalities via deep learning. Specifically, we use Deep Boltzmann Machine (DBM)(2), a deep network with a restricted Boltzmann machine as a building block, to find a latent hierarchical feature representation from a 3D patch, and then devise a systematic method for a joint feature representation from the paired patches of MRI and PET with a multimodal DBM. To validate the effectiveness of the proposed method, we performed experiments on ADNI dataset and compared with the state-of-the-art methods. In three binary classification problems of AD vs. healthy Normal Control (NC), MCI vs. NC, and MCI converter vs. MCI non-converter, we obtained the maximal accuracies of 95.35%, 85.67%, and 74.58%, respectively, outperforming the competing methods. By visual inspection of the trained model, we observed that the proposed method could hierarchically discover the complex latent patterns inherent in both MRI and PET. Copyright © 2014 Elsevier Inc. All rights reserved.

Hierarchical Feature Representation and Multimodal Fusion with Deep Learning for AD/MCI Diagnosis

PubMed Central

Suk, Heung-Il; Lee, Seong-Whan; Shen, Dinggang

2014-01-01

For the last decade, it has been shown that neuroimaging can be a potential tool for the diagnosis of Alzheimer’s Disease (AD) and its prodromal stage, Mild Cognitive Impairment (MCI), and also fusion of different modalities can further provide the complementary information to enhance diagnostic accuracy. Here, we focus on the problems of both feature representation and fusion of multimodal information from Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET). To our best knowledge, the previous methods in the literature mostly used hand-crafted features such as cortical thickness, gray matter densities from MRI, or voxel intensities from PET, and then combined these multimodal features by simply concatenating into a long vector or transforming into a higher-dimensional kernel space. In this paper, we propose a novel method for a high-level latent and shared feature representation from neuroimaging modalities via deep learning. Specifically, we use Deep Boltzmann Machine (DBM)1, a deep network with a restricted Boltzmann machine as a building block, to find a latent hierarchical feature representation from a 3D patch, and then devise a systematic method for a joint feature representation from the paired patches of MRI and PET with a multimodal DBM. To validate the effectiveness of the proposed method, we performed experiments on ADNI dataset and compared with the state-of-the-art methods. In three binary classification problems of AD vs. healthy Normal Control (NC), MCI vs. NC, and MCI converter vs. MCI non-converter, we obtained the maximal accuracies of 95.35%, 85.67%, and 74.58%, respectively, outperforming the competing methods. By visual inspection of the trained model, we observed that the proposed method could hierarchically discover the complex latent patterns inherent in both MRI and PET. PMID:25042445

One-dimensional collision carts computer model and its design ideas for productive experiential learning

NASA Astrophysics Data System (ADS)

Wee, Loo Kang

2012-05-01

We develop an Easy Java Simulation (EJS) model for students to experience the physics of idealized one-dimensional collision carts. The physics model is described and simulated by both continuous dynamics and discrete transition during collision. In designing the simulations, we discuss briefly three pedagogical considerations namely (1) a consistent simulation world view with a pen and paper representation, (2) a data table, scientific graphs and symbolic mathematical representations for ease of data collection and multiple representational visualizations and (3) a game for simple concept testing that can further support learning. We also suggest using a physical world setup augmented by simulation by highlighting three advantages of real collision carts equipment such as a tacit 3D experience, random errors in measurement and the conceptual significance of conservation of momentum applied to just before and after collision. General feedback from the students has been relatively positive, and we hope teachers will find the simulation useful in their own classes.

Full dimensional (15-dimensional) quantum-dynamical simulation of the protonated water-dimer III: Mixed Jacobi-valence parametrization and benchmark results for the zero point energy, vibrationally excited states, and infrared spectrum.

PubMed

Vendrell, Oriol; Brill, Michael; Gatti, Fabien; Lauvergnat, David; Meyer, Hans-Dieter

2009-06-21

Quantum dynamical calculations are reported for the zero point energy, several low-lying vibrational states, and the infrared spectrum of the H(5)O(2)(+) cation. The calculations are performed by the multiconfiguration time-dependent Hartree (MCTDH) method. A new vector parametrization based on a mixed Jacobi-valence description of the system is presented. With this parametrization the potential energy surface coupling is reduced with respect to a full Jacobi description, providing a better convergence of the n-mode representation of the potential. However, new coupling terms appear in the kinetic energy operator. These terms are derived and discussed. A mode-combination scheme based on six combined coordinates is used, and the representation of the 15-dimensional potential in terms of a six-combined mode cluster expansion including up to some 7-dimensional grids is discussed. A statistical analysis of the accuracy of the n-mode representation of the potential at all orders is performed. Benchmark, fully converged results are reported for the zero point energy, which lie within the statistical uncertainty of the reference diffusion Monte Carlo result for this system. Some low-lying vibrationally excited eigenstates are computed by block improved relaxation, illustrating the applicability of the approach to large systems. Benchmark calculations of the linear infrared spectrum are provided, and convergence with increasing size of the time-dependent basis and as a function of the order of the n-mode representation is studied. The calculations presented here make use of recent developments in the parallel version of the MCTDH code, which are briefly discussed. We also show that the infrared spectrum can be computed, to a very good approximation, within D(2d) symmetry, instead of the G(16) symmetry used before, in which the complete rotation of one water molecule with respect to the other is allowed, thus simplifying the dynamical problem.

Parental representations and dimensions of personality: empirical relations and assessment implications.

PubMed

Pincus, A L; Ruiz, M A

1997-04-01

Research on the relations between parental representations, personality traits, and psychopathology was discussed with reference to their integration for clinical personality assessment. Empirical results linking parental representations assessed by the Structural Analysis of Social Behavior and the Five-Factor Model of personality traits in a young adult population supported the position that parental representations significantly relate to adult personality. Individuals whose parental representations were generally affiliative described themselves as less prone to emotional distress (lower neuroticism); more interpersonally oriented and experiencing of positive emotions (higher extraversion); more peaceable and trustworthy (higher agreeableness); and more dutiful, resourceful, and dependable (higher conscientiousness). Parental representations colored by autonomy granting and autonomy taking were related to higher levels of openness to experience but lower levels of conscientiousness and extraversion in self-descriptions. Assessment implications and an integrative assessment strategy were presented along with a clinical case example.

Graphical tensor product reduction scheme for the Lie algebras so(5) = sp(2) , su(3) , and g(2)

NASA Astrophysics Data System (ADS)

Vlasii, N. D.; von Rütte, F.; Wiese, U.-J.

2016-08-01

We develop in detail a graphical tensor product reduction scheme, first described by Antoine and Speiser, for the simple rank 2 Lie algebras so(5) = sp(2) , su(3) , and g(2) . This leads to an efficient practical method to reduce tensor products of irreducible representations into sums of such representations. For this purpose, the 2-dimensional weight diagram of a given representation is placed in a ;landscape; of irreducible representations. We provide both the landscapes and the weight diagrams for a large number of representations for the three simple rank 2 Lie algebras. We also apply the algebraic ;girdle; method, which is much less efficient for calculations by hand for moderately large representations. Computer code for reducing tensor products, based on the graphical method, has been developed as well and is available from the authors upon request.

Two-dimensional beam profiles and one-dimensional projections

NASA Astrophysics Data System (ADS)

Findlay, D. J. S.; Jones, B.; Adams, D. J.

2018-05-01

One-dimensional projections of improved two-dimensional representations of transverse profiles of particle beams are proposed for fitting to data from harp-type monitors measuring beam profiles on particle accelerators. Composite distributions, with tails smoothly matched on to a central (inverted) parabola, are shown to give noticeably better fits than single gaussian and single parabolic distributions to data from harp-type beam profile monitors all along the proton beam transport lines to the two target stations on the ISIS Spallation Neutron Source. Some implications for inferring beam current densities on the beam axis are noted.

Exploration Geophysics

ERIC Educational Resources Information Center

Espey, H. R.

1977-01-01

Describes geophysical techniques such as seismic, gravity, and magnetic surveys of offshare acreage, and land-data gathering from a three-dimensional representation made from closely spaced seismic lines. (MLH)

Mental representation and motor imagery training

PubMed Central

Schack, Thomas; Essig, Kai; Frank, Cornelia; Koester, Dirk

2014-01-01

Research in sports, dance and rehabilitation has shown that basic action concepts (BACs) are fundamental building blocks of mental action representations. BACs are based on chunked body postures related to common functions for realizing action goals. In this paper, we outline issues in research methodology and an experimental method, the structural dimensional analysis of mental representation (SDA-M), to assess action-relevant representational structures that reflect the organization of BACs. The SDA-M reveals a strong relationship between cognitive representation and performance if complex actions are performed. We show how the SDA-M can improve motor imagery training and how it contributes to our understanding of coaching processes. The SDA-M capitalizes on the objective measurement of individual mental movement representations before training and the integration of these results into the motor imagery training. Such motor imagery training based on mental representations (MTMR) has been applied successfully in professional sports such as golf, volleyball, gymnastics, windsurfing, and recently in the rehabilitation of patients who have suffered a stroke. PMID:24904368

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

PubMed

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

2010-06-01

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

Design of a Two Dimensional Planer Pressurized Air Labyrinth Seal Test Rig

DTIC Science & Technology

1993-12-01

identity by block number) Dump Diffuser, Flow Modification, Laser Doppler Velocimeter, Labyrinth Seal , Leakage Prediction, Press --ized air 19 Abstract...reducing this high to low pressure leakage . Figure 1.1 is a two dimensional representation of a 3 dimensional annular labyrinth seal . The object of this... Labyrinth Seal literature, Sneck [2] credits C.A. Parsons with development of the labyrinth seal in concert with Parson’s [31 development of the steam

Color Makes a Difference: Two-Dimensional Object Naming in Literate and Illiterate Subjects

ERIC Educational Resources Information Center

Reis, Alexandra; Faisca, Luis; Ingvar, Martin; Petersson, Karl Magnus

2006-01-01

Previous work has shown that illiterate subjects are better at naming two-dimensional representations of real objects when presented as colored photos as compared to black and white drawings. This raises the question if color or textural details selectively improve object recognition and naming in illiterate compared to literate subjects. In this…

Complementing forest inventory data with information from unmanned aerial vehicle imagery and photogrammetry

Treesearch

Nikolay S. Strigul; Demetrios Gatziolis; Jean F. Liénard; Andre Vogs

2015-01-01

Although a prerequisite for an accurate assessment of tree competition, growth, and morphological plasticity, measurements conducive to three-dimensional (3D) representations of individual trees are seldom part of forest inventory operations. This is in part because until recently our ability to measure the dimensionality, spatial arrangement, and shape of trees and...

Transition density of one-dimensional diffusion with discontinuous drift

NASA Technical Reports Server (NTRS)

Zhang, Weijian

1990-01-01

The transition density of a one-dimensional diffusion process with a discontinuous drift coefficient is studied. A probabilistic representation of the transition density is given, illustrating the close connections between discontinuities of the drift and Brownian local times. In addition, some explicit results are obtained based on the trivariate density of Brownian motion, its occupation, and local times.

A Comparison of Cognitive Teaching Stimuli in a First Grade Classroom.

ERIC Educational Resources Information Center

Sigrest, Christine E.

A study assessed the effectiveness of three cognitive levels of instruction with first graders--three-dimensional (3-D) instruction using real objects, two-dimensional (2-D) instruction using picture representations, and verbal instruction. The study population included 18 first-grade students between the ages of 6 and 8 at a small elementary city…

Children's Schemes for Anticipating the Validity of Nets for Solids

ERIC Educational Resources Information Center

Wright, Vince; Smith, Ken

2017-01-01

There is growing acknowledgement of the importance of spatial abilities to student achievement across a broad range of domains and disciplines. Nets are one way to connect three-dimensional shapes and their two-dimensional representations and are a common focus of geometry curricula. Thirty-four students at year 6 (upper primary school) were…

Spinning particle and gauge theories as integrability conditions

NASA Astrophysics Data System (ADS)

Eisenberg, Yeshayahu

1992-02-01

Starting from a new four dimensional spinning point particle we obtain new representations of the standard four dimensional gauge field equations in terms of a generalized space (Minkowski + light cone). In terms of this new formulation we define linear systems whose integrability conditions imply the massive Dirac-Maxwell and the Yang-Mills equations. Research supported by the Rothschild Fellowship.

Maximum-entropy reconstruction method for moment-based solution of the Boltzmann equation

NASA Astrophysics Data System (ADS)

Summy, Dustin; Pullin, Dale

2013-11-01

We describe a method for a moment-based solution of the Boltzmann equation. This starts with moment equations for a 10 + 9 N , N = 0 , 1 , 2 . . . -moment representation. The partial-differential equations (PDEs) for these moments are unclosed, containing both higher-order moments and molecular-collision terms. These are evaluated using a maximum-entropy construction of the velocity distribution function f (c , x , t) , using the known moments, within a finite-box domain of single-particle-velocity (c) space. Use of a finite-domain alleviates known problems (Junk and Unterreiter, Continuum Mech. Thermodyn., 2002) concerning existence and uniqueness of the reconstruction. Unclosed moments are evaluated with quadrature while collision terms are calculated using a Monte-Carlo method. This allows integration of the moment PDEs in time. Illustrative examples will include zero-space- dimensional relaxation of f (c , t) from a Mott-Smith-like initial condition toward equilibrium and one-space dimensional, finite Knudsen number, planar Couette flow. Comparison with results using the direct-simulation Monte-Carlo method will be presented.

Competition in high dimensional spaces using a sparse approximation of neural fields.

PubMed

Quinton, Jean-Charles; Girau, Bernard; Lefort, Mathieu

2011-01-01

The Continuum Neural Field Theory implements competition within topologically organized neural networks with lateral inhibitory connections. However, due to the polynomial complexity of matrix-based implementations, updating dense representations of the activity becomes computationally intractable when an adaptive resolution or an arbitrary number of input dimensions is required. This paper proposes an alternative to self-organizing maps with a sparse implementation based on Gaussian mixture models, promoting a trade-off in redundancy for higher computational efficiency and alleviating constraints on the underlying substrate.This version reproduces the emergent attentional properties of the original equations, by directly applying them within a continuous approximation of a high dimensional neural field. The model is compatible with preprocessed sensory flows but can also be interfaced with artificial systems. This is particularly important for sensorimotor systems, where decisions and motor actions must be taken and updated in real-time. Preliminary tests are performed on a reactive color tracking application, using spatially distributed color features.

Instantons, quivers and noncommutative Donaldson-Thomas theory

NASA Astrophysics Data System (ADS)

Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.

2011-12-01

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.

Representing and comparing protein structures as paths in three-dimensional space

PubMed Central

Zhi, Degui; Krishna, S Sri; Cao, Haibo; Pevzner, Pavel; Godzik, Adam

2006-01-01

Background Most existing formulations of protein structure comparison are based on detailed atomic level descriptions of protein structures and bypass potential insights that arise from a higher-level abstraction. Results We propose a structure comparison approach based on a simplified representation of proteins that describes its three-dimensional path by local curvature along the generalized backbone of the polypeptide. We have implemented a dynamic programming procedure that aligns curvatures of proteins by optimizing a defined sum turning angle deviation measure. Conclusion Although our procedure does not directly optimize global structural similarity as measured by RMSD, our benchmarking results indicate that it can surprisingly well recover the structural similarity defined by structure classification databases and traditional structure alignment programs. In addition, our program can recognize similarities between structures with extensive conformation changes that are beyond the ability of traditional structure alignment programs. We demonstrate the applications of procedure to several contexts of structure comparison. An implementation of our procedure, CURVE, is available as a public webserver. PMID:17052359

Representing high-dimensional data to intelligent prostheses and other wearable assistive robots: A first comparison of tile coding and selective Kanerva coding.

PubMed

Travnik, Jaden B; Pilarski, Patrick M

2017-07-01

Prosthetic devices have advanced in their capabilities and in the number and type of sensors included in their design. As the space of sensorimotor data available to a conventional or machine learning prosthetic control system increases in dimensionality and complexity, it becomes increasingly important that this data be represented in a useful and computationally efficient way. Well structured sensory data allows prosthetic control systems to make informed, appropriate control decisions. In this study, we explore the impact that increased sensorimotor information has on current machine learning prosthetic control approaches. Specifically, we examine the effect that high-dimensional sensory data has on the computation time and prediction performance of a true-online temporal-difference learning prediction method as embedded within a resource-limited upper-limb prosthesis control system. We present results comparing tile coding, the dominant linear representation for real-time prosthetic machine learning, with a newly proposed modification to Kanerva coding that we call selective Kanerva coding. In addition to showing promising results for selective Kanerva coding, our results confirm potential limitations to tile coding as the number of sensory input dimensions increases. To our knowledge, this study is the first to explicitly examine representations for realtime machine learning prosthetic devices in general terms. This work therefore provides an important step towards forming an efficient prosthesis-eye view of the world, wherein prompt and accurate representations of high-dimensional data may be provided to machine learning control systems within artificial limbs and other assistive rehabilitation technologies.

New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials

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

Marquette, Ian; Quesne, Christiane

2013-04-15

In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape invariant. In this paper, we construct from Hermite and Laguerre EOP and their related quantum systems new 2D superintegrable Hamiltonians with higher-order integrals of motion and the polynomial algebras generated by their integrals of motion. We obtain the finite-dimensional unitary representations of the polynomial algebras and the corresponding energy spectrum. We also point out a new type of degeneracies of the energy levels of these systems that is associated with holes in sequencesmore » of EOP.« less

Parallel log structured file system collective buffering to achieve a compact representation of scientific and/or dimensional data

DOEpatents

Grider, Gary A.; Poole, Stephen W.

2015-09-01

Collective buffering and data pattern solutions are provided for storage, retrieval, and/or analysis of data in a collective parallel processing environment. For example, a method can be provided for data storage in a collective parallel processing environment. The method comprises receiving data to be written for a plurality of collective processes within a collective parallel processing environment, extracting a data pattern for the data to be written for the plurality of collective processes, generating a representation describing the data pattern, and saving the data and the representation.

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

NASA Astrophysics Data System (ADS)

Sakuraba, Takao

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

Quaternionic (super) twistors extensions and general superspaces

NASA Astrophysics Data System (ADS)

Cirilo-Lombardo, Diego Julio; Pervushin, Victor N.

2017-09-01

In a attempt to treat a supergravity as a tensor representation, the four-dimensional N-extended quaternionic superspaces are constructed from the (diffeomorphyc) graded extension of the ordinary Penrose-twistor formulation, performed in a previous work of the authors [D. J. Cirilo-Lombardo and V. N. Pervushin, Int. J. Geom. Methods Mod. Phys., doi: http://dx.doi.org/10.1142/S0219887816501139.], with N = p + k. These quaternionic superspaces have 4 + k(N - k) even-quaternionic coordinates and 4N odd-quaternionic coordinates, where each coordinate is a quaternion composed by four ℂ-fields (bosons and fermions respectively). The fields content as the dimensionality (even and odd sectors) of these superspaces are given and exemplified by selected physical cases. In this case, the number of fields of the supergravity is determined by the number of components of the tensor representation of the four-dimensional N-extended quaternionic superspaces. The role of tensorial central charges for any N even USp(N) = Sp(N, ℍℂ) ∩ U(N, ℍℂ) is elucidated from this theoretical context.

Numerical Zooming Between a NPSS Engine System Simulation and a One-Dimensional High Compressor Analysis Code

NASA Technical Reports Server (NTRS)

Follen, Gregory; auBuchon, M.

2000-01-01

Within NASA's High Performance Computing and Communication (HPCC) program, NASA Glenn Research Center is developing an environment for the analysis/design of aircraft engines called the Numerical Propulsion System Simulation (NPSS). NPSS focuses on the integration of multiple disciplines such as aerodynamics, structures, and heat transfer along with the concept of numerical zooming between zero-dimensional to one-, two-, and three-dimensional component engine codes. In addition, the NPSS is refining the computing and communication technologies necessary to capture complex physical processes in a timely and cost-effective manner. The vision for NPSS is to create a "numerical test cell" enabling full engine simulations overnight on cost-effective computing platforms. Of the different technology areas that contribute to the development of the NPSS Environment, the subject of this paper is a discussion on numerical zooming between a NPSS engine simulation and higher fidelity representations of the engine components (fan, compressor, burner, turbines, etc.). What follows is a description of successfully zooming one-dimensional (row-by-row) high-pressure compressor analysis results back to a zero-dimensional NPSS engine simulation and a discussion of the results illustrated using an advanced data visualization tool. This type of high fidelity system-level analysis, made possible by the zooming capability of the NPSS, will greatly improve the capability of the engine system simulation and increase the level of virtual test conducted prior to committing the design to hardware.

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

On representations of the filiform Lie superalgebra Lm,n

NASA Astrophysics Data System (ADS)

Wang, Qi; Chen, Hongjia; Liu, Wende

2015-11-01

In this paper, we study the representations for the filiform Lie superalgebras Lm,n, a particular class of nilpotent Lie superalgebras. We determine the minimal dimension of a faithful module over Lm,n using the theory of linear algebra. In addition, using the method of Feingold and Frenkel (1985), we construct some finite and infinite dimensional modules over Lm,n on the Grassmann algebra and the mixed Clifford-Weyl algebra.

Application of time series discretization using evolutionary programming for classification of precancerous cervical lesions.

PubMed

Acosta-Mesa, Héctor-Gabriel; Rechy-Ramírez, Fernando; Mezura-Montes, Efrén; Cruz-Ramírez, Nicandro; Hernández Jiménez, Rodolfo

2014-06-01

In this work, we present a novel application of time series discretization using evolutionary programming for the classification of precancerous cervical lesions. The approach optimizes the number of intervals in which the length and amplitude of the time series should be compressed, preserving the important information for classification purposes. Using evolutionary programming, the search for a good discretization scheme is guided by a cost function which considers three criteria: the entropy regarding the classification, the complexity measured as the number of different strings needed to represent the complete data set, and the compression rate assessed as the length of the discrete representation. This discretization approach is evaluated using a time series data based on temporal patterns observed during a classical test used in cervical cancer detection; the classification accuracy reached by our method is compared with the well-known times series discretization algorithm SAX and the dimensionality reduction method PCA. Statistical analysis of the classification accuracy shows that the discrete representation is as efficient as the complete raw representation for the present application, reducing the dimensionality of the time series length by 97%. This representation is also very competitive in terms of classification accuracy when compared with similar approaches. Copyright © 2014 Elsevier Inc. All rights reserved.

A 2-categorical state sum model

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

Baratin, Aristide, E-mail: abaratin@uwaterloo.ca; Freidel, Laurent, E-mail: lfreidel@perimeterinstitute.ca

It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewedmore » a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027–2060 (2007)] which was shown to lead after gauge-fixing to Korepanov’s invariant of 4-manifolds.« less

Virtual Ligand Screening Using PL-PatchSurfer2, a Molecular Surface-Based Protein-Ligand Docking Method.

PubMed

Shin, Woong-Hee; Kihara, Daisuke

2018-01-01

Virtual screening is a computational technique for predicting a potent binding compound for a receptor protein from a ligand library. It has been a widely used in the drug discovery field to reduce the efforts of medicinal chemists to find hit compounds by experiments.Here, we introduce our novel structure-based virtual screening program, PL-PatchSurfer, which uses molecular surface representation with the three-dimensional Zernike descriptors, which is an effective mathematical representation for identifying physicochemical complementarities between local surfaces of a target protein and a ligand. The advantage of the surface-patch description is its tolerance on a receptor and compound structure variation. PL-PatchSurfer2 achieves higher accuracy on apo form and computationally modeled receptor structures than conventional structure-based virtual screening programs. Thus, PL-PatchSurfer2 opens up an opportunity for targets that do not have their crystal structures. The program is provided as a stand-alone program at http://kiharalab.org/plps2 . We also provide files for two ligand libraries, ChEMBL and ZINC Drug-like.

Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: Analytical approximation

NASA Astrophysics Data System (ADS)

Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

2017-09-01

Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. Lü, A. Perkins, C. Pope, and K. Stelle [Phys. Rev. Lett. 114, 171601 (2015), 10.1103/PhysRevLett.114.171601] found a numerical solution describing a spherically symmetric non-Schwarzschild asymptotically flat black hole in Einstein gravity with added higher derivative terms. Using the general and quickly convergent parametrization in terms of the continued fractions, we represent this numerical solution in the analytical form, which is accurate not only near the event horizon or far from the black hole, but in the whole space. Thereby, the obtained analytical form of the metric allows one to study easily all the further properties of the black hole, such as thermodynamics, Hawking radiation, particle motion, accretion, perturbations, stability, quasinormal spectrum, etc. Thus, the found analytical approximate representation can serve in the same way as an exact solution.

Discovering motion primitives for unsupervised grouping and one-shot learning of human actions, gestures, and expressions.

