A fast identification algorithm for Box-Cox transformation based radial basis function neural network.

PubMed

Hong, Xia

2006-07-01

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.

Comparison of l₁-Norm SVR and Sparse Coding Algorithms for Linear Regression.

PubMed

Zhang, Qingtian; Hu, Xiaolin; Zhang, Bo

2015-08-01

Support vector regression (SVR) is a popular function estimation technique based on Vapnik's concept of support vector machine. Among many variants, the l1-norm SVR is known to be good at selecting useful features when the features are redundant. Sparse coding (SC) is a technique widely used in many areas and a number of efficient algorithms are available. Both l1-norm SVR and SC can be used for linear regression. In this brief, the close connection between the l1-norm SVR and SC is revealed and some typical algorithms are compared for linear regression. The results show that the SC algorithms outperform the Newton linear programming algorithm, an efficient l1-norm SVR algorithm, in efficiency. The algorithms are then used to design the radial basis function (RBF) neural networks. Experiments on some benchmark data sets demonstrate the high efficiency of the SC algorithms. In particular, one of the SC algorithms, the orthogonal matching pursuit is two orders of magnitude faster than a well-known RBF network designing algorithm, the orthogonal least squares algorithm.

Generalization of the Jones vector-matrix method and the regularity of the Weigert effect for partially polarized light.

PubMed

Kilosanidze, Barbara

2010-06-01

Generalization of the Jones vector for partially polarized radiation carried out by Kakichashvili is given. Partially polarized light is presented as two noncoherent components of mutually orthogonal polarization. The formal operation of amplitude summation of mutually noncoherent components and the symbol of this operation are introduced. The rules of operating with this symbol are determined. The regularity of the Weigert effect is modified for partial polarization of the inducing light. On this basis the modification of the Jones matrix for partially polarized light is made. The rules for the formation of the resulting matrix from the Jones matrices corresponding to the noncoherent components of partially polarized light are determined.

Symbolic computer vector analysis

NASA Technical Reports Server (NTRS)

Stoutemyer, D. R.

1977-01-01

A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.

Microchip solid-state cylindrical vector lasers with orthogonally polarized dual laser-diode end pumping.

PubMed

Otsuka, Kenju; Chu, Shu-Chun

2013-05-01

We report a simple method for generating cylindrical vector beams directly from laser-diode (LD)-pumped microchip solid-state lasers by using dual end-pumping beams. Radially as well as azimuthally polarized vector field emissions have been generated from the common c-cut Nd:GdVO4 laser cavity merely by controlling the focus positions of orthogonally polarized LD off-axis pump beams. Hyperbolically polarized vector fields have also been observed, in which the cylindrical symmetry of vector fields is broken. Experimental results have been well reproduced by numerical simulations.

A combined representation method for use in band structure calculations. 1: Method

NASA Technical Reports Server (NTRS)

Friedli, C.; Ashcroft, N. W.

1975-01-01

A representation was described whose basis levels combine the important physical aspects of a finite set of plane waves with those of a set of Bloch tight-binding levels. The chosen combination has a particularly simple dependence on the wave vector within the Brillouin Zone, and its use in reducing the standard one-electron band structure problem to the usual secular equation has the advantage that the lattice sums involved in the calculation of the matrix elements are actually independent of the wave vector. For systems with complicated crystal structures, for which the Korringa-Kohn-Rostoker (KKR), Augmented-Plane Wave (APW) and Orthogonalized-Plane Wave (OPW) methods are difficult to apply, the present method leads to results with satisfactory accuracy and convergence.

Modeling global vector fields of chaotic systems from noisy time series with the aid of structure-selection techniques.

PubMed

Xu, Daolin; Lu, Fangfang

2006-12-01

We address the problem of reconstructing a set of nonlinear differential equations from chaotic time series. A method that combines the implicit Adams integration and the structure-selection technique of an error reduction ratio is proposed for system identification and corresponding parameter estimation of the model. The structure-selection technique identifies the significant terms from a pool of candidates of functional basis and determines the optimal model through orthogonal characteristics on data. The technique with the Adams integration algorithm makes the reconstruction available to data sampled with large time intervals. Numerical experiment on Lorenz and Rossler systems shows that the proposed strategy is effective in global vector field reconstruction from noisy time series.

Creating orbiting vorticity vectors in magnetic particle suspensions through field symmetry transitions–a route to multi-axis mixing

DOE PAGES

Martin, James E.; Solis, Kyle Jameson

2015-11-09

It has recently been reported that two types of triaxial electric or magnetic fields can drive vorticity in dielectric or magnetic particle suspensions, respectively. The first type-symmetry -- breaking rational fields -- consists of three mutually orthogonal fields, two alternating and one dc, and the second type -- rational triads -- consists of three mutually orthogonal alternating fields. In each case it can be shown through experiment and theory that the fluid vorticity vector is parallel to one of the three field components. For any given set of field frequencies this axis is invariant, but the sign and magnitude ofmore » the vorticity (at constant field strength) can be controlled by the phase angles of the alternating components and, at least for some symmetry-breaking rational fields, the direction of the dc field. In short, the locus of possible vorticity vectors is a 1-d set that is symmetric about zero and is along a field direction. In this paper we show that continuous, 3-d control of the vorticity vector is possible by progressively transitioning the field symmetry by applying a dc bias along one of the principal axes. Such biased rational triads are a combination of symmetry-breaking rational fields and rational triads. A surprising aspect of these transitions is that the locus of possible vorticity vectors for any given field bias is extremely complex, encompassing all three spatial dimensions. As a result, the evolution of a vorticity vector as the dc bias is increased is complex, with large components occurring along unexpected directions. More remarkable are the elaborate vorticity vector orbits that occur when one or more of the field frequencies are detuned. As a result, these orbits provide the basis for highly effective mixing strategies wherein the vorticity axis periodically explores a range of orientations and magnitudes.« less

Estimation of the chemical rank for the three-way data: a principal norm vector orthogonal projection approach.

PubMed

Hong-Ping, Xie; Jian-Hui, Jiang; Guo-Li, Shen; Ru-Qin, Yu

2002-01-01

A new approach for estimating the chemical rank of the three-way array called the principal norm vector orthogonal projection method has been proposed. The method is based on the fact that the chemical rank of the three-way data array is equal to one of the column space of the unfolded matrix along the spectral or chromatographic mode. A vector with maximum Frobenius norm is selected among all the column vectors of the unfolded matrix as the principal norm vector (PNV). A transformation is conducted for the column vectors with an orthogonal projection matrix formulated by PNV. The mathematical rank of the column space of the residual matrix thus obtained should decrease by one. Such orthogonal projection is carried out repeatedly till the contribution of chemical species to the signal data is all deleted. At this time the decrease of the mathematical rank would equal that of the chemical rank, and the remaining residual subspace would entirely be due to the noise contribution. The chemical rank can be estimated easily by using an F-test. The method has been used successfully to the simulated HPLC-DAD type three-way data array and two real excitation-emission fluorescence data sets of amino acid mixtures and dye mixtures. The simulation with added relatively high level noise shows that the method is robust in resisting the heteroscedastic noise. The proposed algorithm is simple and easy to program with quite light computational burden.

Orthogonal vector algorithm to obtain the solar vector using the single-scattering Rayleigh model.

PubMed

Wang, Yinlong; Chu, Jinkui; Zhang, Ran; Shi, Chao

2018-02-01

Information obtained from a polarization pattern in the sky provides many animals like insects and birds with vital long-distance navigation cues. The solar vector can be derived from the polarization pattern using the single-scattering Rayleigh model. In this paper, an orthogonal vector algorithm, which utilizes the redundancy of the single-scattering Rayleigh model, is proposed. We use the intersection angles between the polarization vectors as the main criteria in our algorithm. The assumption that all polarization vectors can be considered coplanar is used to simplify the three-dimensional (3D) problem with respect to the polarization vectors in our simulation. The surface-normal vector of the plane, which is determined by the polarization vectors after translation, represents the solar vector. Unfortunately, the two-directionality of the polarization vectors makes the resulting solar vector ambiguous. One important result of this study is, however, that this apparent disadvantage has no effect on the complexity of the algorithm. Furthermore, two other universal least-squares algorithms were investigated and compared. A device was then constructed, which consists of five polarized-light sensors as well as a 3D attitude sensor. Both the simulation and experimental data indicate that the orthogonal vector algorithms, if used with a suitable threshold, perform equally well or better than the other two algorithms. Our experimental data reveal that if the intersection angles between the polarization vectors are close to 90°, the solar-vector angle deviations are small. The data also support the assumption of coplanarity. During the 51 min experiment, the mean of the measured solar-vector angle deviations was about 0.242°, as predicted by our theoretical model.

Vector solitons with polarization instability and locked polarization in a fiber laser

NASA Astrophysics Data System (ADS)

Tang, Dingkang; Zhang, Jian-Guo; Liu, Yuanshan

2012-07-01

We investigate the characteristics of vector solitons with and without locked phase velocities of orthogonal polarization components in a specially-designed laser cavity which is formed by a bidirectional fiber loop together with a semiconductor saturable absorber mirror. The characteristics of the two states are compared in the temporal and spectrum domain, respectively. Both of the two states exhibit the characteristic of mode locking while the two orthogonal polarization components are not resolved. However, for the vector soliton with unlocked phase velocities, identical intensity varies after passing through a polarization beam splitter (PBS) outside the laser cavity. Contrary to the polarization rotation locked vector soliton, the intensity does not change periodically. For the polarization-locked vector soliton (PLVS), the identical pulse intensity is still obtained after passing through the PBS and can be observed on the oscilloscope screen after photodetection. A coupler instead of a circulator is integrated in the laser cavity and strong interaction on the polarization resolved spectra of the PLVS is observed. By comparing the two states, we conclude that interaction between the two orthogonal components contributes to the locked phase velocities.

Principle component analysis to separate deformation signals from multiple sources during a 2015 intrusive sequence at Kīlauea Volcano

NASA Astrophysics Data System (ADS)

Johanson, I. A.; Miklius, A.; Poland, M. P.

2016-12-01

A sequence of magmatic events in April-May 2015 at Kīlauea Volcano produced a complex deformation pattern that can be described by multiple deforming sources, active simultaneously. The 2015 intrusive sequence began with inflation in the volcano's summit caldera near Halema`uma`u (HMM) Crater, which continued over a few weeks, followed by rapid deflation of the HMM source and inflation of a source in the south caldera region during the next few days. In Kīlauea Volcano's summit area, multiple deformation centers are active at varying times, and all contribute to the overall pattern observed with GPS, tiltmeters, and InSAR. Isolating the contribution of different signals related to each source is a challenge and complicates the determination of optimal source geometry for the underlying magma bodies. We used principle component analysis of continuous GPS time series from the 2015 intrusion sequence to determine three basis vectors which together account for 83% of the variance in the data set. The three basis vectors are non-orthogonal and not strictly the principle components of the data set. In addition to separating deformation sources in the continuous GPS data, the basis vectors provide a means to scale the contribution of each source in a given interferogram. This provides an additional constraint in a joint model of GPS and InSAR data (COSMO-SkyMed and Sentinel-1A) to determine source geometry. The first basis vector corresponds with inflation in the south caldera region, an area long recognized as the location of a long-term storage reservoir. The second vector represents deformation of the HMM source, which is in the same location as a previously modeled shallow reservoir, however InSAR data suggest a more complicated source. Preliminary modeling of the deformation attributed to the third basis vector shows that it is consistent with inflation of a steeply dipping ellipsoid centered below Keanakāko`i crater, southeast of HMM. Keanakāko`i crater is the locus of a known, intermittently active deformation source, which was not previously recognized to have been active during the 2015 event.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Finding a Hadamard matrix by simulated annealing of spin vectors

NASA Astrophysics Data System (ADS)

Bayu Suksmono, Andriyan

2017-05-01

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

Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors.

PubMed

Xu, Danfeng; Gu, Bing; Rui, Guanghao; Zhan, Qiwen; Cui, Yiping

2016-02-22

We present an arbitrary vector field with hybrid polarization based on the combination of a pair of orthogonal elliptically polarized base vectors on the Poincaré sphere. It is shown that the created vector field is only dependent on the latitude angle 2χ but is independent on the longitude angle 2ψ on the Poincaré sphere. By adjusting the latitude angle 2χ, which is related to two identical waveplates in a common path interferometric arrangement, one could obtain arbitrary type of vector fields. Experimentally, we demonstrate the generation of such kind of vector fields and confirm the distribution of state of polarization by the measurement of Stokes parameters. Besides, we investigate the tight focusing properties of these vector fields. It is found that the additional degree of freedom 2χ provided by arbitrary vector field with hybrid polarization allows one to control the spatial structure of polarization and to engineer the focusing field.

Manipulation of group-velocity-locked vector dissipative solitons and properties of the generated high-order vector soliton structure.

PubMed

Zhu, S N; Wu, Z C; Fu, S N; Zhao, L M

2018-03-20

Details of various composites of the projections originated from a fundamental group-velocity-locked vector dissipative soliton (GVLVDS) are both experimentally and numerically explored. By combining the projections from the orthogonal polarization components of the GVLVDS, a high-order vector soliton structure with a double-humped pulse profile along one polarization and a single-humped pulse profile along the orthogonal polarization can be observed. Moreover, by de-chirping the composite double-humped pulse, the time separation between the two humps is reduced from 15.36 ps to 1.28 ps, indicating that the frequency chirp of the GVLVDS contributes significantly to the shaping of the double-humped pulse profile.

Mixed kernel function support vector regression for global sensitivity analysis

NASA Astrophysics Data System (ADS)

Cheng, Kai; Lu, Zhenzhou; Wei, Yuhao; Shi, Yan; Zhou, Yicheng

2017-11-01

Global sensitivity analysis (GSA) plays an important role in exploring the respective effects of input variables on an assigned output response. Amongst the wide sensitivity analyses in literature, the Sobol indices have attracted much attention since they can provide accurate information for most models. In this paper, a mixed kernel function (MKF) based support vector regression (SVR) model is employed to evaluate the Sobol indices at low computational cost. By the proposed derivation, the estimation of the Sobol indices can be obtained by post-processing the coefficients of the SVR meta-model. The MKF is constituted by the orthogonal polynomials kernel function and Gaussian radial basis kernel function, thus the MKF possesses both the global characteristic advantage of the polynomials kernel function and the local characteristic advantage of the Gaussian radial basis kernel function. The proposed approach is suitable for high-dimensional and non-linear problems. Performance of the proposed approach is validated by various analytical functions and compared with the popular polynomial chaos expansion (PCE). Results demonstrate that the proposed approach is an efficient method for global sensitivity analysis.

Rotation invariants of vector fields from orthogonal moments

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

Yang, Bo; Kostková, Jitka; Flusser, Jan

Vector field images are a type of new multidimensional data that appear in many engineering areas. Although the vector fields can be visualized as images, they differ from graylevel and color images in several aspects. In order to analyze them, special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area. Here, we propose a method for the description and matching of vector field patterns under an unknown rotation of the field. Rotation of a vector field is so-called total rotation, where the action is applied not only on the spatial coordinates but alsomore » on the field values. Invariants of vector fields with respect to total rotation constructed from orthogonal Gaussian–Hermite moments and Zernike moments are introduced. Their numerical stability is shown to be better than that of the invariants published so far. We demonstrate their usefulness in a real world template matching application of rotated vector fields.« less

PCA-LBG-based algorithms for VQ codebook generation

NASA Astrophysics Data System (ADS)

Tsai, Jinn-Tsong; Yang, Po-Yuan

2015-04-01

Vector quantisation (VQ) codebooks are generated by combining principal component analysis (PCA) algorithms with Linde-Buzo-Gray (LBG) algorithms. All training vectors are grouped according to the projected values of the principal components. The PCA-LBG-based algorithms include (1) PCA-LBG-Median, which selects the median vector of each group, (2) PCA-LBG-Centroid, which adopts the centroid vector of each group, and (3) PCA-LBG-Random, which randomly selects a vector of each group. The LBG algorithm finds a codebook based on the better vectors sent to an initial codebook by the PCA. The PCA performs an orthogonal transformation to convert a set of potentially correlated variables into a set of variables that are not linearly correlated. Because the orthogonal transformation efficiently distinguishes test image vectors, the proposed PCA-LBG-based algorithm is expected to outperform conventional algorithms in designing VQ codebooks. The experimental results confirm that the proposed PCA-LBG-based algorithms indeed obtain better results compared to existing methods reported in the literature.

Rotation invariants of vector fields from orthogonal moments

DOE PAGES

Yang, Bo; Kostková, Jitka; Flusser, Jan; ...

2017-09-11

Vector field images are a type of new multidimensional data that appear in many engineering areas. Although the vector fields can be visualized as images, they differ from graylevel and color images in several aspects. In order to analyze them, special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area. Here, we propose a method for the description and matching of vector field patterns under an unknown rotation of the field. Rotation of a vector field is so-called total rotation, where the action is applied not only on the spatial coordinates but alsomore » on the field values. Invariants of vector fields with respect to total rotation constructed from orthogonal Gaussian–Hermite moments and Zernike moments are introduced. Their numerical stability is shown to be better than that of the invariants published so far. We demonstrate their usefulness in a real world template matching application of rotated vector fields.« less

Separation of spatial-temporal patterns ('climatic modes') by combined analysis of really measured and generated numerically vector time series

NASA Astrophysics Data System (ADS)

Feigin, A. M.; Mukhin, D.; Volodin, E. M.; Gavrilov, A.; Loskutov, E. M.

2013-12-01

The new method of decomposition of the Earth's climate system into well separated spatial-temporal patterns ('climatic modes') is discussed. The method is based on: (i) generalization of the MSSA (Multichannel Singular Spectral Analysis) [1] for expanding vector (space-distributed) time series in basis of spatial-temporal empirical orthogonal functions (STEOF), which makes allowance delayed correlations of the processes recorded in spatially separated points; (ii) expanding both real SST data, and longer by several times SST data generated numerically, in STEOF basis; (iii) use of the numerically produced STEOF basis for exclusion of 'too slow' (and thus not represented correctly) processes from real data. The application of the method allows by means of vector time series generated numerically by the INM RAS Coupled Climate Model [2] to separate from real SST anomalies data [3] two climatic modes possessing by noticeably different time scales: 3-5 and 9-11 years. Relations of separated modes to ENSO and PDO are investigated. Possible applications of spatial-temporal climatic patterns concept to prognosis of climate system evolution is discussed. 1. Ghil, M., R. M. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, et al. (2002) "Advanced spectral methods for climatic time series", Rev. Geophys. 40(1), 3.1-3.41. 2. http://83.149.207.89/GCM_DATA_PLOTTING/GCM_INM_DATA_XY_en.htm 3. http://iridl.ldeo.columbia.edu/SOURCES/.KAPLAN/.EXTENDED/.v2/.ssta/

Least-Squares Adaptive Control Using Chebyshev Orthogonal Polynomials

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Burken, John; Ishihara, Abraham

2011-01-01

This paper presents a new adaptive control approach using Chebyshev orthogonal polynomials as basis functions in a least-squares functional approximation. The use of orthogonal basis functions improves the function approximation significantly and enables better convergence of parameter estimates. Flight control simulations demonstrate the effectiveness of the proposed adaptive control approach.

Gram-Schmidt Orthogonalization by Gauss Elimination.

ERIC Educational Resources Information Center

Pursell, Lyle; Trimble, S. Y.

1991-01-01

Described is the hand-calculation method for the orthogonalization of a given set of vectors through the integration of Gaussian elimination with existing algorithms. Although not numerically preferable, this method adds increased precision as well as organization to the solution process. (JJK)

Three-Dimensional Orthogonal Co-ordinates

ERIC Educational Resources Information Center

Astin, J.

1974-01-01

A systematic approach to general orthogonal co-ordinates, suitable for use near the end of a beginning vector analysis course, is presented. It introduces students to tensor quantities and shows how equations and quantities needed in classical problems can be determined. (Author/LS)

Hydrologic Process Regularization for Improved Geoelectrical Monitoring of a Lab-Scale Saline Tracer Experiment

NASA Astrophysics Data System (ADS)

Oware, E. K.; Moysey, S. M.

2016-12-01

Regularization stabilizes the geophysical imaging problem resulting from sparse and noisy measurements that render solutions unstable and non-unique. Conventional regularization constraints are, however, independent of the physics of the underlying process and often produce smoothed-out tomograms with mass underestimation. Cascaded time-lapse (CTL) is a widely used reconstruction technique for monitoring wherein a tomogram obtained from the background dataset is employed as starting model for the inversion of subsequent time-lapse datasets. In contrast, a proper orthogonal decomposition (POD)-constrained inversion framework enforces physics-based regularization based upon prior understanding of the expected evolution of state variables. The physics-based constraints are represented in the form of POD basis vectors. The basis vectors are constructed from numerically generated training images (TIs) that mimic the desired process. The target can be reconstructed from a small number of selected basis vectors, hence, there is a reduction in the number of inversion parameters compared to the full dimensional space. The inversion involves finding the optimal combination of the selected basis vectors conditioned on the geophysical measurements. We apply the algorithm to 2-D lab-scale saline transport experiments with electrical resistivity (ER) monitoring. We consider two transport scenarios with one and two mass injection points evolving into unimodal and bimodal plume morphologies, respectively. The unimodal plume is consistent with the assumptions underlying the generation of the TIs, whereas bimodality in plume morphology was not conceptualized. We compare difference tomograms retrieved from POD with those obtained from CTL. Qualitative comparisons of the difference tomograms with images of their corresponding dye plumes suggest that POD recovered more compact plumes in contrast to those of CTL. While mass recovery generally deteriorated with increasing number of time-steps, POD outperformed CTL in terms of mass recovery accuracy rates. POD is computationally superior requiring only 2.5 mins to complete each inversion compared to 3 hours for CTL to do the same.

The Cross Product of Two Vectors Is Not Just Another Vector--A Major Misconception Being Perpetuated in Calculus and Vector Analysis Textbooks.

ERIC Educational Resources Information Center

Elk, Seymour B.

1997-01-01

Suggests that the cross product of two vectors can be more easily and accurately explained by starting from the perspective of dyadics because then the concept of vector multiplication has a simple geometrical picture that encompasses both the dot and cross products in any number of dimensions in terms of orthogonal unit vector components. (AIM)

Hydrologic Process Parameterization of Electrical Resistivity Imaging of Solute Plumes Using POD McMC

NASA Astrophysics Data System (ADS)

Awatey, M. T.; Irving, J.; Oware, E. K.

2016-12-01

Markov chain Monte Carlo (McMC) inversion frameworks are becoming increasingly popular in geophysics due to their ability to recover multiple equally plausible geologic features that honor the limited noisy measurements. Standard McMC methods, however, become computationally intractable with increasing dimensionality of the problem, for example, when working with spatially distributed geophysical parameter fields. We present a McMC approach based on a sparse proper orthogonal decomposition (POD) model parameterization that implicitly incorporates the physics of the underlying process. First, we generate training images (TIs) via Monte Carlo simulations of the target process constrained to a conceptual model. We then apply POD to construct basis vectors from the TIs. A small number of basis vectors can represent most of the variability in the TIs, leading to dimensionality reduction. A projection of the starting model into the reduced basis space generates the starting POD coefficients. At each iteration, only coefficients within a specified sampling window are resimulated assuming a Gaussian prior. The sampling window grows at a specified rate as the number of iteration progresses starting from the coefficients corresponding to the highest ranked basis to those of the least informative basis. We found this gradual increment in the sampling window to be more stable compared to resampling all the coefficients right from the first iteration. We demonstrate the performance of the algorithm with both synthetic and lab-scale electrical resistivity imaging of saline tracer experiments, employing the same set of basis vectors for all inversions. We consider two scenarios of unimodal and bimodal plumes. The unimodal plume is consistent with the hypothesis underlying the generation of the TIs whereas bimodality in plume morphology was not theorized. We show that uncertainty quantification using McMC can proceed in the reduced dimensionality space while accounting for the physics of the underlying process.