PubMed

Yang, Yang; Saleemi, Imran; Shah, Mubarak

2013-07-01

This paper proposes a novel representation of articulated human actions and gestures and facial expressions. The main goals of the proposed approach are: 1) to enable recognition using very few examples, i.e., one or k-shot learning, and 2) meaningful organization of unlabeled datasets by unsupervised clustering. Our proposed representation is obtained by automatically discovering high-level subactions or motion primitives, by hierarchical clustering of observed optical flow in four-dimensional, spatial, and motion flow space. The completely unsupervised proposed method, in contrast to state-of-the-art representations like bag of video words, provides a meaningful representation conducive to visual interpretation and textual labeling. Each primitive action depicts an atomic subaction, like directional motion of limb or torso, and is represented by a mixture of four-dimensional Gaussian distributions. For one--shot and k-shot learning, the sequence of primitive labels discovered in a test video are labeled using KL divergence, and can then be represented as a string and matched against similar strings of training videos. The same sequence can also be collapsed into a histogram of primitives or be used to learn a Hidden Markov model to represent classes. We have performed extensive experiments on recognition by one and k-shot learning as well as unsupervised action clustering on six human actions and gesture datasets, a composite dataset, and a database of facial expressions. These experiments confirm the validity and discriminative nature of the proposed representation.

On the three-dimensional instability of strained vortices

NASA Technical Reports Server (NTRS)

Waleffe, Fabian

1990-01-01

The three-dimensional (3-D) instability of a two-dimensional (2-D) flow with elliptical streamlines has been proposed as a generic mechanism for the breakdown of many 2-D flows. A physical interpretation for the mechanism is presented together with an analytical treatment of the problem. It is shown that the stability of an elliptical flow is governed by an Ince equation. An analytical representation for a localized solution is given and establishes a direct link with previous computations and experiments.

Graphical classification of DNA sequences of HLA alleles by deep learning.

PubMed

Miyake, Jun; Kaneshita, Yuhei; Asatani, Satoshi; Tagawa, Seiichi; Niioka, Hirohiko; Hirano, Takashi

2018-04-01

Alleles of human leukocyte antigen (HLA)-A DNAs are classified and expressed graphically by using artificial intelligence "Deep Learning (Stacked autoencoder)". Nucleotide sequence data corresponding to the length of 822 bp, collected from the Immuno Polymorphism Database, were compressed to 2-dimensional representation and were plotted. Profiles of the two-dimensional plots indicate that the alleles can be classified as clusters are formed. The two-dimensional plot of HLA-A DNAs gives a clear outlook for characterizing the various alleles.

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.

Multiview alignment hashing for efficient image search.

PubMed

Liu, Li; Yu, Mengyang; Shao, Ling

2015-03-01

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

Transfer of Learning between 2D and 3D Sources during Infancy: Informing Theory and Practice

ERIC Educational Resources Information Center

Barr, Rachel

2010-01-01

The ability to transfer learning across contexts is an adaptive skill that develops rapidly during early childhood. Learning from television is a specific instance of transfer of learning between a two-dimensional (2D) representation and a three-dimensional (3D) object. Understanding the conditions under which young children might accomplish this…

A Prototype Digital Library for 3D Collections: Tools To Capture, Model, Analyze, and Query Complex 3D Data.

ERIC Educational Resources Information Center

Rowe, Jeremy; Razdan, Anshuman

The Partnership for Research in Spatial Modeling (PRISM) project at Arizona State University (ASU) developed modeling and analytic tools to respond to the limitations of two-dimensional (2D) data representations perceived by affiliated discipline scientists, and to take advantage of the enhanced capabilities of three-dimensional (3D) data that…

Symposium on Numerical and Physical Aspects of Aerodynamic Flows, 4th, California State University, Long Beach, Jan. 16-19, 1989, Proceedings

NASA Technical Reports Server (NTRS)

1989-01-01

Papers are presented on the calculation of flows of relevance to aircraft, ships, and missiles, with emphasis on the solution of two-dimensional unsteady and three-dimensional steady equations. Papers are also presented describing experimental work and the representation of the onset of transition from laminar to turbulent flow.

Using Dynamic Mathematics Software to Teach One-Variable Inequalities by the View of Semiotic Registers

ERIC Educational Resources Information Center

Kabaca, Tolga

2013-01-01

Solution set of any inequality or compound inequality, which has one-variable, lies in the real line which is one dimensional. So a difficulty appears when computer assisted graphical representation is intended to use for teaching these topics. Sketching a one-dimensional graph by using computer software is not a straightforward work. In this…

PubMed Central

Baum, S.; Sillem, M.; Ney, J. T.; Baum, A.; Friedrich, M.; Radosa, J.; Kramer, K. M.; Gronwald, B.; Gottschling, S.; Solomayer, E. F.; Rody, A.; Joukhadar, R.

2017-01-01

Introduction Minimally invasive operative techniques are being used increasingly in gynaecological surgery. The expansion of the laparoscopic operation spectrum is in part the result of improved imaging. This study investigates the practical advantages of using 3D cameras in routine surgical practice. Materials and Methods Two different 3-dimensional camera systems were compared with a 2-dimensional HD system; the operating surgeonʼs experiences were documented immediately postoperatively using a questionnaire. Results Significant advantages were reported for suturing and cutting of anatomical structures when using the 3D compared to 2D camera systems. There was only a slight advantage for coagulating. The use of 3D cameras significantly improved the general operative visibility and in particular the representation of spacial depth compared to 2-dimensional images. There was not a significant advantage for image width. Depiction of adhesions and retroperitoneal neural structures was significantly improved by the stereoscopic cameras, though this did not apply to blood vessels, ureter, uterus or ovaries. Conclusion 3-dimensional cameras were particularly advantageous for the depiction of fine anatomical structures due to improved spacial depth representation compared to 2D systems. 3D cameras provide the operating surgeon with a monitor image that more closely resembles actual anatomy, thus simplifying laparoscopic procedures. PMID:28190888

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.

Categorical and dimensional approaches in the evaluation of the relationship between attachment and personality disorders: an empirical study.

PubMed

Chiesa, Marco; Cirasola, Antonella; Williams, Riccardo; Nassisi, Valentina; Fonagy, Peter

2017-04-01

Although several studies have highlighted the relationship between attachment states of mind and personality disorders, their findings have not been consistent, possibly due to the application of the traditional taxonomic classification model of attachment. A more recently developed dimensional classification of attachment representations, including more specific aspects of trauma-related representations, may have advantages. In this study, we compare specific associations and predictive power of the categorical attachment and dimensional models applied to 230 Adult Attachment Interview transcripts obtained from personality disordered and nonpsychiatric subjects. We also investigate the role that current levels of psychiatric distress may have in the prediction of PD. The results showed that both models predict the presence of PD, with the dimensional approach doing better in discriminating overall diagnosis of PD. However, both models are less helpful in discriminating specific PD diagnostic subtypes. Current psychiatric distress was found to be the most consistent predictor of PD capturing a large share of the variance and obscuring the role played by attachment variables. The results suggest that attachment parameters correlate with the presence of PD alone and have no specific associations with particular PD subtypes when current psychiatric distress is taken into account.

Part A: Investigations of the Synthesis of Pyrazinochlorins and Other Porphyrin Derivatives. Part B: investigations of Student Translation Between 2-D/3-D Representations of Molecules

NASA Astrophysics Data System (ADS)

Dean, Michelle L.

This dissertation will be composed of two parts. The first part was completed under the direction of Dr. Christian Bruckner and outlines the synthesis of porphyrins and related derivatives. It explores specifically the synthesis of pyrazinoporphyrin, a pyrrole-modified porphyrin, the use of microwaves for porphyrin synthesis, and the synthesis of a novel building block for use in an expanded porphyrin structure. Lastly, this part will describe a laboratory experiment, suitable for an organic chemistry course, which investigates the photophysical properties of porphyrins using brown eggs as a source of protoporphyrin IX. The second part, under the advisement of Dr. Tyson Miller, will detail research conducted on students' ability to translate between two-dimensional and three-dimensional representations of molecules. Using the Grounded Theory and a formal interview it was investigated what errors students make as they translate from a two-dimensional drawing to a three-dimensional model, and visa versa. This part also seeks to gain an understanding, through the use of phenomenography what was factors contribute to cognitive overload when drawing chiral centers.

Exploring nonlinear feature space dimension reduction and data representation in breast Cadx with Laplacian eigenmaps and t-SNE.

PubMed

Jamieson, Andrew R; Giger, Maryellen L; Drukker, Karen; Li, Hui; Yuan, Yading; Bhooshan, Neha

2010-01-01

In this preliminary study, recently developed unsupervised nonlinear dimension reduction (DR) and data representation techniques were applied to computer-extracted breast lesion feature spaces across three separate imaging modalities: Ultrasound (U.S.) with 1126 cases, dynamic contrast enhanced magnetic resonance imaging with 356 cases, and full-field digital mammography with 245 cases. Two methods for nonlinear DR were explored: Laplacian eigenmaps [M. Belkin and P. Niyogi, "Laplacian eigenmaps for dimensionality reduction and data representation," Neural Comput. 15, 1373-1396 (2003)] and t-distributed stochastic neighbor embedding (t-SNE) [L. van der Maaten and G. Hinton, "Visualizing data using t-SNE," J. Mach. Learn. Res. 9, 2579-2605 (2008)]. These methods attempt to map originally high dimensional feature spaces to more human interpretable lower dimensional spaces while preserving both local and global information. The properties of these methods as applied to breast computer-aided diagnosis (CADx) were evaluated in the context of malignancy classification performance as well as in the visual inspection of the sparseness within the two-dimensional and three-dimensional mappings. Classification performance was estimated by using the reduced dimension mapped feature output as input into both linear and nonlinear classifiers: Markov chain Monte Carlo based Bayesian artificial neural network (MCMC-BANN) and linear discriminant analysis. The new techniques were compared to previously developed breast CADx methodologies, including automatic relevance determination and linear stepwise (LSW) feature selection, as well as a linear DR method based on principal component analysis. Using ROC analysis and 0.632+bootstrap validation, 95% empirical confidence intervals were computed for the each classifier's AUC performance. In the large U.S. data set, sample high performance results include, AUC0.632+ = 0.88 with 95% empirical bootstrap interval [0.787;0.895] for 13 ARD selected features and AUC0.632+ = 0.87 with interval [0.817;0.906] for four LSW selected features compared to 4D t-SNE mapping (from the original 81D feature space) giving AUC0.632+ = 0.90 with interval [0.847;0.919], all using the MCMC-BANN. Preliminary results appear to indicate capability for the new methods to match or exceed classification performance of current advanced breast lesion CADx algorithms. While not appropriate as a complete replacement of feature selection in CADx problems, DR techniques offer a complementary approach, which can aid elucidation of additional properties associated with the data. Specifically, the new techniques were shown to possess the added benefit of delivering sparse lower dimensional representations for visual interpretation, revealing intricate data structure of the feature space.

Evaluating mental workload of two-dimensional and three-dimensional visualization for anatomical structure localization.

PubMed

Foo, Jung-Leng; Martinez-Escobar, Marisol; Juhnke, Bethany; Cassidy, Keely; Hisley, Kenneth; Lobe, Thom; Winer, Eliot

2013-01-01

Visualization of medical data in three-dimensional (3D) or two-dimensional (2D) views is a complex area of research. In many fields 3D views are used to understand the shape of an object, and 2D views are used to understand spatial relationships. It is unclear how 2D/3D views play a role in the medical field. Using 3D views can potentially decrease the learning curve experienced with traditional 2D views by providing a whole representation of the patient's anatomy. However, there are challenges with 3D views compared with 2D. This current study expands on a previous study to evaluate the mental workload associated with both 2D and 3D views. Twenty-five first-year medical students were asked to localize three anatomical structures--gallbladder, celiac trunk, and superior mesenteric artery--in either 2D or 3D environments. Accuracy and time were taken as the objective measures for mental workload. The NASA Task Load Index (NASA-TLX) was used as a subjective measure for mental workload. Results showed that participants viewing in 3D had higher localization accuracy and a lower subjective measure of mental workload, specifically, the mental demand component of the NASA-TLX. Results from this study may prove useful for designing curricula in anatomy education and improving training procedures for surgeons.

Neural correlates of context-independent and context-dependent self-knowledge.

PubMed

Martial, Charlotte; Stawarczyk, David; D'Argembeau, Arnaud

2018-05-25

The self-concept consists of both a general (context-independent) self-representation and a set of context-dependent selves that represent personal attributes in particular contexts (e.g., as a student, as a daughter). To date, however, neuroimaging studies have focused on general self-representations, such that little is known about the neural correlates of context-dependent self-knowledge. The present study aimed at investigating this issue by examining the neural correlates of both kinds of self-knowledge. Participants judged the extent to which trait adjectives described their own personality or the personality of a close friend, either in a specific context (i.e., as a student) or in general. We found that both kinds of self-judgments were associated with common activation in the medial prefrontal cortex (MPFC), as compared to judgments about others. Interestingly, however, there were also notable differences between self-judgments, with context-independent judgments being associated with higher activity in the MPFC, whereas context-dependent judgments were associated with greater activation in posterior brain regions (i.e., the posterior cingulate/retrosplenial cortex). These findings show that context-independent and context-dependent self-referential judgments recruit both common and distinct brain regions, thereby supporting the view that the self-concept is a multi-dimensional knowledge structure that includes a general self-representation and a set of context-specific selves. Copyright © 2018 Elsevier Inc. All rights reserved.

Generalized -deformed correlation functions as spectral functions of hyperbolic geometry

NASA Astrophysics Data System (ADS)

Bonora, L.; Bytsenko, A. A.; Guimarães, M. E. X.

2014-08-01

We analyze the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite-dimensional Lie algebras, MacMahon and Ruelle functions. By definition p-dimensional MacMahon function, with , is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c = 1 CFT, and, as such, they can be generalized to . With some abuse of language we call the latter amplitudes generalized MacMahon functions. In this paper we show that generalized p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of three-dimensional hyperbolic geometry.

Functional specializations in human cerebral cortex analyzed using the Visible Man surface-based atlas

NASA Technical Reports Server (NTRS)

Drury, H. A.; Van Essen, D. C.

1997-01-01

We used surface-based representations to analyze functional specializations in the human cerebral cortex. A computerized reconstruction of the cortical surface of the Visible Man digital atlas was generated and transformed to the Talairach coordinate system. This surface was also flattened and used to establish a surface-based coordinate system that respects the topology of the cortical sheet. The linkage between two-dimensional and three-dimensional representations allows the locations of published neuroimaging activation foci to be stereotaxically projected onto the Visible Man cortical flat map. An analysis of two activation studies related to the hearing and reading of music and of words illustrates how this approach permits the systematic estimation of the degree of functional segregation and of potential functional overlap for different aspects of sensory processing.

A Short Note on the Scaling Function Constant Problem in the Two-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Bothner, Thomas

2018-02-01

We provide a simple derivation of the constant factor in the short-distance asymptotics of the tau-function associated with the 2-point function of the two-dimensional Ising model. This factor was first computed by Tracy (Commun Math Phys 142:297-311, 1991) via an exponential series expansion of the correlation function. Further simplifications in the analysis are due to Tracy and Widom (Commun Math Phys 190:697-721, 1998) using Fredholm determinant representations of the correlation function and Wiener-Hopf approximation results for the underlying resolvent operator. Our method relies on an action integral representation of the tau-function and asymptotic results for the underlying Painlevé-III transcendent from McCoy et al. (J Math Phys 18:1058-1092, 1977).

Support Vector Machine-Based Endmember Extraction

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

Filippi, Anthony M; Archibald, Richard K

Introduced in this paper is the utilization of Support Vector Machines (SVMs) to automatically perform endmember extraction from hyperspectral data. The strengths of SVM are exploited to provide a fast and accurate calculated representation of high-dimensional data sets that may consist of multiple distributions. Once this representation is computed, the number of distributions can be determined without prior knowledge. For each distribution, an optimal transform can be determined that preserves informational content while reducing the data dimensionality, and hence, the computational cost. Finally, endmember extraction for the whole data set is accomplished. Results indicate that this Support Vector Machine-Based Endmembermore » Extraction (SVM-BEE) algorithm has the capability of autonomously determining endmembers from multiple clusters with computational speed and accuracy, while maintaining a robust tolerance to noise.« less

Automatic segmentation of brain MRI in high-dimensional local and non-local feature space based on sparse representation.

PubMed

Khalilzadeh, Mohammad Mahdi; Fatemizadeh, Emad; Behnam, Hamid

2013-06-01

Automatic extraction of the varying regions of magnetic resonance images is required as a prior step in a diagnostic intelligent system. The sparsest representation and high-dimensional feature are provided based on learned dictionary. The classification is done by employing the technique that computes the reconstruction error locally and non-locally of each pixel. The acquired results from the real and simulated images are superior to the best MRI segmentation method with regard to the stability advantages. In addition, it is segmented exactly through a formula taken from the distance and sparse factors. Also, it is done automatically taking sparse factor in unsupervised clustering methods whose results have been improved. Copyright © 2013 Elsevier Inc. All rights reserved.

SA-Search: a web tool for protein structure mining based on a Structural Alphabet

PubMed Central

Guyon, Frédéric; Camproux, Anne-Claude; Hochez, Joëlle; Tufféry, Pierre

2004-01-01

SA-Search is a web tool that can be used to mine for protein structures and extract structural similarities. It is based on a hidden Markov model derived Structural Alphabet (SA) that allows the compression of three-dimensional (3D) protein conformations into a one-dimensional (1D) representation using a limited number of prototype conformations. Using such a representation, classical methods developed for amino acid sequences can be employed. Currently, SA-Search permits the performance of fast 3D similarity searches such as the extraction of exact words using a suffix tree approach, and the search for fuzzy words viewed as a simple 1D sequence alignment problem. SA-Search is available at http://bioserv.rpbs.jussieu.fr/cgi-bin/SA-Search. PMID:15215446

SA-Search: a web tool for protein structure mining based on a Structural Alphabet.

PubMed

Guyon, Frédéric; Camproux, Anne-Claude; Hochez, Joëlle; Tufféry, Pierre

2004-07-01

SA-Search is a web tool that can be used to mine for protein structures and extract structural similarities. It is based on a hidden Markov model derived Structural Alphabet (SA) that allows the compression of three-dimensional (3D) protein conformations into a one-dimensional (1D) representation using a limited number of prototype conformations. Using such a representation, classical methods developed for amino acid sequences can be employed. Currently, SA-Search permits the performance of fast 3D similarity searches such as the extraction of exact words using a suffix tree approach, and the search for fuzzy words viewed as a simple 1D sequence alignment problem. SA-Search is available at http://bioserv.rpbs.jussieu.fr/cgi-bin/SA-Search.

Two-year-olds' understanding of self-symbols.

PubMed

Herold, Katherine; Akhtar, Nameera

2014-09-01

This study investigated 48 2.5-year-olds' ability to map from their own body to a two-dimensional self-representation and also examined relations between parents' talk about body representations and their children's understanding of self-symbols. Children participated in two dual-representation tasks in which they were asked to match body parts between a symbol and its referent. In one task, they used a self-symbol and in the other they used a symbol for a doll. Participants were also read a book about body parts by a parent. As a group, children found the self-symbol task more difficult than the doll-task; however, those whose parents explicitly pointed out the relation between their children's bodies and the symbols in the book performed better on the self-symbol task. The findings demonstrate that 2-year-old children have difficulty comprehending a self-symbol, even when it is two-dimensional and approximately the same size as them, and suggest that parents' talk about self-symbols may facilitate their understanding. © 2014 The British Psychological Society.

Appearance-based representative samples refining method for palmprint recognition

NASA Astrophysics Data System (ADS)

Wen, Jiajun; Chen, Yan

2012-07-01

The sparse representation can deal with the lack of sample problem due to utilizing of all the training samples. However, the discrimination ability will degrade when more training samples are used for representation. We propose a novel appearance-based palmprint recognition method. We aim to find a compromise between the discrimination ability and the lack of sample problem so as to obtain a proper representation scheme. Under the assumption that the test sample can be well represented by a linear combination of a certain number of training samples, we first select the representative training samples according to the contributions of the samples. Then we further refine the training samples by an iteration procedure, excluding the training sample with the least contribution to the test sample for each time. Experiments on PolyU multispectral palmprint database and two-dimensional and three-dimensional palmprint database show that the proposed method outperforms the conventional appearance-based palmprint recognition methods. Moreover, we also explore and find out the principle of the usage for the key parameters in the proposed algorithm, which facilitates to obtain high-recognition accuracy.

Face recognition from unconstrained three-dimensional face images using multitask sparse representation

NASA Astrophysics Data System (ADS)

Bentaieb, Samia; Ouamri, Abdelaziz; Nait-Ali, Amine; Keche, Mokhtar

2018-01-01

We propose and evaluate a three-dimensional (3D) face recognition approach that applies the speeded up robust feature (SURF) algorithm to the depth representation of shape index map, under real-world conditions, using only a single gallery sample for each subject. First, the 3D scans are preprocessed, then SURF is applied on the shape index map to find interest points and their descriptors. Each 3D face scan is represented by keypoints descriptors, and a large dictionary is built from all the gallery descriptors. At the recognition step, descriptors of a probe face scan are sparsely represented by the dictionary. A multitask sparse representation classification is used to determine the identity of each probe face. The feasibility of the approach that uses the SURF algorithm on the shape index map for face identification/authentication is checked through an experimental investigation conducted on Bosphorus, University of Milano Bicocca, and CASIA 3D datasets. It achieves an overall rank one recognition rate of 97.75%, 80.85%, and 95.12%, respectively, on these datasets.

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.

BEYOND THE DYAD: THE RELATIONSHIP BETWEEN PRESCHOOLERS' ATTACHMENT REPRESENTATIONS AND FAMILY TRIADIC INTERACTIONS.

PubMed

C, Francisca Pérez; Moessner, Markus; A, María Pía Santelices

2017-03-01

This study examines the relationship between triadic family interactions and preschoolers' attachment representations, or internal working models (IWMs), from a qualitative and dimensional perspective. Individual, relational, and sociocultural variables were evaluated using two different samples. The results showed that triadic family interactions were linked to preschoolers' attachment security levels in both groups, indicating the reliability of the proposed model. © 2017 Michigan Association for Infant Mental Health.

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Phylogenetic tree construction based on 2D graphical representation

NASA Astrophysics Data System (ADS)

Liao, Bo; Shan, Xinzhou; Zhu, Wen; Li, Renfa

2006-04-01

A new approach based on the two-dimensional (2D) graphical representation of the whole genome sequence [Bo Liao, Chem. Phys. Lett., 401(2005) 196.] is proposed to analyze the phylogenetic relationships of genomes. The evolutionary distances are obtained through measuring the differences among the 2D curves. The fuzzy theory is used to construct phylogenetic tree. The phylogenetic relationships of H5N1 avian influenza virus illustrate the utility of our approach.

The importance of spatial ability and mental models in learning anatomy

NASA Astrophysics Data System (ADS)

Chatterjee, Allison K.

As a foundational course in medical education, gross anatomy serves to orient medical and veterinary students to the complex three-dimensional nature of the structures within the body. Understanding such spatial relationships is both fundamental and crucial for achievement in gross anatomy courses, and is essential for success as a practicing professional. Many things contribute to learning spatial relationships; this project focuses on a few key elements: (1) the type of multimedia resources, particularly computer-aided instructional (CAI) resources, medical students used to study and learn; (2) the influence of spatial ability on medical and veterinary students' gross anatomy grades and their mental models; and (3) how medical and veterinary students think about anatomy and describe the features of their mental models to represent what they know about anatomical structures. The use of computer-aided instruction (CAI) by gross anatomy students at Indiana University School of Medicine (IUSM) was assessed through a questionnaire distributed to the regional centers of the IUSM. Students reported using internet browsing, PowerPoint presentation software, and email on a daily bases to study gross anatomy. This study reveals that first-year medical students at the IUSM make limited use of CAI to study gross anatomy. Such studies emphasize the importance of examining students' use of CAI to study gross anatomy prior to development and integration of electronic media into the curriculum and they may be important in future decisions regarding the development of alternative learning resources. In order to determine how students think about anatomical relationships and describe the features of their mental models, personal interviews were conducted with select students based on students' ROT scores. Five typologies of the characteristics of students' mental models were identified and described: spatial thinking, kinesthetic approach, identification of anatomical structures, problem solving strategies, and study methods. Students with different levels of spatial ability visualize and think about anatomy in qualitatively different ways, which is reflected by the features of their mental models. Low spatial ability students thought about and used two-dimensional images from the textbook. They possessed basic two-dimensional models of anatomical structures; they placed emphasis on diagrams and drawings in their studies; and they re-read anatomical problems many times before answering. High spatial ability students thought fully in three-dimensional and imagined rotation and movement of the structures; they made use of many types of images and text as they studied and solved problems. They possessed elaborate three-dimensional models of anatomical structures which they were able to manipulate to solve problems; and they integrated diagrams, drawings, and written text in their studies. Middle spatial ability students were a mix between both low and high spatial ability students. They imagined two-dimensional images popping out of the flat paper to become more three-dimensional, but still relied on drawings and diagrams. Additionally, high spatial ability students used a higher proportion of anatomical terminology than low spatial ability or middle spatial ability students. This provides additional support to the premise that high spatial students' mental models are a complex mixture of imagistic representations and propositional representations that incorporate correct anatomical terminology. Low spatial ability students focused on the function of structures and ways to group information primarily for the purpose of recall. This supports the theory that low spatial students' mental models will be characterized by more on imagistic representations that are general in nature. (Abstract shortened by UMI.)

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

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

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

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

Digital and optical shape representation and pattern recognition; Proceedings of the Meeting, Orlando, FL, Apr. 4-6, 1988

NASA Technical Reports Server (NTRS)

Juday, Richard D. (Editor)

1988-01-01

The present conference discusses topics in pattern-recognition correlator architectures, digital stereo systems, geometric image transformations and their applications, topics in pattern recognition, filter algorithms, object detection and classification, shape representation techniques, and model-based object recognition methods. Attention is given to edge-enhancement preprocessing using liquid crystal TVs, massively-parallel optical data base management, three-dimensional sensing with polar exponential sensor arrays, the optical processing of imaging spectrometer data, hybrid associative memories and metric data models, the representation of shape primitives in neural networks, and the Monte Carlo estimation of moment invariants for pattern recognition.

Natural representations: diagram and text in Darwin's "On the origin of species".

PubMed

Brink-Roby, Heather

2009-01-01

This article examines Darwin's use of diagram and text in the "Origin" by focusing on their interacting roles in his discussion of natural relations, extinction, and time. Each medium presented opportunities and challenges that depend on the topic in question; indeed, a medium's dimensionality could undermine one claim and make self-evident another. While Darwin divides representational labor between diagram and text, he also creates a constitutive interplay between media. The resulting dynamic alliance of form and content recalls his early evolutionary reflections on representation; image and word could be used not simply to argue for, but also as evidence of, his theory.

The oligonucleotide frequency derived error gradient and its application to the binning of metagenome fragments

PubMed Central

2009-01-01

Background The characterisation, or binning, of metagenome fragments is an important first step to further downstream analysis of microbial consortia. Here, we propose a one-dimensional signature, OFDEG, derived from the oligonucleotide frequency profile of a DNA sequence, and show that it is possible to obtain a meaningful phylogenetic signal for relatively short DNA sequences. The one-dimensional signal is essentially a compact representation of higher dimensional feature spaces of greater complexity and is intended to improve on the tetranucleotide frequency feature space preferred by current compositional binning methods. Results We compare the fidelity of OFDEG against tetranucleotide frequency in both an unsupervised and semi-supervised setting on simulated metagenome benchmark data. Four tests were conducted using assembler output of Arachne and phrap, and for each, performance was evaluated on contigs which are greater than or equal to 8 kbp in length and contigs which are composed of at least 10 reads. Using both G-C content in conjunction with OFDEG gave an average accuracy of 96.75% (semi-supervised) and 95.19% (unsupervised), versus 94.25% (semi-supervised) and 82.35% (unsupervised) for tetranucleotide frequency. Conclusion We have presented an observation of an alternative characteristic of DNA sequences. The proposed feature representation has proven to be more beneficial than the existing tetranucleotide frequency space to the metagenome binning problem. We do note, however, that our observation of OFDEG deserves further anlaysis and investigation. Unsupervised clustering revealed OFDEG related features performed better than standard tetranucleotide frequency in representing a relevant organism specific signal. Further improvement in binning accuracy is given by semi-supervised classification using OFDEG. The emphasis on a feature-driven, bottom-up approach to the problem of binning reveals promising avenues for future development of techniques to characterise short environmental sequences without bias toward cultivable organisms. PMID:19958473

Piecewise parabolic method for simulating one-dimensional shear shock wave propagation in tissue-mimicking phantoms

NASA Astrophysics Data System (ADS)

Tripathi, B. B.; Espíndola, D.; Pinton, G. F.

2017-11-01

The recent discovery of shear shock wave generation and propagation in the porcine brain suggests that this new shock phenomenology may be responsible for a broad range of traumatic injuries. Blast-induced head movement can indirectly lead to shear wave generation in the brain, which could be a primary mechanism for injury. Shear shock waves amplify the local acceleration deep in the brain by up to a factor of 8.5, which may tear and damage neurons. Currently, there are numerical methods that can model compressional shock waves, such as comparatively well-studied blast waves, but there are no numerical full-wave solvers that can simulate nonlinear shear shock waves in soft solids. Unlike simplified representations, e.g., retarded time, full-wave representations describe fundamental physical behavior such as reflection and heterogeneities. Here we present a piecewise parabolic method-based solver for one-dimensional linearly polarized nonlinear shear wave in a homogeneous medium and with empirical frequency-dependent attenuation. This method has the advantage of being higher order and more directly extendable to multiple dimensions and heterogeneous media. The proposed numerical scheme is validated analytically and experimentally and compared to other shock capturing methods. A Riemann step-shock problem is used to characterize the numerical dissipation. This dissipation is then tuned to be negligible with respect to the physical attenuation by choosing an appropriate grid spacing. The numerical results are compared to ultrasound-based experiments that measure planar polarized shear shock wave propagation in a tissue-mimicking gelatin phantom. Good agreement is found between numerical results and experiment across a 40 mm propagation distance. We anticipate that the proposed method will be a starting point for the development of a two- and three-dimensional full-wave code for the propagation of nonlinear shear waves in heterogeneous media.

A Multi-Resolution Data Structure for Two-Dimensional Morse Functions

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

Bremer, P-T; Edelsbrunner, H; Hamann, B

2003-07-30

The efficient construction of simplified models is a central problem in the field of visualization. We combine topological and geometric methods to construct a multi-resolution data structure for functions over two-dimensional domains. Starting with the Morse-Smale complex we build a hierarchy by progressively canceling critical points in pairs. The data structure supports mesh traversal operations similar to traditional multi-resolution representations.

Direct calculation of wall interferences and wall adaptation for two-dimensional flow in wind tunnels with closed walls

NASA Technical Reports Server (NTRS)

Amecke, Juergen

1986-01-01

A method for the direct calculation of the wall induced interference velocity in two dimensional flow based on Cauchy's integral formula was derived. This one-step method allows the calculation of the residual corrections and the required wall adaptation for interference-free flow starting from the wall pressure distribution without any model representation. Demonstrated applications are given.

Portable Body Temperature Conditioner

DTIC Science & Technology

2013-10-18

disposable PVDF turbine flowmeter that is compact in size and capable of accommodating a volumetric flow rate from 0.03 L/min to 2.0 L/min of water . The...pictorial representation of the flowmeter along with a dimensional drawing. 33 Figure 27. Water flowmeter for PBTC As displayed in the dimensional...suitable for military applications. 15. SUBJECT TERMS Hypothermia, Circulating Water -blanket, Trauma, Hyperthermia, Military, Thermal Manikin 16

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.

Fuzzy parametric uncertainty analysis of linear dynamical systems: A surrogate modeling approach

NASA Astrophysics Data System (ADS)

Chowdhury, R.; Adhikari, S.

2012-10-01

Uncertainty propagation engineering systems possess significant computational challenges. This paper explores the possibility of using correlated function expansion based metamodelling approach when uncertain system parameters are modeled using Fuzzy variables. In particular, the application of High-Dimensional Model Representation (HDMR) is proposed for fuzzy finite element analysis of dynamical systems. The HDMR expansion is a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior based on a hierarchy of functions of increasing dimensions. The input variables may be either finite-dimensional (i.e., a vector of parameters chosen from the Euclidean space RM) or may be infinite-dimensional as in the function space CM[0,1]. The computational effort to determine the expansion functions using the alpha cut method scales polynomially with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is integrated with a commercial Finite Element software. Modal analysis of a simplified aircraft wing with Fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations.

Semiclassical initial value representation for the quantum propagator in the Heisenberg interaction representation

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

Petersen, Jakob; Pollak, Eli, E-mail: eli.pollak@weizmann.ac.il

2015-12-14

One of the challenges facing on-the-fly ab initio semiclassical time evolution is the large expense needed to converge the computation. In this paper, we suggest that a significant saving in computational effort may be achieved by employing a semiclassical initial value representation (SCIVR) of the quantum propagator based on the Heisenberg interaction representation. We formulate and test numerically a modification and simplification of the previous semiclassical interaction representation of Shao and Makri [J. Chem. Phys. 113, 3681 (2000)]. The formulation is based on the wavefunction form of the semiclassical propagation instead of the operator form, and so is simpler andmore » cheaper to implement. The semiclassical interaction representation has the advantage that the phase and prefactor vary relatively slowly as compared to the “standard” SCIVR methods. This improves its convergence properties significantly. Using a one-dimensional model system, the approximation is compared with Herman-Kluk’s frozen Gaussian and Heller’s thawed Gaussian approximations. The convergence properties of the interaction representation approach are shown to be favorable and indicate that the interaction representation is a viable way of incorporating on-the-fly force field information within a semiclassical framework.« less

Polio Pictures

MedlinePlus

... dimensional representation of poliovirus. A few examples from public health professionals Child in Nigeria with a leg partly ... for these sites, which offer more images/photos. Public Health Image Library (PHIL) Immunization Action Coalition Polio Eradication ...

Recent Developments In Theory Of Balanced Linear Systems

NASA Technical Reports Server (NTRS)

Gawronski, Wodek

1994-01-01

Report presents theoretical study of some issues of controllability and observability of system represented by linear, time-invariant mathematical model of the form. x = Ax + Bu, y = Cx + Du, x(0) = xo where x is n-dimensional vector representing state of system; u is p-dimensional vector representing control input to system; y is q-dimensional vector representing output of system; n,p, and q are integers; x(0) is intial (zero-time) state vector; and set of matrices (A,B,C,D) said to constitute state-space representation of system.

A novel framework for change detection in bi-temporal polarimetric SAR images

NASA Astrophysics Data System (ADS)

Pirrone, Davide; Bovolo, Francesca; Bruzzone, Lorenzo

2016-10-01

Last years have seen relevant increase of polarimetric Synthetic Aperture Radar (SAR) data availability, thanks to satellite sensors like Sentinel-1 or ALOS-2 PALSAR-2. The augmented information lying in the additional polarimetric channels represents a possibility for better discriminate different classes of changes in change detection (CD) applications. This work aims at proposing a framework for CD in multi-temporal multi-polarization SAR data. The framework includes both a tool for an effective visual representation of the change information and a method for extracting the multiple-change information. Both components are designed to effectively handle the multi-dimensionality of polarimetric data. In the novel representation, multi-temporal intensity SAR data are employed to compute a polarimetric log-ratio. The multitemporal information of the polarimetric log-ratio image is represented in a multi-dimensional features space, where changes are highlighted in terms of magnitude and direction. This representation is employed to design a novel unsupervised multi-class CD approach. This approach considers a sequential two-step analysis of the magnitude and the direction information for separating non-changed and changed samples. The proposed approach has been validated on a pair of Sentinel-1 data acquired before and after the flood in Tamil-Nadu in 2015. Preliminary results demonstrate that the representation tool is effective and that the use of polarimetric SAR data is promising in multi-class change detection applications.

Female Representation in Higher Education: Retrospect and Prospect.

ERIC Educational Resources Information Center

Waldenberg, Adair L.

Female representation in higher education increased significantly at several levels over the past decade. In this paper the trends are analyzed, and the potential role of policy changes that alter female representation is explored. The measure used in the analysis is the proportion of a given group that is female or the ratio of the number of…

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.

Collaborative activity between parietal and dorso-lateral prefrontal cortex in dynamic spatial working memory revealed by fMRI.

PubMed

Diwadkar, V A; Carpenter, P A; Just, M A

2000-07-01

Functional MRI was used to determine how the constituents of the cortical network subserving dynamic spatial working memory respond to two types of increases in task complexity. Participants mentally maintained the most recent location of either one or three objects as the three objects moved discretely in either a two- or three-dimensional array. Cortical activation in the dorsolateral prefrontal (DLPFC) and the parietal cortex increased as a function of the number of object locations to be maintained and the dimensionality of the display. An analysis of the response characteristics of the individual voxels showed that a large proportion were activated only when both the variables imposed the higher level of demand. A smaller proportion were activated specifically in response to increases in task demand associated with each of the independent variables. A second experiment revealed the same effect of dimensionality in the parietal cortex when the movement of objects was signaled auditorily rather than visually, indicating that the additional representational demands induced by 3-D space are independent of input modality. The comodulation of activation in the prefrontal and parietal areas by the amount of computational demand suggests that the collaboration between areas is a basic feature underlying much of the functionality of spatial working memory. Copyright 2000 Academic Press.

Impact of Basal Hydrology Near Grounding Lines: Results from the MISMIP-3D and MISMIP+ Experiments Using the Community Ice Sheet Model

NASA Astrophysics Data System (ADS)

Leguy, G.; Lipscomb, W. H.; Asay-Davis, X.

2017-12-01

Ice sheets and ice shelves are linked by the transition zone, the region where the grounded ice lifts off the bedrock and begins to float. Adequate resolution of the transition zone is necessary for numerically accurate ice sheet-ice shelf simulations. In previous work we have shown that by using a simple parameterization of the basal hydrology, a smoother transition in basal water pressure between floating and grounded ice improves the numerical accuracy of a one-dimensional vertically integrated fixed-grid model. We used a set of experiments based on the Marine Ice Sheet Model Intercomparison Project (MISMIP) to show that reliable grounding-line dynamics at resolutions 1 km is achievable. In this presentation we use the Community Ice Sheet Model (CISM) to demonstrate how the representation of basal lubrication impacts three-dimensional models using the MISMIP-3D and MISMIP+ experiments. To this end we will compare three different Stokes approximations: the Shallow Shelf Approximation (SSA), a depth-integrated higher-order approximation, and the Blatter-Pattyn model. The results from our one-dimensional model carry over to the 3-D models; a resolution of 1 km (and in some cases 2 km) remains sufficient to accurately simulate grounding-line dynamics.

From experimental imaging techniques to virtual embryology.

PubMed

Weninger, Wolfgang J; Tassy, Olivier; Darras, Sébastien; Geyer, Stefan H; Thieffry, Denis

2004-01-01

Modern embryology increasingly relies on descriptive and functional three dimensional (3D) and four dimensional (4D) analysis of physically, optically, or virtually sectioned specimens. To cope with the technical requirements, new methods for high detailed in vivo imaging, as well as the generation of high resolution digital volume data sets for the accurate visualisation of transgene activity and gene product presence, in the context of embryo morphology, were recently developed and are under construction. These methods profoundly change the scientific applicability, appearance and style of modern embryo representations. In this paper, we present an overview of the emerging techniques to create, visualise and administrate embryo representations (databases, digital data sets, 3-4D embryo reconstructions, models, etc.), and discuss the implications of these new methods on the work of modern embryologists, including, research, teaching, the selection of specific model organisms, and potential collaborators.

Galactic Cosmic Rays in the Outer Heliosphere

NASA Technical Reports Server (NTRS)

Florinski, V.; Washimi, H.; Pogorelov, N. V.; Adams, J. H.

2010-01-01

We report a next generation model of galactic cosmic ray (GCR) transport in the three dimensional heliosphere. Our model is based on an accurate three-dimensional representation of the heliospheric interface. This representation is obtained by taking into account the interaction between partially ionized, magnetized plasma flows of the solar wind and the local interstellar medium. Our model reveals that after entering the heliosphere GCRs are stored in the heliosheath for several years. The preferred GCR entry locations are near the nose of the heliopause and at high latitudes. Low-energy (hundreds of MeV) galactic ions observed in the heliosheath have spent, on average, a longer time in the solar wind than those observed in the inner heliosphere, which would explain their cooled-off spectra at these energies. We also discuss radial gradients in the heliosheath and the implications for future Voyager observations

Efficient local representations for three-dimensional palmprint recognition

NASA Astrophysics Data System (ADS)

Yang, Bing; Wang, Xiaohua; Yao, Jinliang; Yang, Xin; Zhu, Wenhua

2013-10-01

Palmprints have been broadly used for personal authentication because they are highly accurate and incur low cost. Most previous works have focused on two-dimensional (2-D) palmprint recognition in the past decade. Unfortunately, 2-D palmprint recognition systems lose the shape information when capturing palmprint images. Moreover, such 2-D palmprint images can be easily forged or affected by noise. Hence, three-dimensional (3-D) palmprint recognition has been regarded as a promising way to further improve the performance of palmprint recognition systems. We have developed a simple, but efficient method for 3-D palmprint recognition by using local features. We first utilize shape index representation to describe the geometry of local regions in 3-D palmprint data. Then, we extract local binary pattern and Gabor wavelet features from the shape index image. The two types of complementary features are finally fused at a score level for further improvements. The experimental results on the Hong Kong Polytechnic 3-D palmprint database, which contains 8000 samples from 400 palms, illustrate the effectiveness of the proposed method.

Asymptotic symmetries of Rindler space at the horizon and null infinity

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

Chung, Hyeyoun

2010-08-15

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler spacemore » at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.« less

Residence-time framework for modeling multicomponent reactive transport in stream hyporheic zones

NASA Astrophysics Data System (ADS)

Painter, S. L.; Coon, E. T.; Brooks, S. C.

2017-12-01

Process-based models for transport and transformation of nutrients and contaminants in streams require tractable representations of solute exchange between the stream channel and biogeochemically active hyporheic zones. Residence-time based formulations provide an alternative to detailed three-dimensional simulations and have had good success in representing hyporheic exchange of non-reacting solutes. We extend the residence-time formulation for hyporheic transport to accommodate general multicomponent reactive transport. To that end, the integro-differential form of previous residence time models is replaced by an equivalent formulation based on a one-dimensional advection dispersion equation along the channel coupled at each channel location to a one-dimensional transport model in Lagrangian travel-time form. With the channel discretized for numerical solution, the associated Lagrangian model becomes a subgrid model representing an ensemble of streamlines that are diverted into the hyporheic zone before returning to the channel. In contrast to the previous integro-differential forms of the residence-time based models, the hyporheic flowpaths have semi-explicit spatial representation (parameterized by travel time), thus allowing coupling to general biogeochemical models. The approach has been implemented as a stream-corridor subgrid model in the open-source integrated surface/subsurface modeling software ATS. We use bedform-driven flow coupled to a biogeochemical model with explicit microbial biomass dynamics as an example to show that the subgrid representation is able to represent redox zonation in sediments and resulting effects on metal biogeochemical dynamics in a tractable manner that can be scaled to reach scales.

Strategies to Evaluate the Visibility Along AN Indoor Path in a Point Cloud Representation

NASA Astrophysics Data System (ADS)

Grasso, N.; Verbree, E.; Zlatanova, S.; Piras, M.

2017-09-01

Many research works have been oriented to the formulation of different algorithms for estimating the paths in indoor environments from three-dimensional representations of space. The architectural configuration, the actions that take place within it, and the location of some objects in the space influence the paths along which is it possible to move, as they may cause visibility problems. To overcome the visibility issue, different methods have been proposed which allow to identify the visible areas and from a certain point of view, but often they do not take into account the user's visual perception of the environment and not allow estimating how much may be complicated to follow a certain path. In the field of space syntax and cognitive science, it has been attempted to describe the characteristics of a building or an urban environment by the isovists and visibility graphs methods; some numerical properties of these representations allow to describe the space as for how it is perceived by a user. However, most of these studies are directed to analyze the environment in a two-dimensional space. In this paper we propose a method to evaluate in a quantitative way the complexity of a certain path within an environment represented by a three-dimensional point cloud, by the combination of some of the previously mentioned techniques, considering the space visible from a certain point of view, depending on the moving agent (pedestrian , people in wheelchairs, UAV, UGV, robot).

Simultaneous Spectral-Spatial Feature Selection and Extraction for Hyperspectral Images.

PubMed

Zhang, Lefei; Zhang, Qian; Du, Bo; Huang, Xin; Tang, Yuan Yan; Tao, Dacheng

2018-01-01

In hyperspectral remote sensing data mining, it is important to take into account of both spectral and spatial information, such as the spectral signature, texture feature, and morphological property, to improve the performances, e.g., the image classification accuracy. In a feature representation point of view, a nature approach to handle this situation is to concatenate the spectral and spatial features into a single but high dimensional vector and then apply a certain dimension reduction technique directly on that concatenated vector before feed it into the subsequent classifier. However, multiple features from various domains definitely have different physical meanings and statistical properties, and thus such concatenation has not efficiently explore the complementary properties among different features, which should benefit for boost the feature discriminability. Furthermore, it is also difficult to interpret the transformed results of the concatenated vector. Consequently, finding a physically meaningful consensus low dimensional feature representation of original multiple features is still a challenging task. In order to address these issues, we propose a novel feature learning framework, i.e., the simultaneous spectral-spatial feature selection and extraction algorithm, for hyperspectral images spectral-spatial feature representation and classification. Specifically, the proposed method learns a latent low dimensional subspace by projecting the spectral-spatial feature into a common feature space, where the complementary information has been effectively exploited, and simultaneously, only the most significant original features have been transformed. Encouraging experimental results on three public available hyperspectral remote sensing datasets confirm that our proposed method is effective and efficient.

Approximation of Optimal Infinite Dimensional Compensators for Flexible Structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.; Adamian, A.; Jabbari, F.

1985-01-01

The infinite dimensional compensator for a large class of flexible structures, modeled as distributed systems are discussed, as well as an approximation scheme for designing finite dimensional compensators to approximate the infinite dimensional compensator. The approximation scheme is applied to develop a compensator for a space antenna model based on wrap-rib antennas being built currently. While the present model has been simplified, it retains the salient features of rigid body modes and several distributed components of different characteristics. The control and estimator gains are represented by functional gains, which provide graphical representations of the control and estimator laws. These functional gains also indicate the convergence of the finite dimensional compensators and show which modes the optimal compensator ignores.

Visualizing second order tensor fields with hyperstreamlines

NASA Technical Reports Server (NTRS)

Delmarcelle, Thierry; Hesselink, Lambertus

1993-01-01

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

Risk Assessment Using the Three Dimensions of Probability (Likelihood), Severity, and Level of Control

NASA Technical Reports Server (NTRS)

Watson, Clifford C.

2011-01-01

Traditional hazard analysis techniques utilize a two-dimensional representation of the results determined by relative likelihood and severity of the residual risk. These matrices present a quick-look at the Likelihood (Y-axis) and Severity (X-axis) of the probable outcome of a hazardous event. A three-dimensional method, described herein, utilizes the traditional X and Y axes, while adding a new, third dimension, shown as the Z-axis, and referred to as the Level of Control. The elements of the Z-axis are modifications of the Hazard Elimination and Control steps (also known as the Hazard Reduction Precedence Sequence). These steps are: 1. Eliminate risk through design. 2. Substitute less risky materials for more hazardous materials. 3. Install safety devices. 4. Install caution and warning devices. 5. Develop administrative controls (to include special procedures and training.) 6. Provide protective clothing and equipment. When added to the two-dimensional models, the level of control adds a visual representation of the risk associated with the hazardous condition, creating a tall-pole for the least-well-controlled failure while establishing the relative likelihood and severity of all causes and effects for an identified hazard. Computer modeling of the analytical results, using spreadsheets and three-dimensional charting gives a visual confirmation of the relationship between causes and their controls.

Risk Presentation Using the Three Dimensions of Likelihood, Severity, and Level of Control

NASA Technical Reports Server (NTRS)

Watson, Clifford

2010-01-01

Traditional hazard analysis techniques utilize a two-dimensional representation of the results determined by relative likelihood and severity of the residual risk. These matrices present a quick-look at the Likelihood (Y-axis) and Severity (X-axis) of the probable outcome of a hazardous event. A three-dimensional method, described herein, utilizes the traditional X and Y axes, while adding a new, third dimension, shown as the Z-axis, and referred to as the Level of Control. The elements of the Z-axis are modifications of the Hazard Elimination and Control steps (also known as the Hazard Reduction Precedence Sequence). These steps are: 1. Eliminate risk through design. 2. Substitute less risky materials for more hazardous materials. 3. Install safety devices. 4. Install caution and warning devices. 5. Develop administrative controls (to include special procedures and training.) 6. Provide protective clothing and equipment. When added to the two-dimensional models, the level of control adds a visual representation of the risk associated with the hazardous condition, creating a tall-pole for the leastwell-controlled failure while establishing the relative likelihood and severity of all causes and effects for an identified hazard. Computer modeling of the analytical results, using spreadsheets and three-dimensional charting gives a visual confirmation of the relationship between causes and their controls.

A strategy for analysis of (molecular) equilibrium simulations: Configuration space density estimation, clustering, and visualization

NASA Astrophysics Data System (ADS)

Hamprecht, Fred A.; Peter, Christine; Daura, Xavier; Thiel, Walter; van Gunsteren, Wilfred F.