A communication-avoiding, hybrid-parallel, rank-revealing orthogonalization method.

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

Hoemmen, Mark

2010-11-01

Orthogonalization consumes much of the run time of many iterative methods for solving sparse linear systems and eigenvalue problems. Commonly used algorithms, such as variants of Gram-Schmidt or Householder QR, have performance dominated by communication. Here, 'communication' includes both data movement between the CPU and memory, and messages between processors in parallel. Our Tall Skinny QR (TSQR) family of algorithms requires asymptotically fewer messages between processors and data movement between CPU and memory than typical orthogonalization methods, yet achieves the same accuracy as Householder QR factorization. Furthermore, in block orthogonalizations, TSQR is faster and more accurate than existing approaches formore » orthogonalizing the vectors within each block ('normalization'). TSQR's rank-revealing capability also makes it useful for detecting deflation in block iterative methods, for which existing approaches sacrifice performance, accuracy, or both. We have implemented a version of TSQR that exploits both distributed-memory and shared-memory parallelism, and supports real and complex arithmetic. Our implementation is optimized for the case of orthogonalizing a small number (5-20) of very long vectors. The shared-memory parallel component uses Intel's Threading Building Blocks, though its modular design supports other shared-memory programming models as well, including computation on the GPU. Our implementation achieves speedups of 2 times or more over competing orthogonalizations. It is available now in the development branch of the Trilinos software package, and will be included in the 10.8 release.« less

Spatial orientation of semicircular canals and afferent sensitivity vectors in pigeons

NASA Technical Reports Server (NTRS)

Dickman, J. D.

1996-01-01

Rotational head motion in vertebrates is detected by the semicircular canal system, whose innervating primary afferent fibers carry information about movement in specific head planes. The semicircular canals have been qualitatively examined over a number of years, and the canal planes have been quantitatively characterized in several animal species. The present study first determined the geometric relationship between individual semicircular canals and between the canals and the stereotactic head planes in pigeons. Stereotactic measurements of multiple points along the circumference of the bony canals were taken, and the measured points fitted with a three-dimensional planar surface. Direction normals to the plane's surface were calculated and used to define angles between semicircular canal pairs. Because of the unusual shape of the anterior semicircular canals in pigeons, two planes, a major and a minor, were fitted to the canal's course. Calculated angle values for all canals indicated that the horizontal and posterior semicircular canals are nearly orthogonal, but the anterior canals have substantial deviations from orthogonality with other canal planes. Next, the responses of the afferent fibers that innervate each of the semicircular canals to 0.5 Hz sinusoidal rotation about an earth-vertical axis were obtained. The head orientation relative to the rotation axis was systematically varied so that directions of maximum sensitivity for each canal afferent could be determined. These sensitivity vectors were then compared with the canal plane direction normals. The afferents that innervated specific semicircular canals formed homogeneous clusters of sensitivity vectors in different head planes. The horizontal and posterior afferents had average sensitivity vectors that were largely co-incident with the innervated canal plane direction normals. Anterior canal afferents, however, appeared to synthesize contributions from the major and minor plane components of the bony canal structure to produce a resultant sensitivity vector that was positioned between the canal planes. Calculated angles between the average canal afferent sensitivity vectors revealed that direction orthogonality is preserved at the afferent signal level, even though deviations from canal plane orthogonality exist.

Ideal flux field dielectric concentrators.

PubMed

García-Botella, Angel

2011-10-01

The concept of the vector flux field was first introduced as a photometrical theory and later developed in the field of nonimaging optics; it has provided new perspectives in the design of concentrators, overcoming standard ray tracing techniques. The flux field method has shown that reflective concentrators with the geometry of the field lines achieve the theoretical limit of concentration. In this paper we study the role of surfaces orthogonal to the field vector J. For rotationally symmetric systems J is orthogonal to its curl, and then a family of surfaces orthogonal to the lines of J exists, which can be called the family of surfaces of constant pseudopotential. Using the concept of the flux tube, it is possible to demonstrate that refractive concentrators with the shape of these pseudopotential surfaces achieve the theoretical limit of concentration.

Deterministic Joint Remote Preparation of Asymmetric Five-Party Three-Qubit Entangled States

NASA Astrophysics Data System (ADS)

Ma, Peng-Cheng; Chen, Gui-Bin; Li, Xiao-Wei; Zhan, You-Bang

2017-04-01

We present two schemes for joint remote state preparation (JRSP) of asymmetric five-party three-qubit entangled states with complex coefficients via three three-qubit and (N+1)-qubit GHZ states as the quantum channel, respectively. In these schemes, two senders(or N senders) share the original state which they wish to help the receiver to remotely prepare. To complete the JRSP schemes, some novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if two senders(or N senders) collaborate with each other, and perform projective measurements under suitable measuring basis on their own qubits respectively, the receiver can reconstruct the original state by means of some appropriate unitary operations. The advantage of the present schemes is that the success probability in all the considered JRSP can reach 1.

Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for Shock-Turbulence Computations

NASA Technical Reports Server (NTRS)

Sjoegreen, B.; Yee, H. C.

2001-01-01

The recently developed essentially fourth-order or higher low dissipative shock-capturing scheme of Yee, Sandham and Djomehri (1999) aimed at minimizing nu- merical dissipations for high speed compressible viscous flows containing shocks, shears and turbulence. To detect non smooth behavior and control the amount of numerical dissipation to be added, Yee et al. employed an artificial compression method (ACM) of Harten (1978) but utilize it in an entirely different context than Harten originally intended. The ACM sensor consists of two tuning parameters and is highly physical problem dependent. To minimize the tuning of parameters and physical problem dependence, new sensors with improved detection properties are proposed. The new sensors are derived from utilizing appropriate non-orthogonal wavelet basis functions and they can be used to completely switch to the extra numerical dissipation outside shock layers. The non-dissipative spatial base scheme of arbitrarily high order of accuracy can be maintained without compromising its stability at all parts of the domain where the solution is smooth. Two types of redundant non-orthogonal wavelet basis functions are considered. One is the B-spline wavelet (Mallat & Zhong 1992) used by Gerritsen and Olsson (1996) in an adaptive mesh refinement method, to determine regions where re nement should be done. The other is the modification of the multiresolution method of Harten (1995) by converting it to a new, redundant, non-orthogonal wavelet. The wavelet sensor is then obtained by computing the estimated Lipschitz exponent of a chosen physical quantity (or vector) to be sensed on a chosen wavelet basis function. Both wavelet sensors can be viewed as dual purpose adaptive methods leading to dynamic numerical dissipation control and improved grid adaptation indicators. Consequently, they are useful not only for shock-turbulence computations but also for computational aeroacoustics and numerical combustion. In addition, these sensors are scheme independent and can be stand alone options for numerical algorithm other than the Yee et al. scheme.

Correlation, Cost Risk, and Geometry

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1992-01-01

The geometric viewpoint identifies the choice of a correlation matrix for the simulation of cost risk with the pairwise choice of data vectors corresponding to the parameters used to obtain cost risk. The correlation coefficient is the cosine of the angle between the data vectors after translation to an origin at the mean and normalization for magnitude. Thus correlation is equivalent to expressing the data in terms of a non orthogonal basis. To understand the many resulting phenomena requires the use of the tensor concept of raising the index to transform the measured and observed covariant components into contravariant components before vector addition can be applied. The geometric viewpoint also demonstrates that correlation and covariance are geometric properties, as opposed to purely statistical properties, of the variates. Thus, variates from different distributions may be correlated, as desired, after selection from independent distributions. By determining the principal components of the correlation matrix, variates with the desired mean, magnitude, and correlation can be generated through linear transforms which include the eigenvalues and the eigenvectors of the correlation matrix. The conversion of the data to a non orthogonal basis uses a compound linear transformation which distorts or stretches the data space. Hence, the correlated data does not have the same properties as the uncorrelated data used to generate it. This phenomena is responsible for seemingly strange observations such as the fact that the marginal distributions of the correlated data can be quite different from the distributions used to generate the data. The joint effect of statistical distributions and correlation remains a fertile area for further research. In terms of application to cost estimating, the geometric approach demonstrates that the estimator must have data and must understand that data in order to properly choose the correlation matrix appropriate for a given estimate. There is a general feeling by employers and managers that the field of cost requires little technical or mathematical background. Contrary to that opinion, this paper demonstrates that a background in mathematics equivalent to that needed for typical engineering and scientific disciplines at the masters or doctorate level is appropriate within the field of cost risk.

Boosting with Averaged Weight Vectors

NASA Technical Reports Server (NTRS)

Oza, Nikunj C.; Clancy, Daniel (Technical Monitor)

2002-01-01

AdaBoost is a well-known ensemble learning algorithm that constructs its constituent or base models in sequence. A key step in AdaBoost is constructing a distribution over the training examples to create each base model. This distribution, represented as a vector, is constructed to be orthogonal to the vector of mistakes made by the previous base model in the sequence. The idea is to make the next base model's errors uncorrelated with those of the previous model. Some researchers have pointed out the intuition that it is probably better to construct a distribution that is orthogonal to the mistake vectors of all the previous base models, but that this is not always possible. We present an algorithm that attempts to come as close as possible to this goal in an efficient manner. We present experimental results demonstrating significant improvement over AdaBoost and the Totally Corrective boosting algorithm, which also attempts to satisfy this goal.

Wavefront analysis from its slope data

NASA Astrophysics Data System (ADS)

Mahajan, Virendra N.; Acosta, Eva

2017-08-01

In the aberration analysis of a wavefront over a certain domain, the polynomials that are orthogonal over and represent balanced wave aberrations for this domain are used. For example, Zernike circle polynomials are used for the analysis of a circular wavefront. Similarly, the annular polynomials are used to analyze the annular wavefronts for systems with annular pupils, as in a rotationally symmetric two-mirror system, such as the Hubble space telescope. However, when the data available for analysis are the slopes of a wavefront, as, for example, in a Shack- Hartmann sensor, we can integrate the slope data to obtain the wavefront data, and then use the orthogonal polynomials to obtain the aberration coefficients. An alternative is to find vector functions that are orthogonal to the gradients of the wavefront polynomials, and obtain the aberration coefficients directly as the inner products of these functions with the slope data. In this paper, we show that an infinite number of vector functions can be obtained in this manner. We show further that the vector functions that are irrotational are unique and propagate minimum uncorrelated additive random noise from the slope data to the aberration coefficients.

Polarization rotation locking of vector solitons in a fiber ring laser.

PubMed

Zhao, L M; Tang, D Y; Zhang, H; Wu, X

2008-07-07

Polarization rotation of vector solitons in a fiber ring laser was experimentally studied. It was observed that the period of vector soliton polarization rotation could be locked to the cavity roundtrip time or multiple of it. We further show that multiple vector solitons can be formed in a fiber laser, and all the vector solitons have the same group velocity in cavity, however, their instantaneous polarization ellipse orientations could be orthogonal.

No need for external orthogonality in subsystem density-functional theory.

PubMed

Unsleber, Jan P; Neugebauer, Johannes; Jacob, Christoph R

2016-08-03

Recent reports on the necessity of using externally orthogonal orbitals in subsystem density-functional theory (SDFT) [Annu. Rep. Comput. Chem., 8, 2012, 53; J. Phys. Chem. A, 118, 2014, 9182] are re-investigated. We show that in the basis-set limit, supermolecular Kohn-Sham-DFT (KS-DFT) densities can exactly be represented as a sum of subsystem densities, even if the subsystem orbitals are not externally orthogonal. This is illustrated using both an analytical example and in basis-set free numerical calculations for an atomic test case. We further show that even with finite basis sets, SDFT calculations using accurate reconstructed potentials can closely approach the supermolecular KS-DFT density, and that the deviations between SDFT and KS-DFT decrease as the basis-set limit is approached. Our results demonstrate that formally, there is no need to enforce external orthogonality in SDFT, even though this might be a useful strategy when developing projection-based DFT embedding schemes.

Lossless and Sufficient - Invariant Decomposition of Deterministic Target

NASA Astrophysics Data System (ADS)

Paladini, Riccardo; Ferro Famil, Laurent; Pottier, Eric; Martorella, Marco; Berizzi, Fabrizio

2011-03-01

The symmetric radar scattering matrix of a reciprocal target is projected on the circular polarization basis and is decomposed into four orientation invariant parameters, relative phase and relative orientation. The physical interpretation of this results is found in the wave-particle nature of radar scattering due to the circular polarization nature of elemental packets of energy. The proposed decomposition, is based on left orthogonal to left Special Unitary basis, providing the target description in term of a unitary vector. A comparison between the proposed CTD and Cameron, Kennaugh and Krogager decompositions is also pointed out. A validation by the use of both anechoic chamber data and airborne EMISAR data of DTU is used to show the effectiveness of this decomposition for the analysis of coherent targets. In the second paper we will show the application of the rotation group U(3) for the decomposition of distributed targets into nine meaningful parameters.

Schemes for deterministic joint remote preparation of an arbitrary tripartite four-qubit entangled state

NASA Astrophysics Data System (ADS)

Ma, Peng-Cheng; Chen, Gui-Bin; Li, Xiao-Wei; Zhan, You-Bang

2016-10-01

We present two schemes for the joint remote state preparation (JRSP) of an arbitrary tripartite four-qubit entangled state with complex coefficients via four and two three-qubit GHZ states as the quantum channel, respectively. In these schemes, the two senders share the original state which they wish to help the receiver remotely prepare. To complete the JRSP schemes, some novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if the two senders collaborate with each other, and perform projective measurements under a suitable measuring basis on their own qubits respectively, can the receiver reconstruct the original state by means of some appropriate unitary operations. We demonstrate, in our both schemes, the total success probability of the JRSP can reach 1. Moreover, compared with the first scheme in this paper, the advantage of the second scheme is that the entanglement resource can be reduced.

Some fundamentals regarding kinematics and generalized forces for multibody dynamics

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.

1990-01-01

In order to illustrate the various forms in which generalized forces can arise from diverse subsystem analyses in multibody dynamics, intrinsic dynamical equations for the rotational dynamics of a rigid body are derived from Hamilton's principle. Two types of generalized forces are derived: (1) those associated with the virtual rotation vector in some orthogonal basis, and (2) those associated with varying generalized coordinates. As one physical or kinematical result (such as a frequency or a specific direction cosine) cannot rely on this selection, a 'blind' coupling of two models in which generalized forces are calculated in different ways would be wrong. Both types should use the same rotational coordinates and should denote the virtual rotation on a similar basis according to method 1, or in terms of common rotational coordinates and their diversifications as in method 2. Alternatively, the generalized forces and coordinates of one model may be transformed to those of the other.

Equivalent Vectors

ERIC Educational Resources Information Center

Levine, Robert

2004-01-01

The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…

Minimal parameter solution of the orthogonal matrix differential equation

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.; Markley, F. Landis

1990-01-01

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed emplying the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Minimal parameter solution of the orthogonal matrix differential equation

NASA Technical Reports Server (NTRS)

Baritzhack, Itzhack Y.; Markley, F. Landis

1988-01-01

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Teleporting an unknown quantum state with unit fidelity and unit probability via a non-maximally entangled channel and an auxiliary system

NASA Astrophysics Data System (ADS)

Rashvand, Taghi

2016-11-01

We present a new scheme for quantum teleportation that one can teleport an unknown state via a non-maximally entangled channel with certainly, using an auxiliary system. In this scheme depending on the state of the auxiliary system, one can find a class of orthogonal vectors set as a basis which by performing von Neumann measurement in each element of this class Alice can teleport an unknown state with unit fidelity and unit probability. A comparison of our scheme with some previous schemes is given and we will see that our scheme has advantages that the others do not.

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.

Timelike Killing vectors and ergo surfaces in non-asymptotically flat spacetimes

NASA Astrophysics Data System (ADS)

Pelavas, N.

2005-02-01

Ergo surfaces are investigated in spacetimes with a cosmological constant. We find the existence of multiple timelike Killing vectors, each corresponding to a distinct ergo surface, with no one being preferred. Using a kinematic invariant, which provides a measure of hypersurface orthogonality, we explore its potential role in selecting a preferred timelike Killing vector and consequently a unique ergo surface.

A unified development of several techniques for the representation of random vectors and data sets

NASA Technical Reports Server (NTRS)

Bundick, W. T.

1973-01-01

Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.

Direct calculation of modal parameters from matrix orthogonal polynomials

NASA Astrophysics Data System (ADS)

El-Kafafy, Mahmoud; Guillaume, Patrick

2011-10-01

The object of this paper is to introduce a new technique to derive the global modal parameter (i.e. system poles) directly from estimated matrix orthogonal polynomials. This contribution generalized the results given in Rolain et al. (1994) [5] and Rolain et al. (1995) [6] for scalar orthogonal polynomials to multivariable (matrix) orthogonal polynomials for multiple input multiple output (MIMO) system. Using orthogonal polynomials improves the numerical properties of the estimation process. However, the derivation of the modal parameters from the orthogonal polynomials is in general ill-conditioned if not handled properly. The transformation of the coefficients from orthogonal polynomials basis to power polynomials basis is known to be an ill-conditioned transformation. In this paper a new approach is proposed to compute the system poles directly from the multivariable orthogonal polynomials. High order models can be used without any numerical problems. The proposed method will be compared with existing methods (Van Der Auweraer and Leuridan (1987) [4] Chen and Xu (2003) [7]). For this comparative study, simulated as well as experimental data will be used.

Nested Krylov methods and preserving the orthogonality

NASA Technical Reports Server (NTRS)

Desturler, Eric; Fokkema, Diederik R.

1993-01-01

Recently the GMRESR inner-outer iteraction scheme for the solution of linear systems of equations was proposed by Van der Vorst and Vuik. Similar methods have been proposed by Axelsson and Vassilevski and Saad (FGMRES). The outer iteration is GCR, which minimizes the residual over a given set of direction vectors. The inner iteration is GMRES, which at each step computes a new direction vector by approximately solving the residual equation. However, the optimality of the approximation over the space of outer search directions is ignored in the inner GMRES iteration. This leads to suboptimal corrections to the solution in the outer iteration, as components of the outer iteration directions may reenter in the inner iteration process. Therefore we propose to preserve the orthogonality relations of GCR in the inner GMRES iteration. This gives optimal corrections; however, it involves working with a singular, non-symmetric operator. We will discuss some important properties, and we will show by experiments that, in terms of matrix vector products, this modification (almost) always leads to better convergence. However, because we do more orthogonalizations, it does not always give an improved performance in CPU-time. Furthermore, we will discuss efficient implementations as well as the truncation possibilities of the outer GCR process. The experimental results indicate that for such methods it is advantageous to preserve the orthogonality in the inner iteration. Of course we can also use iteration schemes other than GMRES as the inner method; methods with short recurrences like GICGSTAB are of interest.

Beamspace dual signal space projection (bDSSP): a method for selective detection of deep sources in MEG measurements.

PubMed

Sekihara, Kensuke; Adachi, Yoshiaki; Kubota, Hiroshi K; Cai, Chang; Nagarajan, Srikantan S

2018-06-01

Magnetoencephalography (MEG) has a well-recognized weakness at detecting deeper brain activities. This paper proposes a novel algorithm for selective detection of deep sources by suppressing interference signals from superficial sources in MEG measurements. The proposed algorithm combines the beamspace preprocessing method with the dual signal space projection (DSSP) interference suppression method. A prerequisite of the proposed algorithm is prior knowledge of the location of the deep sources. The proposed algorithm first derives the basis vectors that span a local region just covering the locations of the deep sources. It then estimates the time-domain signal subspace of the superficial sources by using the projector composed of these basis vectors. Signals from the deep sources are extracted by projecting the row space of the data matrix onto the direction orthogonal to the signal subspace of the superficial sources. Compared with the previously proposed beamspace signal space separation (SSS) method, the proposed algorithm is capable of suppressing much stronger interference from superficial sources. This capability is demonstrated in our computer simulation as well as experiments using phantom data. The proposed bDSSP algorithm can be a powerful tool in studies of physiological functions of midbrain and deep brain structures.

Beamspace dual signal space projection (bDSSP): a method for selective detection of deep sources in MEG measurements

NASA Astrophysics Data System (ADS)

Sekihara, Kensuke; Adachi, Yoshiaki; Kubota, Hiroshi K.; Cai, Chang; Nagarajan, Srikantan S.

2018-06-01

Objective. Magnetoencephalography (MEG) has a well-recognized weakness at detecting deeper brain activities. This paper proposes a novel algorithm for selective detection of deep sources by suppressing interference signals from superficial sources in MEG measurements. Approach. The proposed algorithm combines the beamspace preprocessing method with the dual signal space projection (DSSP) interference suppression method. A prerequisite of the proposed algorithm is prior knowledge of the location of the deep sources. The proposed algorithm first derives the basis vectors that span a local region just covering the locations of the deep sources. It then estimates the time-domain signal subspace of the superficial sources by using the projector composed of these basis vectors. Signals from the deep sources are extracted by projecting the row space of the data matrix onto the direction orthogonal to the signal subspace of the superficial sources. Main results. Compared with the previously proposed beamspace signal space separation (SSS) method, the proposed algorithm is capable of suppressing much stronger interference from superficial sources. This capability is demonstrated in our computer simulation as well as experiments using phantom data. Significance. The proposed bDSSP algorithm can be a powerful tool in studies of physiological functions of midbrain and deep brain structures.

Locally indistinguishable orthogonal product bases in arbitrary bipartite quantum system

PubMed Central

Xu, Guang-Bao; Yang, Ying-Hui; Wen, Qiao-Yan; Qin, Su-Juan; Gao, Fei

2016-01-01

As we know, unextendible product basis (UPB) is an incomplete basis whose members cannot be perfectly distinguished by local operations and classical communication. However, very little is known about those incomplete and locally indistinguishable product bases that are not UPBs. In this paper, we first construct a series of orthogonal product bases that are completable but not locally distinguishable in a general m ⊗ n (m ≥ 3 and n ≥ 3) quantum system. In particular, we give so far the smallest number of locally indistinguishable states of a completable orthogonal product basis in arbitrary quantum systems. Furthermore, we construct a series of small and locally indistinguishable orthogonal product bases in m ⊗ n (m ≥ 3 and n ≥ 3). All the results lead to a better understanding of the structures of locally indistinguishable product bases in arbitrary bipartite quantum system. PMID:27503634

Derivation of a formula for the resonance integral for a nonorthogonal basis set

PubMed Central

Yim, Yung-Chang; Eyring, Henry

1981-01-01

In a self-consistent field calculation, a formula for the off-diagonal matrix elements of the core Hamiltonian is derived for a nonorthogonal basis set by a polyatomic approach. A set of parameters is then introduced for the repulsion integral formula of Mataga-Nishimoto to fit the experimental data. The matrix elements computed for the nonorthogonal basis set in the π-electron approximation are transformed to those for an orthogonal basis set by the Löwdin symmetrical orthogonalization. PMID:16593009

On real-space Density Functional Theory for non-orthogonal crystal systems: Kronecker product formulation of the kinetic energy operator

NASA Astrophysics Data System (ADS)

Sharma, Abhiraj; Suryanarayana, Phanish

2018-05-01

We present an accurate and efficient real-space Density Functional Theory (DFT) framework for the ab initio study of non-orthogonal crystal systems. Specifically, employing a local reformulation of the electrostatics, we develop a novel Kronecker product formulation of the real-space kinetic energy operator that significantly reduces the number of operations associated with the Laplacian-vector multiplication, the dominant cost in practical computations. In particular, we reduce the scaling with respect to finite-difference order from quadratic to linear, thereby significantly bridging the gap in computational cost between non-orthogonal and orthogonal systems. We verify the accuracy and efficiency of the proposed methodology through selected examples.