2001-02-01

We propose an approach for summarizing the output of long simulations of complex systems, affording a rapid overview and interpretation. First, multidimensional scaling techniques are used in conjunction with dimension reduction methods to obtain a low-dimensional representation of the configuration space explored by the system. A nonparametric estimate of the density of states in this subspace is then obtained using kernel methods. The free energy surface is calculated from that density, and the configurations produced in the simulation are then clustered according to the topography of that surface, such that all configurations belonging to one local free energy minimum form one class. This topographical cluster analysis is performed using basin spanning trees which we introduce as subgraphs of Delaunay triangulations. Free energy surfaces obtained in dimensions lower than four can be visualized directly using iso-contours and -surfaces. Basin spanning trees also afford a glimpse of higher-dimensional topographies. The procedure is illustrated using molecular dynamics simulations on the reversible folding of peptide analoga. Finally, we emphasize the intimate relation of density estimation techniques to modern enhanced sampling algorithms.

Topology in colored tensor models via crystallization theory

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

Assessment of WENO-extended two-fluid modelling in compressible multiphase flows

NASA Astrophysics Data System (ADS)

Kitamura, Keiichi; Nonomura, Taku

2017-03-01

The two-fluid modelling based on an advection-upwind-splitting-method (AUSM)-family numerical flux function, AUSM+-up, following the work by Chang and Liou [Journal of Computational Physics 2007;225: 840-873], has been successfully extended to the fifth order by weighted-essentially-non-oscillatory (WENO) schemes. Then its performance is surveyed in several numerical tests. The results showed a desired performance in one-dimensional benchmark test problems: Without relying upon an anti-diffusion device, the higher-order two-fluid method captures the phase interface within a fewer grid points than the conventional second-order method, as well as a rarefaction wave and a very weak shock. At a high pressure ratio (e.g. 1,000), the interpolated variables appeared to affect the performance: the conservative-variable-based characteristic-wise WENO interpolation showed less sharper but more robust representations of the shocks and expansions than the primitive-variable-based counterpart did. In two-dimensional shock/droplet test case, however, only the primitive-variable-based WENO with a huge void fraction realised a stable computation.

Exploring nonlinear feature space dimension reduction and data representation in breast CADx with Laplacian eigenmaps and t-SNE

PubMed Central

Jamieson, Andrew R.; Giger, Maryellen L.; Drukker, Karen; Li, Hui; Yuan, Yading; Bhooshan, Neha

2010-01-01

Purpose: In this preliminary study, recently developed unsupervised nonlinear dimension reduction (DR) and data representation techniques were applied to computer-extracted breast lesion feature spaces across three separate imaging modalities: Ultrasound (U.S.) with 1126 cases, dynamic contrast enhanced magnetic resonance imaging with 356 cases, and full-field digital mammography with 245 cases. Two methods for nonlinear DR were explored: Laplacian eigenmaps [M. Belkin and P. Niyogi, “Laplacian eigenmaps for dimensionality reduction and data representation,” Neural Comput. 15, 1373–1396 (2003)] and t-distributed stochastic neighbor embedding (t-SNE) [L. van der Maaten and G. Hinton, “Visualizing data using t-SNE,” J. Mach. Learn. Res. 9, 2579–2605 (2008)]. Methods: These methods attempt to map originally high dimensional feature spaces to more human interpretable lower dimensional spaces while preserving both local and global information. The properties of these methods as applied to breast computer-aided diagnosis (CADx) were evaluated in the context of malignancy classification performance as well as in the visual inspection of the sparseness within the two-dimensional and three-dimensional mappings. Classification performance was estimated by using the reduced dimension mapped feature output as input into both linear and nonlinear classifiers: Markov chain Monte Carlo based Bayesian artificial neural network (MCMC-BANN) and linear discriminant analysis. The new techniques were compared to previously developed breast CADx methodologies, including automatic relevance determination and linear stepwise (LSW) feature selection, as well as a linear DR method based on principal component analysis. Using ROC analysis and 0.632+bootstrap validation, 95% empirical confidence intervals were computed for the each classifier’s AUC performance. Results: In the large U.S. data set, sample high performance results include, AUC0.632+=0.88 with 95% empirical bootstrap interval [0.787;0.895] for 13 ARD selected features and AUC0.632+=0.87 with interval [0.817;0.906] for four LSW selected features compared to 4D t-SNE mapping (from the original 81D feature space) giving AUC0.632+=0.90 with interval [0.847;0.919], all using the MCMC-BANN. Conclusions: Preliminary results appear to indicate capability for the new methods to match or exceed classification performance of current advanced breast lesion CADx algorithms. While not appropriate as a complete replacement of feature selection in CADx problems, DR techniques offer a complementary approach, which can aid elucidation of additional properties associated with the data. Specifically, the new techniques were shown to possess the added benefit of delivering sparse lower dimensional representations for visual interpretation, revealing intricate data structure of the feature space. PMID:20175497

Continuous versus discontinuous albedo representations in a simple diffusive climate model

NASA Astrophysics Data System (ADS)

Simmons, P. A.; Griffel, D. H.

1988-07-01

A one-dimensional annually and zonally averaged energy-balance model, with diffusive meridional heat transport and including icealbedo feedback, is considered. This type of model is found to be very sensitive to the form of albedo used. The solutions for a discontinuous step-function albedo are compared to those for a more realistic smoothly varying albedo. The smooth albedo gives a closer fit to present conditions, but the discontinuous form gives a better representation of climates in earlier epochs.

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

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

Kulish, P.P.; Reshetikin N.Y.

1986-09-01

GL/sub 3/-invariant, finite-dimensional solutions of the Yang-Baxter equations acting in the tensor product of two irreducible representations of the group GL/sub 3/ are investigated. A number of relations are obtained for the transfer matrices which demonstrate the connection of representation theory and the Bethe Ansatz in GL/sub 3/invariant models. Some of the most interesting quantum and classical integrable systems connected with GL/sub 3/-invariant solutions of the Yang-Baxter equation are presented.

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

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

Kulish, P.P.; Reshetikhin, N.Yu.

1986-09-10

GL/sub 3/-invariant, finite-dimensional solutions of the Yang-Baxter equations acting in the tensor product of two irreducible representations of the group GL/sub 3/ are investigated. A number of relations are obtained for the transfer matrices which demonstrate the connection of representation theory and the Bethe Ansatz in GL/sub 3/-invariant models. Some of the most interesting quantum and classical integrable systems connected with GL/sub 3/-invariant solutions of the Yang-Baxter equation are presented.

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

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

Kulish, P.P.; Reshetikhin, N.Yu.

1987-05-20

The authors investigate the GL/sub 3/-invariant finite-dimensional solutions of the Yang-Baxter equation acting in the tensor product of two irreducible representations of the GL/sub 3/ group. Relationships obtained for the transfer matrices demonstrate the link between representation theory and the Bethe ansatz in GL/sub 3/-invariant models. Some examples of quantum and classical integrable systems associated with GL/sub 3/-invariant solutions of the Yang-Baxter equation are given.

A topological hierarchy for functions on triangulated surfaces.

PubMed

Bremer, Peer-Timo; Edelsbrunner, Herbert; Hamann, Bernd; Pascucci, Valerio

2004-01-01

We combine topological and geometric methods to construct a multiresolution representation for a function over a two-dimensional domain. In a preprocessing stage, we create the Morse-Smale complex of the function and progressively simplify its topology by cancelling pairs of critical points. Based on a simple notion of dependency among these cancellations, we construct a hierarchical data structure supporting traversal and reconstruction operations similarly to traditional geometry-based representations. We use this data structure to extract topologically valid approximations that satisfy error bounds provided at runtime.

Techniques for increasing the efficiency of Earth gravity calculations for precision orbit determination

NASA Technical Reports Server (NTRS)

Smith, R. L.; Lyubomirsky, A. S.

1981-01-01

Two techniques were analyzed. The first is a representation using Chebyshev expansions in three-dimensional cells. The second technique employs a temporary file for storing the components of the nonspherical gravity force. Computer storage requirements and relative CPU time requirements are presented. The Chebyshev gravity representation can provide a significant reduction in CPU time in precision orbit calculations, but at the cost of a large amount of direct-access storage space, which is required for a global model.

Geo3DML: A standard-based exchange format for 3D geological models

NASA Astrophysics Data System (ADS)

Wang, Zhangang; Qu, Honggang; Wu, Zixing; Wang, Xianghong

2018-01-01

A geological model (geomodel) in three-dimensional (3D) space is a digital representation of the Earth's subsurface, recognized by geologists and stored in resultant geological data (geodata). The increasing demand for data management and interoperable applications of geomodelscan be addressed by developing standard-based exchange formats for the representation of not only a single geological object, but also holistic geomodels. However, current standards such as GeoSciML cannot incorporate all the geomodel-related information. This paper presents Geo3DML for the exchange of 3D geomodels based on the existing Open Geospatial Consortium (OGC) standards. Geo3DML is based on a unified and formal representation of structural models, attribute models and hierarchical structures of interpreted resultant geodata in different dimensional views, including drills, cross-sections/geomaps and 3D models, which is compatible with the conceptual model of GeoSciML. Geo3DML aims to encode all geomodel-related information integrally in one framework, including the semantic and geometric information of geoobjects and their relationships, as well as visual information. At present, Geo3DML and some supporting tools have been released as a data-exchange standard by the China Geological Survey (CGS).

Spacetime representation of topological phononics

NASA Astrophysics Data System (ADS)

Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.

2018-05-01

Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

Acoustic basis for recognition of aspect-dependent three-dimensional targets by an echolocating bottlenose dolphin.

PubMed

Helweg, D A; Au, W W; Roitblat, H L; Nachtigall, P E

1996-04-01

The relationships between acoustic features of target echoes and the cognitive representations of the target formed by an echolocating dolphin will influence the ease with which the dolphin can recognize a target. A blindfolded Atlantic bottlenose dolphin (Tursiops truncatus) learned to match aspect-dependent three-dimensional targets (such as a cube) at haphazard orientations, although with some difficulty. This task may have been difficult because aspect-dependent targets produce different echoes at different orientations, which required the dolphin to have some capability for object constancy across changes in echo characteristics. Significant target-related differences in echo amplitude, rms bandwidth, and distributions of interhighlight intervals were observed among echoes collected when the dolphin was performing the task. Targets could be classified using a combination of energy flux density and rms bandwidth by a linear discriminant analysis and a nearest centroid classifier. Neither statistical model could classify targets without amplitude information, but the highest accuracy required spectral information as well. This suggests that the dolphin recognized the targets using a multidimensional representation containing amplitude and spectral information and that dolphins can form stable representations of targets regardless of orientation based on varying sensory properties.

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.

Manifold decoding for neural representations of face viewpoint and gaze direction using magnetoencephalographic data.

PubMed

Kuo, Po-Chih; Chen, Yong-Sheng; Chen, Li-Fen

2018-05-01

The main challenge in decoding neural representations lies in linking neural activity to representational content or abstract concepts. The transformation from a neural-based to a low-dimensional representation may hold the key to encoding perceptual processes in the human brain. In this study, we developed a novel model by which to represent two changeable features of faces: face viewpoint and gaze direction. These features are embedded in spatiotemporal brain activity derived from magnetoencephalographic data. Our decoding results demonstrate that face viewpoint and gaze direction can be represented by manifold structures constructed from brain responses in the bilateral occipital face area and right superior temporal sulcus, respectively. Our results also show that the superposition of brain activity in the manifold space reveals the viewpoints of faces as well as directions of gazes as perceived by the subject. The proposed manifold representation model provides a novel opportunity to gain further insight into the processing of information in the human brain. © 2018 Wiley Periodicals, Inc.

Design principles of the sparse coding network and the role of “sister cells” in the olfactory system of Drosophila

PubMed Central

Zhang, Danke; Li, Yuanqing; Wu, Si; Rasch, Malte J.

2013-01-01

Sensory systems face the challenge to represent sensory inputs in a way to allow easy readout of sensory information by higher brain areas. In the olfactory system of the fly drosopohila melanogaster, projection neurons (PNs) of the antennal lobe (AL) convert a dense activation of glomeruli into a sparse, high-dimensional firing pattern of Kenyon cells (KCs) in the mushroom body (MB). Here we investigate the design principles of the olfactory system of drosophila in regard to the capabilities to discriminate odor quality from the MB representation and its robustness to different types of noise. We focus on understanding the role of highly correlated homotypic projection neurons (“sister cells”) found in the glomeruli of flies. These cells are coupled by gap-junctions and receive almost identical sensory inputs, but target randomly different KCs in MB. We show that sister cells might play a crucial role in increasing the robustness of the MB odor representation to noise. Computationally, sister cells thus might help the system to improve the generalization capabilities in face of noise without impairing the discriminability of odor quality at the same time. PMID:24167488

Entanglement entropy for 2D gauge theories with matters

NASA Astrophysics Data System (ADS)

Aoki, Sinya; Iizuka, Norihiro; Tamaoka, Kotaro; Yokoya, Tsuyoshi

2017-08-01

We investigate the entanglement entropy in 1 +1 -dimensional S U (N ) gauge theories with various matter fields using the lattice regularization. Here we use extended Hilbert space definition for entanglement entropy, which contains three contributions; (1) classical Shannon entropy associated with superselection sector distribution, where sectors are labeled by irreducible representations of boundary penetrating fluxes, (2) logarithm of the dimensions of their representations, which is associated with "color entanglement," and (3) EPR Bell pairs, which give "genuine" entanglement. We explicitly show that entanglement entropies (1) and (2) above indeed appear for various multiple "meson" states in gauge theories with matter fields. Furthermore, we employ transfer matrix formalism for gauge theory with fundamental matter field and analyze its ground state using hopping parameter expansion (HPE), where the hopping parameter K is roughly the inverse square of the mass for the matter. We evaluate the entanglement entropy for the ground state and show that all (1), (2), (3) above appear in the HPE, though the Bell pair part (3) appears in higher order than (1) and (2) do. With these results, we discuss how the ground state entanglement entropy in the continuum limit can be understood from the lattice ground state obtained in the HPE.

Convolutional neural network features based change detection in satellite images

NASA Astrophysics Data System (ADS)

Mohammed El Amin, Arabi; Liu, Qingjie; Wang, Yunhong

2016-07-01

With the popular use of high resolution remote sensing (HRRS) satellite images, a huge research efforts have been placed on change detection (CD) problem. An effective feature selection method can significantly boost the final result. While hand-designed features have proven difficulties to design features that effectively capture high and mid-level representations, the recent developments in machine learning (Deep Learning) omit this problem by learning hierarchical representation in an unsupervised manner directly from data without human intervention. In this letter, we propose approaching the change detection problem from a feature learning perspective. A novel deep Convolutional Neural Networks (CNN) features based HR satellite images change detection method is proposed. The main guideline is to produce a change detection map directly from two images using a pretrained CNN. This method can omit the limited performance of hand-crafted features. Firstly, CNN features are extracted through different convolutional layers. Then, a concatenation step is evaluated after an normalization step, resulting in a unique higher dimensional feature map. Finally, a change map was computed using pixel-wise Euclidean distance. Our method has been validated on real bitemporal HRRS satellite images according to qualitative and quantitative analyses. The results obtained confirm the interest of the proposed method.

The Representation and Pay of Women and Minorities in Higher Education Administration: Institutions That Are Getting It Right. A CUPA-HR Research Brief

ERIC Educational Resources Information Center

McChesney, Jasper

2017-01-01

Earlier this year, College and University Professional Association for Human Resources (CUPA-HR) published research briefs on representation and pay equity for women and racial/ethnic minority administrators in higher education, using data from 15 years of salary surveys. Although there were a few successes highlighted, gains in representation and…

Physiological Feedback Method and System

NASA Technical Reports Server (NTRS)

Pope, Alan T. (Inventor); Severance, Kurt E. (Inventor)

2002-01-01

A method and system provide physiological feedback for a patient and/or physician. At least one physiological effect experienced by a body part of a patient is measured noninvasively. A three-dimensional graphics model serving as an analogous representation of the body part is altered in accordance with the measurements. A binocular image signal representative of the three-dimensional graphics model so-altered is displayed for the patient and/or physician in a virtual reality environment.

The influence of ligament modelling strategies on the predictive capability of finite element models of the human knee joint.

PubMed

Naghibi Beidokhti, Hamid; Janssen, Dennis; van de Groes, Sebastiaan; Hazrati, Javad; Van den Boogaard, Ton; Verdonschot, Nico

2017-12-08

In finite element (FE) models knee ligaments can represented either by a group of one-dimensional springs, or by three-dimensional continuum elements based on segmentations. Continuum models closer approximate the anatomy, and facilitate ligament wrapping, while spring models are computationally less expensive. The mechanical properties of ligaments can be based on literature, or adjusted specifically for the subject. In the current study we investigated the effect of ligament modelling strategy on the predictive capability of FE models of the human knee joint. The effect of literature-based versus specimen-specific optimized material parameters was evaluated. Experiments were performed on three human cadaver knees, which were modelled in FE models with ligaments represented either using springs, or using continuum representations. In spring representation collateral ligaments were each modelled with three and cruciate ligaments with two single-element bundles. Stiffness parameters and pre-strains were optimized based on laxity tests for both approaches. Validation experiments were conducted to evaluate the outcomes of the FE models. Models (both spring and continuum) with subject-specific properties improved the predicted kinematics and contact outcome parameters. Models incorporating literature-based parameters, and particularly the spring models (with the representations implemented in this study), led to relatively high errors in kinematics and contact pressures. Using a continuum modelling approach resulted in more accurate contact outcome variables than the spring representation with two (cruciate ligaments) and three (collateral ligaments) single-element-bundle representations. However, when the prediction of joint kinematics is of main interest, spring ligament models provide a faster option with acceptable outcome. Copyright © 2017 Elsevier Ltd. All rights reserved.

Multiple Kernel Sparse Representation based Orthogonal Discriminative Projection and Its Cost-Sensitive Extension.

PubMed

Zhang, Guoqing; Sun, Huaijiang; Xia, Guiyu; Sun, Quansen

2016-07-07

Sparse representation based classification (SRC) has been developed and shown great potential for real-world application. Based on SRC, Yang et al. [10] devised a SRC steered discriminative projection (SRC-DP) method. However, as a linear algorithm, SRC-DP cannot handle the data with highly nonlinear distribution. Kernel sparse representation-based classifier (KSRC) is a non-linear extension of SRC and can remedy the drawback of SRC. KSRC requires the use of a predetermined kernel function and selection of the kernel function and its parameters is difficult. Recently, multiple kernel learning for SRC (MKL-SRC) [22] has been proposed to learn a kernel from a set of base kernels. However, MKL-SRC only considers the within-class reconstruction residual while ignoring the between-class relationship, when learning the kernel weights. In this paper, we propose a novel multiple kernel sparse representation-based classifier (MKSRC), and then we use it as a criterion to design a multiple kernel sparse representation based orthogonal discriminative projection method (MK-SR-ODP). The proposed algorithm aims at learning a projection matrix and a corresponding kernel from the given base kernels such that in the low dimension subspace the between-class reconstruction residual is maximized and the within-class reconstruction residual is minimized. Furthermore, to achieve a minimum overall loss by performing recognition in the learned low-dimensional subspace, we introduce cost information into the dimensionality reduction method. The solutions for the proposed method can be efficiently found based on trace ratio optimization method [33]. Extensive experimental results demonstrate the superiority of the proposed algorithm when compared with the state-of-the-art methods.

Stochastic solution to quantum dynamics

NASA Technical Reports Server (NTRS)

John, Sarah; Wilson, John W.

1994-01-01

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms

NASA Astrophysics Data System (ADS)

Sá, Lucas

2017-03-01

Maxwell’s equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell’s equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism.

The V-Scope: An "Oscilloscope" for Motion.

ERIC Educational Resources Information Center

Ronen, Miky; Lipman, Aharon

1991-01-01

Proposes the V-Scope as a teaching aid to measure, analyze, and display three-dimensional multibody motion. Describes experiment setup considerations, how measurements are calculated, graphic representation capabilities, and modes of operation of this microcomputer-based system. (MDH)

Two-Dimensional Optical Processing Of One-Dimensional Acoustic Data

NASA Astrophysics Data System (ADS)

Szu, Harold H.

1982-10-01

The concept of carrier-mean-frequency-selective convolution is introduced to solve the undersea problem of passive acoustic surveillance (PAS) and compared with the conventional notion of difference-frequency Doppler-corrected correlation. The former results in the cross-Wigner distribution function (WD), and the latter results in the cross-ambiguity function (AF). When the persistent time of a sound emitter is more important than the characteristic tone of the sound emitter, WD will be more useful than AF for PAS activity detection, and vice versa. Their mutual relationships with the instantaneous power spectrum (IPS) show the importance of the phase information that must be kept in any 2-D representation of a 1 -D signal. If a square-law detector is used, or an unsymmetric version of WD or AF is gener-ated, then one must produce the other 2-D representations directly, rather than transform one to the other.

Terahertz emission from the intrinsic Josephson junctions of high-symmetry thermally-managed Bi2Sr2CaCu2O8+δ microstrip antennas

NASA Astrophysics Data System (ADS)

Klemm, Richard A.; Davis, Andrew E.; Wang, Qing X.; Yamamoto, Takashi; Cerkoney, Daniel P.; Reid, Candy; Koopman, Maximiliaan L.; Minami, Hidetoshi; Kashiwagi, Takanari; Rain, Joseph R.; Doty, Constance M.; Sedlack, Michael A.; Morales, Manuel A.; Watanabe, Chiharu; Tsujimoto, Manabu; Delfanazari, Kaveh; Kadowaki, Kazuo

2017-12-01

We show for high-symmetry disk, square, or equilateral triangular thin microstrip antennas of any composition respectively obeying C ∞v , C 4v , and C 3v point group symmetries, that the transverse magnetic electromagnetic cavity mode wave functions are restricted in form to those that are one-dimensional representations of those point groups. Plots of the common nodal points of the ten lowest-energy non-radiating two-dimensional representations of each of these three symmetries are presented. For comparison with symmetry-broken disk intrinsic Josephson junction microstrip antennas constructed from the highly anisotropic layered superconductor Bi2Sr2CaCu2O8+δ (BSCCO), we present plots of the ten lowest frequency orthonormal wave functions and of their emission power angular distributions. These results are compared with previous results for square and equilateral triangular thin microstrip antennas.

Harmonic-phase path-integral approximation of thermal quantum correlation functions

NASA Astrophysics Data System (ADS)

Robertson, Christopher; Habershon, Scott

2018-03-01

We present an approximation to the thermal symmetric form of the quantum time-correlation function in the standard position path-integral representation. By transforming to a sum-and-difference position representation and then Taylor-expanding the potential energy surface of the system to second order, the resulting expression provides a harmonic weighting function that approximately recovers the contribution of the phase to the time-correlation function. This method is readily implemented in a Monte Carlo sampling scheme and provides exact results for harmonic potentials (for both linear and non-linear operators) and near-quantitative results for anharmonic systems for low temperatures and times that are likely to be relevant to condensed phase experiments. This article focuses on one-dimensional examples to provide insights into convergence and sampling properties, and we also discuss how this approximation method may be extended to many-dimensional systems.

The harmonic oscillator and nuclear physics

NASA Technical Reports Server (NTRS)

Rowe, D. J.

1993-01-01

The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.

Cosmic Ray Modulation in the Outer Heliosphere During the Minimum of Solar Cycle 23/24

NASA Technical Reports Server (NTRS)

Adams, James H., Jr.; Florinski, V.; Washimi, H.; Pogorelov, N. V.

2011-01-01

We report a next generation model of galactic cosmic ray (GCR) transport in the three dimensional heliosphere. Our model is based on an accurate three-dimensional representation of the heliospheric interface. This representation is obtained by taking into account the interaction between partially ionized, magnetized plasma flows of the solar wind and the local interstellar medium. Our model reveals that after entering the heliosphere GCRs are stored in the heliosheath for several years. The preferred GCR entry locations are near the nose of the heliopause and at high latitudes. Low-energy (hundreds of MeV) galactic ions observed in the heliosheath have spent, on average, a longer time in the solar wind than those observed in the inner heliosphere, which would explain their cooled-off spectra at these energies. We also discuss radial gradients in the heliosheath and the implications for future Voyager observations.

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

PubMed Central

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

2015-01-01

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

Sampling-free Bayesian inversion with adaptive hierarchical tensor representations

NASA Astrophysics Data System (ADS)

Eigel, Martin; Marschall, Manuel; Schneider, Reinhold

2018-03-01

A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model. This becomes feasible due to the complete treatment in function spaces, which requires an efficient model reduction technique for numerical computations. The advocated perspective yields the crucial benefit that error bounds can be derived for all occuring approximations, leading to provable convergence subject to the discretization parameters. Moreover, it enables a fully adaptive a posteriori control with automatic problem-dependent adjustments of the employed discretizations. The method is discussed in the context of modern hierarchical tensor representations, which are used for the evaluation of a random PDE (the forward model) and the subsequent high-dimensional quadrature of the log-likelihood, alleviating the ‘curse of dimensionality’. Numerical experiments demonstrate the performance and confirm the theoretical results.