Representation of magnetic fields in space

NASA Technical Reports Server (NTRS)

Stern, D. P.

1975-01-01

Several methods by which a magnetic field in space can be represented are reviewed with particular attention to problems of the observed geomagnetic field. Time dependence is assumed to be negligible, and five main classes of representation are described by vector potential, scalar potential, orthogonal vectors, Euler potentials, and expanded magnetic field.

Multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials

NASA Astrophysics Data System (ADS)

Odake, Satoru; Sasaki, Ryu

2017-04-01

As the fourth stage of the project multi-indexed orthogonal polynomials, we present the multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials in the framework of ‘discrete quantum mechanics’ with real shifts defined on the semi-infinite lattice in one dimension. They are obtained, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier, from the quantum mechanical systems corresponding to the original orthogonal polynomials by multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of virtual state vectors. The virtual state vectors are the solutions of the matrix Schrödinger equation on all the lattice points having negative energies and infinite norm. This is in good contrast to the (q-)Racah systems defined on a finite lattice, in which the ‘virtual state’ vectors satisfy the matrix Schrödinger equation except for one of the two boundary points.

SH c realization of minimal model CFT: triality, poset and Burge condition

NASA Astrophysics Data System (ADS)

Fukuda, M.; Nakamura, S.; Matsuo, Y.; Zhu, R.-D.

2015-11-01

Recently an orthogonal basis of {{W}}_N -algebra (AFLT basis) labeled by N-tuple Young diagrams was found in the context of 4D/2D duality. Recursion relations among the basis are summarized in the form of an algebra SH c which is universal for any N. We show that it has an {{S}}_3 automorphism which is referred to as triality. We study the level-rank duality between minimal models, which is a special example of the automorphism. It is shown that the nonvanishing states in both systems are described by N or M Young diagrams with the rows of boxes appropriately shuffled. The reshuffling of rows implies there exists partial ordering of the set which labels them. For the simplest example, one can compute the partition functions for the partially ordered set (poset) explicitly, which reproduces the Rogers-Ramanujan identities. We also study the description of minimal models by SH c . Simple analysis reproduces some known properties of minimal models, the structure of singular vectors and the N-Burge condition in the Hilbert space.

Observation of High-Order Polarization-Locked Vector Solitons in a Fiber Laser

NASA Astrophysics Data System (ADS)

Tang, D. Y.; Zhang, H.; Zhao, L. M.; Wu, X.

2008-10-01

We report on the experimental observation of a new type of polarization-locked vector soliton in a passively mode-locked fiber laser. The vector soliton is characterized by the fact that not only are the two orthogonally polarized soliton components phase-locked, but also one of the components has a double-humped intensity profile. Multiple phase-locked high-order vector solitons with identical soliton parameters and harmonic mode locking of the vector solitons were also obtained in the laser. Numerical simulations confirmed the existence of stable high-order vector solitons in the fiber laser.

Observation of high-order polarization-locked vector solitons in a fiber laser.

PubMed

Tang, D Y; Zhang, H; Zhao, L M; Wu, X

2008-10-10

We report on the experimental observation of a new type of polarization-locked vector soliton in a passively mode-locked fiber laser. The vector soliton is characterized by the fact that not only are the two orthogonally polarized soliton components phase-locked, but also one of the components has a double-humped intensity profile. Multiple phase-locked high-order vector solitons with identical soliton parameters and harmonic mode locking of the vector solitons were also obtained in the laser. Numerical simulations confirmed the existence of stable high-order vector solitons in the fiber laser.

A novel optimal configuration form redundant MEMS inertial sensors based on the orthogonal rotation method.

PubMed

Cheng, Jianhua; Dong, Jinlu; Landry, Rene; Chen, Daidai

2014-07-29

In order to improve the accuracy and reliability of micro-electro mechanical systems (MEMS) navigation systems, an orthogonal rotation method-based nine-gyro redundant MEMS configuration is presented. By analyzing the accuracy and reliability characteristics of an inertial navigation system (INS), criteria for redundant configuration design are introduced. Then the orthogonal rotation configuration is formed through a two-rotation of a set of orthogonal inertial sensors around a space vector. A feasible installation method is given for the real engineering realization of this proposed configuration. The performances of the novel configuration and another six configurations are comprehensively compared and analyzed. Simulation and experimentation are also conducted, and the results show that the orthogonal rotation configuration has the best reliability, accuracy and fault detection and isolation (FDI) performance when the number of gyros is nine.

On orthogonal projectors induced by compact groups and Haar measures

NASA Astrophysics Data System (ADS)

Niezgoda, Marek

2008-02-01

We study the difference of two orthogonal projectors induced by compact groups of linear operators acting on a vector space. An upper bound for the difference is derived using the Haar measures of the groups. A particular attention is paid to finite groups. Some applications are given for complex matrices and unitarily invariant norms. Majorization inequalities of Fan and Hoffmann and of Causey are rediscovered.

Anatomical Reconstruction and Functional Imaging Reveal an Ordered Array of Skylight Polarization Detectors in Drosophila

PubMed Central

Bleul, Christiane; Baumann-Klausener, Franziska; Labhart, Thomas; Dickinson, Michael H.

2016-01-01

Many insects exploit skylight polarization as a compass cue for orientation and navigation. In the fruit fly, Drosophila melanogaster, photoreceptors R7 and R8 in the dorsal rim area (DRA) of the compound eye are specialized to detect the electric vector (e-vector) of linearly polarized light. These photoreceptors are arranged in stacked pairs with identical fields of view and spectral sensitivities, but mutually orthogonal microvillar orientations. As in larger flies, we found that the microvillar orientation of the distal photoreceptor R7 changes in a fan-like fashion along the DRA. This anatomical arrangement suggests that the DRA constitutes a detector for skylight polarization, in which different e-vectors maximally excite different positions in the array. To test our hypothesis, we measured responses to polarized light of varying e-vector angles in the terminals of R7/8 cells using genetically encoded calcium indicators. Our data confirm a progression of preferred e-vector angles from anterior to posterior in the DRA, and a strict orthogonality between the e-vector preferences of paired R7/8 cells. We observed decreased activity in photoreceptors in response to flashes of light polarized orthogonally to their preferred e-vector angle, suggesting reciprocal inhibition between photoreceptors in the same medullar column, which may serve to increase polarization contrast. Together, our results indicate that the polarization-vision system relies on a spatial map of preferred e-vector angles at the earliest stage of sensory processing. SIGNIFICANCE STATEMENT The fly's visual system is an influential model system for studying neural computation, and much is known about its anatomy, physiology, and development. The circuits underlying motion processing have received the most attention, but researchers are increasingly investigating other functions, such as color perception and object recognition. In this work, we investigate the early neural processing of a somewhat exotic sense, called polarization vision. Because skylight is polarized in an orientation that is rigidly determined by the position of the sun, this cue provides compass information. Behavioral experiments have shown that many species use the polarization pattern in the sky to direct locomotion. Here we describe the input stage of the fly's polarization-vision system. PMID:27170135

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.

Efficient schemes for deterministic joint remote preparation of an arbitrary four-qubit W-type entangled state

NASA Astrophysics Data System (ADS)

Fu, Hao; Ma, Peng-Cheng; Chen, Gui-Bin; Li, Xiao-Wei; Zhan, You-Bang

2017-06-01

We present three schemes for the joint remote state preparation (JRSP) of an arbitrary four-qubit W-type entangled state with complex coefficients via four and two three-qubit GHZ states as the quantum channel. In these schemes, two senders (or N senders) share the original state which they wish to help the receiver to remotely prepare. To complete the JRSP schemes, some novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if two senders (or N senders) collaborate with each other, and perform projective measurements under suitable measuring basis on their own qubits, the receiver can reconstruct the original state by means of some appropriate unitary operations. It is shown that, in all our schemes, the total success probability of the JRSP can reach 1. Specially, compared with the first scheme in our paper, the entanglement resource in the second scheme can be reduced. This means that the scheme is more efficient and economical.

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

Munitions Detection Using Unmanned Underwater Vehicles Equipped with Advanced Sensors

DTIC Science & Technology

2012-06-29

buried target. The RTG is a small passive magnetic sensor using fluxgate magnetometers measuring 3- orthogonal magnetic-field vector components at 3...surveys. Figure 6 shows the RTG magnetic sensor in both an open (showing the fluxgate magnetometers ) and enclosed state (mode for integration onto...7.6 Real-time Tracking Gradiometer (RTG) System The RTG is a small passive magnetic sensor using fluxgate magnetometers measuring 3- orthogonal

Optical/Infrared Signatures for Space-Based Remote Sensing

DTIC Science & Technology

2007-11-01

Vanderbilt et al., 1985a, 1985b]. So, first linear polarization was introduced, followed by progress toward a full vector theory of polarization ...radiance profiles taken 30 s apart in a view direction orthogonal to the velocity vector , showing considerable structure due to radiance layers in the...6 Figure 3. The northern polar region and locations of the MSX

On the Partitioning of Squared Euclidean Distance and Its Applications in Cluster Analysis.

ERIC Educational Resources Information Center

Carter, Randy L.; And Others

1989-01-01

The partitioning of squared Euclidean--E(sup 2)--distance between two vectors in M-dimensional space into the sum of squared lengths of vectors in mutually orthogonal subspaces is discussed. Applications to specific cluster analysis problems are provided (i.e., to design Monte Carlo studies for performance comparisons of several clustering methods…

Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays

NASA Astrophysics Data System (ADS)

Meier, Joachim; Hudock, Jared; Christodoulides, Demetrios; Stegeman, George; Silberberg, Y.; Morandotti, R.; Aitchison, J. S.

2003-10-01

We report the first experimental observation of discrete vector solitons in AlGaAs nonlinear waveguide arrays. These self-trapped states are possible through the coexistence of two orthogonally polarized fields and are stable in spite of the presence of four-wave mixing effects. We demonstrate that at sufficiently high power levels the two polarizations lock into a highly localized vector discrete soliton that would have been otherwise impossible in the absence of either one of these two components.

Face Hallucination with Linear Regression Model in Semi-Orthogonal Multilinear PCA Method

NASA Astrophysics Data System (ADS)

Asavaskulkiet, Krissada

2018-04-01

In this paper, we propose a new face hallucination technique, face images reconstruction in HSV color space with a semi-orthogonal multilinear principal component analysis method. This novel hallucination technique can perform directly from tensors via tensor-to-vector projection by imposing the orthogonality constraint in only one mode. In our experiments, we use facial images from FERET database to test our hallucination approach which is demonstrated by extensive experiments with high-quality hallucinated color faces. The experimental results assure clearly demonstrated that we can generate photorealistic color face images by using the SO-MPCA subspace with a linear regression model.

Decentralized Dimensionality Reduction for Distributed Tensor Data Across Sensor Networks.

PubMed

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

2016-11-01

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

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

DOE PAGES

Nourgaliev, R.; Luo, H.; Weston, B.; ...

2015-11-11

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as wellmore » as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.« less

Anatomical Reconstruction and Functional Imaging Reveal an Ordered Array of Skylight Polarization Detectors in Drosophila.

PubMed

Weir, Peter T; Henze, Miriam J; Bleul, Christiane; Baumann-Klausener, Franziska; Labhart, Thomas; Dickinson, Michael H

2016-05-11

Many insects exploit skylight polarization as a compass cue for orientation and navigation. In the fruit fly, Drosophila melanogaster, photoreceptors R7 and R8 in the dorsal rim area (DRA) of the compound eye are specialized to detect the electric vector (e-vector) of linearly polarized light. These photoreceptors are arranged in stacked pairs with identical fields of view and spectral sensitivities, but mutually orthogonal microvillar orientations. As in larger flies, we found that the microvillar orientation of the distal photoreceptor R7 changes in a fan-like fashion along the DRA. This anatomical arrangement suggests that the DRA constitutes a detector for skylight polarization, in which different e-vectors maximally excite different positions in the array. To test our hypothesis, we measured responses to polarized light of varying e-vector angles in the terminals of R7/8 cells using genetically encoded calcium indicators. Our data confirm a progression of preferred e-vector angles from anterior to posterior in the DRA, and a strict orthogonality between the e-vector preferences of paired R7/8 cells. We observed decreased activity in photoreceptors in response to flashes of light polarized orthogonally to their preferred e-vector angle, suggesting reciprocal inhibition between photoreceptors in the same medullar column, which may serve to increase polarization contrast. Together, our results indicate that the polarization-vision system relies on a spatial map of preferred e-vector angles at the earliest stage of sensory processing. The fly's visual system is an influential model system for studying neural computation, and much is known about its anatomy, physiology, and development. The circuits underlying motion processing have received the most attention, but researchers are increasingly investigating other functions, such as color perception and object recognition. In this work, we investigate the early neural processing of a somewhat exotic sense, called polarization vision. Because skylight is polarized in an orientation that is rigidly determined by the position of the sun, this cue provides compass information. Behavioral experiments have shown that many species use the polarization pattern in the sky to direct locomotion. Here we describe the input stage of the fly's polarization-vision system. Copyright © 2016 the authors 0270-6474/16/365397-08$15.00/0.

Improved resistivity imaging of groundwater solute plumes using POD-based inversion

NASA Astrophysics Data System (ADS)

Oware, E. K.; Moysey, S. M.; Khan, T.

2012-12-01

We propose a new approach for enforcing physics-based regularization in electrical resistivity imaging (ERI) problems. The approach utilizes a basis-constrained inversion where an optimal set of basis vectors is extracted from training data by Proper Orthogonal Decomposition (POD). The key aspect of the approach is that Monte Carlo simulation of flow and transport is used to generate a training dataset, thereby intrinsically capturing the physics of the underlying flow and transport models in a non-parametric form. POD allows for these training data to be projected onto a subspace of the original domain, resulting in the extraction of a basis for the inversion that captures characteristics of the groundwater flow and transport system, while simultaneously allowing for dimensionality reduction of the original problem in the projected space We use two different synthetic transport scenarios in heterogeneous media to illustrate how the POD-based inversion compares with standard Tikhonov and coupled inversion. The first scenario had a single source zone leading to a unimodal solute plume (synthetic #1), whereas, the second scenario had two source zones that produced a bimodal plume (synthetic #2). For both coupled inversion and the POD approach, the conceptual flow and transport model used considered only a single source zone for both scenarios. Results were compared based on multiple metrics (concentration root-mean square error (RMSE), peak concentration, and total solute mass). In addition, results for POD inversion based on 3 different data densities (120, 300, and 560 data points) and varying number of selected basis images (100, 300, and 500) were compared. For synthetic #1, we found that all three methods provided qualitatively reasonable reproduction of the true plume. Quantitatively, the POD inversion performed best overall for each metric considered. Moreover, since synthetic #1 was consistent with the conceptual transport model, a small number of basis vectors (100) contained enough a priori information to constrain the inversion. Increasing the amount of data or number of selected basis images did not translate into significant improvement in imaging results. For synthetic #2, the RMSE and error in total mass were lowest for the POD inversion. However, the peak concentration was significantly overestimated by the POD approach. Regardless, the POD-based inversion was the only technique that could capture the bimodality of the plume in the reconstructed image, thus providing critical information that could be used to reconceptualize the transport problem. We also found that, in the case of synthetic #2, increasing the number of resistivity measurements and the number of selected basis vectors allowed for significant improvements in the reconstructed images.

Absence of internal conical refraction with the spatially dispersive index surface of fluorine; discussion of the orthogonality of the Poynting vector to the index surface.

PubMed

Dettwiller, Luc

2006-04-17

Since 2001 the intrinsic birefringence of fluorine has been accessible to experiment. It is known that its intrinsic anisotropy is entirely due to spatial dispersion, and that the index surface of fluorine and crystals with the same symmetry has seven optical axes, four of them intersecting this surface at pairs of conical points. I point out the fact that there is no internal conical refraction, but only simple refraction (and without walkoff), with these conical points. I also explain why the rays are not a priori normal to the index surface in the case of fluorine because of its spatial dispersion; and I discuss two particular cases of spatial dispersion where the Poynting vector remains orthogonal to the index surface.

Morphing of spatial objects in real time with interpolation by functions of radial and orthogonal basis

NASA Astrophysics Data System (ADS)

Kosnikov, Yu N.; Kuzmin, A. V.; Ho, Hoang Thai

2018-05-01

The article is devoted to visualization of spatial objects’ morphing described by the set of unordered reference points. A two-stage model construction is proposed to change object’s form in real time. The first (preliminary) stage is interpolation of the object’s surface by radial basis functions. Initial reference points are replaced by new spatially ordered ones. Reference points’ coordinates change patterns during the process of morphing are assigned. The second (real time) stage is surface reconstruction by blending functions of orthogonal basis. Finite differences formulas are applied to increase the productivity of calculations.

Vertical amplitude phase structure of a low-frequency acoustic field in shallow water

NASA Astrophysics Data System (ADS)

Kuznetsov, G. N.; Lebedev, O. V.; Stepanov, A. N.

2016-11-01

We obtain in integral and analytic form the relations for calculating the amplitude and phase characteristics of an interference structure of orthogonal projections of the oscillation velocity vector in shallow water. For different frequencies and receiver depths, we numerically study the source depth dependences of the effective phase velocities of an equivalent plane wave, the orthogonal projections of the sound pressure phase gradient, and the projections of the oscillation velocity vector. We establish that at low frequencies in zones of interference maxima, independently of source depth, weakly varying effective phase velocity values are observed, which exceed the sound velocity in water by 5-12%. We show that the angles of arrival of the equivalent plane wave and the oscillation velocity vector in the general case differ; however, they virtually coincide in the zone of the interference maximum of the sound pressure under the condition that the horizontal projections of the oscillation velocity appreciably exceed the value of the vertical projection. We give recommendations on using the sound field characteristics in zones with maximum values for solving rangefinding and signal-detection problems.

Mutually orthogonal Latin squares from the inner products of vectors in mutually unbiased bases

NASA Astrophysics Data System (ADS)

Hall, Joanne L.; Rao, Asha

2010-04-01

Mutually unbiased bases (MUBs) are important in quantum information theory. While constructions of complete sets of d + 1 MUBs in {\\bb C}^d are known when d is a prime power, it is unknown if such complete sets exist in non-prime power dimensions. It has been conjectured that complete sets of MUBs only exist in {\\bb C}^d if a maximal set of mutually orthogonal Latin squares (MOLS) of side length d also exists. There are several constructions (Roy and Scott 2007 J. Math. Phys. 48 072110; Paterek, Dakić and Brukner 2009 Phys. Rev. A 79 012109) of complete sets of MUBs from specific types of MOLS, which use Galois fields to construct the vectors of the MUBs. In this paper, two known constructions of MUBs (Alltop 1980 IEEE Trans. Inf. Theory 26 350-354 Wootters and Fields 1989 Ann. Phys. 191 363-381), both of which use polynomials over a Galois field, are used to construct complete sets of MOLS in the odd prime case. The MOLS come from the inner products of pairs of vectors in the MUBs.

Characteristics of a dry, pulsating microburst at Denver Stapleton Airport

NASA Technical Reports Server (NTRS)

Proctor, Fred H.

1994-01-01

This study examines the influence of ambient vertical wind shear on microburst intensity, asymmetry, and translation. Results show that microburst asymmetry is influenced by the magnitude of the low-level ambient vertical shear. The microburst outflow elongates in the direction of the shear vector (which is not necessarily in the direction of translation), and generates the greatest hazard (for commercial jet transports) along paths orthogonal to the shear vector. The model results also show that the asymmetry increases with increasing shear magnitude. One implication of these results concerns the detection of a microburst by a ground-based doppler systems. These systems may underestimate the hazard for landing and departing aircraft that are on trajectories orthogonal to both the sensor beam and shear vector, especially if the magnitude of the shear is large. Another implication is that microburst are more likely to be asymmetrical in regions (seasons) where there is climatologically a significant low-level shear. The model results also show that the rotor microbursts and severe wind damage can be a product of the microburst interaction with strong ambient wind shear.

Dual comb generation from a mode-locked fiber laser with orthogonally polarized interlaced pulses.

PubMed

Akosman, Ahmet E; Sander, Michelle Y

2017-08-07

Ultra-high precision dual-comb spectroscopy traditionally requires two mode-locked, fully stabilized lasers with complex feedback electronics. We present a novel mode-locked operation regime in a thulium-holmium co-doped fiber laser, a frequency-halved state with orthogonally polarized interlaced pulses, for dual comb generation from a single source. In a linear fiber laser cavity, an ultrafast pulse train composed of co-generated, equal intensity and orthogonally polarized consecutive pulses at half of the fundamental repetition rate is demonstrated based on vector solitons. Upon optical interference of the orthogonally polarized pulse trains, two stable microwave RF beat combs are formed, effectively down-converting the optical properties into the microwave regime. These co-generated, dual polarization interlaced pulse trains, from one all-fiber laser configuration with common mode suppression, thus provide an attractive compact source for dual-comb spectroscopy, optical metrology and polarization entanglement measurements.

On the Hilbert-Huang Transform Theoretical Developments

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Blank, Karin; Flatley, Thomas; Huang, Norden E.; Patrick, David; Hestnes, Phyllis

2005-01-01

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposition data, the HHT allows spectrum analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a near orthogonal adaptive basis, a basis that is derived from the data. The IMFs can be further analyzed for spectrum interpretation by the classical Hilbert Transform. A new engineering spectrum analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications post additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs near orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the developments of new HHT processing options, such as real-time and 2-D processing using Field Programmable Array (FPGA) computational resources, enhanced HHT synthesis, and broaden the scope of HHT applications for signal processing.

Hyperbolic-symmetry vector fields.

PubMed

Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2015-12-14

We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.

Properties of a vector soliton laser passively mode-locked by a fiber-based semiconductor saturable absorber operating in transmission

NASA Astrophysics Data System (ADS)

Ouyang, Chunmei; Wang, Honghai; Shum, Ping; Fu, Songnian; Wong, Jia Haur; Wu, Kan; Lim, Desmond Rodney Chin Siong; Wong, Vincent Kwok Huei; Lee, Kenneth Eng Kian

2011-01-01

We experimentally demonstrate a passively mode-locked fiber laser employing a fiber-based semiconductor saturable absorber (SSA) operating in transmission. Polarization rotation locked vector solitons are observed in the laser. Due to the intrinsic dynamic feature of the laser, period-doubling of these vector solitons has also been observed. Furthermore, extra spectral sidebands are formed on the optical spectrum, caused by the energy exchange between the two orthogonal polarization components of the vector solitons. By careful reduction of the pump power together with fine adjustment to the cavity birefringence, period-one state can further be obtained. Additionally, the phase noise properties of the vector soliton fiber laser have also been characterized experimentally and analytically.

Group-velocity-locked vector soliton molecules in fiber lasers.

PubMed

Luo, Yiyang; Cheng, Jianwei; Liu, Bowen; Sun, Qizhen; Li, Lei; Fu, Songnian; Tang, Dingyuan; Zhao, Luming; Liu, Deming

2017-05-24

Physics phenomena of multi-soliton complexes have enriched the life of dissipative solitons in fiber lasers. By developing a birefringence-enhanced fiber laser, we report the first experimental observation of group-velocity-locked vector soliton (GVLVS) molecules. The birefringence-enhanced fiber laser facilitates the generation of GVLVSs, where the two orthogonally polarized components are coupled together to form a multi-soliton complex. Moreover, the interaction of repulsive and attractive forces between multiple pulses binds the particle-like GVLVSs together in time domain to further form compound multi-soliton complexes, namely GVLVS molecules. By adopting the polarization-resolved measurement, we show that the two orthogonally polarized components of the GVLVS molecules are both soliton molecules supported by the strongly modulated spectral fringes and the double-humped intensity profiles. Additionally, GVLVS molecules with various soliton separations are also observed by adjusting the pump power and the polarization controller.

Multiple mechanisms in the perception of face gender: Effect of sex-irrelevant features.

PubMed

Komori, Masashi; Kawamura, Satoru; Ishihara, Shigekazu

2011-06-01

Effects of sex-relevant and sex-irrelevant facial features on the evaluation of facial gender were investigated. Participants rated masculinity of 48 male facial photographs and femininity of 48 female facial photographs. Eighty feature points were measured on each of the facial photographs. Using a generalized Procrustes analysis, facial shapes were converted into multidimensional vectors, with the average face as a starting point. Each vector was decomposed into a sex-relevant subvector and a sex-irrelevant subvector which were, respectively, parallel and orthogonal to the main male-female axis. Principal components analysis (PCA) was performed on the sex-irrelevant subvectors. One principal component was negatively correlated with both perceived masculinity and femininity, and another was correlated only with femininity, though both components were orthogonal to the male-female dimension (and thus by definition sex-irrelevant). These results indicate that evaluation of facial gender depends on sex-irrelevant as well as sex-relevant facial features.

Sparse Reconstruction of Regional Gravity Signal Based on Stabilized Orthogonal Matching Pursuit (SOMP)

NASA Astrophysics Data System (ADS)

Saadat, S. A.; Safari, A.; Needell, D.

2016-06-01

The main role of gravity field recovery is the study of dynamic processes in the interior of the Earth especially in exploration geophysics. In this paper, the Stabilized Orthogonal Matching Pursuit (SOMP) algorithm is introduced for sparse reconstruction of regional gravity signals of the Earth. In practical applications, ill-posed problems may be encountered regarding unknown parameters that are sensitive to the data perturbations. Therefore, an appropriate regularization method needs to be applied to find a stabilized solution. The SOMP algorithm aims to regularize the norm of the solution vector, while also minimizing the norm of the corresponding residual vector. In this procedure, a convergence point of the algorithm that specifies optimal sparsity-level of the problem is determined. The results show that the SOMP algorithm finds the stabilized solution for the ill-posed problem at the optimal sparsity-level, improving upon existing sparsity based approaches.

Domain walls of linear polarization in isotropic Kerr media

NASA Astrophysics Data System (ADS)

Louis, Y.; Sheppard, A. P.; Haelterman, M.

1997-09-01

We present a new type of domain-wall vector solitary waves in isotropic self-defocusing Kerr media. These domain walls consist of localized structures separating uniform field domains of orthogonal linear polarizations. They result from the interplay between diffraction, self-phase modulation and cross-phase modulation in cases where the nonlinear birefringence coefficient B = {χxyyx(3)}/{χxxxx(3)} is negative. Numerical simulations show that these new vector solitary waves are stable.

Eigenanalysis and Graph Theory Combined to Determine the Seasonal and Solar-Cycle Variations of Polar Magnetic Fields

NASA Astrophysics Data System (ADS)

Shore, R. M.; Freeman, M. P.; Gjerloev, J. W.

2017-12-01

We apply the meteorological analysis method of Empirical Orthogonal Functions (EOF) to ground magnetometer measurements, and subsequently use graph theory to classify the results. The EOF method is used to characterise and separate contributions to the variability of the Earth's external magnetic field (EMF) in the northern polar region. EOFs decompose the noisy EMF data into a small number of independent spatio-temporal basis functions, which collectively describe the majority of the magnetic field variance. We use these basis functions (computed monthly) to infill where data are missing, providing a self-consistent description of the EMF at 5-minute resolution spanning 1997-2009 (solar cycle 23). The EOF basis functions are calculated independently for each of the 144 months (i.e. 1997-2009) analysed. Since (by definition) the basis vectors are ranked by their contribution to the total variance, their rank will change from month to month. We use graph theory to find clusters of quantifiably-similar spatial basis functions, and thereby track similar patterns throughout the span of 144 months. We find that the discovered clusters can be associated with well-known individual Disturbance Polar (DP)-type equivalent current systems (e.g. DP2, DP1, DPY, NBZ), or with the motion of these systems. Via this method, we thus describe the varying behaviour of these current systems over solar cycle 23. We present their seasonal and solar cycle variations and examine the response of each current system to solar wind driving.

Comparison Analysis of Recognition Algorithms of Forest-Cover Objects on Hyperspectral Air-Borne and Space-Borne Images

NASA Astrophysics Data System (ADS)

Kozoderov, V. V.; Kondranin, T. V.; Dmitriev, E. V.

2017-12-01

The basic model for the recognition of natural and anthropogenic objects using their spectral and textural features is described in the problem of hyperspectral air-borne and space-borne imagery processing. The model is based on improvements of the Bayesian classifier that is a computational procedure of statistical decision making in machine-learning methods of pattern recognition. The principal component method is implemented to decompose the hyperspectral measurements on the basis of empirical orthogonal functions. Application examples are shown of various modifications of the Bayesian classifier and Support Vector Machine method. Examples are provided of comparing these classifiers and a metrical classifier that operates on finding the minimal Euclidean distance between different points and sets in the multidimensional feature space. A comparison is also carried out with the " K-weighted neighbors" method that is close to the nonparametric Bayesian classifier.

Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene.

PubMed

Oettinger, D; Mendoza, M; Herrmann, H J

2013-07-01

We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as the weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, which satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential the electronic fluid behaves as if it increases its effective viscosity.

JRSP of three-particle state via three tripartite GHZ class in quantum noisy channels

NASA Astrophysics Data System (ADS)

Falaye, Babatunde James; Sun, Guo-Hua; Camacho-Nieto, Oscar; Dong, Shi-Hai

2016-10-01

We present a scheme for joint remote state preparation (JRSP) of three-particle state via three tripartite Greenberger-Horne-Zeilinger (GHZ) entangled states as the quantum channel linking the parties. We use eight-qubit mutually orthogonal basis vector as measurement point of departure. The likelihood of success for this scheme has been found to be 1/8. However, by putting some special cases into consideration, the chances can be ameliorated to 1/4 and 1. The effects of amplitude-damping noise, phase-damping noise and depolarizing noise on this scheme have been scrutinized and the analytical derivations of fidelities for the quantum noisy channels have been presented. We found that for 0.55≤η≤1, the states conveyed through depolarizing channel lose more information than phase-damping channel while the information loss through amplitude damping channel is most minimal.

Intelligent Design of Metal Oxide Gas Sensor Arrays Using Reciprocal Kernel Support Vector Regression

NASA Astrophysics Data System (ADS)

Dougherty, Andrew W.

Metal oxides are a staple of the sensor industry. The combination of their sensitivity to a number of gases, and the electrical nature of their sensing mechanism, make the particularly attractive in solid state devices. The high temperature stability of the ceramic material also make them ideal for detecting combustion byproducts where exhaust temperatures can be high. However, problems do exist with metal oxide sensors. They are not very selective as they all tend to be sensitive to a number of reduction and oxidation reactions on the oxide's surface. This makes sensors with large numbers of sensors interesting to study as a method for introducing orthogonality to the system. Also, the sensors tend to suffer from long term drift for a number of reasons. In this thesis I will develop a system for intelligently modeling metal oxide sensors and determining their suitability for use in large arrays designed to analyze exhaust gas streams. It will introduce prior knowledge of the metal oxide sensors' response mechanisms in order to produce a response function for each sensor from sparse training data. The system will use the same technique to model and remove any long term drift from the sensor response. It will also provide an efficient means for determining the orthogonality of the sensor to determine whether they are useful in gas sensing arrays. The system is based on least squares support vector regression using the reciprocal kernel. The reciprocal kernel is introduced along with a method of optimizing the free parameters of the reciprocal kernel support vector machine. The reciprocal kernel is shown to be simpler and to perform better than an earlier kernel, the modified reciprocal kernel. Least squares support vector regression is chosen as it uses all of the training points and an emphasis was placed throughout this research for extracting the maximum information from very sparse data. The reciprocal kernel is shown to be effective in modeling the sensor responses in the time, gas and temperature domains, and the dual representation of the support vector regression solution is shown to provide insight into the sensor's sensitivity and potential orthogonality. Finally, the dual weights of the support vector regression solution to the sensor's response are suggested as a fitness function for a genetic algorithm, or some other method for efficiently searching large parameter spaces.

Quantitative tissue polarimetry using polar decomposition of 3 x 3 Mueller matrix

NASA Astrophysics Data System (ADS)

Swami, M. K.; Manhas, S.; Buddhiwant, P.; Ghosh, N.; Uppal, A.; Gupta, P. K.

2007-05-01

Polarization properties of any optical system are completely described by a sixteen-element (4 x 4) matrix called Mueller matrix, which transform the Stokes vector describing the polarization properties of incident light to the stokes vector of scattered light. Measurement of all the elements of the matrix requires a minimum of sixteen measurements involving both linear and circularly polarized light. However, for many diagnostic applications, it would be useful if all the polarization parameters of the medium (depolarization (Δ), differential attenuation of two orthogonal polarizations, that is, diattenuation (d), and differential phase retardance of two orthogonal polarizations, i.e., retardance (δ )) can be quantified with linear polarization measurements alone. In this paper we show that for a turbid medium, like biological tissue, where the depolarization of linearly polarized light arises primarily due to the randomization of the field vector's direction by multiple scattering, the polarization parameters of the medium can be obtained from the nine Mueller matrix elements involving linear polarization measurements only. Use of the approach for measurement of polarization parameters (Δ, d and δ) of normal and malignant (squamous cell carcinoma) tissues resected from human oral cavity are presented.

Doppler Global Velocimeter Development for the Large Wind Tunnels at Ames Research Center

NASA Technical Reports Server (NTRS)

Reinath, Michael S.

1997-01-01

Development of an optical, laser-based flow-field measurement technique for large wind tunnels is described. The technique uses laser sheet illumination and charged coupled device detectors to rapidly measure flow-field velocity distributions over large planar regions of the flow. Sample measurements are presented that illustrate the capability of the technique. An analysis of measurement uncertainty, which focuses on the random component of uncertainty, shows that precision uncertainty is not dependent on the measured velocity magnitude. For a single-image measurement, the analysis predicts a precision uncertainty of +/-5 m/s. When multiple images are averaged, this uncertainty is shown to decrease. For an average of 100 images, for example, the analysis shows that a precision uncertainty of +/-0.5 m/s can be expected. Sample applications show that vectors aligned with an orthogonal coordinate system are difficult to measure directly. An algebraic transformation is presented which converts measured vectors to the desired orthogonal components. Uncertainty propagation is then used to show how the uncertainty propagates from the direct measurements to the orthogonal components. For a typical forward-scatter viewing geometry, the propagation analysis predicts precision uncertainties of +/-4, +/-7, and +/-6 m/s, respectively, for the U, V, and W components at 68% confidence.

Reduced Order Model Basis Vector Generation: Generates Basis Vectors fro ROMs

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

Arrighi, Bill

2016-03-03

libROM is a library that implements order reduction via singular value decomposition (SVD) of sampled state vectors. It implements 2 parallel, incremental SVD algorithms and one serial, non-incremental algorithm. It also provides a mechanism for adaptive sampling of basis vectors.

LETTER TO THE EDITOR: A theorem on topologically massive gravity

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Nutku, Y.

1996-03-01

We show that for three dimensional spacetimes admitting a hypersurface orthogonal Killing vector field, Deser, Jackiw and Templeton's vacuum field equations of topologically massive gravity allow only the trivial flat spacetime solution. Thus spin is necessary to support topological mass.

Projection correlation between two random vectors.

PubMed

Zhu, Liping; Xu, Kai; Li, Runze; Zhong, Wei

2017-12-01

We propose the use of projection correlation to characterize dependence between two random vectors. Projection correlation has several appealing properties. It equals zero if and only if the two random vectors are independent, it is not sensitive to the dimensions of the two random vectors, it is invariant with respect to the group of orthogonal transformations, and its estimation is free of tuning parameters and does not require moment conditions on the random vectors. We show that the sample estimate of the projection correction is [Formula: see text]-consistent if the two random vectors are independent and root-[Formula: see text]-consistent otherwise. Monte Carlo simulation studies indicate that the projection correlation has higher power than the distance correlation and the ranks of distances in tests of independence, especially when the dimensions are relatively large or the moment conditions required by the distance correlation are violated.

Pre-stack separation of PP and split PS waves in HTI media

NASA Astrophysics Data System (ADS)

Lu, Jun; Wang, Yun; Yang, Yuyong; Chen, Jingyi

2017-07-01

Separation of PP and split PS waves in transversely isotropic media with a horizontal axis of symmetry is crucial for imaging subsurface targets and for fracture prediction in a multicomponent seismic survey using P-wave sources. In conventional multicomponent processing, when a low velocity zone is present near the surface, it is often assumed that the vertical Z-component mainly records P modes and that the horizontal X- and Y-components record S modes, including split PS waves. However, this assumption does not hold when the ubiquitous presence of azimuthal anisotropy makes near surface velocity structures more complicated. Seismic wavefields recorded in each component therefore generally represent a complex waveform formed by PP and split PS waves, seriously distorting velocity analysis and seismic imaging. Most previous studies on wave separation have tended to separate P and S modes using pre-stack data and to separate split S modes using post-stack sections, under the assumption of orthogonal polarization. However, split S modes can hardly maintain their original orthogonal polarizations during propagation to the surface due to stratigraphic heterogeneity. Here, without assuming orthogonal polarization, we present a method for pre-stack separation of PP, PS1 and PS2 waves using all three components. The core of our method is the rotation of wave vectors from the Cartesian coordinate system established by Z-, R- and T-axes to a coordinate system established by the true PP-, PS1- and PS2-wave vector directions. Further, we propose a three-component superposition approach to obtain base wave vectors for the coordinate system transformation. Synthetic data testing results confirm that the performance of our wave separation method is stable under different noise levels. Application to field data from Southwest China reveals the potential of our proposed method.

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus

NASA Astrophysics Data System (ADS)

Ortega-Quijano, Noé; Fade, Julien; Roche, Muriel; Parnet, François; Alouini, Mehdi

2016-04-01

Polarimetric sensing by orthogonality breaking has been recently proposed as an alternative technique for performing direct and fast polarimetric measurements using a specific dual-frequency dual-polarization (DFDP) source. Based on the instantaneous Stokes-Mueller formalism to describe the high-frequency evolution of the DFDP beam intensity, we thoroughly analyze the interaction of such a beam with birefringent, dichroic and depolarizing samples. This allows us to confirm that orthogonality breaking is produced by the sample diattenuation, whereas this technique is immune to both birefringence and diagonal depolarization. We further analyze the robustness of this technique when polarimetric sensing is performed through a birefringent waveguide, and the optimal DFDP source configuration for fiber-based endoscopic measurements is subsequently identified. Finally, we consider a stochastic depolarization model based on an ensemble of random linear diattenuators, which makes it possible to understand the progressive vanishing of the detected orthogonality breaking signal as the spatial heterogeneity of the sample increases, thus confirming the insensitivity of this method to diagonal depolarization. The fact that the orthogonality breaking signal is exclusively due to the sample dichroism is an advantageous feature for the precise decoupled characterization of such an anisotropic parameter in samples showing several simultaneous effects.

Soliton trapping in fiber lasers.

PubMed

Zhao, L M; Tang, D Y; Zhang, H; Wu, X; Xiang, N

2008-06-23

We report on the soliton trapping in a fiber ring laser modelocked with a SESAM. It was observed that solitons along the two orthogonal polarization directions of the cavity with fairly large difference in central frequency and energy could be coupled together to form a group velocity locked vector soliton. In particular, due to that each of the coupled solitons forms its own soliton sidebands, two sets of soliton sidebands could be observed on the vector soliton spectrum. Numerical simulations have well confirmed the experimental observations.

Lightning Tests on the WC-130 Research Aircraft.

DTIC Science & Technology

1982-12-01

in the WC-136 tests at various times.) E- Feild Fiber Optic Test Article Sensor Transmitter (Typ)WiePr Indtuced Voltag Sensor"" *Fiber I"=Current optic...well-characterized. 5.1 Skin Current Measurements Skin current vectors were measured at five fuselage locations on the left side of the WC-130 at a...MGL-S7) which were mounted so that they sampled two orthogonal components of the skin current vector . The measured responses were then inte- grated

Beam-centroid tracking instrument for ion thrusters

NASA Astrophysics Data System (ADS)

Pollard, J. E.

1995-03-01

Thrust vector stability for an electrostatic ion engine can be measured with improved sensitivity and time resolution by the method described here. Four double-wire Langmuir probes, aligned in the form of a cross, are placed in the exhaust plume and are translated by a motorized positioning system to balance the currents collected along two orthogonal axes. The thrust vector position is thereby measured with an angular resolution of less than 0.01 deg and a response time of less than 5 sec.

Deterministic Joint Assisted Cloning of Unknown Two-Qubit Entangled States

NASA Astrophysics Data System (ADS)

Zhan, You-Bang

2012-06-01

We present two schemes for perfect cloning unknown two-qubit and general two-qubit entangled states with assistance from two state preparers, respectively. In the schemes, the sender wish to teleport an unknown two-qubit (or general two-qubit) entangled state which from two state preparers to a remote receiver, and then create a perfect copy of the unknown state at her place. The schemes include two stages. The first stage of the schemes requires usual teleportation. In the second stage, to help the sender realize the quantum cloning, two state preparers perform two-qubit projective measurements on their own qubits which from the sender, then the sender can acquire a perfect copy of the unknown state. To complete the assisted cloning schemes, several novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if two state preparers collaborate with each other, and perform projective measurements under suitable measuring basis on their own qubit respectively, the sender can create a copy of the unknown state by means of some appropriate unitary operations. The advantage of the present schemes is that the total success probability for assisted cloning a perfect copy of the unknown state can reach 1.

EEG-distributed inverse solutions for a spherical head model

NASA Astrophysics Data System (ADS)

Riera, J. J.; Fuentes, M. E.; Valdés, P. A.; Ohárriz, Y.

1998-08-01

The theoretical study of the minimum norm solution to the MEG inverse problem has been carried out in previous papers for the particular case of spherical symmetry. However, a similar study for the EEG is remarkably more difficult due to the very complicated nature of the expression relating the voltage differences on the scalp to the primary current density (PCD) even for this simple symmetry. This paper introduces the use of the electric lead field (ELF) on the dyadic formalism in the spherical coordinate system to overcome such a drawback using an expansion of the ELF in terms of longitudinal and orthogonal vector fields. This approach allows us to represent EEG Fourier coefficients on a 2-sphere in terms of a current multipole expansion. The choice of a suitable basis for the Hilbert space of the PCDs on the brain region allows the current multipole moments to be related by spatial transfer functions to the PCD spectral coefficients. Properties of the most used distributed inverse solutions are explored on the basis of these results. Also, a part of the ELF null space is completely characterized and those spherical components of the PCD which are possible silent candidates are discussed.

An accelerated training method for back propagation networks

NASA Technical Reports Server (NTRS)

Shelton, Robert O. (Inventor)

1993-01-01

The principal objective is to provide a training procedure for a feed forward, back propagation neural network which greatly accelerates the training process. A set of orthogonal singular vectors are determined from the input matrix such that the standard deviations of the projections of the input vectors along these singular vectors, as a set, are substantially maximized, thus providing an optimal means of presenting the input data. Novelty exists in the method of extracting from the set of input data, a set of features which can serve to represent the input data in a simplified manner, thus greatly reducing the time/expense to training the system.

Initial evaluation of discrete orthogonal basis reconstruction of ECT images

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

Moody, E.B.; Donohue, K.D.

1996-12-31

Discrete orthogonal basis restoration (DOBR) is a linear, non-iterative, and robust method for solving inverse problems for systems characterized by shift-variant transfer functions. This simulation study evaluates the feasibility of using DOBR for reconstructing emission computed tomographic (ECT) images. The imaging system model uses typical SPECT parameters and incorporates the effects of attenuation, spatially-variant PSF, and Poisson noise in the projection process. Sample reconstructions and statistical error analyses for a class of digital phantoms compare the DOBR performance for Hartley and Walsh basis functions. Test results confirm that DOBR with either basis set produces images with good statistical properties. Nomore » problems were encountered with reconstruction instability. The flexibility of the DOBR method and its consistent performance warrants further investigation of DOBR as a means of ECT image reconstruction.« less

Dielectric and permeability

NASA Technical Reports Server (NTRS)

Cole, K. D.

1982-01-01

Using the unabridged Maxwell equations (including vectors D, E and H) new effects in collisionless plasmas are uncovered. In a steady state, it is found that spatially varying energy density of the electric field (E perpendicular) orthogonal to B produces electric current leading, under certain conditions, to the relationship P perpendicular+B(2)/8 pi-epsilon E perpendicular(2)/8 pi = constant, where epsilon is the dielectric constant of the plasma for fields orthogonal to B. In steady state quasi-two-dimensional flows in plasmas, a general relationship between the components of electric field parallel and perpendicular to B is found. These effects are significant in goephysical and astrophysical plasmas. The general conditions for a steady state in collisionless plasma are deduced. With time variations in a plasma, slow compared to ion-gyroperiod, there is a general current, (j*), which includes the well-known polarisation current, given by J*=d/dt (ExM)+(PxB)xB B(-2) where M and P are the magnetization and polarization vectors respectively.

A robust variant of block Jacobi-Davidson for extracting a large number of eigenpairs: Application to grid-based real-space density functional theory

NASA Astrophysics Data System (ADS)

Lee, M.; Leiter, K.; Eisner, C.; Breuer, A.; Wang, X.

2017-09-01

In this work, we investigate a block Jacobi-Davidson (J-D) variant suitable for sparse symmetric eigenproblems where a substantial number of extremal eigenvalues are desired (e.g., ground-state real-space quantum chemistry). Most J-D algorithm variations tend to slow down as the number of desired eigenpairs increases due to frequent orthogonalization against a growing list of solved eigenvectors. In our specification of block J-D, all of the steps of the algorithm are performed in clusters, including the linear solves, which allows us to greatly reduce computational effort with blocked matrix-vector multiplies. In addition, we move orthogonalization against locked eigenvectors and working eigenvectors outside of the inner loop but retain the single Ritz vector projection corresponding to the index of the correction vector. Furthermore, we minimize the computational effort by constraining the working subspace to the current vectors being updated and the latest set of corresponding correction vectors. Finally, we incorporate accuracy thresholds based on the precision required by the Fermi-Dirac distribution. The net result is a significant reduction in the computational effort against most previous block J-D implementations, especially as the number of wanted eigenpairs grows. We compare our approach with another robust implementation of block J-D (JDQMR) and the state-of-the-art Chebyshev filter subspace (CheFSI) method for various real-space density functional theory systems. Versus CheFSI, for first-row elements, our method yields competitive timings for valence-only systems and 4-6× speedups for all-electron systems with up to 10× reduced matrix-vector multiplies. For all-electron calculations on larger elements (e.g., gold) where the wanted spectrum is quite narrow compared to the full spectrum, we observe 60× speedup with 200× fewer matrix-vector multiples vs. CheFSI.

A robust variant of block Jacobi-Davidson for extracting a large number of eigenpairs: Application to grid-based real-space density functional theory.

PubMed

Lee, M; Leiter, K; Eisner, C; Breuer, A; Wang, X

2017-09-21

In this work, we investigate a block Jacobi-Davidson (J-D) variant suitable for sparse symmetric eigenproblems where a substantial number of extremal eigenvalues are desired (e.g., ground-state real-space quantum chemistry). Most J-D algorithm variations tend to slow down as the number of desired eigenpairs increases due to frequent orthogonalization against a growing list of solved eigenvectors. In our specification of block J-D, all of the steps of the algorithm are performed in clusters, including the linear solves, which allows us to greatly reduce computational effort with blocked matrix-vector multiplies. In addition, we move orthogonalization against locked eigenvectors and working eigenvectors outside of the inner loop but retain the single Ritz vector projection corresponding to the index of the correction vector. Furthermore, we minimize the computational effort by constraining the working subspace to the current vectors being updated and the latest set of corresponding correction vectors. Finally, we incorporate accuracy thresholds based on the precision required by the Fermi-Dirac distribution. The net result is a significant reduction in the computational effort against most previous block J-D implementations, especially as the number of wanted eigenpairs grows. We compare our approach with another robust implementation of block J-D (JDQMR) and the state-of-the-art Chebyshev filter subspace (CheFSI) method for various real-space density functional theory systems. Versus CheFSI, for first-row elements, our method yields competitive timings for valence-only systems and 4-6× speedups for all-electron systems with up to 10× reduced matrix-vector multiplies. For all-electron calculations on larger elements (e.g., gold) where the wanted spectrum is quite narrow compared to the full spectrum, we observe 60× speedup with 200× fewer matrix-vector multiples vs. CheFSI.