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

NASA Astrophysics Data System (ADS)

Cyganek, Boguslaw; Smolka, Bogdan

2015-02-01

In this paper a system for real-time recognition of objects in multidimensional video signals is proposed. Object recognition is done by pattern projection into the tensor subspaces obtained from the factorization of the signal tensors representing the input signal. However, instead of taking only the intensity signal the novelty of this paper is first to build the Extended Structural Tensor representation from the intensity signal that conveys information on signal intensities, as well as on higher-order statistics of the input signals. This way the higher-order input pattern tensors are built from the training samples. Then, the tensor subspaces are built based on the Higher-Order Singular Value Decomposition of the prototype pattern tensors. Finally, recognition relies on measurements of the distance of a test pattern projected into the tensor subspaces obtained from the training tensors. Due to high-dimensionality of the input data, tensor based methods require high memory and computational resources. However, recent achievements in the technology of the multi-core microprocessors and graphic cards allows real-time operation of the multidimensional methods as is shown and analyzed in this paper based on real examples of object detection in digital images.

Information jet: Handling noisy big data from weakly disconnected network

NASA Astrophysics Data System (ADS)

Aurongzeb, Deeder

Sudden aggregation (information jet) of large amount of data is ubiquitous around connected social networks, driven by sudden interacting and non-interacting events, network security threat attacks, online sales channel etc. Clustering of information jet based on time series analysis and graph theory is not new but little work is done to connect them with particle jet statistics. We show pre-clustering based on context can element soft network or network of information which is critical to minimize time to calculate results from noisy big data. We show difference between, stochastic gradient boosting and time series-graph clustering. For disconnected higher dimensional information jet, we use Kallenberg representation theorem (Kallenberg, 2005, arXiv:1401.1137) to identify and eliminate jet similarities from dense or sparse graph.

Numerical simulation of unsteady generalized Newtonian blood flow through differently shaped distensible arterial stenoses.

PubMed

Sarifuddin; Chakravarty, S; Mandal, P K; Layek, G C

2008-01-01

An updated numerical simulation of unsteady generalized Newtonian blood flow through differently shaped distensible arterial stenoses is developed. A shear-thinning fluid modelling the deformation dependent viscosity of blood is considered for the characterization of generalized Newtonian behaviour of blood. The arterial model is treated as two-dimensional and axisymmetric with an outline of the stenosis obtained from a three-dimensional casting of a mildly stenosed artery. The full Navier-Stokes equations governing blood flow are written in the dimensionless form and the solution is accomplished by finite time-step advancement through their finite difference staggered grid representations. The marker and cell (MAC) method comprising the use of a set of marker particles moving with the fluid is used for the purpose. Results are obtained for three differently shaped stenoses - irregular, smooth and cosine curve representations. The present results do agree well with those of existing investigations in the steady state, but contrary to their conclusions the present findings demonstrate that the excess pressure drop across the cosine and the smooth stenoses is caused by neither their smoothness nor their higher degree of symmetry relative to the irregular stenosis, but is rather an effect of area cover with respect to the irregular stenosis. This effect clearly prevails throughout the entire physiological range of Reynolds numbers. Further the in-depth study in flow patterns reveals the development of flow separation zones in the diverging part of the stenosis towards the arterial wall, and they are influenced by non-Newtonian blood rheology, distensibility of the wall and flow unsteadiness in order to validate the applicability of the present model.

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.

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

Xie, T., E-mail: xietao@ustc.edu.cn; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026; Qin, H.

A unified ballooning theory, constructed on the basis of two special theories [Zhang et al., Phys. Fluids B 4, 2729 (1992); Y. Z. Zhang and T. Xie, Nucl. Fusion Plasma Phys. 33, 193 (2013)], shows that a weak up-down asymmetric mode structure is normally formed in an up-down symmetric equilibrium; the weak up-down asymmetry in mode structure is the manifestation of non-trivial higher order effects beyond the standard ballooning equation. It is shown that the asymmetric mode may have even higher growth rate than symmetric modes. The salient features of the theory are illustrated by investigating a fluid model formore » the ion temperature gradient (ITG) mode. The two dimensional (2D) analytical form of the ITG mode, solved in ballooning representation, is then converted into the radial-poloidal space to provide the natural boundary condition for solving the 2D mathematical local eigenmode problem. We find that the analytical expression of the mode structure is in a good agreement with finite difference solution. This sets a reliable framework for quasi-linear computation.« less

Satellite Observations for Detecting and Tracking Changes in Atmospheric Composition

EPA Science Inventory

The international scientific community's Integrated Global Atmosphere Chemistry Observation System report outlined a plan for ground-based, airborne and satellite Measurements, and models to integrate the observations into a 4-dimensional representation of the atmosphere (space a...

30 CFR 250.105 - Definitions.

Code of Federal Regulations, 2012 CFR

2012-07-01

... include, but is not limited to, identification of lithologic and fossil content, core analysis, laboratory... means geological knowledge, often in the form of schematic cross sections, 3-dimensional representations... information. Interpreted geophysical information means geophysical knowledge, often in the form of schematic...

30 CFR 551.1 - Definitions.

Code of Federal Regulations, 2014 CFR

2014-07-01

... been analyzed. Analysis may include, but is not limited to, identification of lithologic and fossil... the form of schematic cross sections, 3-dimensional representations, and maps, developed by.... Interpreted geophysical information means knowledge, often in the form of seismic cross sections, 3...

30 CFR 551.1 - Definitions.

Code of Federal Regulations, 2013 CFR

2013-07-01

... been analyzed. Analysis may include, but is not limited to, identification of lithologic and fossil... the form of schematic cross sections, 3-dimensional representations, and maps, developed by.... Interpreted geophysical information means knowledge, often in the form of seismic cross sections, 3...

30 CFR 551.1 - Definitions.

Code of Federal Regulations, 2012 CFR

2012-07-01

... been analyzed. Analysis may include, but is not limited to, identification of lithologic and fossil... the form of schematic cross sections, 3-dimensional representations, and maps, developed by.... Interpreted geophysical information means knowledge, often in the form of seismic cross sections, 3...

Holographic Imaging In Dense Artificial Fog

NASA Technical Reports Server (NTRS)

Liu, Hua-Kuang; Marzwell, Neville

1996-01-01

Artificial fog serves as volume-projection medium for display of three-dimensional image. Projection technique enables display of images for variety of purposes, possibly including entertainment, indoor and outdoor advertising, medical diagnostics and image representations for surgical procedures, and education.

A novel representation for planning 3-D collision-free paths

NASA Technical Reports Server (NTRS)

Bonner, Susan; Kelley, Robert B.

1990-01-01

A new scheme for the representation of objects, the successive spherical approximation (SSA), facilitates the rapid planning of collision-free paths in a dynamic three-dimensional environment. The hierarchical nature of the SSA allows collisions to be determined efficiently while still providing an exact representation of objects. The rapidity with which collisions can be detected, less than 1 sec per environment object per path, makes it possible to use a generate-and-test path-planning strategy driven by human conceptual knowledge to determine collision-free paths in a matter of seconds on a Sun 3/180 computer. A hierarchy of rules, based on the concept of a free space cell, is used to find heuristically satisfying collision-free paths in a structured environment.

The Role of High-Dimensional Diffusive Search, Stabilization, and Frustration in Protein Folding

PubMed Central

Rimratchada, Supreecha; McLeish, Tom C.B.; Radford, Sheena E.; Paci, Emanuele

2014-01-01

Proteins are polymeric molecules with many degrees of conformational freedom whose internal energetic interactions are typically screened to small distances. Therefore, in the high-dimensional conformation space of a protein, the energy landscape is locally relatively flat, in contrast to low-dimensional representations, where, because of the induced entropic contribution to the full free energy, it appears funnel-like. Proteins explore the conformation space by searching these flat subspaces to find a narrow energetic alley that we call a hypergutter and then explore the next, lower-dimensional, subspace. Such a framework provides an effective representation of the energy landscape and folding kinetics that does justice to the essential characteristic of high-dimensionality of the search-space. It also illuminates the important role of nonnative interactions in defining folding pathways. This principle is here illustrated using a coarse-grained model of a family of three-helix bundle proteins whose conformations, once secondary structure has formed, can be defined by six rotational degrees of freedom. Two folding mechanisms are possible, one of which involves an intermediate. The stabilization of intermediate subspaces (or states in low-dimensional projection) in protein folding can either speed up or slow down the folding rate depending on the amount of native and nonnative contacts made in those subspaces. The folding rate increases due to reduced-dimension pathways arising from the mere presence of intermediate states, but decreases if the contacts in the intermediate are very stable and introduce sizeable topological or energetic frustration that needs to be overcome. Remarkably, the hypergutter framework, although depending on just a few physically meaningful parameters, can reproduce all the types of experimentally observed curvature in chevron plots for realizations of this fold. PMID:24739172

A solution for two-dimensional Fredholm integral equations of the second kind with periodic, semiperiodic, or nonperiodic kernels. [integral representation of the stationary Navier-Stokes problem

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

A numerical scheme for solving two dimensional Fredholm integral equations of the second kind is developed. The proof of the convergence of the numerical scheme is shown for three cases: the case of periodic kernels, the case of semiperiodic kernels, and the case of nonperiodic kernels. Applications to the incompressible, stationary Navier-Stokes problem are of primary interest.

Memory color of natural familiar objects: effects of surface texture and 3-D shape.

PubMed

Vurro, Milena; Ling, Yazhu; Hurlbert, Anya C

2013-06-28

Natural objects typically possess characteristic contours, chromatic surface textures, and three-dimensional shapes. These diagnostic features aid object recognition, as does memory color, the color most associated in memory with a particular object. Here we aim to determine whether polychromatic surface texture, 3-D shape, and contour diagnosticity improve memory color for familiar objects, separately and in combination. We use solid three-dimensional familiar objects rendered with their natural texture, which participants adjust in real time to match their memory color for the object. We analyze mean, accuracy, and precision of the memory color settings relative to the natural color of the objects under the same conditions. We find that in all conditions, memory colors deviate slightly but significantly in the same direction from the natural color. Surface polychromaticity, shape diagnosticity, and three dimensionality each improve memory color accuracy, relative to uniformly colored, generic, or two-dimensional shapes, respectively. Shape diagnosticity improves the precision of memory color also, and there is a trend for polychromaticity to do so as well. Differently from other studies, we find that the object contour alone also improves memory color. Thus, enhancing the naturalness of the stimulus, in terms of either surface or shape properties, enhances the accuracy and precision of memory color. The results support the hypothesis that memory color representations are polychromatic and are synergistically linked with diagnostic shape representations.

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

Steiner, J.L.; Lime, J.F.; Elson, J.S.

One dimensional TRAC transient calculations of the process inherent ultimate safety (PIUS) advanced reactor design were performed for a pump-trip SCRAM. The TRAC calculations showed that the reactor power response and shutdown were in qualitative agreement with the one-dimensional analyses presented in the PIUS Preliminary Safety Information Document (PSID) submitted by Asea Brown Boveri (ABB) to the US Nuclear Regulatory Commission for preapplication safety review. The PSID analyses were performed with the ABB-developed RIGEL code. The TRAC-calculated phenomena and trends were also similar to those calculated with another one-dimensional PIUS model, the Brookhaven National Laboratory developed PIPA code. A TRACmore » pump-trip SCRAM transient has also been calculated with a TRAC model containing a multi-dimensional representation of the PIUS intemal flow structures and core region. The results obtained using the TRAC fully one-dimensional PIUS model are compared to the RIGEL, PIPA, and TRAC multi-dimensional results.« less

High-School Chemistry Students' Performance and Gender Differences in a Computerized Molecular Modeling Learning Environment

NASA Astrophysics Data System (ADS)

Barnea, Nitza; Dori, Yehudit J.

1999-12-01

Computerized molecular modeling (CMM) contributes to the development of visualization skills via vivid animation of three dimensional representations. Its power to illustrate and explore phenomena in chemistry teaching stems from the convenience and simplicity of building molecules of any size and color in a number of presentation styles. A new CMM-based learning environment for teaching and learning chemistry in Israeli high schools has been designed and implemented. Three tenth grade experimental classes used this discovery CMM approach, while two other classes, who studied the same topic in the customary approach, served as a control group. We investigated the effects of using molecular modeling on students' spatial ability, understanding of new concepts related to geometric and symbolic representations and students' perception of the model concept. Each variable was examined for gender differences. Students of the experimental group performed better than control group students in all three performance aspects. Experimental group students scored higher than the control group students in the achievement test on structure and bonding. Students' spatial ability improved in both groups, but students from the experimental group scored higher. For the average students in the two groups the improvement in all three spatial ability sub-tests —paper folding, card rotation, and cube comparison—was significantly higher for the experimental group. Experimental group students gained better insight into the model concept than the control group and could explain more phenomena with the aid of a variety of models. Hence, CMM helps in particular to improve the examined cognitive aspects of the average student population. In most of the achievement and spatial ability tests no significant differences between the genders were found, but in some aspects of model perception and verbal argumentation differences still exist. Experimental group females improved their model perception more than the control group females in understanding ways to create models and in the role of models as mental structures and prediction tools. Teachers' and students' feedback on the CMM learning environment was found to be positive, as it helped them understand concepts in molecular geometry and bonding. The results of this study suggest that teaching/learning of topics in chemistry that are related to three dimensional structures can be improved by using a discovery approach in a computerized learning environment.

Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation

NASA Astrophysics Data System (ADS)

Debusschere, Bert J.; Najm, Habib N.; Matta, Alain; Knio, Omar M.; Ghanem, Roger G.; Le Maître, Olivier P.

2003-08-01

This paper presents a model for two-dimensional electrochemical microchannel flow including the propagation of uncertainty from model parameters to the simulation results. For a detailed representation of electroosmotic and pressure-driven microchannel flow, the model considers the coupled momentum, species transport, and electrostatic field equations, including variable zeta potential. The chemistry model accounts for pH-dependent protein labeling reactions as well as detailed buffer electrochemistry in a mixed finite-rate/equilibrium formulation. Uncertainty from the model parameters and boundary conditions is propagated to the model predictions using a pseudo-spectral stochastic formulation with polynomial chaos (PC) representations for parameters and field quantities. Using a Galerkin approach, the governing equations are reformulated into equations for the coefficients in the PC expansion. The implementation of the physical model with the stochastic uncertainty propagation is applied to protein-labeling in a homogeneous buffer, as well as in two-dimensional electrochemical microchannel flow. The results for the two-dimensional channel show strong distortion of sample profiles due to ion movement and consequent buffer disturbances. The uncertainty in these results is dominated by the uncertainty in the applied voltage across the channel.

Embedding and Publishing Interactive, 3-Dimensional, Scientific Figures in Portable Document Format (PDF) Files

PubMed Central

Barnes, David G.; Vidiassov, Michail; Ruthensteiner, Bernhard; Fluke, Christopher J.; Quayle, Michelle R.; McHenry, Colin R.

2013-01-01

With the latest release of the S2PLOT graphics library, embedding interactive, 3-dimensional (3-d) scientific figures in Adobe Portable Document Format (PDF) files is simple, and can be accomplished without commercial software. In this paper, we motivate the need for embedding 3-d figures in scholarly articles. We explain how 3-d figures can be created using the S2PLOT graphics library, exported to Product Representation Compact (PRC) format, and included as fully interactive, 3-d figures in PDF files using the movie15 LaTeX package. We present new examples of 3-d PDF figures, explain how they have been made, validate them, and comment on their advantages over traditional, static 2-dimensional (2-d) figures. With the judicious use of 3-d rather than 2-d figures, scientists can now publish, share and archive more useful, flexible and faithful representations of their study outcomes. The article you are reading does not have embedded 3-d figures. The full paper, with embedded 3-d figures, is recommended and is available as a supplementary download from PLoS ONE (File S2). PMID:24086243

Embedding and publishing interactive, 3-dimensional, scientific figures in Portable Document Format (PDF) files.

PubMed

Barnes, David G; Vidiassov, Michail; Ruthensteiner, Bernhard; Fluke, Christopher J; Quayle, Michelle R; McHenry, Colin R

2013-01-01

With the latest release of the S2PLOT graphics library, embedding interactive, 3-dimensional (3-d) scientific figures in Adobe Portable Document Format (PDF) files is simple, and can be accomplished without commercial software. In this paper, we motivate the need for embedding 3-d figures in scholarly articles. We explain how 3-d figures can be created using the S2PLOT graphics library, exported to Product Representation Compact (PRC) format, and included as fully interactive, 3-d figures in PDF files using the movie15 LaTeX package. We present new examples of 3-d PDF figures, explain how they have been made, validate them, and comment on their advantages over traditional, static 2-dimensional (2-d) figures. With the judicious use of 3-d rather than 2-d figures, scientists can now publish, share and archive more useful, flexible and faithful representations of their study outcomes. The article you are reading does not have embedded 3-d figures. The full paper, with embedded 3-d figures, is recommended and is available as a supplementary download from PLoS ONE (File S2).

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables

NASA Astrophysics Data System (ADS)

Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino

2013-12-01

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables.

PubMed

Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino

2013-12-07

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

Regression-based adaptive sparse polynomial dimensional decomposition for sensitivity analysis

NASA Astrophysics Data System (ADS)

Tang, Kunkun; Congedo, Pietro; Abgrall, Remi

2014-11-01

Polynomial dimensional decomposition (PDD) is employed in this work for global sensitivity analysis and uncertainty quantification of stochastic systems subject to a large number of random input variables. Due to the intimate structure between PDD and Analysis-of-Variance, PDD is able to provide simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to polynomial chaos (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of the standard method unaffordable for real engineering applications. In order to address this problem of curse of dimensionality, this work proposes a variance-based adaptive strategy aiming to build a cheap meta-model by sparse-PDD with PDD coefficients computed by regression. During this adaptive procedure, the model representation by PDD only contains few terms, so that the cost to resolve repeatedly the linear system of the least-square regression problem is negligible. The size of the final sparse-PDD representation is much smaller than the full PDD, since only significant terms are eventually retained. Consequently, a much less number of calls to the deterministic model is required to compute the final PDD coefficients.

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

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

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

2014-01-15

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

Back in the USSR: Path Dependence Effects in Student Representation in Russia

ERIC Educational Resources Information Center

Chirikov, Igor; Gruzdev, Ivan

2014-01-01

This paper analyses the current state of student representation in Russia as deeply rooted in the institutional structure of the Soviet higher education system. The study traces the origins of existing institutional arrangements for student representation at the level of university governance and analyses how representation practices have been…

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.

Uncovering the Images and Meanings of International Organizations (IOs) in Higher Education Research

ERIC Educational Resources Information Center

Shahjahan, Riyad A.; Madden, Meggan

2015-01-01

Employing Stuart Hall's concept of representation, we examine how international organizations (IOs) are presented in the higher education literature. This paper examines how IOs, such as the World Bank, OECD, and UNESCO, are conceptualized and represented by higher education researchers. We focus on three main representations of IOs in the higher…

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

PubMed

Harris, W F

1997-06-01

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

Beyond Point Clouds and Virtual Reality. Innovative Methods and Technologies for the Protection and Promotion of Cultural Heritage

NASA Astrophysics Data System (ADS)

Canevese, E. P.; De Gottardo, T.

2017-05-01

The morphometric and photogrammetric knowledge, combined with the historical research, are the indispensable prerequisites for the protection and enhancement of historical, architectural and cultural heritage. Nowadays the use of BIM (Building Information Modeling) as a supporting tool for restoration and conservation purposes is becoming more and more popular. However this tool is not fully adequate in this context because of its simplified representation of three-dimensional models, resulting from solid modelling techniques (mostly used in virtual reality) causing the loss of important morphometric information. One solution to this problem is imagining new advanced tools and methods that enable the building of effective and efficient three-dimensional representations backing the correct geometric analysis of the built model. Twenty-year of interdisciplinary research activities implemented by Virtualgeo focused on developing new methods and tools for 3D modeling that go beyond the simplified digital-virtual reconstruction used in standard solid modeling. Methods and tools allowing the creation of informative and true to life three-dimensional representations, that can be further used by various academics or industry professionals to carry out diverse analysis, research and design activities. Virtualgeo applied research activities, in line with the European Commission 2013's directives of Reflective 7 - Horizon 2020 Project, gave birth to GeomaticsCube Ecosystem, an ecosystem resulting from different technologies based on experiences garnered from various fields, metrology in particular, a discipline used in the automotive and aviation industry, and in general mechanical engineering. The implementation of the metrological functionality is only possible if the 3D model is created with special modeling techniques, based on surface modeling that allow, as opposed to solid modeling, a 3D representation of the manufact that is true to life. The advantages offered by metrological analysis are varied and important because they permit a precise and detailed overview of the 3D model's characteristics, and especially the over time monitoring of the model itself, these informations are impossible to obtain from a three-dimensional representation produced with solid modelling techniques. The applied research activities are also focused on the possibility of obtaining a photogrammetric and informative 3D model., Two distinct applications have been developed for this purpose, the first allows the classification of each individual element and the association of its material characteristics during the 3D modelling phase, whilst the second allows segmentations of the photogrammetric 3D model in its diverse aspects (materic, related to decay, chronological) with the possibility to make use and to populate the database, associated with the 3D model, with all types of multimedia contents.

Towards a gestural 3D interaction for tangible and three-dimensional GIS visualizations

NASA Astrophysics Data System (ADS)

Partsinevelos, Panagiotis; Agadakos, Ioannis; Pattakos, Nikolas; Maragakis, Michail

2014-05-01

The last decade has been characterized by a significant increase of spatially dependent applications that require storage, visualization, analysis and exploration of geographic information. GIS analysis of spatiotemporal geographic data is operated by highly trained personnel under an abundance of software and tools, lacking interoperability and friendly user interaction. Towards this end, new forms of querying and interaction are emerging, including gestural interfaces. Three-dimensional GIS representations refer to either tangible surfaces or projected representations. Making a 3D tangible geographic representation touch-sensitive may be a convenient solution, but such an approach raises the cost significantly and complicates the hardware and processing required to combine touch-sensitive material (for pinpointing points) with deformable material (for displaying elevations). In this study, a novel interaction scheme upon a three dimensional visualization of GIS data is proposed. While gesture user interfaces are not yet fully acceptable due to inconsistencies and complexity, a non-tangible GIS system where 3D visualizations are projected, calls for interactions that are based on three-dimensional, non-contact and gestural procedures. Towards these objectives, we use the Microsoft Kinect II system which includes a time of flight camera, allowing for a robust and real time depth map generation, along with the capturing and translation of a variety of predefined gestures from different simultaneous users. By incorporating these features into our system architecture, we attempt to create a natural way for users to operate on GIS data. Apart from the conventional pan and zoom features, the key functions addressed for the 3-D user interface is the ability to pinpoint particular points, lines and areas of interest, such as destinations, waypoints, landmarks, closed areas, etc. The first results shown, concern a projected GIS representation where the user selects points and regions of interest while the GIS component responds accordingly by changing the scenario in a natural disaster application. Creating a 3D model representation of geospatial data provides a natural way for users to perceive and interact with space. To the best of our knowledge it is the first attempt to use Kinect II for GIS applications and generally virtual environments using novel Human Computer Interaction methods. Under a robust decision support system, the users are able to interact, combine and computationally analyze information in three dimensions using gestures. This study promotes geographic awareness and education and will prove beneficial for a wide range of geoscience applications including natural disaster and emergency management. Acknowledgements: This work is partially supported under the framework of the "Cooperation 2011" project ATLANTAS (11_SYN_6_1937) funded from the Operational Program "Competitiveness and Entrepreneurship" (co-funded by the European Regional Development Fund (ERDF)) and managed by the Greek General Secretariat for Research and Technology.

30 CFR 251.1 - Definitions.

Code of Federal Regulations, 2011 CFR

2011-07-01

..., identification of lithologic and fossil content, core analyses, laboratory analyses of physical and chemical..., often in the form of schematic cross sections, 3-dimensional representations, and maps, developed by.... Interpreted geophysical information means knowledge, often in the form of seismic cross sections, 3...

30 CFR 250.105 - Definitions.

Code of Federal Regulations, 2013 CFR

2013-07-01

... include, but is not limited to, identification of lithologic and fossil content, core analysis, laboratory.... Interpreted geological information means geological knowledge, often in the form of schematic cross sections... knowledge, often in the form of schematic cross sections, 3-dimensional representations, and maps, developed...

30 CFR 250.105 - Definitions.

Code of Federal Regulations, 2014 CFR

2014-07-01

... include, but is not limited to, identification of lithologic and fossil content, core analysis, laboratory.... Interpreted geological information means geological knowledge, often in the form of schematic cross sections... knowledge, often in the form of schematic cross sections, 3-dimensional representations, and maps, developed...

30 CFR 251.1 - Definitions.

Code of Federal Regulations, 2010 CFR

2010-07-01

.... Analysis may include, but is not limited to, identification of lithologic and fossil content, core analyses... the form of schematic cross sections, 3-dimensional representations, and maps, developed by.... Interpreted geophysical information means knowledge, often in the form of seismic cross sections, 3...