Nonlinear Reduced-Order Simulation Using An Experimentally Guided Modal Basis

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2012-01-01

A procedure is developed for using nonlinear experimental response data to guide the modal basis selection in a nonlinear reduced-order simulation. The procedure entails using nonlinear acceleration response data to first identify proper orthogonal modes. Special consideration is given to cases in which some of the desired response data is unavailable. Bases consisting of linear normal modes are then selected to best represent the experimentally determined transverse proper orthogonal modes and either experimentally determined inplane proper orthogonal modes or the special case of numerically computed in-plane companions. The bases are subsequently used in nonlinear modal reduction and dynamic response simulations. The experimental data used in this work is simulated to allow some practical considerations, such as the availability of in-plane response data and non-idealized test conditions, to be explored. Comparisons of the nonlinear reduced-order simulations are made with the surrogate experimental data to demonstrate the effectiveness of the approach.

Inelastic Vector Soliton Collisions: A Lattice-Based Quantum Representation

DTIC Science & Technology

2004-01-01

components in these orthogonal polarizations will travel at slightly different speeds. It can be shown (Lakshmanan & Kanna 2001) that the slowly varying...media. Phys. Rev. E 58, 6752-6758. Kivshar, Y. S. & Agrawal, G. P. 2003 Optical solitons. Academic. Lakshmanan, M. & Kanna , T. 2001 Shape changing

Visualization of flow by vector analysis of multidirectional cine MR velocity mapping.

PubMed

Mohiaddin, R H; Yang, G Z; Kilner, P J

1994-01-01

We describe a noninvasive method for visualization of flow and demonstrate its application in a flow phantom and in the great vessels of healthy volunteers and patients with aortic and pulmonary arterial disease. The technique uses multidirectional MR velocity mapping acquired in selected planes. Maps of orthogonal velocity components were then processed into a graphic form immediately recognizable as flow. Cine MR velocity maps of orthogonal velocity components in selected planes were acquired in a flow phantom, 10 healthy volunteers, and 13 patients with dilated great vessels. Velocities were presented by multiple computer-generated streaks whose orientation, length, and movement corresponded to velocity vectors in the chosen plane. The velocity vector maps allowed visualization of complex patterns of primary and secondary flow in the thoracic aorta and pulmonary arteries. The technique revealed coherent, helical forward blood movements in the normal thoracic aorta during midsystole and a reverse flow during early diastole. Abnormal flow patterns with secondary vortices were seen in patients with dilated arteries. The potential of MR velocity vector mapping for in vitro and in vivo visualization of flow patterns is demonstrated. Although this study was limited to two-directional flow in a single anatomical plane, the method provides information that might advance our understanding of the human vascular system in health and disease. Further developments to reduce the acquisition time and the handling and presenting of three-directional velocity data are required to enhance the capability of this method.

On the description of conical intersections—A continuous representation of the local topography of seams of conical intersection of three or more electronic states: A generalization of the two state result

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

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

2014-11-07

For conical intersections of two states (I,J = I + 1) the vectors defining the branching or g-h plane, the energy difference gradient vector g{sup I,J}, and the interstate coupling vector h{sup I,J}, can be made orthogonal by a one parameter rotation of the degenerate electronic eigenstates. The representation obtained from this rotation is used to construct the parameters that describe the vicinity of the conical intersection seam, the conical parameters, s{sup I,J}{sub x} (R), s{sup I,J}{sub y} (R), g{sup I,J}(R), and h{sup I,J}(R). As a result of the orthogonalization these parameters can be made continuous functions of R, themore » internuclear coordinates. In this work we generalize this notion to construct continuous parametrizations of conical intersection seams of three or more states. The generalization derives from a recently introduced procedure for using non-degenerate electronic states to construct coupled diabatic states that represent adiabatic states coupled by conical intersections. The procedure is illustrated using the seam of conical intersections of three states in parazolyl as an example.« less

Symmetry of semi-reduced lattices.

PubMed

Stróż, Kazimierz

2015-05-01

The main result of this work is extension of the famous characterization of Bravais lattices according to their metrical, algebraic and geometric properties onto a wide class of primitive lattices (including Buerger-reduced, nearly Buerger-reduced and a substantial part of Delaunay-reduced) related to low-restricted semi-reduced descriptions (s.r.d.'s). While the `geometric' operations in Bravais lattices map the basis vectors into themselves, the `arithmetic' operators in s.r.d. transform the basis vectors into cell vectors (basis vectors, face or space diagonals) and are represented by matrices from the set {\\bb V} of all 960 matrices with the determinant ±1 and elements {0, ±1} of the matrix powers. A lattice is in s.r.d. if the moduli of off-diagonal elements in both the metric tensors M and M(-1) are smaller than corresponding diagonal elements sharing the same column or row. Such lattices are split into 379 s.r.d. types relative to the arithmetic holohedries. Metrical criteria for each type do not need to be explicitly given but may be modelled as linear derivatives {\\bb M}(p,q,r), where {\\bb M} denotes the set of 39 highest-symmetry metric tensors, and p,q,r describe changes of appropriate interplanar distances. A sole filtering of {\\bb V} according to an experimental s.r.d. metric and subsequent geometric interpretation of the filtered matrices lead to mathematically stable and rich information on the Bravais-lattice symmetry and deviations from the exact symmetry. The emphasis on the crystallographic features of lattices was obtained by shifting the focus (i) from analysis of a lattice metric to analysis of symmetry matrices [Himes & Mighell (1987). Acta Cryst. A43, 375-384], (ii) from the isometric approach and invariant subspaces to the orthogonality concept {some ideas in Le Page [J. Appl. Cryst. (1982), 15, 255-259]} and splitting indices [Stróż (2011). Acta Cryst. A67, 421-429] and (iii) from fixed cell transformations to transformations derivable via geometric information (Himes & Mighell, 1987; Le Page, 1982). It is illustrated that corresponding arithmetic and geometric holohedries share space distribution of symmetry elements. Moreover, completeness of the s.r.d. types reveals their combinatorial structure and simplifies the crystallographic description of structural phase transitions, especially those observed with the use of powder diffraction. The research proves that there are excellent theoretical and practical reasons for looking at crystal lattice symmetry from an entirely new and surprising point of view - the combinatorial set {\\bb V} of matrices, their semi-reduced lattice context and their geometric properties.

Group velocity locked vector dissipative solitons in a high repetition rate fiber laser

NASA Astrophysics Data System (ADS)

Luo, Yiyang; Li, Lei; Liu, Deming; Sun, Qizhen; Wu, Zhichao; Xu, Zhilin; Tang, Dingyuan; Fu, Songnian; Zhao, Luming

2016-08-01

Vectorial nature of dissipative solitons (DSs) with high repetition rates is studied for the first time in a normal-dispersion fiber laser. Despite the fact that the formed DSs are strongly chirped and the repetition rate is greater than 100 MHz, polarization locked and polarization rotating group velocity locked vector DSs can be formed under 129.3 MHz fundamental mode-locking and 258.6 MHz harmonic mode-locking of the fiber laser, respectively. The two orthogonally polarized components of these vector DSs possess distinctly different central wavelengths and travel together at the same group velocity in the laser cavity, resulting in a gradual spectral edge and small steps on the optical spectra, which can be considered as an auxiliary indicator of the group velocity locked vector DSs.

Searches For Pair Production of Heavy Vector-Like Quarks in pp Collisions at √s =13 Tev with the Atlas Detector

NASA Astrophysics Data System (ADS)

Marley, Daniel Edison

A summary of two orthogonal and complementary searches for pair production of heavy vector-like quarks is presented. The first analysis considers final states with 1-lepton and hadronic jets that can be used to reconstruct the vector-like quark system after identifying the boosted decay of W bosons and building the neutrino from the missing transverse momentum. Control and signal regions constrain the uncertainties associated with top quark production that most negatively impact this analysis. The second analysis searches in the fully-hadronic final state where no leptons are considered. An explicit veto on the lepton number ensures orthogonality between the analyses. The analysis uses a deep neural network to reconstruct the decays of heavy objects and a data-driven technique to estimate the dominant multi-jet background. Data were recorded by the ATLAS experiment in sqrt(s)=13 TeV proton-proton collisions delivered by the Large Hadron Collider in 2015 and 2016. No excess above the Standard Model background is observed in either analysis. The results from the 1-lepton analysis are interpreted assuming vector-like quarks decay TT¯ → Wb + X. The 0-lepton analysis assumes both types of pair produced vector-like quarks TT and BB that decay to T → Wb, Ht, Zt and B → Wt, Hb, Zb. The 1-lepton analysis observes a 95% CL lower limit on the T mass of 1090 (810) GeV assuming the scenario BR(T → Wb)=1 (SU(2) singlet). The strongest observed 95% CL lower limits in the 0-lepton analysis are 850 GeV and 903 GeV in the BR(T → Ht) = 1 and BR(B → Hb)=1 decays, respectively.

Method for multi-axis, non-contact mixing of magnetic particle suspensions

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

Martin, James E.; Solis, Kyle J.

Continuous, three-dimensional control of the vorticity vector is possible by progressively transitioning the field symmetry by applying or removing a dc bias along one of the principal axes of mutually orthogonal alternating fields. By exploiting this transition, the vorticity vector can be oriented in a wide range of directions that comprise all three spatial dimensions. Detuning one or more field components to create phase modulation causes the vorticity vector to trace out complex orbits of a wide variety, creating very robust multiaxial stirring. This multiaxial, non-contact stirring is particularly attractive for applications where the fluid volume has complex boundaries, ormore » is congested.« less

Novel analytical approach for strongly coupled waveguide arrays

NASA Astrophysics Data System (ADS)

Kohli, Niharika; Srivastava, Sangeeta; Sharma, Enakshi K.

2018-02-01

Coupled Mode theory and Variational methods are the most extensively used analytical methods for the study of coupled optical waveguides. In this paper we have discussed a variation of the Ritz Galerkin Variational method (RGVM) wherein the trial field is a superposition of an orthogonal basis set which in turn is generated from superposition of the individual waveguide modal fields using Gram Schmidt Orthogonalization Procedure (GSOP). The conventional coupled mode theory (CCMT), a modified coupled mode theory (MCMT) incorporating interaction terms that are neglected in CCMT, and an RGVM using orthogonal basis set (RG-GSOP) are compared for waveguide arrays of different materials. The exact effective indices values for these planar waveguide arrays are also studied. The different materials have their index-contrasts ranging between the GaAs/ AlGaAs system to Si/SiO2 system. It has been shown that the error in the effective indices values obtained from MCMT and CCMT is higher than RGVM-GSOP especially in the case of higher index-contrast. Therefore, for accurate calculations of the modal characteristics of planar waveguide arrays, even at higher index-contrasts, RGVM-GSOP is the best choice. Moreover, we obtain obviously orthogonal supermode fields and Hermitian matrix from RGVM-GSOP.

Communication: Density functional theory embedding with the orthogonality constrained basis set expansion procedure

NASA Astrophysics Data System (ADS)

Culpitt, Tanner; Brorsen, Kurt R.; Hammes-Schiffer, Sharon

2017-06-01

Density functional theory (DFT) embedding approaches have generated considerable interest in the field of computational chemistry because they enable calculations on larger systems by treating subsystems at different levels of theory. To circumvent the calculation of the non-additive kinetic potential, various projector methods have been developed to ensure the orthogonality of molecular orbitals between subsystems. Herein the orthogonality constrained basis set expansion (OCBSE) procedure is implemented to enforce this subsystem orbital orthogonality without requiring a level shifting parameter. This scheme is a simple alternative to existing parameter-free projector-based schemes, such as the Huzinaga equation. The main advantage of the OCBSE procedure is that excellent convergence behavior is attained for DFT-in-DFT embedding without freezing any of the subsystem densities. For the three chemical systems studied, the level of accuracy is comparable to or higher than that obtained with the Huzinaga scheme with frozen subsystem densities. Allowing both the high-level and low-level DFT densities to respond to each other during DFT-in-DFT embedding calculations provides more flexibility and renders this approach more generally applicable to chemical systems. It could also be useful for future extensions to embedding approaches combining wavefunction theories and DFT.

Alternative Modal Basis Selection Procedures for Nonlinear Random Response Simulation

NASA Technical Reports Server (NTRS)

Przekop, Adam; Guo, Xinyun; Rizzi, Stephen A.

2010-01-01

Three procedures to guide selection of an efficient modal basis in a nonlinear random response analysis are examined. One method is based only on proper orthogonal decomposition, while the other two additionally involve smooth orthogonal decomposition. Acoustic random response problems are employed to assess the performance of the three modal basis selection approaches. A thermally post-buckled beam exhibiting snap-through behavior, a shallowly curved arch in the auto-parametric response regime and a plate structure are used as numerical test articles. The results of the three reduced-order analyses are compared with the results of the computationally taxing simulation in the physical degrees of freedom. For the cases considered, all three methods are shown to produce modal bases resulting in accurate and computationally efficient reduced-order nonlinear simulations.

Mathematics of Quantization and Quantum Fields

NASA Astrophysics Data System (ADS)

Dereziński, Jan; Gérard, Christian

2013-03-01

Preface; 1. Vector spaces; 2. Operators in Hilbert spaces; 3. Tensor algebras; 4. Analysis in L2(Rd); 5. Measures; 6. Algebras; 7. Anti-symmetric calculus; 8. Canonical commutation relations; 9. CCR on Fock spaces; 10. Symplectic invariance of CCR in finite dimensions; 11. Symplectic invariance of the CCR on Fock spaces; 12. Canonical anti-commutation relations; 13. CAR on Fock spaces; 14. Orthogonal invariance of CAR algebras; 15. Clifford relations; 16. Orthogonal invariance of the CAR on Fock spaces; 17. Quasi-free states; 18. Dynamics of quantum fields; 19. Quantum fields on space-time; 20. Diagrammatics; 21. Euclidean approach for bosons; 22. Interacting bosonic fields; Subject index; Symbols index.

The Pioneer XI high field fluxgate magnetometer

NASA Technical Reports Server (NTRS)

Acuna, M. A.; Ness, N. F.

1975-01-01

The high field fluxgate magnetometer experiment flown aboard the Pioneer XI spacecraft is described. This extremely simple instrument was used to extend the spacecraft's upper-limit measurement capability by approximately an order of magnitude (from 0.14 mT to 1.00 mT) with minimum power and volume requirements. This magnetometer was designed to complement the low-field measurements provided by a helium vector magnetometer and utilizes magnetic ring core sensors with biaxial orthogonal sense coils. The instrument is a single-range, triaxial-fluxgate magnetometer capable of measuring fields of up to 1 mT along each orthogonal axis, with a maximum resolution of 1 microT.

Reciprocity relationships in vector acoustics and their application to vector field calculations.

PubMed

Deal, Thomas J; Smith, Kevin B

2017-08-01

The reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. A similar equation that governs the orthogonal components of the particle velocity field is needed to enable this computational method to be used for acoustic vector sensors. This paper derives a general reciprocity equation that accounts for both monopole and dipole sources. This vector-scalar reciprocity equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each vector field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-dependent environment using a parabolic equation model.

Reviving the shear-free perfect fluid conjecture in general relativity

NASA Astrophysics Data System (ADS)

Sikhonde, Muzikayise E.; Dunsby, Peter K. S.

2017-12-01

Employing a Mathematica symbolic computer algebra package called xTensor, we present (1+3) -covariant special case proofs of the shear-free perfect fluid conjecture in general relativity. We first present the case where the pressure is constant, and where the acceleration is parallel to the vorticity vector. These cases were first presented in their covariant form by Senovilla et al. We then provide a covariant proof for the case where the acceleration and vorticity vectors are orthogonal, which leads to the existence of a Killing vector along the vorticity. This Killing vector satisfies the new constraint equations resulting from the vanishing of the shear. Furthermore, it is shown that in order for the conjecture to be true, this Killing vector must have a vanishing spatially projected directional covariant derivative along the velocity vector field. This in turn implies the existence of another basic vector field along the direction of the vorticity for the conjecture to hold. Finally, we show that in general, there exists a basic vector field parallel to the acceleration for which the conjecture is true.

Risky Group Decision-Making Method for Distribution Grid Planning

NASA Astrophysics Data System (ADS)

Li, Cunbin; Yuan, Jiahang; Qi, Zhiqiang

2015-12-01

With rapid speed on electricity using and increasing in renewable energy, more and more research pay attention on distribution grid planning. For the drawbacks of existing research, this paper proposes a new risky group decision-making method for distribution grid planning. Firstly, a mixing index system with qualitative and quantitative indices is built. On the basis of considering the fuzziness of language evaluation, choose cloud model to realize "quantitative to qualitative" transformation and construct interval numbers decision matrices according to the "3En" principle. An m-dimensional interval numbers decision vector is regarded as super cuboids in m-dimensional attributes space, using two-level orthogonal experiment to arrange points uniformly and dispersedly. The numbers of points are assured by testing numbers of two-level orthogonal arrays and these points compose of distribution points set to stand for decision-making project. In order to eliminate the influence of correlation among indices, Mahalanobis distance is used to calculate the distance from each solutions to others which means that dynamic solutions are viewed as the reference. Secondly, due to the decision-maker's attitude can affect the results, this paper defines the prospect value function based on SNR which is from Mahalanobis-Taguchi system and attains the comprehensive prospect value of each program as well as the order. At last, the validity and reliability of this method is illustrated by examples which prove the method is more valuable and superiority than the other.

Orthogonal basis with a conicoid first mode for shape specification of optical surfaces.

PubMed

Ferreira, Chelo; López, José L; Navarro, Rafael; Sinusía, Ester Pérez

2016-03-07

A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different polynomials. Here we present results for surfaces with circular apertures when the first basis function (mode) is a conicoid. The system for aspheres with rotational symmetry is obtained applying an appropriate change of variables to Legendre polynomials, whereas the system for general freeform case is obtained applying a similar procedure to spherical harmonics. Numerical comparisons with standard systems, such as Forbes and Zernike polynomials, are performed and discussed.

Extending the length and time scales of Gram-Schmidt Lyapunov vector computations

NASA Astrophysics Data System (ADS)

Costa, Anthony B.; Green, Jason R.

2013-08-01

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram-Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N2 (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram-Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard-Jones fluids from N=100 to 1300 between Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram-Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra.

Multiuser receiver for DS-CDMA signals in multipath channels: an enhanced multisurface method.

PubMed

Mahendra, Chetan; Puthusserypady, Sadasivan

2006-11-01

This paper deals with the problem of multiuser detection in direct-sequence code-division multiple-access (DS-CDMA) systems in multipath environments. The existing multiuser detectors can be divided into two categories: (1) low-complexity poor-performance linear detectors and (2) high-complexity good-performance nonlinear detectors. In particular, in channels where the orthogonality of the code sequences is destroyed by multipath, detectors with linear complexity perform much worse than the nonlinear detectors. In this paper, we propose an enhanced multisurface method (EMSM) for multiuser detection in multipath channels. EMSM is an intermediate piecewise linear detection scheme with a run-time complexity linear in the number of users. Its bit error rate performance is compared with existing linear detectors, a nonlinear radial basis function detector trained by the new support vector learning algorithm, and Verdu's optimal detector. Simulations in multipath channels, for both synchronous and asynchronous cases, indicate that it always outperforms all other linear detectors, performing nearly as well as nonlinear detectors.

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

Romano, J.D.; Woan, G.

Data from the Laser Interferometer Space Antenna (LISA) is expected to be dominated by frequency noise from its lasers. However, the noise from any one laser appears more than once in the data and there are combinations of the data that are insensitive to this noise. These combinations, called time delay interferometry (TDI) variables, have received careful study and point the way to how LISA data analysis may be performed. Here we approach the problem from the direction of statistical inference, and show that these variables are a direct consequence of a principal component analysis of the problem. We presentmore » a formal analysis for a simple LISA model and show that there are eigenvectors of the noise covariance matrix that do not depend on laser frequency noise. Importantly, these orthogonal basis vectors correspond to linear combinations of TDI variables. As a result we show that the likelihood function for source parameters using LISA data can be based on TDI combinations of the data without loss of information.« less

SU-E-J-45: The Correlation Between CBCT Flat Panel Misalignment and 3D Image Guidance Accuracy

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

Kenton, O; Valdes, G; Yin, L

Purpose To simulate the impact of CBCT flat panel misalignment on the image quality, the calculated correction vectors in 3D image guided proton therapy and to determine if these calibration errors can be caught in our QA process. Methods The X-ray source and detector geometrical calibration (flexmap) file of the CBCT system in the AdaPTinsight software (IBA proton therapy) was edited to induce known changes in the rotational and translational calibrations of the imaging panel. Translations of up to ±10 mm in the x, y and z directions (see supplemental) and rotational errors of up to ±3° were induced. Themore » calibration files were then used to reconstruct the CBCT image of a pancreatic patient and CatPhan phantom. Correction vectors were calculated for the patient using the software’s auto match system and compared to baseline values. The CatPhan CBCT images were used for quantitative evaluation of image quality for each type of induced error. Results Translations of 1 to 3 mm in the x and y calibration resulted in corresponding correction vector errors of equal magnitude. Similar 10mm shifts were seen in the y-direction; however, in the x-direction, the image quality was too degraded for a match. These translational errors can be identified through differences in isocenter from orthogonal kV images taken during routine QA. Errors in the z-direction had no effect on the correction vector and image quality.Rotations of the imaging panel calibration resulted in corresponding correction vector rotations of the patient images. These rotations also resulted in degraded image quality which can be identified through quantitative image quality metrics. Conclusion Misalignment of CBCT geometry can lead to incorrect translational and rotational patient correction vectors. These errors can be identified through QA of the imaging isocenter as compared to orthogonal images combined with monitoring of CBCT image quality.« less

Reply to ''Comment on 'Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models'''

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

Paterek, Tomasz; Dakic, Borivoje; Brukner, Caslav

In this Reply to the preceding Comment by Hall and Rao [Phys. Rev. A 83, 036101 (2011)], we motivate terminology of our original paper and point out that further research is needed in order to (dis)prove the claimed link between every orthogonal Latin square of order being a power of a prime and a mutually unbiased basis.

Spatial attenuation of different sound field components in a water layer and shallow-water sediments

NASA Astrophysics Data System (ADS)

Belov, A. I.; Kuznetsov, G. N.

2017-11-01

The paper presents the results of an experimental study of spatial attenuation of low-frequency vector-scalar sound fields in shallow water. The experiments employed a towed pneumatic cannon and spatially separated four-component vector-scalar receiver modules. Narrowband analysis of received signals made it possible to estimate the attenuation coefficients of the first three modes in the frequency of range of 26-182 Hz and calculate the frequency dependences of the sound absorption coefficients in the upper part of bottom sediments. We analyze the experimental and calculated (using acoustic calibration of the waveguide) laws of the drop in sound pressure and orthogonal vector projections of the oscillation velocity. It is shown that the vertical projection of the oscillation velocity vector decreases significantly faster than the sound pressure field.

Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

NASA Astrophysics Data System (ADS)

Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

2013-09-01

Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are presented to compare the output from the MCPI library to current state-of-practice numerical integration methods. It is shown that MCPI is capable of out-performing the state-of-practice in terms of computational cost and accuracy.