Boundary Quantum Knizhnik-Zamolodchikov Equations and Bethe Vectors

NASA Astrophysics Data System (ADS)

Reshetikhin, Nicolai; Stokman, Jasper; Vlaar, Bart

2015-06-01

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

Self-organized Evaluation of Dynamic Hand Gestures for Sign Language Recognition

NASA Astrophysics Data System (ADS)

Buciu, Ioan; Pitas, Ioannis

Two main theories exist with respect to face encoding and representation in the human visual system (HVS). The first one refers to the dense (holistic) representation of the face, where faces have "holon"-like appearance. The second one claims that a more appropriate face representation is given by a sparse code, where only a small fraction of the neural cells corresponding to face encoding is activated. Theoretical and experimental evidence suggest that the HVS performs face analysis (encoding, storing, face recognition, facial expression recognition) in a structured and hierarchical way, where both representations have their own contribution and goal. According to neuropsychological experiments, it seems that encoding for face recognition, relies on holistic image representation, while a sparse image representation is used for facial expression analysis and classification. From the computer vision perspective, the techniques developed for automatic face and facial expression recognition fall into the same two representation types. Like in Neuroscience, the techniques which perform better for face recognition yield a holistic image representation, while those techniques suitable for facial expression recognition use a sparse or local image representation. The proposed mathematical models of image formation and encoding try to simulate the efficient storing, organization and coding of data in the human cortex. This is equivalent with embedding constraints in the model design regarding dimensionality reduction, redundant information minimization, mutual information minimization, non-negativity constraints, class information, etc. The presented techniques are applied as a feature extraction step followed by a classification method, which also heavily influences the recognition results.

Geometric actions for three-dimensional gravity

NASA Astrophysics Data System (ADS)

Barnich, G.; González, H. A.; Salgado-Rebolledo, P.

2018-01-01

The solution space of three-dimensional asymptotically anti-de Sitter or flat Einstein gravity is given by the coadjoint representation of two copies of the Virasoro group in the former and the centrally extended BMS3 group in the latter case. Dynamical actions that control these solution spaces are usually constructed by starting from the Chern–Simons formulation and imposing all boundary conditions. In this note, an alternative route is followed. We study in detail how to derive these actions from a group-theoretical viewpoint by constructing geometric actions for each of the coadjoint orbits, including the appropriate Hamiltonians. We briefly sketch relevant generalizations and potential applications beyond three-dimensional gravity.

User's manual for master: Modeling of aerodynamic surfaces by 3-dimensional explicit representation. [input to three dimensional computational fluid dynamics

NASA Technical Reports Server (NTRS)

Gibson, S. G.

1983-01-01

A system of computer programs was developed to model general three dimensional surfaces. Surfaces are modeled as sets of parametric bicubic patches. There are also capabilities to transform coordinates, to compute mesh/surface intersection normals, and to format input data for a transonic potential flow analysis. A graphical display of surface models and intersection normals is available. There are additional capabilities to regulate point spacing on input curves and to compute surface/surface intersection curves. Input and output data formats are described; detailed suggestions are given for user input. Instructions for execution are given, and examples are shown.

Protein space: a natural method for realizing the nature of protein universe.

PubMed

Yu, Chenglong; Deng, Mo; Cheng, Shiu-Yuen; Yau, Shek-Chung; He, Rong L; Yau, Stephen S-T

2013-02-07

Current methods cannot tell us what the nature of the protein universe is concretely. They are based on different models of amino acid substitution and multiple sequence alignment which is an NP-hard problem and requires manual intervention. Protein structural analysis also gives a direction for mapping the protein universe. Unfortunately, now only a minuscule fraction of proteins' 3-dimensional structures are known. Furthermore, the phylogenetic tree representations are not unique for any existing tree construction methods. Here we develop a novel method to realize the nature of protein universe. We show the protein universe can be realized as a protein space in 60-dimensional Euclidean space using a distance based on a normalized distribution of amino acids. Every protein is in one-to-one correspondence with a point in protein space, where proteins with similar properties stay close together. Thus the distance between two points in protein space represents the biological distance of the corresponding two proteins. We also propose a natural graphical representation for inferring phylogenies. The representation is natural and unique based on the biological distances of proteins in protein space. This will solve the fundamental question of how proteins are distributed in the protein universe. Copyright © 2012 Elsevier Ltd. All rights reserved.

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.

Supervoxels for graph cuts-based deformable image registration using guided image filtering

NASA Astrophysics Data System (ADS)

Szmul, Adam; Papież, Bartłomiej W.; Hallack, Andre; Grau, Vicente; Schnabel, Julia A.

2017-11-01

We propose combining a supervoxel-based image representation with the concept of graph cuts as an efficient optimization technique for three-dimensional (3-D) deformable image registration. Due to the pixels/voxels-wise graph construction, the use of graph cuts in this context has been mainly limited to two-dimensional (2-D) applications. However, our work overcomes some of the previous limitations by posing the problem on a graph created by adjacent supervoxels, where the number of nodes in the graph is reduced from the number of voxels to the number of supervoxels. We demonstrate how a supervoxel image representation combined with graph cuts-based optimization can be applied to 3-D data. We further show that the application of a relaxed graph representation of the image, followed by guided image filtering over the estimated deformation field, allows us to model "sliding motion." Applying this method to lung image registration results in highly accurate image registration and anatomically plausible estimations of the deformations. Evaluation of our method on a publicly available computed tomography lung image dataset leads to the observation that our approach compares very favorably with state of the art methods in continuous and discrete image registration, achieving target registration error of 1.16 mm on average per landmark.

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

Robust and efficient anomaly detection using heterogeneous representations

NASA Astrophysics Data System (ADS)

Hu, Xing; Hu, Shiqiang; Xie, Jinhua; Zheng, Shiyou

2015-05-01

Various approaches have been proposed for video anomaly detection. Yet these approaches typically suffer from one or more limitations: they often characterize the pattern using its internal information, but ignore its external relationship which is important for local anomaly detection. Moreover, the high-dimensionality and the lack of robustness of pattern representation may lead to problems, including overfitting, increased computational cost and memory requirements, and high false alarm rate. We propose a video anomaly detection framework which relies on a heterogeneous representation to account for both the pattern's internal information and external relationship. The internal information is characterized by slow features learned by slow feature analysis from low-level representations, and the external relationship is characterized by the spatial contextual distances. The heterogeneous representation is compact, robust, efficient, and discriminative for anomaly detection. Moreover, both the pattern's internal information and external relationship can be taken into account in the proposed framework. Extensive experiments demonstrate the robustness and efficiency of our approach by comparison with the state-of-the-art approaches on the widely used benchmark datasets.

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.

Modern cosmology and the origin of our three dimensionality.

PubMed

Woodbury, M A; Woodbury, M F

1998-01-01

We are three dimensional egocentric beings existing within a specific space/time continuum and dimensionality which we assume wrongly is the same for all times and places throughout the entire universe. Physicists name Omnipoint the origin of the universe at Dimension zero, which exploded as a Big Bang of energy proceeding at enormous speed along one dimension which eventually curled up into matter: particles, atoms, molecules and Galaxies which exist in two dimensional space. Finally from matter spread throughout the cosmos evolved life generating eventually the DNA molecules which control the construction of brains complex enough to construct our three dimensional Body Representation from which is extrapolated what we perceive as a 3-D universe. The whole interconnected structures which conjure up our three dimensionality are as fragile as Humpty Dumpty, capable of breaking apart with terrifying effects for the individual patient during a psychotic panic, revealing our three dimensionality to be but "maya", an illusion, which we psychiatrists work at putting back together.

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

DOE PAGES

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

2018-03-20

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

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

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

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

Dark and bright solitons for the two-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch system with time-dependent coefficient

NASA Astrophysics Data System (ADS)

Shaikhova, G.; Ozat, N.; Yesmakhanova, K.; Bekova, G.

2018-02-01

In this work, we present Lax pair for two-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch (cmKdV-MB) system with the time-dependent coefficient. Dark and bright soliton solutions for the cmKdV-MB system with variable coefficient are received by Darboux transformation. Moreover, the determinant representation of the one-fold and two-fold Darboux transformation for the cmKdV-MB system with time-dependent coefficient is presented.

Mass gap in the weak coupling limit of (2 +1 )-dimensional SU(2) lattice gauge theory

NASA Astrophysics Data System (ADS)

Anishetty, Ramesh; Sreeraj, T. P.

2018-04-01

We develop the dual description of (2 +1 )-dimensional SU(2) lattice gauge theory as interacting "Abelian-like" electric loops by using Schwinger bosons. "Point splitting" of the lattice enables us to construct explicit Hilbert space for the gauge invariant theory which in turn makes dynamics more transparent. Using path integral representation in phase space, the interacting closed loop dynamics is analyzed in the weak coupling limit to get the mass gap.

Australian Indigenous Higher Education: Politics, Policy and Representation

ERIC Educational Resources Information Center

Wilson, Katie; Wilks, Judith

2015-01-01

The growth of Aboriginal and Torres Strait Islander participation in Australian higher education from 1959 to the present is notable statistically, but below population parity. Distinct patterns in government policy-making and programme development, inconsistent funding and political influences, together with Indigenous representation during the…

The use of virtual reality to reimagine two-dimensional representations of three-dimensional spaces

NASA Astrophysics Data System (ADS)

Fath, Elaine

2015-03-01

A familiar realm in the world of two-dimensional art is the craft of taking a flat canvas and creating, through color, size, and perspective, the illusion of a three-dimensional space. Using well-explored tricks of logic and sight, impossible landscapes such as those by surrealists de Chirico or Salvador Dalí seem to be windows into new and incredible spaces which appear to be simultaneously feasible and utterly nonsensical. As real-time 3D imaging becomes increasingly prevalent as an artistic medium, this process takes on an additional layer of depth: no longer is two-dimensional space restricted to strategies of light, color, line and geometry to create the impression of a three-dimensional space. A digital interactive environment is a space laid out in three dimensions, allowing the user to explore impossible environments in a way that feels very real. In this project, surrealist two-dimensional art was researched and reimagined: what would stepping into a de Chirico or a Magritte look and feel like, if the depth and distance created by light and geometry were not simply single-perspective illusions, but fully formed and explorable spaces? 3D environment-building software is allowing us to step into these impossible spaces in ways that 2D representations leave us yearning for. This art project explores what we gain--and what gets left behind--when these impossible spaces become doors, rather than windows. Using sketching, Maya 3D rendering software, and the Unity Engine, surrealist art was reimagined as a fully navigable real-time digital environment. The surrealist movement and its key artists were researched for their use of color, geometry, texture, and space and how these elements contributed to their work as a whole, which often conveys feelings of unexpectedness or uneasiness. The end goal was to preserve these feelings while allowing the viewer to actively engage with the space.

Using Stereoscopy to Teach Complex Biological Concepts

ERIC Educational Resources Information Center

Ferdig, Richard; Blank, James; Kratcoski, Annette; Clements, Robert

2015-01-01

Used effectively, stereoscopic three-dimensional (3D) technologies can engage students with complex disciplinary content as they are presented with informative representations of abstract concepts. In addition, preliminary evidence suggests that stereoscopy may enhance learning and retention in some educational settings. Biological concepts…

30 CFR 580.1 - What definitions apply to this part?

Code of Federal Regulations, 2014 CFR

2014-07-01

... of lithologic and fossil content, core analyses, laboratory analyses of physical and chemical... the form of schematic cross sections, 3-dimensional representations, and maps, developed by.... Interpreted geophysical information means knowledge, often in the form of seismic cross sections, 3...

30 CFR 580.1 - What definitions apply to this part?

Code of Federal Regulations, 2013 CFR

2013-07-01

... of lithologic and fossil content, core analyses, laboratory analyses of physical and chemical... the form of schematic cross sections, 3-dimensional representations, and maps, developed by.... Interpreted geophysical information means knowledge, often in the form of seismic cross sections, 3...

30 CFR 580.1 - What definitions apply to this part?

Code of Federal Regulations, 2012 CFR

2012-07-01

... of lithologic and fossil content, core analyses, laboratory analyses of physical and chemical... the form of schematic cross sections, 3-dimensional representations, and maps, developed by.... Interpreted geophysical information means knowledge, often in the form of seismic cross sections, 3...

An Introduction to Educational Holography.

ERIC Educational Resources Information Center

Lloyd, R. Scott

Holograms are capable of taking the two-dimensional ways of envisioning information to another dimension of presentation, representation, and conceptualization. Educational holography is joining display holography, holographic testing of materials, and holographic optical elements as a fourth major field in holography. Holograms are explored as…

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

PubMed

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

2015-03-01

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

Real-time ligand binding pocket database search using local surface descriptors.

PubMed

Chikhi, Rayan; Sael, Lee; Kihara, Daisuke

2010-07-01

Because of the increasing number of structures of unknown function accumulated by ongoing structural genomics projects, there is an urgent need for computational methods for characterizing protein tertiary structures. As functions of many of these proteins are not easily predicted by conventional sequence database searches, a legitimate strategy is to utilize structure information in function characterization. Of particular interest is prediction of ligand binding to a protein, as ligand molecule recognition is a major part of molecular function of proteins. Predicting whether a ligand molecule binds a protein is a complex problem due to the physical nature of protein-ligand interactions and the flexibility of both binding sites and ligand molecules. However, geometric and physicochemical complementarity is observed between the ligand and its binding site in many cases. Therefore, ligand molecules which bind to a local surface site in a protein can be predicted by finding similar local pockets of known binding ligands in the structure database. Here, we present two representations of ligand binding pockets and utilize them for ligand binding prediction by pocket shape comparison. These representations are based on mapping of surface properties of binding pockets, which are compactly described either by the two-dimensional pseudo-Zernike moments or the three-dimensional Zernike descriptors. These compact representations allow a fast real-time pocket searching against a database. Thorough benchmark studies employing two different datasets show that our representations are competitive with the other existing methods. Limitations and potentials of the shape-based methods as well as possible improvements are discussed.

Independent psychophysical measurement of experimental modulations in the somatotopy of cutaneous heat-pain stimuli.

PubMed

Trojan, Jörg; Kleinböhl, Dieter; Stolle, Annette M; Andersen, Ole K; Hölzl, Rupert; Arendt-Nielsen, Lars

2009-03-01

Distortions of the body image have been repeatedly reported for various clinical conditions, but direct experimental analyses of the perceptual changes involved are still scarce. In addition, most experimental studies rely on cerebral activation patterns to assess neuroplastic changes in central representation, although the relationship between cerebral topography and the topology of the perceptual space is not clear. This study examines whether the direct psychophysical mapping approach we introduced recently (Trojan et al., Brain Res 2006;1120:106-113) is capable of tracking perceptual distortions in the somatotopic representation of heat-pain stimuli. Eleven healthy participants indicated the perceived positions of CO(2) laser stimuli, repetitively presented to the dorsal forearm, with a 3D tracking system in two consecutive sessions, separated by the topical application of capsaicin cream. In line with earlier reports, we expected that the resulting individual perceptual maps (i.e., one-dimensional projections of the perceived positions onto the forearm surface) would be subject to modulation through the altered sensory input, to be measured in terms of altered topological parameters. We found that the topology and metrics of the somatotopic representation were well preserved in the second session, but that the perceptual map was compressed to a smaller range in 9 out of 11 participants. By providing dimensional measures of perceptual representations, perceptual maps constitute an independent, genuinely psychological complement to the topography of cortical activations measured with neuroimaging methods. In addition, we expect them to be useful in diagnosing pathological changes in body perception accompanying chronic pain and other disorders.

Computational effects of inlet representation on powered hypersonic, airbreathing models

NASA Technical Reports Server (NTRS)

Huebner, Lawrence D.; Tatum, Kenneth E.

1993-01-01

Computational results are presented to illustrate the powered aftbody effects of representing the scramjet inlet on a generic hypersonic vehicle with a fairing, to divert the external flow, as compared to an operating flow-through scramjet inlet. This study is pertinent to the ground testing of hypersonic, airbreathing models employing scramjet exhaust flow simulation in typical small-scale hypersonic wind tunnels. The comparison of aftbody effects due to inlet representation is well-suited for computational study, since small model size typically precludes the ability to ingest flow into the inlet and perform exhaust simulation at the same time. Two-dimensional analysis indicates that, although flowfield differences exist for the two types of inlet representations, little, if any, difference in surface aftbody characteristics is caused by fairing over the inlet.

Research on knowledge representation, machine learning, and knowledge acquisition

NASA Technical Reports Server (NTRS)

Buchanan, Bruce G.

1987-01-01

Research in knowledge representation, machine learning, and knowledge acquisition performed at Knowledge Systems Lab. is summarized. The major goal of the research was to develop flexible, effective methods for representing the qualitative knowledge necessary for solving large problems that require symbolic reasoning as well as numerical computation. The research focused on integrating different representation methods to describe different kinds of knowledge more effectively than any one method can alone. In particular, emphasis was placed on representing and using spatial information about three dimensional objects and constraints on the arrangement of these objects in space. Another major theme is the development of robust machine learning programs that can be integrated with a variety of intelligent systems. To achieve this goal, learning methods were designed, implemented and experimented within several different problem solving environments.

Decomposition of the polynomial kernel of arbitrary higher spin Dirac operators

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

Eelbode, D., E-mail: David.Eelbode@ua.ac.be; Raeymaekers, T., E-mail: Tim.Raeymaekers@UGent.be; Van der Jeugt, J., E-mail: Joris.VanderJeugt@UGent.be

2015-10-15

In a series of recent papers, we have introduced higher spin Dirac operators, which are generalisations of the classical Dirac operator. Whereas the latter acts on spinor-valued functions, the former acts on functions taking values in arbitrary irreducible half-integer highest weight representations for the spin group. In this paper, we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group. We will hereby make use of results from representation theory.

Snow stratigraphic heterogeneity within ground-based passive microwave radiometer footprints: Implications for emission modeling

NASA Astrophysics Data System (ADS)

Rutter, Nick; Sandells, Mel; Derksen, Chris; Toose, Peter; Royer, Alain; Montpetit, Benoit; Langlois, Alex; Lemmetyinen, Juha; Pulliainen, Jouni

2014-03-01

Two-dimensional measurements of snowpack properties (stratigraphic layering, density, grain size, and temperature) were used as inputs to the multilayer Helsinki University of Technology (HUT) microwave emission model at a centimeter-scale horizontal resolution, across a 4.5 m transect of ground-based passive microwave radiometer footprints near Churchill, Manitoba, Canada. Snowpack stratigraphy was complex (between six and eight layers) with only three layers extending continuously throughout the length of the transect. Distributions of one-dimensional simulations, accurately representing complex stratigraphic layering, were evaluated using measured brightness temperatures. Large biases (36 to 68 K) between simulated and measured brightness temperatures were minimized (-0.5 to 0.6 K), within measurement accuracy, through application of grain scaling factors (2.6 to 5.3) at different combinations of frequencies, polarizations, and model extinction coefficients. Grain scaling factors compensated for uncertainty relating optical specific surface area to HUT effective grain size inputs and quantified relative differences in scattering and absorption properties of various extinction coefficients. The HUT model required accurate representation of ice lenses, particularly at horizontal polarization, and large grain scaling factors highlighted the need to consider microstructure beyond the size of individual grains. As variability of extinction coefficients was strongly influenced by the proportion of large (hoar) grains in a vertical profile, it is important to consider simulations from distributions of one-dimensional profiles rather than single profiles, especially in sub-Arctic snowpacks where stratigraphic variability can be high. Model sensitivity experiments suggested that the level of error in field measurements and the new methodological framework used to apply them in a snow emission model were satisfactory. Layer amalgamation showed that a three-layer representation of snowpack stratigraphy reduced the bias of a one-layer representation by about 50%.

Optical frequency selective surface design using a GPU accelerated finite element boundary integral method

NASA Astrophysics Data System (ADS)

Ashbach, Jason A.

Periodic metallodielectric frequency selective surface (FSS) designs have historically seen widespread use in the microwave and radio frequency spectra. By scaling the dimensions of an FSS unit cell for use in a nano-fabrication process, these concepts have recently been adapted for use in optical applications as well. While early optical designs have been limited to wellunderstood geometries or optimized pixelated screens, nano-fabrication, lithographic and interconnect technology has progressed to a point where it is possible to fabricate metallic screens of arbitrary geometries featuring curvilinear or even three-dimensional characteristics that are only tens of nanometers wide. In order to design an FSS featuring such characteristics, it is important to have a robust numerical solver that features triangular elements in purely two-dimensional geometries and prismatic or tetrahedral elements in three-dimensional geometries. In this dissertation, a periodic finite element method code has been developed which features prismatic elements whose top and bottom boundaries are truncated by numerical integration of the boundary integral as opposed to an approximate representation found in a perfectly matched layer. However, since no exact solution exists for the calculation of triangular elements in a boundary integral, this process can be time consuming. To address this, these calculations were optimized for parallelization such that they may be done on a graphics processor, which provides a large increase in computational speed. Additionally, a simple geometrical representation using a Bezier surface is presented which provides generality with few variables. With a fast numerical solver coupled with a lowvariable geometric representation, a heuristic optimization algorithm has been used to develop several optical designs such as an absorber, a circular polarization filter, a transparent conductive surface and an enhanced, optical modulator.

A comprehensive three-dimensional cortical map of vowel space.

PubMed

Scharinger, Mathias; Idsardi, William J; Poe, Samantha

2011-12-01

Mammalian cortex is known to contain various kinds of spatial encoding schemes for sensory information including retinotopic, somatosensory, and tonotopic maps. Tonotopic maps are especially interesting for human speech sound processing because they encode linguistically salient acoustic properties. In this study, we mapped the entire vowel space of a language (Turkish) onto cortical locations by using the magnetic N1 (M100), an auditory-evoked component that peaks approximately 100 msec after auditory stimulus onset. We found that dipole locations could be structured into two distinct maps, one for vowels produced with the tongue positioned toward the front of the mouth (front vowels) and one for vowels produced in the back of the mouth (back vowels). Furthermore, we found spatial gradients in lateral-medial, anterior-posterior, and inferior-superior dimensions that encoded the phonetic, categorical distinctions between all the vowels of Turkish. Statistical model comparisons of the dipole locations suggest that the spatial encoding scheme is not entirely based on acoustic bottom-up information but crucially involves featural-phonetic top-down modulation. Thus, multiple areas of excitation along the unidimensional basilar membrane are mapped into higher dimensional representations in auditory cortex.

Attachment in families with Huntington's disease. A paradigm in clinical genetics.

PubMed

Van der Meer, Lucienne; Timman, Reinier; Trijsburg, Wim; Duisterhof, Marleen; Erdman, Ruud; Van Elderen, Thérèse; Tibben, Aad

2006-10-01

Based on the premise that attachment experiences lead to a working model for social relationships throughout life, this study investigates if there is a difference between adult attachment representations in individuals who were brought up by a parent with Huntington's disease (HD), compared to a non-clinical population. Specific events in the parents' disease process, especially those leading to trauma and loss will receive attention. Using the Adult Attachment Interview, adult attachment representations were investigated in 32 unaffected adults at 50% risk for HD who were raised by an affected parent. We found a lower percentage of secure attachment representations, a higher percentage of preoccupied representations, and a higher percentage of unresolved/disorganized representations in our sample, compared to a non-clinical population. A relatively late start of the parent's HD career was associated with a secure adult attachment representation. Death of the HD parent before the child's 18th birthday was associated with an unresolved/disorganized adult attachment representation. Growing up in a family where one of the parents has Huntington's disease appears to affect the offspring's adult attachment representation. This study can be of relevance for genetic counselling, as well as for counselling and intervention in childrearing matters.

Characteristics of a Two-Dimensional Hydrogenlike Atom

NASA Astrophysics Data System (ADS)

Skobelev, V. V.

2018-06-01

Using the customary and well-known representation of the radiation probability of a hydrogen-like atom in the three-dimensional case, a general expression for the probability of single-photon emission of a twodimensional atom has been obtained along with an expression for the particular case of the transition from the first excited state to the ground state, in the latter case in comparison with corresponding expressions for the three-dimensional atom and the one-dimensional atom. Arguments are presented in support of the claim that this method of calculation gives a value of the probability that is identical to the value given by exact methods of QED extended to the subspace {0, 1, 2}. Relativistic corrections (Zα)4 to the usual Schrödinger value of the energy ( (Zα)2) are also discussed.

Three-dimensional perspective software for representation of digital imagery data. [Olympic National Park, Washington

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1980-01-01

A generalized three dimensional perspective software capability was developed within the framework of a low cost computer oriented geographically based information system using the Earth Resources Laboratory Applications Software (ELAS) operating subsystem. This perspective software capability, developed primarily to support data display requirements at the NASA/NSTL Earth Resources Laboratory, provides a means of displaying three dimensional feature space object data in two dimensional picture plane coordinates and makes it possible to overlay different types of information on perspective drawings to better understand the relationship of physical features. An example topographic data base is constructed and is used as the basic input to the plotting module. Examples are shown which illustrate oblique viewing angles that convey spatial concepts and relationships represented by the topographic data planes.

Space-time topology and quantum gravity.

NASA Astrophysics Data System (ADS)

Friedman, J. L.

Characteristic features are discussed of a theory of quantum gravity that allows space-time with a non-Euclidean topology. The review begins with a summary of the manifolds that can occur as classical vacuum space-times and as space-times with positive energy. Local structures with non-Euclidean topology - topological geons - collapse, and one may conjecture that in asymptotically flat space-times non-Euclidean topology is hiden from view. In the quantum theory, large diffeos can act nontrivially on the space of states, leading to state vectors that transform as representations of the corresponding symmetry group π0(Diff). In particular, in a quantum theory that, at energies E < EPlanck, is a theory of the metric alone, there appear to be ground states with half-integral spin, and in higher-dimensional gravity, with the kinematical quantum numbers of fundamental fermions.

The link between mental rotation ability and basic numerical representations

PubMed Central

Thompson, Jacqueline M.; Nuerk, Hans-Christoph; Moeller, Korbinian; Cohen Kadosh, Roi

2013-01-01

Mental rotation and number representation have both been studied widely, but although mental rotation has been linked to higher-level mathematical skills, to date it has not been shown whether mental rotation ability is linked to the most basic mental representation and processing of numbers. To investigate the possible connection between mental rotation abilities and numerical representation, 43 participants completed four tasks: 1) a standard pen-and-paper mental rotation task; 2) a multi-digit number magnitude comparison task assessing the compatibility effect, which indicates separate processing of decade and unit digits; 3) a number-line mapping task, which measures precision of number magnitude representation; and 4) a random number generation task, which yields measures both of executive control and of spatial number representations. Results show that mental rotation ability correlated significantly with both size of the compatibility effect and with number mapping accuracy, but not with any measures from the random number generation task. Together, these results suggest that higher mental rotation abilities are linked to more developed number representation, and also provide further evidence for the connection between spatial and numerical abilities. PMID:23933002

Real three-dimensional objects: effects on mental rotation.

PubMed

Felix, Michael C; Parker, Joshua D; Lee, Charles; Gabriel, Kara I

2011-08-01

The current experiment investigated real three-dimensional (3D) objects with regard to performance on a mental rotation task and whether the appearance of sex differences may be mediated by experiences with spatially related activities. 40 men and 40 women were presented with alternating timed trials consisting of real-3D objects or two-dimensional illustrations of 3D objects. Sex differences in spatially related activities did not significantly influence the finding that men outperformed women on mental rotation of either stimulus type. However, on measures related to spatial activities, self-reported proficiency using maps correlated positively with performance only on trials with illustrations whereas self-reported proficiency using GPS correlated negatively with performance regardless of stimulus dimensionality. Findings may be interpreted as suggesting that rotating real-3D objects utilizes distinct but overlapping spatial skills compared to rotating two-dimensional representations of 3D objects, and real-3D objects can enhance mental rotation performance.

Leadership and Strategic Choices: Female Professors in Australia and Turkey

ERIC Educational Resources Information Center

Ozkanli, Ozlem; White, Kate

2008-01-01

This study explores leadership styles and gender in higher education (HE) by examining representation of female professors in Australian and Turkish universities and identifying barriers to achieving seniority. The paper explores factors, including leadership styles, which explain the higher representation of female professors in Turkey, despite…

Cross-sectional mapping for refined beam elements with applications to shell-like structures

NASA Astrophysics Data System (ADS)

Pagani, A.; de Miguel, A. G.; Carrera, E.

2017-06-01

This paper discusses the use of higher-order mapping functions for enhancing the physical representation of refined beam theories. Based on the Carrera unified formulation (CUF), advanced one-dimensional models are formulated by expressing the displacement field as a generic expansion of the generalized unknowns. According to CUF, a novel physically/geometrically consistent model is devised by employing Legendre-like polynomial sets to approximate the generalized unknowns at the cross-sectional level, whereas a local mapping technique based on the blending functions method is used to describe the exact physical boundaries of the cross-section domain. Classical and innovative finite element methods, including hierarchical p-elements and locking-free integration schemes, are utilized to solve the governing equations of the unified beam theory. Several numerical applications accounting for small displacements/rotations and strains are discussed, including beam structures with cross-sectional curved edges, cylindrical shells, and thin-walled aeronautical wing structures with reinforcements. The results from the proposed methodology are widely assessed by comparisons with solutions from the literature and commercial finite element software tools. The attention is focussed on the high computational efficiency and the marked capabilities of the present beam model, which can deal with a broad spectrum of structural problems with unveiled accuracy in terms of geometrical representation of the domain boundaries.

Construction of non-Markovian coarse-grained models employing the Mori-Zwanzig formalism and iterative Boltzmann inversion

NASA Astrophysics Data System (ADS)

Yoshimoto, Yuta; Li, Zhen; Kinefuchi, Ikuya; Karniadakis, George Em

2017-12-01

We propose a new coarse-grained (CG) molecular simulation technique based on the Mori-Zwanzig (MZ) formalism along with the iterative Boltzmann inversion (IBI). Non-Markovian dissipative particle dynamics (NMDPD) taking into account memory effects is derived in a pairwise interaction form from the MZ-guided generalized Langevin equation. It is based on the introduction of auxiliary variables that allow for the replacement of a non-Markovian equation with a Markovian one in a higher dimensional space. We demonstrate that the NMDPD model exploiting MZ-guided memory kernels can successfully reproduce the dynamic properties such as the mean square displacement and velocity autocorrelation function of a Lennard-Jones system, as long as the memory kernels are appropriately evaluated based on the Volterra integral equation using the force-velocity and velocity-velocity correlations. Furthermore, we find that the IBI correction of a pair CG potential significantly improves the representation of static properties characterized by a radial distribution function and pressure, while it has little influence on the dynamic processes. Our findings suggest that combining the advantages of both the MZ formalism and IBI leads to an accurate representation of both the static and dynamic properties of microscopic systems that exhibit non-Markovian behavior.

The Use of Modelling for Improving Pupils' Learning about Cells.

ERIC Educational Resources Information Center

Tregidgo, David; Ratcliffe, Mary

2000-01-01

Outlines the use of modeling in science teaching. Describes a study in which two parallel groups of year seven pupils modeled concepts of cell structure and function as they produced two- or three-dimensional representations of plant and animal cells. (Author/CCM)

30 CFR 280.1 - What definitions apply to this part?

Code of Federal Regulations, 2010 CFR

2010-07-01

... of lithologic and fossil content, core analyses, laboratory analyses of physical and chemical..., or sulphur. Interpreted geological information means the knowledge, often in the form of schematic... information means knowledge, often in the form of seismic cross sections, 3-dimensional representations, and...

Loop-Extended Symbolic Execution on Binary Programs

DTIC Science & Technology

2009-03-02

1434. Based on its speci- fication [35], one valid message format contains 2 fields: a header byte of value 4, followed by a string giving a database ...potentially become expensive. For instance the polyhedron technique [16] requires costly conversion operations on a multi-dimensional abstract representation

Explorations in Context Space: Words, Sentences, Discourse.

ERIC Educational Resources Information Center

Burgess, Curt; Livesay, Kay; Lund, Kevin

1998-01-01

Describes a computational model of high-dimensional context space: the Hyperspace Analog to Language (HAL). Shows that HAL provides sufficient information to make semantic, grammatical, and abstract distinctions. Demonstrates the cognitive compatibility of the representations with human processing; and introduces a new methodology that extracts…

SIMPLE METHOD FOR THE REPRESENTATION, QUANTIFICATION, AND COMPARISON OF THE VOLUMES AND SHAPES OF CHEMICAL COMPOUNDS

EPA Science Inventory

A conceptually and computationally simple method for the definition, display, quantification, and comparison of the shapes of three-dimensional mathematical molecular models is presented. Molecular or solvent-accessible volume and surface area can also be calculated. Algorithms, ...

Multigrid one shot methods for optimal control problems: Infinite dimensional control

NASA Technical Reports Server (NTRS)

Arian, Eyal; Taasan, Shlomo

1994-01-01

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

Three-dimensional digital mapping of the optic nerve head cupping in glaucoma

NASA Astrophysics Data System (ADS)

Mitra, Sunanda; Ramirez, Manuel; Morales, Jose

1992-08-01

Visualization of the optic nerve head cupping is clinically achieved by stereoscopic viewing of a fundus image pair of the suspected eye. A novel algorithm for three-dimensional digital surface representation of the optic nerve head, using fusion of stereo depth map with a linearly stretched intensity image of a stereo fundus image pair, is presented. Prior to depth map acquisition, a number of preprocessing tasks including feature extraction, registration by cepstral analysis, and correction for intensity variations are performed. The depth map is obtained by using a coarse to fine strategy for obtaining disparities between corresponding areas. The required matching techniques to obtain the translational differences in every step, uses cepstral analysis and correlation-like scanning technique in the spatial domain for the finest details. The quantitative and precise representation of the optic nerve head surface topography following this algorithm is not computationally intensive and should provide more useful information than just qualitative stereoscopic viewing of the fundus as one of the diagnostic criteria for diagnosis of glaucoma.

Palm vein recognition based on directional empirical mode decomposition

NASA Astrophysics Data System (ADS)

Lee, Jen-Chun; Chang, Chien-Ping; Chen, Wei-Kuei

2014-04-01

Directional empirical mode decomposition (DEMD) has recently been proposed to make empirical mode decomposition suitable for the processing of texture analysis. Using DEMD, samples are decomposed into a series of images, referred to as two-dimensional intrinsic mode functions (2-D IMFs), from finer to large scale. A DEMD-based 2 linear discriminant analysis (LDA) for palm vein recognition is proposed. The proposed method progresses through three steps: (i) a set of 2-D IMF features of various scale and orientation are extracted using DEMD, (ii) the 2LDA method is then applied to reduce the dimensionality of the feature space in both the row and column directions, and (iii) the nearest neighbor classifier is used for classification. We also propose two strategies for using the set of 2-D IMF features: ensemble DEMD vein representation (EDVR) and multichannel DEMD vein representation (MDVR). In experiments using palm vein databases, the proposed MDVR-based 2LDA method achieved recognition accuracy of 99.73%, thereby demonstrating its feasibility for palm vein recognition.

Initial Systematic Investigations of the Weakly Coupled Free Fermionic Heterotic String Landscape Statistics

NASA Astrophysics Data System (ADS)

Renner, Timothy

2011-12-01

A C++ framework was constructed with the explicit purpose of systematically generating string models using the Weakly Coupled Free Fermionic Heterotic String (WCFFHS) method. The software, optimized for speed, generality, and ease of use, has been used to conduct preliminary systematic investigations of WCFFHS vacua. Documentation for this framework is provided in the Appendix. After an introduction to theoretical and computational aspects of WCFFHS model building, a study of ten-dimensional WCFFHS models is presented. Degeneracies among equivalent expressions of each of the known models are investigated and classified. A study of more phenomenologically realistic four-dimensional models based on the well known "NAHE" set is then presented, with statistics being reported on gauge content, matter representations, and space-time supersymmetries. The final study is a parallel to the NAHE study in which a variation of the NAHE set is systematically extended and examined statistically. Special attention is paid to models with "mirroring"---identical observable and hidden sector gauge groups and matter representations.

Semiclassical propagation of Wigner functions.

PubMed

Dittrich, T; Gómez, E A; Pachón, L A

2010-06-07

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrodinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo-Metropolis algorithms suitable for high-dimensional systems.

Geometry of the generalized Bloch sphere for qutrits

NASA Astrophysics Data System (ADS)

Goyal, Sandeep K.; Neethi Simon, B.; Singh, Rajeev; Simon, Sudhavathani

2016-04-01

The geometry of the generalized Bloch sphere Ω3, the state space of a qutrit, is studied. Closed form expressions for Ω3, its boundary ∂Ω3, and the set of extremals {{{Ω }}}3{{ext}} are obtained by use of an elementary observation. These expressions and analytic methods are used to classify the 28 two-sections and the 56 three-sections of Ω3 into unitary equivalence classes, completing the works of earlier authors. It is shown, in particular, that there are families of two-sections and of three-sections which are equivalent geometrically but not unitarily, a feature that does not appear to have been appreciated earlier. A family of three-sections of obese-tetrahedral shape whose symmetry corresponds to the 24-element tetrahedral point group T d is examined in detail. This symmetry is traced to the natural reduction of the adjoint representation of SU(3), the symmetry underlying Ω3, into direct sum of the two-dimensional and the two (inequivalent) three-dimensional irreducible representations of T d .

Reinforcement learning in multidimensional environments relies on attention mechanisms.

PubMed

Niv, Yael; Daniel, Reka; Geana, Andra; Gershman, Samuel J; Leong, Yuan Chang; Radulescu, Angela; Wilson, Robert C

2015-05-27

In recent years, ideas from the computational field of reinforcement learning have revolutionized the study of learning in the brain, famously providing new, precise theories of how dopamine affects learning in the basal ganglia. However, reinforcement learning algorithms are notorious for not scaling well to multidimensional environments, as is required for real-world learning. We hypothesized that the brain naturally reduces the dimensionality of real-world problems to only those dimensions that are relevant to predicting reward, and conducted an experiment to assess by what algorithms and with what neural mechanisms this "representation learning" process is realized in humans. Our results suggest that a bilateral attentional control network comprising the intraparietal sulcus, precuneus, and dorsolateral prefrontal cortex is involved in selecting what dimensions are relevant to the task at hand, effectively updating the task representation through trial and error. In this way, cortical attention mechanisms interact with learning in the basal ganglia to solve the "curse of dimensionality" in reinforcement learning. Copyright © 2015 the authors 0270-6474/15/358145-13$15.00/0.

Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems

NASA Astrophysics Data System (ADS)

Ivanova, Violeta M.; Sousa, Rita; Murrihy, Brian; Einstein, Herbert H.

2014-06-01

This paper presents results from research conducted at MIT during 2010-2012 on modeling of natural rock fracture systems with the GEOFRAC three-dimensional stochastic model. Following a background summary of discrete fracture network models and a brief introduction of GEOFRAC, the paper provides a thorough description of the newly developed mathematical and computer algorithms for fracture intensity, aperture, and intersection representation, which have been implemented in MATLAB. The new methods optimize, in particular, the representation of fracture intensity in terms of cumulative fracture area per unit volume, P32, via the Poisson-Voronoi Tessellation of planes into polygonal fracture shapes. In addition, fracture apertures now can be represented probabilistically or deterministically whereas the newly implemented intersection algorithms allow for computing discrete pathways of interconnected fractures. In conclusion, results from a statistical parametric study, which was conducted with the enhanced GEOFRAC model and the new MATLAB-based Monte Carlo simulation program FRACSIM, demonstrate how fracture intensity, size, and orientations influence fracture connectivity.

Characterizing psychopathy using DSM-5 personality traits.

PubMed

Strickland, Casey M; Drislane, Laura E; Lucy, Megan; Krueger, Robert F; Patrick, Christopher J

2013-06-01

Despite its importance historically and contemporarily, psychopathy is not recognized in the current Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, Text Revised (DSM-IV-TR). Its closest counterpart, antisocial personality disorder, includes strong representation of behavioral deviance symptoms but weak representation of affective-interpersonal features considered central to psychopathy. The current study evaluated the extent to which psychopathy and its distinctive facets, indexed by the Triarchic Psychopathy Measure, can be assessed effectively using traits from the dimensional model of personality pathology developed for DSM-5, operationalized by the Personality Inventory for DSM-5 (PID-5). Results indicate that (a) facets of psychopathy entailing impulsive externalization and callous aggression are well-represented by traits from the PID-5 considered relevant to antisocial personality disorder, and (b) the boldness facet of psychopathy can be effectively captured using additional PID-5 traits. These findings provide evidence that the dimensional model of personality pathology embodied in the PID-5 provides effective trait-based coverage of psychopathy and its facets.

Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios

NASA Astrophysics Data System (ADS)

Hobrecht, Hendrik; Hucht, Alfred

2017-02-01

We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function Z on an L× M square lattice, wrapped around a torus with aspect ratio ρ =L/M . By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a 2× 2 transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films ρ \\to 0 . Additionally, for the cylinder at criticality our results confirm the predictions from conformal field theory.

Extracting semantic representations from word co-occurrence statistics: stop-lists, stemming, and SVD.

PubMed

Bullinaria, John A; Levy, Joseph P

2012-09-01

In a previous article, we presented a systematic computational study of the extraction of semantic representations from the word-word co-occurrence statistics of large text corpora. The conclusion was that semantic vectors of pointwise mutual information values from very small co-occurrence windows, together with a cosine distance measure, consistently resulted in the best representations across a range of psychologically relevant semantic tasks. This article extends that study by investigating the use of three further factors--namely, the application of stop-lists, word stemming, and dimensionality reduction using singular value decomposition (SVD)--that have been used to provide improved performance elsewhere. It also introduces an additional semantic task and explores the advantages of using a much larger corpus. This leads to the discovery and analysis of improved SVD-based methods for generating semantic representations (that provide new state-of-the-art performance on a standard TOEFL task) and the identification and discussion of problems and misleading results that can arise without a full systematic study.

Joint Acoustic and Modulation Frequency

NASA Astrophysics Data System (ADS)

Atlas, Les; Shamma, Shihab A.

2003-12-01

There is a considerable evidence that our perception of sound uses important features which is related to underlying signal modulations. This topic has been studied extensively via perceptual experiments, yet there are few, if any, well-developed signal processing methods which capitalize on or model these effects. We begin by summarizing evidence of the importance of modulation representations from psychophysical, physiological, and other sources. The concept of a two-dimensional joint acoustic and modulation frequency representation is proposed. A simple single sinusoidal amplitude modulator of a sinusoidal carrier is then used to illustrate properties of an unconstrained and ideal joint representation. Added constraints are required to remove or reduce undesired interference terms and to provide invertibility. It is then noted that the constraints would also apply to more general and complex cases of broader modulation and carriers. Applications in single-channel speaker separation and in audio coding are used to illustrate the applicability of this joint representation. Other applications in signal analysis and filtering are suggested.

The tensor hierarchy algebra

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

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

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

Using Wikipedia to learn semantic feature representations of concrete concepts in neuroimaging experiments

PubMed Central

Pereira, Francisco; Botvinick, Matthew; Detre, Greg

2012-01-01

In this paper we show that a corpus of a few thousand Wikipedia articles about concrete or visualizable concepts can be used to produce a low-dimensional semantic feature representation of those concepts. The purpose of such a representation is to serve as a model of the mental context of a subject during functional magnetic resonance imaging (fMRI) experiments. A recent study [19] showed that it was possible to predict fMRI data acquired while subjects thought about a concrete concept, given a representation of those concepts in terms of semantic features obtained with human supervision. We use topic models on our corpus to learn semantic features from text in an unsupervised manner, and show that those features can outperform those in [19] in demanding 12-way and 60-way classification tasks. We also show that these features can be used to uncover similarity relations in brain activation for different concepts which parallel those relations in behavioral data from human subjects. PMID:23243317

Simulation of multivariate stationary stochastic processes using dimension-reduction representation methods

NASA Astrophysics Data System (ADS)

Liu, Zhangjun; Liu, Zenghui; Peng, Yongbo

2018-03-01

In view of the Fourier-Stieltjes integral formula of multivariate stationary stochastic processes, a unified formulation accommodating spectral representation method (SRM) and proper orthogonal decomposition (POD) is deduced. By introducing random functions as constraints correlating the orthogonal random variables involved in the unified formulation, the dimension-reduction spectral representation method (DR-SRM) and the dimension-reduction proper orthogonal decomposition (DR-POD) are addressed. The proposed schemes are capable of representing the multivariate stationary stochastic process with a few elementary random variables, bypassing the challenges of high-dimensional random variables inherent in the conventional Monte Carlo methods. In order to accelerate the numerical simulation, the technique of Fast Fourier Transform (FFT) is integrated with the proposed schemes. For illustrative purposes, the simulation of horizontal wind velocity field along the deck of a large-span bridge is proceeded using the proposed methods containing 2 and 3 elementary random variables. Numerical simulation reveals the usefulness of the dimension-reduction representation methods.

Graph representation of hepatic vessel based on centerline extraction and junction detection

NASA Astrophysics Data System (ADS)

Zhang, Xing; Tian, Jie; Deng, Kexin; Li, Xiuli; Yang, Fei

2012-02-01

In the area of computer-aided diagnosis (CAD), segmentation and analysis of hepatic vessel is a prerequisite for hepatic diseases diagnosis and surgery planning. For liver surgery planning, it is crucial to provide the surgeon with a patient-individual three-dimensional representation of the liver along with its vasculature and lesions. The representation allows an exploration of the vascular anatomy and the measurement of vessel diameters, following by intra-patient registration, as well as the analysis of the shape and volume of vascular territories. In this paper, we present an approach for generation of hepatic vessel graph based on centerline extraction and junction detection. The proposed approach involves the following concepts and methods: 1) Flux driven automatic centerline extraction; 2) Junction detection on the centerline using hollow sphere filtering; 3) Graph representation of hepatic vessel based on the centerline and junction. The approach is evaluated on contrast-enhanced liver CT datasets to demonstrate its availability and effectiveness.

A reduced basis approach for implementing thermodynamic phase-equilibria information in geophysical and geodynamic studies

NASA Astrophysics Data System (ADS)

Afonso, J. C.; Zlotnik, S.; Diez, P.

2015-12-01

We present a flexible, general and efficient approach for implementing thermodynamic phase equilibria information (in the form of sets of physical parameters) into geophysical and geodynamic studies. The approach is based on multi-dimensional decomposition methods, which transform the original multi-dimensional discrete information into a dimensional-separated representation. This representation has the property of increasing the number of coefficients to be stored linearly with the number of dimensions (opposite to a full multi-dimensional cube requiring exponential storage depending on the number of dimensions). Thus, the amount of information to be stored in memory during a numerical simulation or geophysical inversion is drastically reduced. Accordingly, the amount and resolution of the thermodynamic information that can be used in a simulation or inversion increases substantially. In addition, the method is independent of the actual software used to obtain the primary thermodynamic information, and therefore it can be used in conjunction with any thermodynamic modeling program and/or database. Also, the errors associated with the decomposition procedure are readily controlled by the user, depending on her/his actual needs (e.g. preliminary runs vs full resolution runs). We illustrate the benefits, generality and applicability of our approach with several examples of practical interest for both geodynamic modeling and geophysical inversion/modeling. Our results demonstrate that the proposed method is a competitive and attractive candidate for implementing thermodynamic constraints into a broad range of geophysical and geodynamic studies.

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.

Qualitative aspects of representational competence among college chemistry students: Multiple representations and their role in the understanding of ideal gases

NASA Astrophysics Data System (ADS)

Madden, Sean Patrick

This study examined the role of multiple representations of chemical phenomena, specifically, the temperature-pressure relationship of ideal gases, in the problem solving strategies of college chemistry students. Volunteers included students enrolled in a first semester general chemistry course at a western university. Two additional volunteers from the same university were asked to participate and serve as models of greater sophistication. One was a senior chemistry major; another was a junior science writing major. Volunteers completed an initial screening task involving multiple representations of concentration and dilution concepts. Based on the results of this screening instrument a smaller set of subjects were asked to complete a think aloud session involving multiple representations of the temperature-pressure relationship. Data consisted of the written work of the volunteers and transcripts from videotaped think aloud sessions. The data were evaluated by the researcher and two other graduate students in chemical education using a coding scheme (Kozma, Schank, Coppola, Michalchik, and Allen. 2000). This coding scheme was designed to identify essential features of representational competence and differences in uses of multiple representations. The results indicate that students tend to have a strong preference for one type of representation. Students scoring low on representational competence, as measured by the rubric, ignored important features of some representations or acknowledged them only superficially. Students scoring higher on representational competence made meaningful connections among representations. The more advanced students, those who rated highly on representational competence, tended to use their preferred representation in a heuristic manner to establish meaning for other representations. The more advanced students also reflected upon the problem at greater length before beginning work. Molecular level sketches seemed to be the most difficult type of representation for students to interpret. Most subjects scored higher on representational competence when engaged in creating graphs and sketches than when evaluating provided representations. This study suggests that students may benefit from an instruction that emphasizes heuristic use of multiple representations in chemistry problem solving. An instructional strategy that makes use of a variety of representations and requires students to create their own representations may have measurable benefits to chemistry students.

Dimensional Representation and Gradient Boosting for Seismic Event Classification

NASA Astrophysics Data System (ADS)

Semmelmayer, F. C.; Kappedal, R. D.; Magana-Zook, S. A.

2017-12-01

In this research, we conducted experiments of representational structures on 5009 seismic signals with the intent of finding a method to classify signals as either an explosion or an earthquake in an automated fashion. We also applied a gradient boosted classifier. While perfect classification was not attained (approximately 88% was our best model), some cases demonstrate that many events can be filtered out as very high probability being explosions or earthquakes, diminishing subject-matter experts'(SME) workload for first stage analysis. It is our hope that these methods can be refined, further increasing the classification probability.