On Certain Theoretical Developments Underlying the Hilbert-Huang Transform

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Blank, Karin; Flatley, Thomas; Huang, Norden E.; Petrick, David; Hestness, Phyllis

2006-01-01

One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real-value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a nearly orthogonal derived from the data (adaptive) basis. The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2-D processing using Field Programmable Gate Array (FPGA) computational resources,

Alternative Modal Basis Selection Procedures For Reduced-Order Nonlinear Random Response Simulation

NASA Technical Reports Server (NTRS)

Przekop, Adam; Guo, Xinyun; Rizi, Stephen A.

2012-01-01

Three procedures to guide selection of an efficient modal basis in a nonlinear random response analysis are examined. One method is based only on proper orthogonal decomposition, while the other two additionally involve smooth orthogonal decomposition. Acoustic random response problems are employed to assess the performance of the three modal basis selection approaches. A thermally post-buckled beam exhibiting snap-through behavior, a shallowly curved arch in the auto-parametric response regime and a plate structure are used as numerical test articles. The results of a computationally taxing full-order analysis in physical degrees of freedom are taken as the benchmark for comparison with the results from the three reduced-order analyses. For the cases considered, all three methods are shown to produce modal bases resulting in accurate and computationally efficient reduced-order nonlinear simulations.

Dissipative vector soliton in a dispersion-managed fiber laser with normal dispersion.

PubMed

Wang, Siming; Fan, Xuliang; Zhao, Luming; Wang, Yong; Tang, Dingyuan; Shen, Deyuan

2014-12-10

We numerically study the vector dynamics of dissipative solitons (DSs) in a 2 μm dispersion-managed fiber laser mode locked by a semiconductor saturable absorber mirror and operated in the normal dispersion regime. It is shown that the effective gain bandwidth is crucial for the DS generation. The steep spectral edges of DSs are the consequence of the interaction among the normal dispersion, fiber nonlinearity, gain and loss, and gain dispersion effect, etc. We numerically duplicate the experimental results and further explore the vector features of the generated DSs. Two DSs formed along the two orthogonal polarization directions which, incoherently coupled with each other, could propagate in the birefringent cavity with the same group velocity.

Method and apparatus for second-rank tensor generation

NASA Technical Reports Server (NTRS)

Liu, Hua-Kuang (Inventor)

1991-01-01

A method and apparatus are disclosed for generation of second-rank tensors using a photorefractive crystal to perform the outer-product between two vectors via four-wave mixing, thereby taking 2n input data to a control n squared output data points. Two orthogonal amplitude modulated coherent vector beams x and y are expanded and then parallel sides of the photorefractive crystal in exact opposition. A beamsplitter is used to direct a coherent pumping beam onto the crystal at an appropriate angle so as to produce a conjugate beam that is the matrix product of the vector beam that propagates in the exact opposite direction from the pumping beam. The conjugate beam thus separated is the tensor output xy (sup T).

Simple, Effective Computation of Principal Eigen-Vectors and Their Eigenvalues and Application to High-Resolution Estimation of Frequencies

DTIC Science & Technology

1985-10-01

written 3 as follows: m 4 cg ° + C + + - c =0n-1u-1 n C + c 2 g 1 +. . c 0 clg o Cngn-1 cn+ 1 (10a) cng° + Cn+11 + + C 2n-lgn_1 + C 2 n 0 or in...matrix form, C " I = 0 (10b) A non-zero solution is possible if the determinant of C is zero. From the theory of Prony’s method [133 g (k1 = % n + kn... g , ki + go = 0 II) hence the polynomial coefficient vector g is also orthogonal to the vector (1 X i ki 2 .Xik)T where %i’s are the

Seismic transmission operator reciprocity - II: impedance-operator symmetry via elastic lateral modes

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2015-08-01

The properties of the overburden transmission response are of particular interest for the analysis of reflectivity illumination or blurring in seismic depth imaging. The first step to showing a transmission-operator reciprocity property is to identify the symmetry of the so-called displacement-to-traction operators. The latter are analogous to Dirichlet-to-Neumann operators and they may also be called impedance operators. Their symmetry is deduced here after development of a formal spectral or modal theory of lateral wavefunctions in a laterally heterogeneous generally anisotropic elastic medium. The elastic lateral modes are displacement-traction 6-vectors and they are built from two auxiliary 3-vector lateral-mode bases. These auxiliary modes arise from Hermitian and anti-Hermitian operators, so they have familiar properties such as orthogonality. There is no assumption of down/up symmetry of the elasticity tensor, but basic assumptions are made about the existence and completeness of the elastic modes. A point-symmetry property appears and plays a central role. The 6-vector elastic modes have a symplectic orthogonality property, which facilitates the development of modal expansions for 6-vector functions of the lateral coordinates when completeness is assumed. While the elastic modal theory is consistent with the laterally homogeneous case, numerical work would provide confidence that it is correct in general. An appendix contains an introductory overview of acoustic lateral modes that were studied by other authors, given from the perspective of this new work. A distinction is drawn between unit normalization of scalar auxiliary modes and a separate energy-flux normalization of 2-vector acoustic modes. Neither is crucial to the form of acoustic pressure-to-velocity or impedance operators. This statement carries over to the elastic case for the 3-vector auxiliary- and 6-vector elastic-mode normalizations. The modal theory is used to construct the kernel of the elastic displacement-to-traction or impedance operator. Symmetry properties of this operator are then deduced, which is the main goal of this paper. The implications of elastic impedance-operator symmetry and the symplectic property for the transmission and reflection responses of finite regions are described in a companion paper.

Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops

NASA Astrophysics Data System (ADS)

Fan, Yiyun; Gnutzmann, Sven; Liang, Yuqi

2017-12-01

We consider two coupled quantum tops with angular momentum vectors L and M . The coupling Hamiltonian defines the Feingold-Peres model, which is a known paradigm of quantum chaos. We show that this model has a nonstandard symmetry with respect to the Altland-Zirnbauer tenfold symmetry classification of quantum systems, which extends the well-known threefold way of Wigner and Dyson (referred to as "standard" symmetry classes here). We identify the nonstandard symmetry classes BD I0 (chiral orthogonal class with no zero modes), BD I1 (chiral orthogonal class with one zero mode), and C I (antichiral orthogonal class) as well as the standard symmetry class A I (orthogonal class). We numerically analyze the specific spectral quantum signatures of chaos related to the nonstandard symmetries. In the microscopic density of states and in the distribution of the lowest positive energy eigenvalue, we show that the Feingold-Peres model follows the predictions of the Gaussian ensembles of random-matrix theory in the appropriate symmetry class if the corresponding classical dynamics is chaotic. In a crossover to mixed and near-integrable classical dynamics, we show that these signatures disappear or strongly change.

Unveiling the signals from extremely noisy microseismic data for high-resolution hydraulic fracturing monitoring.

PubMed

Huang, Weilin; Wang, Runqiu; Li, Huijian; Chen, Yangkang

2017-09-20

Microseismic method is an essential technique for monitoring the dynamic status of hydraulic fracturing during the development of unconventional reservoirs. However, one of the challenges in microseismic monitoring is that those seismic signals generated from micro seismicity have extremely low amplitude. We develop a methodology to unveil the signals that are smeared in the strong ambient noise and thus facilitate a more accurate arrival-time picking that will ultimately improve the localization accuracy. In the proposed technique, we decompose the recorded data into several morphological multi-scale components. In order to unveil weak signal, we propose an orthogonalization operator which acts as a time-varying weighting in the morphological reconstruction. The orthogonalization operator is obtained using an inversion process. This orthogonalized morphological reconstruction can be interpreted as a projection of the higher-dimensional vector. We first test the proposed technique using a synthetic dataset. Then the proposed technique is applied to a field dataset recorded in a project in China, in which the signals induced from hydraulic fracturing are recorded by twelve three-component (3-C) geophones in a monitoring well. The result demonstrates that the orthogonalized morphological reconstruction can make the extremely weak microseismic signals detectable.

Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops.

PubMed

Fan, Yiyun; Gnutzmann, Sven; Liang, Yuqi

2017-12-01

We consider two coupled quantum tops with angular momentum vectors L and M. The coupling Hamiltonian defines the Feingold-Peres model, which is a known paradigm of quantum chaos. We show that this model has a nonstandard symmetry with respect to the Altland-Zirnbauer tenfold symmetry classification of quantum systems, which extends the well-known threefold way of Wigner and Dyson (referred to as "standard" symmetry classes here). We identify the nonstandard symmetry classes BDI_{0} (chiral orthogonal class with no zero modes), BDI_{1} (chiral orthogonal class with one zero mode), and CI (antichiral orthogonal class) as well as the standard symmetry class AI (orthogonal class). We numerically analyze the specific spectral quantum signatures of chaos related to the nonstandard symmetries. In the microscopic density of states and in the distribution of the lowest positive energy eigenvalue, we show that the Feingold-Peres model follows the predictions of the Gaussian ensembles of random-matrix theory in the appropriate symmetry class if the corresponding classical dynamics is chaotic. In a crossover to mixed and near-integrable classical dynamics, we show that these signatures disappear or strongly change.

The Magsat precision vector magnetometer

NASA Technical Reports Server (NTRS)

Acuna, M. H.

1980-01-01

This paper examines the Magsat precision vector magnetometer which is designed to measure projections of the ambient field in three orthogonal directions. The system contains a highly stable and linear triaxial fluxgate magnetometer with a dynamic range of + or - 2000 nT (1 nT = 10 to the -9 weber per sq m). The magnetometer electronics, analog-to-digital converter, and digitally controlled current sources are implemented with redundant designs to avoid a loss of data in case of failures. Measurements are carried out with an accuracy of + or - 1 part in 64,000 in magnitude and 5 arcsec in orientation (1 arcsec = 0.00028 deg).

Multi-indexed (q-)Racah polynomials

NASA Astrophysics Data System (ADS)

Odake, Satoru; Sasaki, Ryu

2012-09-01

As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of ‘discrete quantum mechanics’ with real shifts in one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from the (q-)Racah polynomials by the multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of ‘virtual state’ vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier. The virtual state vectors are the ‘solutions’ of the matrix Schrödinger equation with negative ‘eigenvalues’, except for one of the two boundary points.

Fully-Implicit Reconstructed Discontinuous Galerkin Method for Stiff Multiphysics Problems

NASA Astrophysics Data System (ADS)

Nourgaliev, Robert

2015-11-01

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method's capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing. We focus on the method's accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and funded by the LDRD at LLNL under project tracking code 13-SI-002.

Analysis of structural response data using discrete modal filters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Freudinger, Lawrence C.

1991-01-01

The application of reciprocal modal vectors to the analysis of structural response data is described. Reciprocal modal vectors are constructed using an existing experimental modal model and an existing frequency response matrix of a structure, and can be assembled into a matrix that effectively transforms the data from the physical space to a modal space within a particular frequency range. In other words, the weighting matrix necessary for modal vector orthogonality (typically the mass matrix) is contained within the reciprocal model matrix. The underlying goal of this work is mostly directed toward observing the modal state responses in the presence of unknown, possibly closed loop forcing functions, thus having an impact on both operating data analysis techniques and independent modal space control techniques. This study investigates the behavior of reciprocol modal vectors as modal filters with respect to certain calculation parameters and their performance with perturbed system frequency response data.

Some Applications Of Semigroups And Computer Algebra In Discrete Structures

NASA Astrophysics Data System (ADS)

Bijev, G.

2009-11-01

An algebraic approach to the pseudoinverse generalization problem in Boolean vector spaces is used. A map (p) is defined, which is similar to an orthogonal projection in linear vector spaces. Some other important maps with properties similar to those of the generalized inverses (pseudoinverses) of linear transformations and matrices corresponding to them are also defined and investigated. Let Ax = b be an equation with matrix A and vectors x and b Boolean. Stochastic experiments for solving the equation, which involves the maps defined and use computer algebra methods, have been made. As a result, the Hamming distance between vectors Ax = p(b) and b is equal or close to the least possible. We also share our experience in using computer algebra systems for teaching discrete mathematics and linear algebra and research. Some examples for computations with binary relations using Maple are given.

Aspects of QCD current algebra on a null plane

NASA Astrophysics Data System (ADS)

Beane, S. R.; Hobbs, T. J.

2016-09-01

Consequences of QCD current algebra formulated on a light-like hyperplane are derived for the forward scattering of vector and axial-vector currents on an arbitrary hadronic target. It is shown that current algebra gives rise to a special class of sum rules that are direct consequences of the independent chiral symmetry that exists at every point on the two-dimensional transverse plane orthogonal to the lightlike direction. These sum rules are obtained by exploiting the closed, infinite-dimensional algebra satisfied by the transverse moments of null-plane axial-vector and vector charge distributions. In the special case of a nucleon target, this procedure leads to the Adler-Weisberger, Gerasimov-Drell-Hearn, Cabibbo-Radicati and Fubini-Furlan-Rossetti sum rules. Matching to the dispersion-theoretic language which is usually invoked in deriving these sum rules, the moment sum rules are shown to be equivalent to algebraic constraints on forward S-matrix elements in the Regge limit.

On load paths and load bearing topology from finite element analysis

NASA Astrophysics Data System (ADS)

Kelly, D.; Reidsema, C.; Lee, M.

2010-06-01

Load paths can be mapped from vector plots of 'pointing stress vectors'. They define a path along which a component of load remains constant as it traverses the solution domain. In this paper the theory for the paths is first defined. Properties of the plots that enable a designer to interpret the structural behavior from the contours are then identified. Because stress is a second order tensor defined on an orthogonal set of axes, the vector plots define separate paths for load transfer in each direction of the set of axes. An algorithm is therefore presented that combines the vectors to define a topology to carry the loads. The algorithm is shown to straighten the paths reducing bending moments and removing stress concentration. Application to a bolted joint, a racing car body and a yacht hull demonstrate the usefulness of the plots.

Efficient modeling of vector hysteresis using a novel Hopfield neural network implementation of Stoner–Wohlfarth-like operators

PubMed Central

Adly, Amr A.; Abd-El-Hafiz, Salwa K.

2012-01-01

Incorporation of hysteresis models in electromagnetic analysis approaches is indispensable to accurate field computation in complex magnetic media. Throughout those computations, vector nature and computational efficiency of such models become especially crucial when sophisticated geometries requiring massive sub-region discretization are involved. Recently, an efficient vector Preisach-type hysteresis model constructed from only two scalar models having orthogonally coupled elementary operators has been proposed. This paper presents a novel Hopfield neural network approach for the implementation of Stoner–Wohlfarth-like operators that could lead to a significant enhancement in the computational efficiency of the aforementioned model. Advantages of this approach stem from the non-rectangular nature of these operators that substantially minimizes the number of operators needed to achieve an accurate vector hysteresis model. Details of the proposed approach, its identification and experimental testing are presented in the paper. PMID:25685446

Polarization locked vector solitons and axis instability in optical fiber.

PubMed

Cundiff, Steven T.; Collings, Brandon C.; Bergman, Keren

2000-09-01

We experimentally observe polarization-locked vector solitons in optical fiber. Polarization locked-vector solitons use nonlinearity to preserve their polarization state despite the presence of birefringence. To achieve conditions where the delicate balance between nonlinearity and birefringence can survive, we studied the polarization evolution of the pulses circulating in a laser constructed entirely of optical fiber. We observe two distinct states with fixed polarization. This first state occurs for very small values birefringence and is elliptically polarized. We measure the relative phase between orthogonal components along the two principal axes to be +/-pi/2. The relative amplitude varies linearly with the magnitude of the birefringence. This state is a polarization locked vector soliton. The second, linearly polarized, state occurs for larger values of birefringence. The second state is due to the fast axis instability. We provide complete characterization of these states, and present a physical explanation of both of these states and the stability of the polarization locked vector solitons. (c) 2000 American Institute of Physics.

Polarization locked vector solitons and axis instability in optical fiber

NASA Astrophysics Data System (ADS)

Cundiff, Steven T.; Collings, Brandon C.; Bergman, Keren

2000-09-01

We experimentally observe polarization-locked vector solitons in optical fiber. Polarization locked-vector solitons use nonlinearity to preserve their polarization state despite the presence of birefringence. To achieve conditions where the delicate balance between nonlinearity and birefringence can survive, we studied the polarization evolution of the pulses circulating in a laser constructed entirely of optical fiber. We observe two distinct states with fixed polarization. This first state occurs for very small values birefringence and is elliptically polarized. We measure the relative phase between orthogonal components along the two principal axes to be ±π/2. The relative amplitude varies linearly with the magnitude of the birefringence. This state is a polarization locked vector soliton. The second, linearly polarized, state occurs for larger values of birefringence. The second state is due to the fast axis instability. We provide complete characterization of these states, and present a physical explanation of both of these states and the stability of the polarization locked vector solitons.

A Higher-Order Generalized Singular Value Decomposition for Comparison of Global mRNA Expression from Multiple Organisms

PubMed Central

Ponnapalli, Sri Priya; Saunders, Michael A.; Van Loan, Charles F.; Alter, Orly

2011-01-01

The number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing in many areas of science, accompanied by a need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. The only such framework to date, the generalized singular value decomposition (GSVD), is limited to two matrices. We mathematically define a higher-order GSVD (HO GSVD) for N≥2 matrices , each with full column rank. Each matrix is exactly factored as Di = UiΣiVT, where V, identical in all factorizations, is obtained from the eigensystem SV = VΛ of the arithmetic mean S of all pairwise quotients of the matrices , i≠j. We prove that this decomposition extends to higher orders almost all of the mathematical properties of the GSVD. The matrix S is nondefective with V and Λ real. Its eigenvalues satisfy λk≥1. Equality holds if and only if the corresponding eigenvector vk is a right basis vector of equal significance in all matrices Di and Dj, that is σi,k/σj,k = 1 for all i and j, and the corresponding left basis vector ui,k is orthogonal to all other vectors in Ui for all i. The eigenvalues λk = 1, therefore, define the “common HO GSVD subspace.” We illustrate the HO GSVD with a comparison of genome-scale cell-cycle mRNA expression from S. pombe, S. cerevisiae and human. Unlike existing algorithms, a mapping among the genes of these disparate organisms is not required. We find that the approximately common HO GSVD subspace represents the cell-cycle mRNA expression oscillations, which are similar among the datasets. Simultaneous reconstruction in the common subspace, therefore, removes the experimental artifacts, which are dissimilar, from the datasets. In the simultaneous sequence-independent classification of the genes of the three organisms in this common subspace, genes of highly conserved sequences but significantly different cell-cycle peak times are correctly classified. PMID:22216090

NOTE: Circular symmetry in topologically massive gravity

NASA Astrophysics Data System (ADS)

Deser, S.; Franklin, J.

2010-05-01

We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null.

Wavefront Reconstruction and Mirror Surface Optimizationfor Adaptive Optics

DTIC Science & Technology

2014-06-01

TERMS Wavefront reconstruction, Adaptive optics , Wavelets, Atmospheric turbulence , Branch points, Mirror surface optimization, Space telescope, Segmented...contribution adapts the proposed algorithm to work when branch points are present from significant atmospheric turbulence . An analysis of vector spaces...estimate the distortion of the collected light caused by the atmosphere and corrected by adaptive optics . A generalized orthogonal wavelet wavefront

Elementary properties of triangle in normed spaces

NASA Astrophysics Data System (ADS)

Triana, Deri; Yunus, Mahmud

2018-03-01

Based on concepts of trigonometric on plane, In this paper we generalized those concept in normed spaces. About the orthogonality concept between two vectors already well known, we are interested to develop elementary properties of triangle, especially the properties of its angle. We propose a non-linear (Wilson) functional to define an angle and explore its properties.

Lunar surface magnetometers

NASA Technical Reports Server (NTRS)

Dyal, P.; Gordon, D. I.

1973-01-01

Discussion of the properties of both the stationary and portable magnetometers used in the Apollo program to measure static and dynamic fields on the lunar surface. A stationary magnetometer is described in which the three orthogonal vector components of the magnetic field are measured by three fluxgate sensors which are located at the ends of three orthogonal booms and contain ferromagnetic cores driven to saturation by means of a periodic current. In the Apollo 16 magnetometer special high-stability ring-core sensors were used which provided an output voltage to the analog-to-digital converter which is proportional to the magnetic field. A portable magnetometer is described which consists of a set of three orthogonal fluxgate sensors mounted on top of a tripod connected to an electronics box by a ribbon cable. The above-mentioned stationary magnetometer simultaneously measured the time-varying components of the field which were later subtracted from the portable magnetometer measurements to give the desired resultant steady field values caused by the magnetized crustal material.

On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations

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

Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em, E-mail: george_karniadakis@brown.edu

2014-08-01

The Karhunen–Lòeve (KL) decomposition provides a low-dimensional representation for random fields as it is optimal in the mean square sense. Although for many stochastic systems of practical interest, described by stochastic partial differential equations (SPDEs), solutions possess this low-dimensional character, they also have a strongly time-dependent form and to this end a fixed-in-time basis may not describe the solution in an efficient way. Motivated by this limitation of standard KL expansion, Sapsis and Lermusiaux (2009) [26] developed the dynamically orthogonal (DO) field equations which allow for the simultaneous evolution of both the spatial basis where uncertainty ‘lives’ but also themore » stochastic characteristics of uncertainty. Recently, Cheng et al. (2013) [28] introduced an alternative approach, the bi-orthogonal (BO) method, which performs the exact same tasks, i.e. it evolves the spatial basis and the stochastic characteristics of uncertainty. In the current work we examine the relation of the two approaches and we prove theoretically and illustrate numerically their equivalence, in the sense that one method is an exact reformulation of the other. We show this by deriving a linear and invertible transformation matrix described by a matrix differential equation that connects the BO and the DO solutions. We also examine a pathology of the BO equations that occurs when two eigenvalues of the solution cross, resulting in an instantaneous, infinite-speed, internal rotation of the computed spatial basis. We demonstrate that despite the instantaneous duration of the singularity this has important implications on the numerical performance of the BO approach. On the other hand, it is observed that the BO is more stable in nonlinear problems involving a relatively large number of modes. Several examples, linear and nonlinear, are presented to illustrate the DO and BO methods as well as their equivalence.« less

Stochastic dynamics of time correlation in complex systems with discrete time

NASA Astrophysics Data System (ADS)

Yulmetyev, Renat; Hänggi, Peter; Gafarov, Fail

2000-11-01

In this paper we present the concept of description of random processes in complex systems with discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations for time correlation functions (TCFs). We have introduced the dynamic (time dependent) information Shannon entropy Si(t) where i=0,1,2,3,..., as an information measure of stochastic dynamics of time correlation (i=0) and time memory (i=1,2,3,...). The set of functions Si(t) constitute the quantitative measure of time correlation disorder (i=0) and time memory disorder (i=1,2,3,...) in complex system. The theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states. We examine two stochastic processes involving the creation and annihilation of time correlation (or time memory) in details. We carry out the analysis of vectors' dynamics employing finite-difference equations for random variables and the evolution operator describing their natural motion. The existence of TCF results in the construction of the set of projection operators by the usage of scalar product operation. Harnessing the infinite set of orthogonal dynamic random variables on a basis of Gram-Shmidt orthogonalization procedure tends to creation of infinite chain of finite-difference non-Markov kinetic equations for discrete TCFs and memory functions (MFs). The solution of the equations above thereof brings to the recurrence relations between the TCF and MF of senior and junior orders. This offers new opportunities for detecting the frequency spectra of power of entropy function Si(t) for time correlation (i=0) and time memory (i=1,2,3,...). The results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems. Application of this technique on the analysis of stochastic dynamics of RR intervals from human ECG's shows convincing evidence for a non-Markovian phenomemena associated with a peculiarities in short- and long-range scaling. This method may be of use in distinguishing healthy from pathologic data sets based in differences in these non-Markovian properties.

Extending the length and time scales of Gram–Schmidt Lyapunov vector computations

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

Costa, Anthony B., E-mail: acosta@northwestern.edu; Green, Jason R., E-mail: jason.green@umb.edu; Department of Chemistry, University of Massachusetts Boston, Boston, MA 02125

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram–Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N{sup 2} (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram–Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard–Jones fluids from N=100 to 1300 betweenmore » Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram–Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra.« less

Synthetic Aperture Sonar Processing with MMSE Estimation of Image Sample Values

DTIC Science & Technology

2016-12-01

UNCLASSIFIED/UNLIMITED 13. SUPPLEMENTARY NOTES 14. ABSTRACT MMSE (minimum mean- square error) target sample estimation using non-orthogonal basis...orthogonal, they can still be used in a minimum mean‐ square  error (MMSE)  estimator that models the object echo as a weighted sum of the multi‐aspect basis...problem.                     3    Introduction      Minimum mean‐ square  error (MMSE) estimation is applied to target imaging with synthetic aperture

The generalized formula for angular velocity vector of the moving coordinate system

NASA Astrophysics Data System (ADS)

Ermolin, Vladislav S.; Vlasova, Tatyana V.

2018-05-01

There are various ways for introducing the concept of the instantaneous angular velocity vector. In this paper we propose a method based on introducing of this concept by construction of the solution for the system of kinematic equations. These equations connect the function vectors defining the motion of the basis, and their derivatives. Necessary and sufficient conditions for the existence and uniqueness of the solution of this system are established. The instantaneous angular velocity vector is a solution of the algebraic system of equations. It is built explicitly. The derived formulas for the angular velocity vector generalize the earlier results, both for a basis of an affine oblique coordinate system and for an orthonormal basis.

The application of vector concepts on two skew lines

NASA Astrophysics Data System (ADS)

Alghadari, F.; Turmudi; Herman, T.

2018-01-01

The purpose of this study is knowing how to apply vector concepts on two skew lines in three-dimensional (3D) coordinate and its utilization. Several mathematical concepts have a related function for the other, but the related between the concept of vector and 3D have not applied in learning classroom. In fact, there are studies show that female students have difficulties in learning of 3D than male. It is because of personal spatial intelligence. The relevance of vector concepts creates both learning achievement and mathematical ability of male and female students enables to be balanced. The distance like on a cube, cuboid, or pyramid whose are drawn on the rectangular coordinates of a point in space. Two coordinate points of the lines can be created a vector. The vector of two skew lines has the shortest distance and the angle. Calculating of the shortest distance is started to create two vectors as a representation of line by vector position concept, next to determining a norm-vector of two vector which was obtained by cross-product, and then to create a vector from two combination of pair-points which was passed by two skew line, the shortest distance is scalar orthogonal projection of norm-vector on a vector which is a combination of pair-points. While calculating the angle are used two vectors as a representation of line to dot-product, and the inverse of cosine is yield. The utilization of its application on mathematics learning and orthographic projection method.

Induced solitons formed by cross-polarization coupling in a birefringent cavity fiber laser.

PubMed

Zhang, H; Tang, D Y; Zhao, L M; Tam, H Y

2008-10-15

We report on the experimental observation of induced solitons in a passively mode-locked fiber ring laser with a birefringence cavity. Owing to the cross coupling between the two orthogonal polarization components of the laser, it was found that if a soliton was formed along one cavity polarization axis, a weak soliton was also induced along the orthogonal polarization axis, and depending on the net cavity birefringence, the induced soliton could have either the same or different center wavelengths to that of the inducing soliton. Moreover, the induced soliton always had the same group velocity as that of the inducing soliton. They formed a vector soliton in the cavity. Numerical simulations confirmed the experimental observations.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

A convenient basis for the Izergin-Korepin model

NASA Astrophysics Data System (ADS)

Qiao, Yi; Zhang, Xin; Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Wen-Li; Shi, Kangjie

2018-05-01

We propose a convenient orthogonal basis of the Hilbert space for the quantum spin chain associated with the A2(2) algebra (or the Izergin-Korepin model). It is shown that compared with the original basis the monodromy-matrix elements acting on this basis take relatively simple forms, which is quite similar as that for the quantum spin chain associated with An algebra in the so-called F-basis. As an application of our general results, we present the explicit recursive expressions of the Bethe states in this basis for the Izergin-Korepin model.

AveBoost2: Boosting for Noisy Data

NASA Technical Reports Server (NTRS)

Oza, Nikunj C.

2004-01-01

AdaBoost is a well-known ensemble learning algorithm that constructs its constituent or base models in sequence. A key step in AdaBoost is constructing a distribution over the training examples to create each base model. This distribution, represented as a vector, is constructed to be orthogonal to the vector of mistakes made by the pre- vious base model in the sequence. The idea is to make the next base model's errors uncorrelated with those of the previous model. In previous work, we developed an algorithm, AveBoost, that constructed distributions orthogonal to the mistake vectors of all the previous models, and then averaged them to create the next base model s distribution. Our experiments demonstrated the superior accuracy of our approach. In this paper, we slightly revise our algorithm to allow us to obtain non-trivial theoretical results: bounds on the training error and generalization error (difference between training and test error). Our averaging process has a regularizing effect which, as expected, leads us to a worse training error bound for our algorithm than for AdaBoost but a superior generalization error bound. For this paper, we experimented with the data that we used in both as originally supplied and with added label noise-a small fraction of the data has its original label changed. Noisy data are notoriously difficult for AdaBoost to learn. Our algorithm's performance improvement over AdaBoost is even greater on the noisy data than the original data.

Manifold angles, the concept of self-similarity, and angle-enhanced bifurcation diagrams

PubMed Central

Beims, Marcus W.; Gallas, Jason A. C.

2016-01-01

Chaos and regularity are routinely discriminated by using Lyapunov exponents distilled from the norm of orthogonalized Lyapunov vectors, propagated during the temporal evolution of the dynamics. Such exponents are mean-field-like averages that, for each degree of freedom, squeeze the whole temporal evolution complexity into just a single number. However, Lyapunov vectors also contain a step-by-step record of what exactly happens with the angles between stable and unstable manifolds during the whole evolution, a big-data information permanently erased by repeated orthogonalizations. Here, we study changes of angles between invariant subspaces as observed during temporal evolution of Hénon’s system. Such angles are calculated numerically and analytically and used to characterize self-similarity of a chaotic attractor. In addition, we show how standard tools of dynamical systems may be angle-enhanced by dressing them with informations not difficult to extract. Such angle-enhanced tools reveal unexpected and practical facts that are described in detail. For instance, we present a video showing an angle-enhanced bifurcation diagram that exposes from several perspectives the complex geometrical features underlying the attractors. We believe such findings to be generic for extended classes of systems. PMID:26732416

Manifold angles, the concept of self-similarity, and angle-enhanced bifurcation diagrams

NASA Astrophysics Data System (ADS)

Beims, Marcus W.; Gallas, Jason A. C.

2016-01-01

Chaos and regularity are routinely discriminated by using Lyapunov exponents distilled from the norm of orthogonalized Lyapunov vectors, propagated during the temporal evolution of the dynamics. Such exponents are mean-field-like averages that, for each degree of freedom, squeeze the whole temporal evolution complexity into just a single number. However, Lyapunov vectors also contain a step-by-step record of what exactly happens with the angles between stable and unstable manifolds during the whole evolution, a big-data information permanently erased by repeated orthogonalizations. Here, we study changes of angles between invariant subspaces as observed during temporal evolution of Hénon’s system. Such angles are calculated numerically and analytically and used to characterize self-similarity of a chaotic attractor. In addition, we show how standard tools of dynamical systems may be angle-enhanced by dressing them with informations not difficult to extract. Such angle-enhanced tools reveal unexpected and practical facts that are described in detail. For instance, we present a video showing an angle-enhanced bifurcation diagram that exposes from several perspectives the complex geometrical features underlying the attractors. We believe such findings to be generic for extended classes of systems.

Vector rectangular-shape laser based on reduced graphene oxide interacting with a long fiber taper.

PubMed

Gao, Lei; Zhu, Tao; Huang, Wei; Zeng, Jing

2014-10-01

A vector dual-wavelength rectangular-shape laser (RSL) based on a long fiber taper deposited with reduced graphene oxide is proposed, where nonlinearity is enhanced due to a large evanescent-field-interacting length and strong field confinement of an 8 mm fiber taper with a waist diameter of 4 μm. Graphene flakes are deposited uniformly on the taper waist with light pressure effect, so this structure guarantees both excellent saturable absorption and high nonlinearity. The RSL with a repetition rate of 7.9 MHz shows fast polarization switching in two orthogonal polarization directions, and temporal and spectral characteristics are investigated.

A hyperspectral imagery anomaly detection algorithm based on local three-dimensional orthogonal subspace projection

NASA Astrophysics Data System (ADS)

Zhang, Xing; Wen, Gongjian

2015-10-01

Anomaly detection (AD) becomes increasingly important in hyperspectral imagery analysis with many practical applications. Local orthogonal subspace projection (LOSP) detector is a popular anomaly detector which exploits local endmembers/eigenvectors around the pixel under test (PUT) to construct background subspace. However, this subspace only takes advantage of the spectral information, but the spatial correlat ion of the background clutter is neglected, which leads to the anomaly detection result sensitive to the accuracy of the estimated subspace. In this paper, a local three dimensional orthogonal subspace projection (3D-LOSP) algorithm is proposed. Firstly, under the jointly use of both spectral and spatial information, three directional background subspaces are created along the image height direction, the image width direction and the spectral direction, respectively. Then, the three corresponding orthogonal subspaces are calculated. After that, each vector along three direction of the local cube is projected onto the corresponding orthogonal subspace. Finally, a composite score is given through the three direction operators. In 3D-LOSP, the anomalies are redefined as the target not only spectrally different to the background, but also spatially distinct. Thanks to the addition of the spatial information, the robustness of the anomaly detection result has been improved greatly by the proposed 3D-LOSP algorithm. It is noteworthy that the proposed algorithm is an expansion of LOSP and this ideology can inspire many other spectral-based anomaly detection methods. Experiments with real hyperspectral images have proved the stability of the detection result.

Remote beating of parallel or orthogonally polarized dual-wavelength optical carriers for 5G millimeter-wave radio-over-fiber link.

PubMed

Wang, Huai-Yung; Chi, Yu-Chieh; Lin, Gong-Ru

2016-08-08

A novel millimeter-wave radio over fiber (MMW-RoF) link at carrier frequency of 35-GHz is proposed with the use of remotely beating MMW generation from reference master and injected slave colorless laser diode (LD) carriers at orthogonally polarized dual-wavelength injection-locking. The slave colorless LD supports lasing one of the dual-wavelength master modes with orthogonal polarizations, which facilitates the single-mode direct modulation of the quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) data. Such an injected single-carrier encoding and coupled dual-carrier transmission with orthogonal polarization effectively suppresses the cross-heterodyne mode-beating intensity noise, the nonlinear modulation (NLM) and four-wave mixing (FWM) sidemodes during injection locking and fiber transmission. In 25-km single-mode fiber (SMF) based wireline system, the dual-carrier under single-mode encoding provides baseband 24-Gbit/s 64-QAM OFDM transmission with an error vector magnitude (EVM) of 8.8%, a bit error rate (BER) of 3.7 × 10^-3, a power penalty of <1.5 dB. After remotely self-beating for wireless transmission, the beat MMW carrier at 35 GHz can deliver the passband 16-QAM OFDM at 4 Gbit/s to show corresponding EVM and BER of 15.5% and 1.4 × 10^-3, respectively, after 25-km SMF and 1.6-m free-space transmission.

Orthogonal Reflections on Computer Microworlds, Constructivism, Play and Mathematical Understanding.

ERIC Educational Resources Information Center

Kieren, Thomas E.

1994-01-01

Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…

Matrix-Inversion-Free Compressed Sensing With Variable Orthogonal Multi-Matching Pursuit Based on Prior Information for ECG Signals.

PubMed

Cheng, Yih-Chun; Tsai, Pei-Yun; Huang, Ming-Hao

2016-05-19

Low-complexity compressed sensing (CS) techniques for monitoring electrocardiogram (ECG) signals in wireless body sensor network (WBSN) are presented. The prior probability of ECG sparsity in the wavelet domain is first exploited. Then, variable orthogonal multi-matching pursuit (vOMMP) algorithm that consists of two phases is proposed. In the first phase, orthogonal matching pursuit (OMP) algorithm is adopted to effectively augment the support set with reliable indices and in the second phase, the orthogonal multi-matching pursuit (OMMP) is employed to rescue the missing indices. The reconstruction performance is thus enhanced with the prior information and the vOMMP algorithm. Furthermore, the computation-intensive pseudo-inverse operation is simplified by the matrix-inversion-free (MIF) technique based on QR decomposition. The vOMMP-MIF CS decoder is then implemented in 90 nm CMOS technology. The QR decomposition is accomplished by two systolic arrays working in parallel. The implementation supports three settings for obtaining 40, 44, and 48 coefficients in the sparse vector. From the measurement result, the power consumption is 11.7 mW at 0.9 V and 12 MHz. Compared to prior chip implementations, our design shows good hardware efficiency and is suitable for low-energy applications.

Spatially Common Sparsity Based Adaptive Channel Estimation and Feedback for FDD Massive MIMO

NASA Astrophysics Data System (ADS)

Gao, Zhen; Dai, Linglong; Wang, Zhaocheng; Chen, Sheng

2015-12-01

This paper proposes a spatially common sparsity based adaptive channel estimation and feedback scheme for frequency division duplex based massive multi-input multi-output (MIMO) systems, which adapts training overhead and pilot design to reliably estimate and feed back the downlink channel state information (CSI) with significantly reduced overhead. Specifically, a non-orthogonal downlink pilot design is first proposed, which is very different from standard orthogonal pilots. By exploiting the spatially common sparsity of massive MIMO channels, a compressive sensing (CS) based adaptive CSI acquisition scheme is proposed, where the consumed time slot overhead only adaptively depends on the sparsity level of the channels. Additionally, a distributed sparsity adaptive matching pursuit algorithm is proposed to jointly estimate the channels of multiple subcarriers. Furthermore, by exploiting the temporal channel correlation, a closed-loop channel tracking scheme is provided, which adaptively designs the non-orthogonal pilot according to the previous channel estimation to achieve an enhanced CSI acquisition. Finally, we generalize the results of the multiple-measurement-vectors case in CS and derive the Cramer-Rao lower bound of the proposed scheme, which enlightens us to design the non-orthogonal pilot signals for the improved performance. Simulation results demonstrate that the proposed scheme outperforms its counterparts, and it is capable of approaching the performance bound.

Tensor calculus in polar coordinates using Jacobi polynomials

NASA Astrophysics Data System (ADS)

Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.

2016-11-01

Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.

Relativistic distribution function for particles with spin at local thermodynamical equilibrium

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

Becattini, F., E-mail: becattini@fi.infn.it; INFN Sezione di Firenze, Florence; Universität Frankfurt, Frankfurt am Main

2013-11-15

We present an extension of relativistic single-particle distribution function for weakly interacting particles at local thermodynamical equilibrium including spin degrees of freedom, for massive spin 1/2 particles. We infer, on the basis of the global equilibrium case, that at local thermodynamical equilibrium particles acquire a net polarization proportional to the vorticity of the inverse temperature four-vector field. The obtained formula for polarization also implies that a steady gradient of temperature entails a polarization orthogonal to particle momentum. The single-particle distribution function in momentum space extends the so-called Cooper–Frye formula to particles with spin 1/2 and allows us to predict theirmore » polarization in relativistic heavy ion collisions at the freeze-out. -- Highlights: •Single-particle distribution function in local thermodynamical equilibrium with spin. •Polarization of spin 1/2 particles in a fluid at local thermodynamical equilibrium. •Prediction of a new effect: a steady gradient of temperature induces a polarization. •Application to the calculation of polarization in relativistic heavy ion collisions.« less

Krylov-Subspace Recycling via the POD-Augmented Conjugate-Gradient Method

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

Carlberg, Kevin; Forstall, Virginia; Tuminaro, Ray

This paper presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric-positive-definite matrices. As opposed to typical truncation strategies used in recycling such as deflation, we propose a truncation method inspired by goal-oriented proper orthogonal decomposition (POD) from model reduction. This idea is based on the observation that model reduction aims to compute a low-dimensional subspace that contains an accurate solution; as such, we expect the proposed method to generate a low-dimensional subspace that is well suited for computing solutions that can satisfy inexact tolerances. In particular, we proposemore » specific goal-oriented POD `ingredients' that align the optimality properties of POD with the objective of Krylov-subspace recycling. To compute solutions in the resulting 'augmented' POD subspace, we propose a hybrid direct/iterative three-stage method that leverages 1) the optimal ordering of POD basis vectors, and 2) well-conditioned reduced matrices. Numerical experiments performed on solid-mechanics problems highlight the benefits of the proposed method over existing approaches for Krylov-subspace recycling.« less

Krylov-Subspace Recycling via the POD-Augmented Conjugate-Gradient Method

DOE PAGES

Carlberg, Kevin; Forstall, Virginia; Tuminaro, Ray

2016-01-01

This paper presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric-positive-definite matrices. As opposed to typical truncation strategies used in recycling such as deflation, we propose a truncation method inspired by goal-oriented proper orthogonal decomposition (POD) from model reduction. This idea is based on the observation that model reduction aims to compute a low-dimensional subspace that contains an accurate solution; as such, we expect the proposed method to generate a low-dimensional subspace that is well suited for computing solutions that can satisfy inexact tolerances. In particular, we proposemore » specific goal-oriented POD `ingredients' that align the optimality properties of POD with the objective of Krylov-subspace recycling. To compute solutions in the resulting 'augmented' POD subspace, we propose a hybrid direct/iterative three-stage method that leverages 1) the optimal ordering of POD basis vectors, and 2) well-conditioned reduced matrices. Numerical experiments performed on solid-mechanics problems highlight the benefits of the proposed method over existing approaches for Krylov-subspace recycling.« less

Setting local rank constraints by orthogonal projections for image resolution analysis: application to the determination of a low dose pharmaceutical compound.

PubMed

Boiret, Mathieu; de Juan, Anna; Gorretta, Nathalie; Ginot, Yves-Michel; Roger, Jean-Michel

2015-09-10

Raman chemical imaging provides chemical and spatial information about pharmaceutical drug product. By using resolution methods on acquired spectra, the objective is to calculate pure spectra and distribution maps of image compounds. With multivariate curve resolution-alternating least squares, constraints are used to improve the performance of the resolution and to decrease the ambiguity linked to the final solution. Non negativity and spatial local rank constraints have been identified as the most powerful constraints to be used. In this work, an alternative method to set local rank constraints is proposed. The method is based on orthogonal projections pretreatment. For each drug product compound, raw Raman spectra are orthogonally projected to a basis including all the variability from the formulation compounds other than the product of interest. Presence or absence of the compound of interest is obtained by observing the correlations between the orthogonal projected spectra and a pure spectrum orthogonally projected to the same basis. By selecting an appropriate threshold, maps of presence/absence of compounds can be set up for all the product compounds. This method appears as a powerful approach to identify a low dose compound within a pharmaceutical drug product. The maps of presence/absence of compounds can be used as local rank constraints in resolution methods, such as multivariate curve resolution-alternating least squares process in order to improve the resolution of the system. The method proposed is particularly suited for pharmaceutical systems, where the identity of all compounds in the formulations is known and, therefore, the space of interferences can be well defined. Copyright © 2015 Elsevier B.V. All rights reserved.

Spontaneous generation of vortex and coherent vector beams from a thin-slice c-cut Nd:GdVO4 laser with wide-aperture laser-diode end pumping: application to highly sensitive rotational and translational Doppler velocimetry

NASA Astrophysics Data System (ADS)

Otsuka, Kenju; Chu, Shu-Chun

2017-07-01

Selective excitation of Laguerre-Gauss modes (optical vortices: helical LG0,2 and LG0,1), reflecting their weak transverse cross-saturation of population inversions against a preceding higher-order Ince-Gauss (IG0,2) or Hermite-Gauss (HG2,1) mode, was observed in a thin-slice c-cut Nd:GdVO4 laser with wide-aperture laser-diode end pumping. Single-frequency coherent vector beams were generated through the transverse mode locking of a pair of orthogonally polarized IG2,0 and LG0,2 or HG2,1 and LG0,1 modes. Highly sensitive self-mixing rotational and translational Doppler velocimetry is demonstrated by using vortex and coherent vector beams.

PCA determination of the radiometric noise of high spectral resolution infrared observations from spectral residuals: Application to IASI

NASA Astrophysics Data System (ADS)

Serio, C.; Masiello, G.; Camy-Peyret, C.; Jacquette, E.; Vandermarcq, O.; Bermudo, F.; Coppens, D.; Tobin, D.

2018-02-01

The problem of characterizing and estimating the instrumental or radiometric noise of satellite high spectral resolution infrared spectrometers directly from Earth observations is addressed in this paper. An approach has been developed, which relies on the Principal Component Analysis (PCA) with a suitable criterion to select the optimal number of PC scores. Different selection criteria have been set up and analysed, which is based on the estimation theory of Least Squares and/or Maximum Likelihood Principle. The approach is independent of any forward model and/or radiative transfer calculations. The PCA is used to define an orthogonal basis, which, in turn, is used to derive an optimal linear reconstruction of the observations. The residual vector that is the observation vector minus the calculated or reconstructed one is then used to estimate the instrumental noise. It will be shown that the use of the spectral residuals to assess the radiometric instrumental noise leads to efficient estimators, which are largely independent of possible departures of the true noise from that assumed a priori to model the observational covariance matrix. Application to the Infrared Atmospheric Sounder Interferometer (IASI) has been considered. A series of case studies has been set up, which make use of IASI observations. As a major result, the analysis confirms the high stability and radiometric performance of IASI. The approach also proved to be efficient in characterizing noise features due to mechanical micro-vibrations of the beam splitter of the IASI instrument.

Quantum secret sharing using orthogonal multiqudit entangled states

NASA Astrophysics Data System (ADS)

Bai, Chen-Ming; Li, Zhi-Hui; Liu, Cheng-Ji; Li, Yong-Ming

2017-12-01

In this work, we investigate the distinguishability of orthogonal multiqudit entangled states under restricted local operations and classical communication. According to these properties, we propose a quantum secret sharing scheme to realize three types of access structures, i.e., the ( n, n)-threshold, the restricted (3, n)-threshold and restricted (4, n)-threshold schemes (called LOCC-QSS scheme). All cooperating players in the restricted threshold schemes are from two disjoint groups. In the proposed protocol, the participants use the computational basis measurement and classical communication to distinguish between those orthogonal states and reconstruct the original secret. Furthermore, we also analyze the security of our scheme in four primary quantum attacks and give a simple encoding method in order to better prevent the participant conspiracy attack.

Generalized sidelobe canceller beamforming method for ultrasound imaging.

PubMed

Wang, Ping; Li, Na; Luo, Han-Wu; Zhu, Yong-Kun; Cui, Shi-Gang

2017-03-01

A modified generalized sidelobe canceller (IGSC) algorithm is proposed to enhance the resolution and robustness against the noise of the traditional generalized sidelobe canceller (GSC) and coherence factor combined method (GSC-CF). In the GSC algorithm, weighting vector is divided into adaptive and non-adaptive parts, while the non-adaptive part does not block all the desired signal. A modified steer vector of the IGSC algorithm is generated by the projection of the non-adaptive vector on the signal space constructed by the covariance matrix of received data. The blocking matrix is generated based on the orthogonal complementary space of the modified steer vector and the weighting vector is updated subsequently. The performance of IGSC was investigated by simulations and experiments. Through simulations, IGSC outperformed GSC-CF in terms of spatial resolution by 0.1 mm regardless there is noise or not, as well as the contrast ratio respect. The proposed IGSC can be further improved by combining with CF. The experimental results also validated the effectiveness of the proposed algorithm with dataset provided by the University of Michigan.