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.

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

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

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

1992-10-20

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

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.

Learning from graphically integrated 2D and 3D representations improves retention of neuroanatomy

NASA Astrophysics Data System (ADS)

Naaz, Farah

Visualizations in the form of computer-based learning environments are highly encouraged in science education, especially for teaching spatial material. Some spatial material, such as sectional neuroanatomy, is very challenging to learn. It involves learning the two dimensional (2D) representations that are sampled from the three dimensional (3D) object. In this study, a computer-based learning environment was used to explore the hypothesis that learning sectional neuroanatomy from a graphically integrated 2D and 3D representation will lead to better learning outcomes than learning from a sequential presentation. The integrated representation explicitly demonstrates the 2D-3D transformation and should lead to effective learning. This study was conducted using a computer graphical model of the human brain. There were two learning groups: Whole then Sections, and Integrated 2D3D. Both groups learned whole anatomy (3D neuroanatomy) before learning sectional anatomy (2D neuroanatomy). The Whole then Sections group then learned sectional anatomy using 2D representations only. The Integrated 2D3D group learned sectional anatomy from a graphically integrated 3D and 2D model. A set of tests for generalization of knowledge to interpreting biomedical images was conducted immediately after learning was completed. The order of presentation of the tests of generalization of knowledge was counterbalanced across participants to explore a secondary hypothesis of the study: preparation for future learning. If the computer-based instruction programs used in this study are effective tools for teaching anatomy, the participants should continue learning neuroanatomy with exposure to new representations. A test of long-term retention of sectional anatomy was conducted 4-8 weeks after learning was completed. The Integrated 2D3D group was better than the Whole then Sections group in retaining knowledge of difficult instances of sectional anatomy after the retention interval. The benefit of learning from an integrated 2D3D representation suggests that there are some spatial transformations which are better retained if they are learned through an explicit demonstration. Participants also showed evidence of continued learning on the tests of generalization with the help of cues and practice, even without feedback. This finding suggests that the computer-based learning programs used in this study were good tools for instruction of neuroanatomy.

Three-dimensional visual feature representation in the primary visual cortex

PubMed Central

Tanaka, Shigeru; Moon, Chan-Hong; Fukuda, Mitsuhiro; Kim, Seong-Gi

2011-01-01

In the cat primary visual cortex, it is accepted that neurons optimally responding to similar stimulus orientations are clustered in a column extending from the superficial to deep layers. The cerebral cortex is, however, folded inside a skull, which makes gyri and fundi. The primary visual area of cats, area 17, is located on the fold of the cortex called the lateral gyrus. These facts raise the question of how to reconcile the tangential arrangement of the orientation columns with the curvature of the gyrus. In the present study, we show a possible configuration of feature representation in the visual cortex using a three-dimensional (3D) self-organization model. We took into account preferred orientation, preferred direction, ocular dominance and retinotopy, assuming isotropic interaction. We performed computer simulation only in the middle layer at the beginning and expanded the range of simulation gradually to other layers, which was found to be a unique method in the present model for obtaining orientation columns spanning all the layers in the flat cortex. Vertical columns of preferred orientations were found in the flat parts of the model cortex. On the other hand, in the curved parts, preferred orientations were represented in wedge-like columns rather than straight columns, and preferred directions were frequently reversed in the deeper layers. Singularities associated with orientation representation appeared as warped lines in the 3D model cortex. Direction reversal appeared on the sheets that were delimited by orientation-singularity lines. These structures emerged from the balance between periodic arrangements of preferred orientations and vertical alignment of same orientations. Our theoretical predictions about orientation representation were confirmed by multi-slice, high-resolution functional MRI in the cat visual cortex. We obtained a close agreement between theoretical predictions and experimental observations. The present study throws a doubt about the conventional columnar view of orientation representation, although more experimental data are needed. PMID:21724370

Three-dimensional visual feature representation in the primary visual cortex.

PubMed

Tanaka, Shigeru; Moon, Chan-Hong; Fukuda, Mitsuhiro; Kim, Seong-Gi

2011-12-01

In the cat primary visual cortex, it is accepted that neurons optimally responding to similar stimulus orientations are clustered in a column extending from the superficial to deep layers. The cerebral cortex is, however, folded inside a skull, which makes gyri and fundi. The primary visual area of cats, area 17, is located on the fold of the cortex called the lateral gyrus. These facts raise the question of how to reconcile the tangential arrangement of the orientation columns with the curvature of the gyrus. In the present study, we show a possible configuration of feature representation in the visual cortex using a three-dimensional (3D) self-organization model. We took into account preferred orientation, preferred direction, ocular dominance and retinotopy, assuming isotropic interaction. We performed computer simulation only in the middle layer at the beginning and expanded the range of simulation gradually to other layers, which was found to be a unique method in the present model for obtaining orientation columns spanning all the layers in the flat cortex. Vertical columns of preferred orientations were found in the flat parts of the model cortex. On the other hand, in the curved parts, preferred orientations were represented in wedge-like columns rather than straight columns, and preferred directions were frequently reversed in the deeper layers. Singularities associated with orientation representation appeared as warped lines in the 3D model cortex. Direction reversal appeared on the sheets that were delimited by orientation-singularity lines. These structures emerged from the balance between periodic arrangements of preferred orientations and vertical alignment of the same orientations. Our theoretical predictions about orientation representation were confirmed by multi-slice, high-resolution functional MRI in the cat visual cortex. We obtained a close agreement between theoretical predictions and experimental observations. The present study throws a doubt about the conventional columnar view of orientation representation, although more experimental data are needed. Copyright © 2011 Elsevier Ltd. All rights reserved.

An automatic panoramic image reconstruction scheme from dental computed tomography images

PubMed Central

Papakosta, Thekla K; Savva, Antonis D; Economopoulos, Theodore L; Gröhndal, H G

2017-01-01

Objectives: Panoramic images of the jaws are extensively used for dental examinations and/or surgical planning because they provide a general overview of the patient's maxillary and mandibular regions. Panoramic images are two-dimensional projections of three-dimensional (3D) objects. Therefore, it should be possible to reconstruct them from 3D radiographic representations of the jaws, produced by CBCT scanning, obviating the need for additional exposure to X-rays, should there be a need of panoramic views. The aim of this article is to present an automated method for reconstructing panoramic dental images from CBCT data. Methods: The proposed methodology consists of a series of sequential processing stages for detecting a fitting dental arch which is used for projecting the 3D information of the CBCT data to the two-dimensional plane of the panoramic image. The detection is based on a template polynomial which is constructed from a training data set. Results: A total of 42 CBCT data sets of real clinical pre-operative and post-operative representations from 21 patients were used. Eight data sets were used for training the system and the rest for testing. Conclusions: The proposed methodology was successfully applied to CBCT data sets, producing corresponding panoramic images, suitable for examining pre-operatively and post-operatively the patients' maxillary and mandibular regions. PMID:28112548

A two dimensional power spectral estimate for some nonstationary processes. M.S. Thesis

NASA Technical Reports Server (NTRS)

Smith, Gregory L.

1989-01-01

A two dimensional estimate for the power spectral density of a nonstationary process is being developed. The estimate will be applied to helicopter noise data which is clearly nonstationary. The acoustic pressure from the isolated main rotor and isolated tail rotor is known to be periodically correlated (PC) and the combined noise from the main and tail rotors is assumed to be correlation autoregressive (CAR). The results of this nonstationary analysis will be compared with the current method of assuming that the data is stationary and analyzing it as such. Another method of analysis is to introduce a random phase shift into the data as shown by Papoulis to produce a time history which can then be accurately modeled as stationary. This method will also be investigated for the helicopter data. A method used to determine the period of a PC process when the period is not know is discussed. The period of a PC process must be known in order to produce an accurate spectral representation for the process. The spectral estimate is developed. The bias and variability of the estimate are also discussed. Finally, the current method for analyzing nonstationary data is compared to that of using a two dimensional spectral representation. In addition, the method of phase shifting the data is examined.

Learning structure-property relationship in crystalline materials: A study of lanthanide-transition metal alloys

NASA Astrophysics Data System (ADS)

Pham, Tien-Lam; Nguyen, Nguyen-Duong; Nguyen, Van-Doan; Kino, Hiori; Miyake, Takashi; Dam, Hieu-Chi

2018-05-01

We have developed a descriptor named Orbital Field Matrix (OFM) for representing material structures in datasets of multi-element materials. The descriptor is based on the information regarding atomic valence shell electrons and their coordination. In this work, we develop an extension of OFM called OFM1. We have shown that these descriptors are highly applicable in predicting the physical properties of materials and in providing insights on the materials space by mapping into a low embedded dimensional space. Our experiments with transition metal/lanthanide metal alloys show that the local magnetic moments and formation energies can be accurately reproduced using simple nearest-neighbor regression, thus confirming the relevance of our descriptors. Using kernel ridge regressions, we could accurately reproduce formation energies and local magnetic moments calculated based on first-principles, with mean absolute errors of 0.03 μB and 0.10 eV/atom, respectively. We show that meaningful low-dimensional representations can be extracted from the original descriptor using descriptive learning algorithms. Intuitive prehension on the materials space, qualitative evaluation on the similarities in local structures or crystalline materials, and inference in the designing of new materials by element substitution can be performed effectively based on these low-dimensional representations.

SU(N) affine Toda solitons and breathers from transparent Dirac potentials

NASA Astrophysics Data System (ADS)

Thies, Michael

2017-05-01

Transparent scalar and pseudoscalar potentials in the one-dimensional Dirac equation play an important role as self-consistent mean fields in 1  +  1 dimensional four-fermion theories (Gross-Neveu, Nambu-Jona Lasinio models) and quasi-one dimensional superconductors (Bogoliubov-de Gennes equation). Here, we show that they also serve as seed to generate a large class of classical multi-soliton and multi-breather solutions of su(N) affine Toda field theories, including the Lax representation and the corresponding vector. This generalizes previous findings about the relationship between real kinks in the Gross-Neveu model and classical solitons of the sinh-Gordon equation to complex twisted kinks.

Perfect 3-D movies and stereoscopic movies on TV and projection screens: an appraisement

NASA Astrophysics Data System (ADS)

Klein, Susanne; Dultz, Wolfgang

1990-09-01

Since the invention of stereoscopy (WHEATSTONE 1838) reasons for and against 3-dimensional images have occupied the literature, but there has never been much doubt about the preference of autostereoscopic systems showing a scene which is 3-dimensional and true to life from all sides (perfect 3-dimensional image, HESSE 1939), especially since most stereoscopic movies of the past show serious imperfections with respect to image quality and technical operation. Leave aside that no convincing perfect 3D-TV-system is in sight, there are properties f the stereoscopic movie which are advantageous to certain representations on TV and important for the 3-dimensional motion picture. In this paper we investigate the influence of apparent motions of 3-dimensional images and classify the different projection systems with respect to presence and absence of these spectacular illusions. Apparent motions bring dramatic effects into stereoscopic movies which cannot be created with perfect 3-dimensional systems. In this study we describe their applications and limits for television.

Digital elevation modeling via curvature interpolation for lidar data

USDA-ARS?s Scientific Manuscript database

Digital elevation model (DEM) is a three-dimensional (3D) representation of a terrain's surface - for a planet (including Earth), moon, or asteroid - created from point cloud data which measure terrain elevation. Its modeling requires surface reconstruction for the scattered data, which is an ill-p...

Discovering Structure in High-Dimensional Data Through Correlation Explanation

DTIC Science & Technology

2014-12-08

transforming complex data into simpler, more meaningful forms goes under the rubric of representation learning [2] which shares many goals with...Zhivotovsky, and M.W. Feldman. Genetic structure of human populations. Science, 298(5602):2381–2385, 2002. [14] K. Bache and M. Lichman. UCI machine

30 CFR 280.1 - What definitions apply to this part?

Code of Federal Regulations, 2011 CFR

2011-07-01

... include, but are not limited to, identification of lithologic and fossil content, core analyses.... Interpreted geological information means the knowledge, often in the form of schematic cross sections, 3..., often in the form of seismic cross sections, 3-dimensional representations, and maps, developed by...

Exploring high dimensional data with Butterfly: a novel classification algorithm based on discrete dynamical systems.

PubMed

Geraci, Joseph; Dharsee, Moyez; Nuin, Paulo; Haslehurst, Alexandria; Koti, Madhuri; Feilotter, Harriet E; Evans, Ken

2014-03-01

We introduce a novel method for visualizing high dimensional data via a discrete dynamical system. This method provides a 2D representation of the relationship between subjects according to a set of variables without geometric projections, transformed axes or principal components. The algorithm exploits a memory-type mechanism inherent in a certain class of discrete dynamical systems collectively referred to as the chaos game that are closely related to iterative function systems. The goal of the algorithm was to create a human readable representation of high dimensional patient data that was capable of detecting unrevealed subclusters of patients from within anticipated classifications. This provides a mechanism to further pursue a more personalized exploration of pathology when used with medical data. For clustering and classification protocols, the dynamical system portion of the algorithm is designed to come after some feature selection filter and before some model evaluation (e.g. clustering accuracy) protocol. In the version given here, a univariate features selection step is performed (in practice more complex feature selection methods are used), a discrete dynamical system is driven by this reduced set of variables (which results in a set of 2D cluster models), these models are evaluated for their accuracy (according to a user-defined binary classification) and finally a visual representation of the top classification models are returned. Thus, in addition to the visualization component, this methodology can be used for both supervised and unsupervised machine learning as the top performing models are returned in the protocol we describe here. Butterfly, the algorithm we introduce and provide working code for, uses a discrete dynamical system to classify high dimensional data and provide a 2D representation of the relationship between subjects. We report results on three datasets (two in the article; one in the appendix) including a public lung cancer dataset that comes along with the included Butterfly R package. In the included R script, a univariate feature selection method is used for the dimension reduction step, but in the future we wish to use a more powerful multivariate feature reduction method based on neural networks (Kriesel, 2007). A script written in R (designed to run on R studio) accompanies this article that implements this algorithm and is available at http://butterflygeraci.codeplex.com/. For details on the R package or for help installing the software refer to the accompanying document, Supporting Material and Appendix.

Female Representation in the Higher Education of Geography in Hungary. Symposium

ERIC Educational Resources Information Center

Timar, Judit; Jelenszkyne, Ildiko Fabian

2004-01-01

This paper charts the changing female representation in the higher education of geography, connecting it with the faltering development of feminist geography in Hungary. The transition from socialism to capitalism has compounded gender inequalities while many of the relevant statistical data display gender blindness. Gender issues fail to form a…

Review of Zero-D and 1-D Models of Blood Flow in the Cardiovascular System

PubMed Central

2011-01-01

Background Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models. Method and Results The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository http://models.cellml.org/. They are freely available to the research and education communities. Conclusion Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application. PMID:21521508

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Several examples where turbulence models fail in inlet flow field analysis

NASA Technical Reports Server (NTRS)

Anderson, Bernhard H.

1993-01-01

Computational uncertainties in turbulence modeling for three dimensional inlet flow fields include flows approaching separation, strength of secondary flow field, three dimensional flow predictions of vortex liftoff, and influence of vortex-boundary layer interactions; computational uncertainties in vortex generator modeling include representation of generator vorticity field and the relationship between generator and vorticity field. The objectives of the inlet flow field studies presented in this document are to advance the understanding, prediction, and control of intake distortion and to study the basic interactions that influence this design problem.

Measurement of entanglement entropy in the two-dimensional Potts model using wavelet analysis.

PubMed

Tomita, Yusuke

2018-05-01

A method is introduced to measure the entanglement entropy using a wavelet analysis. Using this method, the two-dimensional Haar wavelet transform of a configuration of Fortuin-Kasteleyn (FK) clusters is performed. The configuration represents a direct snapshot of spin-spin correlations since spin degrees of freedom are traced out in FK representation. A snapshot of FK clusters loses image information at each coarse-graining process by the wavelet transform. It is shown that the loss of image information measures the entanglement entropy in the Potts model.

Coherent States for the Two-Dimensional Dirac-Moshinsky Oscillator Coupled to an External Magnetic Field

NASA Astrophysics Data System (ADS)

Ojeda-Guillén, D.; Mota, R. D.; Granados, V. D.

2015-03-01

We show that the (2+1)-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field can be treated algebraically with the SU(1,1) group theory and its group basis. We use the su(1,1) irreducible representation theory to find the energy spectrum and the eigenfunctions. Also, with the su(1,1) group basis we construct the relativistic coherent states in a closed form for this problem. Supported by SNI-México, COFAA-IPN, EDI-IPN, EDD-IPN, SIP-IPN project number 20140598

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases.

PubMed

D'Amico, María Belén; Calandrini, Guillermo L

2015-11-01

Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases

NASA Astrophysics Data System (ADS)

D'Amico, María Belén; Calandrini, Guillermo L.

2015-11-01

Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

Three dimensional simulation of spatial and temporal variability of stratospheric hydrogen chloride

NASA Technical Reports Server (NTRS)

Kaye, Jack A.; Rood, Richard B.; Jackman, Charles H.; Allen, Dale J.; Larson, Edmund M.

1989-01-01

Spatial and temporal variability of atmospheric HCl columns are calculated for January 1979 using a three-dimensional chemistry-transport model designed to provide the best possible representation of stratospheric transport. Large spatial and temporal variability of the HCl columns is shown to be correlated with lower stratospheric potential vorticity and thus to be of dynamical origin. Systematic longitudinal structure is correlated with planetary wave structure. These results can help place spatially and temporally isolated column and profile measurements in a regional and/or global perspective.

Quantum superintegrable system with a novel chain structure of quadratic algebras

NASA Astrophysics Data System (ADS)

Liao, Yidong; Marquette, Ian; Zhang, Yao-Zhong

2018-06-01

We analyse the n-dimensional superintegrable Kepler–Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. We identify the elements for each sub-structure and obtain the algebra relations satisfied by them and the corresponding Casimir operators. These quadratic sub-algebras are realized in terms of a chain of deformed oscillators with factorized structure functions. We construct the finite-dimensional unitary representations of the deformed oscillators, and give an algebraic derivation of the energy spectrum of the superintegrable system.

Renormalized asymptotic enumeration of Feynman diagrams

NASA Astrophysics Data System (ADS)

Borinsky, Michael

2017-10-01

A method to obtain all-order asymptotic results for the coefficients of perturbative expansions in zero-dimensional quantum field is described. The focus is on the enumeration of the number of skeleton or primitive diagrams of a certain QFT and its asymptotics. The procedure heavily applies techniques from singularity analysis. To utilize singularity analysis, a representation of the zero-dimensional path integral as a generalized hyperelliptic curve is deduced. As applications the full asymptotic expansions of the number of disconnected, connected, 1PI and skeleton Feynman diagrams in various theories are given.

The Development and Evaluation of Color Display Systems for Airborne Applications. Phase 1. Fundamental Visual, Perceptual, and Display System Considerations

DTIC Science & Technology

1985-07-18

Element Predictions 28 2.1.1.2-9 CIELUV Color Difference Derivation Graphically Described In a Three-Dimensional Rectangular Coordinate System 31...in CIE 1976 Coordinates 141 2.2.2-3 Derivation of CIE (L*, U*, V*) Coordinates 145 2.2.2-4 Three-Dimensional Representation of CIELUV Color...Difference Estimates 145 2.2.2-5 Application of CIELUV for Estimating Color Difference on an Electronic Color Display 146 2.2.2-6 Color Performance Envelopes

3D Feature Extraction for Unstructured Grids

NASA Technical Reports Server (NTRS)

Silver, Deborah

1996-01-01

Visualization techniques provide tools that help scientists identify observed phenomena in scientific simulation. To be useful, these tools must allow the user to extract regions, classify and visualize them, abstract them for simplified representations, and track their evolution. Object Segmentation provides a technique to extract and quantify regions of interest within these massive datasets. This article explores basic algorithms to extract coherent amorphous regions from two-dimensional and three-dimensional scalar unstructured grids. The techniques are applied to datasets from Computational Fluid Dynamics and those from Finite Element Analysis.

Face recognition by applying wavelet subband representation and kernel associative memory.

PubMed

Zhang, Bai-Ling; Zhang, Haihong; Ge, Shuzhi Sam

2004-01-01

In this paper, we propose an efficient face recognition scheme which has two features: 1) representation of face images by two-dimensional (2-D) wavelet subband coefficients and 2) recognition by a modular, personalised classification method based on kernel associative memory models. Compared to PCA projections and low resolution "thumb-nail" image representations, wavelet subband coefficients can efficiently capture substantial facial features while keeping computational complexity low. As there are usually very limited samples, we constructed an associative memory (AM) model for each person and proposed to improve the performance of AM models by kernel methods. Specifically, we first applied kernel transforms to each possible training pair of faces sample and then mapped the high-dimensional feature space back to input space. Our scheme using modular autoassociative memory for face recognition is inspired by the same motivation as using autoencoders for optical character recognition (OCR), for which the advantages has been proven. By associative memory, all the prototypical faces of one particular person are used to reconstruct themselves and the reconstruction error for a probe face image is used to decide if the probe face is from the corresponding person. We carried out extensive experiments on three standard face recognition datasets, the FERET data, the XM2VTS data, and the ORL data. Detailed comparisons with earlier published results are provided and our proposed scheme offers better recognition accuracy on all of the face datasets.

Representation of photon limited data in emission tomography using origin ensembles

NASA Astrophysics Data System (ADS)

Sitek, A.

2008-06-01

Representation and reconstruction of data obtained by emission tomography scanners are challenging due to high noise levels in the data. Typically, images obtained using tomographic measurements are represented using grids. In this work, we define images as sets of origins of events detected during tomographic measurements; we call these origin ensembles (OEs). A state in the ensemble is characterized by a vector of 3N parameters Y, where the parameters are the coordinates of origins of detected events in a three-dimensional space and N is the number of detected events. The 3N-dimensional probability density function (PDF) for that ensemble is derived, and we present an algorithm for OE image estimation from tomographic measurements. A displayable image (e.g. grid based image) is derived from the OE formulation by calculating ensemble expectations based on the PDF using the Markov chain Monte Carlo method. The approach was applied to computer-simulated 3D list-mode positron emission tomography data. The reconstruction errors for a 10 000 000 event acquisition for simulated ranged from 0.1 to 34.8%, depending on object size and sampling density. The method was also applied to experimental data and the results of the OE method were consistent with those obtained by a standard maximum-likelihood approach. The method is a new approach to representation and reconstruction of data obtained by photon-limited emission tomography measurements.

Arrowheaded enhanced multivariance products representation for matrices (AEMPRM): Specifically focusing on infinite matrices and converting arrowheadedness to tridiagonality

NASA Astrophysics Data System (ADS)

Özdemir, Gizem; Demiralp, Metin

2015-12-01

In this work, Enhanced Multivariance Products Representation (EMPR) approach which is a Demiralp-and-his- group extension to the Sobol's High Dimensional Model Representation (HDMR) has been used as the basic tool. Their discrete form have also been developed and used in practice by Demiralp and his group in addition to some other authors for the decomposition of the arrays like vectors, matrices, or multiway arrays. This work specifically focuses on the decomposition of infinite matrices involving denumerable infinitely many rows and columns. To this end the target matrix is first decomposed to the sum of certain outer products and then each outer product is treated by Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) which has been developed by Demiralp and his group. The result is a three-matrix- factor-product whose kernel (the middle factor) is an arrowheaded matrix while the pre and post factors are invertable matrices decomposed of the support vectors of TMEMPR. This new method is called as Arrowheaded Enhanced Multivariance Products Representation for Matrices. The general purpose is approximation of denumerably infinite matrices with the new method.

Indicators that influence prospective mathematics teachers representational and reasoning abilities

NASA Astrophysics Data System (ADS)

Darta; Saputra, J.

2018-01-01

Representational and mathematical reasoning ability are very important ability as basic in mathematics learning process. The 2013 curriculum suggests that the use of a scientific approach emphasizes higher order thinking skills. Therefore, a scientific approach is required in mathematics learning to improve ability of representation and mathematical reasoning. The objectives of this research are: (1) to analyze representational and reasoning abilities, (2) to analyze indicators affecting the ability of representation and mathematical reasoning, (3) to analyze scientific approaches that can improve the ability of representation and mathematical reasoning. The subject of this research is the students of mathematics prospective teachers in the first semester at Private Higher Education of Bandung City. The research method of this research was descriptive analysis. The research data were collected using reasoning and representation tests on sixty-one students. Data processing was done by descriptive analysis specified based on the indicators of representation ability and mathematical reasoning that influenced it. The results of this first-year study showed that students still had many weaknesses in reasoning and mathematical representation that were influenced by the ability to understand the indicators of both capabilities. After observing the results of the first-year research, then in the second and third year, the development of teaching materials with a scientific approach in accordance with the needs of prospective students was planned.