Quantum coherent switch utilizing commensurate nanoelectrode and charge density periodicities

DOEpatents

Harrison,; Neil, Singleton [Santa Fe, NM; John, Migliori [Los Alamos, NM; Albert, [Santa Fe, NM

2008-08-05

A quantum coherent switch having a substrate formed from a density wave (DW) material capable of having a periodic electron density modulation or spin density modulation, a dielectric layer formed onto a surface of the substrate that is orthogonal to an intrinsic wave vector of the DW material; and structure for applying an external spatially periodic electrostatic potential over the dielectric layer.

Measuring the orthogonality error of coil systems

USGS Publications Warehouse

Heilig, B.; Csontos, A.; Pajunpää, K.; White, Tim; St. Louis, B.; Calp, D.

2012-01-01

Recently, a simple method was proposed for the determination of pitch angle between two coil axes by means of a total field magnetometer. The method is applicable when the homogeneous volume in the centre of the coil system is large enough to accommodate the total field sensor. Orthogonality of calibration coil systems used for calibrating vector magnetometers can be attained by this procedure. In addition, the method can be easily automated and applied to the calibration of delta inclination–delta declination (dIdD) magnetometers. The method was tested by several independent research groups, having a variety of test equipment, and located at differing geomagnetic observatories, including: Nurmijärvi, Finland; Hermanus, South Africa; Ottawa, Canada; Tihany, Hungary. This paper summarizes the test results, and discusses the advantages and limitations of the method.

Ground states of partially connected binary neural networks

NASA Technical Reports Server (NTRS)

Baram, Yoram

1990-01-01

Neural networks defined by outer products of vectors over (-1, 0, 1) are considered. Patterns over (-1, 0, 1) define by their outer products partially connected neural networks consisting of internally strongly connected, externally weakly connected subnetworks. Subpatterns over (-1, 1) define subnetworks, and their combinations that agree in the common bits define permissible words. It is shown that the permissible words are locally stable states of the network, provided that each of the subnetworks stores mutually orthogonal subwords, or, at most, two subwords. It is also shown that when each of the subnetworks stores two mutually orthogonal binary subwords at most, the permissible words, defined as the combinations of the subwords (one corresponding to each subnetwork), that agree in their common bits are the unique ground states of the associated energy function.

Lazy orbits: An optimization problem on the sphere

NASA Astrophysics Data System (ADS)

Vincze, Csaba

2018-01-01

Non-transitive subgroups of the orthogonal group play an important role in the non-Euclidean geometry. If G is a closed subgroup in the orthogonal group such that the orbit of a single Euclidean unit vector does not cover the (Euclidean) unit sphere centered at the origin then there always exists a non-Euclidean Minkowski functional such that the elements of G preserve the Minkowskian length of vectors. In other words the Minkowski geometry is an alternative of the Euclidean geometry for the subgroup G. It is rich of isometries if G is "close enough" to the orthogonal group or at least to one of its transitive subgroups. The measure of non-transitivity is related to the Hausdorff distances of the orbits under the elements of G to the Euclidean sphere. Its maximum/minimum belongs to the so-called lazy/busy orbits, i.e. they are the solutions of an optimization problem on the Euclidean sphere. The extremal distances allow us to characterize the reducible/irreducible subgroups. We also formulate an upper and a lower bound for the ratio of the extremal distances. As another application of the analytic tools we introduce the rank of a closed non-transitive group G. We shall see that if G is of maximal rank then it is finite or reducible. Since the reducible and the finite subgroups form two natural prototypes of non-transitive subgroups, the rank seems to be a fundamental notion in their characterization. Closed, non-transitive groups of rank n - 1 will be also characterized. Using the general results we classify all their possible types in lower dimensional cases n = 2 , 3 and 4. Finally we present some applications of the results to the holonomy group of a metric linear connection on a connected Riemannian manifold.

Reduced basis technique for evaluating the sensitivity coefficients of the nonlinear tire response

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Tanner, John A.; Peters, Jeanne M.

1992-01-01

An efficient reduced-basis technique is proposed for calculating the sensitivity of nonlinear tire response to variations in the design variables. The tire is modeled using a 2-D, moderate rotation, laminated anisotropic shell theory, including the effects of variation in material and geometric parameters. The vector of structural response and its first-order and second-order sensitivity coefficients are each expressed as a linear combination of a small number of basis vectors. The effectiveness of the basis vectors used in approximating the sensitivity coefficients is demonstrated by a numerical example involving the Space Shuttle nose-gear tire, which is subjected to uniform inflation pressure.

Multiple-image encryption based on double random phase encoding and compressive sensing by using a measurement array preprocessed with orthogonal-basis matrices

NASA Astrophysics Data System (ADS)

Zhang, Luozhi; Zhou, Yuanyuan; Huo, Dongming; Li, Jinxi; Zhou, Xin

2018-09-01

A method is presented for multiple-image encryption by using the combination of orthogonal encoding and compressive sensing based on double random phase encoding. As an original thought in optical encryption, it is demonstrated theoretically and carried out by using the orthogonal-basis matrices to build a modified measurement array, being projected onto the images. In this method, all the images can be compressed in parallel into a stochastic signal and be diffused to be a stationary white noise. Meanwhile, each single-image can be separately reestablished by adopting a proper decryption key combination through the block-reconstruction rather than the entire-rebuilt, for its costs of data and decryption time are greatly decreased, which may be promising both in multi-user multiplexing and huge-image encryption/decryption. Besides, the security of this method is characterized by using the bit-length of key, and the parallelism is investigated as well. The simulations and discussions are also made on the effects of decryption as well as the correlation coefficient by using a series of sampling rates, occlusion attacks, keys with various error rates, etc.

Critical Analysis of the Mathematical Formalism of Theoretical Physics. II. Foundations of Vector Calculus

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2014-03-01

A critical analysis of the foundations of standard vector calculus is proposed. The methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is proved that the vector calculus is incorrect theory because: (a) it is not based on a correct methodological basis - the unity of formal logic and of rational dialectics; (b) it does not contain the correct definitions of ``movement,'' ``direction'' and ``vector'' (c) it does not take into consideration the dimensions of physical quantities (i.e., number names, denominate numbers, concrete numbers), characterizing the concept of ''physical vector,'' and, therefore, it has no natural-scientific meaning; (d) operations on ``physical vectors'' and the vector calculus propositions relating to the ''physical vectors'' are contrary to formal logic.

Linear and nonlinear properties of numerical methods for the rotating shallow water equations

NASA Astrophysics Data System (ADS)

Eldred, Chris

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. It is desirable that numerical models posses similar properties, and the prototypical example of such a scheme is the 1981 Arakawa and Lamb (AL81) staggered (C-grid) total energy and potential enstrophy conserving scheme, based on the vector invariant form of the continuous equations. However, this scheme is restricted to a subset of logically square, orthogonal grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos and others) and Discrete Exterior Calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp and others). It is also possible to obtain these properties (along with arguably superior wave dispersion properties) through the use of a collocated (Z-grid) scheme based on the vorticity-divergence form of the continuous equations. Unfortunately, existing examples of these schemes in the literature for general, spherical grids either contain computational modes; or do not conserve total energy and potential enstrophy. This dissertation extends an existing scheme for planar grids to spherical grids, through the use of Nambu brackets (as pioneered by Rick Salmon). To compare these two schemes, the linear modes (balanced states, stationary modes and propagating modes; with and without dissipation) are examined on both uniform planar grids (square, hexagonal) and quasi-uniform spherical grids (geodesic, cubed-sphere). In addition to evaluating the linear modes, the results of the two schemes applied to a set of standard shallow water test cases and a recently developed forced-dissipative turbulence test case from John Thuburn (intended to evaluate the ability the suitability of schemes as the basis for a climate model) on both hexagonal-pentagonal icosahedral grids and cubed-sphere grids are presented. Finally, some remarks and thoughts about the suitability of these two schemes as the basis for atmospheric dynamical development are given.

Polytopic vector analysis in igneous petrology: Application to lunar petrogenesis

NASA Technical Reports Server (NTRS)

Shervais, John W.; Ehrlich, R.

1993-01-01

Lunar samples represent a heterogeneous assemblage of rocks with complex inter-relationships that are difficult to decipher using standard petrogenetic approaches. These inter-relationships reflect several distinct petrogenetic trends as well as thermomechanical mixing of distinct components. Additional complications arise from the unequal quality of chemical analyses and from the fact that many samples (e.g., breccia clasts) are too small to be representative of the system from which they derived. Polytopic vector analysis (PVA) is a multi-variate procedure used as a tool for exploratory data analysis. PVA allows the analyst to classify samples and clarifies relationships among heterogenous samples with complex petrogenetic histories. It differs from orthogonal factor analysis in that it uses non-orthogonal multivariate sample vectors to extract sample endmember compositions. The output from a Q-mode (sample based) factor analysis is the initial step in PVA. The Q-mode analysis, using criteria established by Miesch and Klovan and Miesch, is used to determine the number of endmembers in the data system. The second step involves determination of endmembers and mixing proportions with all output expressed in the same geochemical variable as the input. The composition of endmembers is derived by analysis of the variability of the data set. Endmembers need not be present in the data set, nor is it necessary for their composition to be known a priori. A set of any endmembers defines a 'polytope' or classification figure (triangle for a three component system, tetrahedron for a four component system, a 'five-tope' in four dimensions for five component system, et cetera).

Semiautomated skeletonization of the pulmonary arterial tree in micro-CT images

NASA Astrophysics Data System (ADS)

Hanger, Christopher C.; Haworth, Steven T.; Molthen, Robert C.; Dawson, Christopher A.

2001-05-01

We present a simple and robust approach that utilizes planar images at different angular rotations combined with unfiltered back-projection to locate the central axes of the pulmonary arterial tree. Three-dimensional points are selected interactively by the user. The computer calculates a sub- volume unfiltered back-projection orthogonal to the vector connecting the two points and centered on the first point. Because more x-rays are absorbed at the thickest portion of the vessel, in the unfiltered back-projection, the darkest pixel is assumed to be the center of the vessel. The computer replaces this point with the newly computer-calculated point. A second back-projection is calculated around the original point orthogonal to a vector connecting the newly-calculated first point and user-determined second point. The darkest pixel within the reconstruction is determined. The computer then replaces the second point with the XYZ coordinates of the darkest pixel within this second reconstruction. Following a vector based on a moving average of previously determined 3- dimensional points along the vessel's axis, the computer continues this skeletonization process until stopped by the user. The computer estimates the vessel diameter along the set of previously determined points using a method similar to the full width-half max algorithm. On all subsequent vessels, the process works the same way except that at each point, distances between the current point and all previously determined points along different vessels are determined. If the difference is less than the previously estimated diameter, the vessels are assumed to branch. This user/computer interaction continues until the vascular tree has been skeletonized.

Research on polarization vector characteristics in a microfiber-based graphene fiber laser

NASA Astrophysics Data System (ADS)

Han, Mengmeng; Zhang, Shumin; Li, Xingliang; Han, Huiyun; Liu, Jingmin; Yan, Dan

2016-11-01

We experimentally investigated the polarization vector characteristics in an Er-doped fiber laser based on graphene that was deposited on microfiber. A variety of dynamic states, including polarization locked fundamental soliton, and polarization domain wall square pulses and their harmonic mode locked counterparts have all been observed with different pump powers and polarization states. These results indicated that the microfiber-based graphene not only could act as a saturable absorber but also could provide high nonlinearity, which is favorable for the cross coupling between the two orthogonal polarization components. It was worth to mention that it is the first time to obtain the polarization domain wall solitons in a mode locked fiber laser.

Constrained multibody system dynamics: An automated approach

NASA Technical Reports Server (NTRS)

Kamman, J. W.; Huston, R. L.

1982-01-01

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.

The Influence Function of Principal Component Analysis by Self-Organizing Rule.

PubMed

Higuchi; Eguchi

1998-07-28

This article is concerned with a neural network approach to principal component analysis (PCA). An algorithm for PCA by the self-organizing rule has been proposed and its robustness observed through the simulation study by Xu and Yuille (1995). In this article, the robustness of the algorithm against outliers is investigated by using the theory of influence function. The influence function of the principal component vector is given in an explicit form. Through this expression, the method is shown to be robust against any directions orthogonal to the principal component vector. In addition, a statistic generated by the self-organizing rule is proposed to assess the influence of data in PCA.

Alignment of a vector magnetometer to an optical prism

NASA Astrophysics Data System (ADS)

Dietrich, M. R.; Bailey, K. G.; O'Connor, T. P.

2017-05-01

A method for alignment of a vector magnetometer to a rigidly attached prism is presented. This enables optical comparison of the magnetometer axes to physical surfaces in the apparatus, and thus an absolute determination of the magnetic field direction in space. This is in contrast with more common techniques, which focus on precise determination of the relative angles between magnetometer axes, and so are more suited to measuring differences in the direction of magnetic fields. Here we demonstrate precision better than 500 μrad on a fluxgate magnetometer, which also gives the coil orthogonality errors to a similar precision. The relative sensitivity of the three axes is also determined, with a precision of about 5 ×10 -4 .

Magnetic measurement of soft magnetic composites material under 3D SVPWM excitation

NASA Astrophysics Data System (ADS)

Zhang, Changgeng; Jiang, Baolin; Li, Yongjian; Yang, Qingxin

2018-05-01

The magnetic properties measurement and analysis of soft magnetic material under the rotational space-vector pulse width modulation (SVPWM) excitation are key factors in design and optimization of the adjustable speed motor. In this paper, a three-dimensional (3D) magnetic properties testing system fit for SVPWM excitation is built, which includes symmetrical orthogonal excitation magnetic circuit and cubic field-metric sensor. Base on the testing system, the vector B and H loci of soft magnetic composite (SMC) material under SVPWM excitation are measured and analyzed by proposed 3D SVPWM control method. Alternating and rotating core losses under various complex excitation with different magnitude modulation ratio are calculated and compared.

A discrimination method for the detection of pneumonia using chest radiograph.

PubMed

Noor, Norliza Mohd; Rijal, Omar Mohd; Yunus, Ashari; Abu-Bakar, S A R

2010-03-01

This paper presents a statistical method for the detection of lobar pneumonia when using digitized chest X-ray films. Each region of interest was represented by a vector of wavelet texture measures which is then multiplied by the orthogonal matrix Q(2). The first two elements of the transformed vectors were shown to have a bivariate normal distribution. Misclassification probabilities were estimated using probability ellipsoids and discriminant functions. The result of this study recommends the detection of pneumonia by constructing probability ellipsoids or discriminant function using maximum energy and maximum column sum energy texture measures where misclassification probabilities were less than 0.15. 2009 Elsevier Ltd. All rights reserved.

Navigational potential of e-vector sensing by marine animals

NASA Astrophysics Data System (ADS)

Waterman, Talbot H.

1993-02-01

This essay documents an informal talk about the central theme in the author's research career. That has mainly related to the visual physiology and orientation of aquatic animals, particularly with regard to underwater polarized light. This required pioneer measurements of underwater polarized light patterns, proof that oriented behavior could be determined by e- vector direction independently of intensity patterns or other secondary clues and a demonstration of the retinal dichroic mechanism involved, at least in crustacean compound eyes. The relevant visual data processing by two orthogonal channels was also analyzed with regard to oriented swimming behavior. Some current research by others and major unsolved problems are mentioned and the relevant part of the author's bibliography is appended.

Strategy for Improved Representation of Magnetospheric Electric Potential Structure on a Polar-Capped Ionosphere

NASA Astrophysics Data System (ADS)

Schulz, M.

2016-12-01

In some simple models of magnetospheric electrodynamics [e.g., Volland, Ann. Géophys., 31, 159-173, 1975], the normal component of the convection electric field is discontinuous across the boundary between closed and open magnetic field lines, and this discontinuity facilitates the formation of auroral arcs there. The requisite discontinuity in E is achieved by making the scalar potential proportional to a positive power (typically 1 or 2) of L on closed field lines and to a negative power (typically -1/2) of L on open (i.e., polar-cap) field lines. This suggests that it may be advantageous to construct more realistic (and thus more complicated) empirical magnetospheric and ionospheric electric-field models from superpositions of mutually orthogonal (or not) vector basis functions having this same analytical property (i.e., discontinuity at L = L*, the boundary surface between closed and open magnetic field lines). The present work offers a few examples of such constructions. A major challenge in this project has been to devise a coordinate system that simplifies the required analytical expansions of electric scalar potentials and accommodates the anti-sunward offset of each polar-cap boundary's centroid with respect to the corresponding magnetic pole. For circular northern and southern polar caps containing equal amounts of magnetic flux, one can imagine a geometrical construction of nested circular (but non-concentric) contours of constant quasi-latitude whose centers converge toward the magnetic poles as the contours themselves approach the magnetic equator. For more general polar-cap shapes and (in any case) to assure mutual orthogonality of respective coordinate surfaces on a spherical ionosphere, a formulation based on harmonic coordinates (expanded from eigen-solutions of the two-dimensional Laplace equation) may be preferable.

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

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

A simple suboptimal least-squares algorithm for attitude determination with multiple sensors

NASA Technical Reports Server (NTRS)

Brozenec, Thomas F.; Bender, Douglas J.

1994-01-01

Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is faster than all but a similarly specialized version of the QUEST algorithm. We also introduce a novel measurement averaging technique which reduces the n-measurement case to the two measurement case for our particular application, a star tracker and earth sensor mounted on an earth-pointed geosynchronous communications satellite. Using this technique, many n-measurement problems reduce to less than or equal to 3 measurements; this reduces the amount of required calculation without significant degradation in accuracy. Finally, we present the results of some tests which compare the least-squares algorithm with the QUEST and FOAM algorithms in the two-measurement case. For our example case, all three algorithms performed with similar accuracy.

A new transform for the analysis of complex fractionated atrial electrograms

PubMed Central

2011-01-01

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

Dynamic trapping of a polarization rotation vector soliton in a fiber laser.

PubMed

Liu, Meng; Luo, Ai-Ping; Luo, Zhi-Chao; Xu, Wen-Cheng

2017-01-15

Ultrafast fiber laser, as a dissipative nonlinear optical system, plays an important role in investigating various nonlinear phenomena and soliton dynamics. Vector features of solitons, including polarization locked and polarization rotation vector solitons (PRVSs), are interesting nonlinear dynamics in ultrafast fiber lasers. Herein, we experimentally reveal the trapping characteristics of PRVSs for the first time, to the best of our best knowledge. We show that, for the conventional soliton trapping in the ultrafast fiber laser, the soliton central wavelengths of the two polarization components are constant at the laser output port. However, it is found that the dynamic trapping can be observed for the PRVS. That is, the peak frequencies along the two orthogonal polarization directions are dynamically alternating, depending on the relative intensities of the two polarization components. The obtained results would further unveil the physical mechanism of PRVSs.

A straightforward characterization of non-modal effects from the evolution of linear dynamical systems

NASA Astrophysics Data System (ADS)

Arratia, Cristobal

2014-11-01

A simple construction will be shown, which reveals a general property satisfied by the evolution in time of a state vector composed by a superposition of orthogonal eigenmodes of a linear dynamical system. This property results from the conservation of the inner product between such state vectors evolving forward and backwards in time, and it can be simply evaluated from the state vector and its first and second time derivatives. This provides an efficient way to characterize, instantaneously along any specific phase-space trajectory of the linear system, the relevance of the non-normality of the linearized Navier-Stokes operator on the energy (or any other norm) gain or decay of small perturbations. Examples of this characterization applied to stationary or time dependent base flows will be shown. CONICYT, Concurso de Apoyo al Retorno de Investigadores del Extranjero, folio 821320055.

Measurement of the topological charge and index of vortex vector optical fields with a space-variant half-wave plate.

PubMed

Liu, Gui-Geng; Wang, Ke; Lee, Yun-Han; Wang, Dan; Li, Ping-Ping; Gou, Fangwang; Li, Yongnan; Tu, Chenghou; Wu, Shin-Tson; Wang, Hui-Tian

2018-02-15

Vortex vector optical fields (VVOFs) refer to a kind of vector optical field with an azimuth-variant polarization and a helical phase, simultaneously. Such a VVOF is defined by the topological index of the polarization singularity and the topological charge of the phase vortex. We present a simple method to measure the topological charge and index of VVOFs by using a space-variant half-wave plate (SV-HWP). The geometric phase grating of the SV-HWP diffracts a VVOF into ±1 orders with orthogonally left- and right-handed circular polarizations. By inserting a polarizer behind the SV-HWP, the two circular polarization states project into the linear polarization and then interfere with each other to form the interference pattern, which enables the direct measurement of the topological charge and index of VVOFs.

Extrema of mass, first law of black hole mechanics, and a staticity theorem in Einstein-Maxwell-axion-dilaton gravity

NASA Astrophysics Data System (ADS)

Rogatko, Marek

1998-08-01

Using the ADM formulation of the Einstein-Maxwell axion-dilaton gravity we derive the formulas for the variation of mass and other asymptotic conserved quantities in the theory under consideration. Generalizing this kind of reasoning to the initial data for the manifold with an interior boundary we get the generalized first law of black hole mechanics. We consider an asymptotically flat solution to the Einstein-Maxwell axion-dilaton gravity describing a black hole with a Killing vector field timelike at infinity, the horizon of which comprises a bifurcate Killing horizon with a bifurcate surface. Supposing that the Killing vector field is asymptotically orthogonal to the static hypersurface with boundary S and a compact interior, we find that the solution is static in the exterior world, when the timelike vector field is normal to the horizon and has vanishing electric and axion-electric fields on static slices.

An efficient calibration method for SQUID measurement system using three orthogonal Helmholtz coils

NASA Astrophysics Data System (ADS)

Hua, Li; Shu-Lin, Zhang; Chao-Xiang, Zhang; Xiang-Yan, Kong; Xiao-Ming, Xie

2016-06-01

For a practical superconducting quantum interference device (SQUID) based measurement system, the Tesla/volt coefficient must be accurately calibrated. In this paper, we propose a highly efficient method of calibrating a SQUID magnetometer system using three orthogonal Helmholtz coils. The Tesla/volt coefficient is regarded as the magnitude of a vector pointing to the normal direction of the pickup coil. By applying magnetic fields through a three-dimensional Helmholtz coil, the Tesla/volt coefficient can be directly calculated from magnetometer responses to the three orthogonally applied magnetic fields. Calibration with alternating current (AC) field is normally used for better signal-to-noise ratio in noisy urban environments and the results are compared with the direct current (DC) calibration to avoid possible effects due to eddy current. In our experiment, a calibration relative error of about 6.89 × 10-4 is obtained, and the error is mainly caused by the non-orthogonality of three axes of the Helmholtz coils. The method does not need precise alignment of the magnetometer inside the Helmholtz coil. It can be used for the multichannel magnetometer system calibration effectively and accurately. Project supported by the “Strategic Priority Research Program (B)” of the Chinese Academy of Sciences (Grant No. XDB04020200) and the Shanghai Municipal Science and Technology Commission Project, China (Grant No. 15DZ1940902).

Three-dimensional flow field measurements in a radial inflow turbine scroll using LDV

NASA Technical Reports Server (NTRS)

Malak, M. F.; Hamed, A.; Tabakoff, W.

1986-01-01

The results of an experimental study of the three-dimensional flow field in a radial inflow turbine scroll are presented. A two-color LDV system was used in the measurement of three orthogonal velocity components at 758 points located throughout the scroll and the unvaned portion of the nozzle. The cold flow experimental results are presented for through-flow velocity contours and the cross velocity vectors.

Increasing Slew Performance of Reaction Wheel Attitude Control Systems

DTIC Science & Technology

2013-09-01

vectors in any arbitrary direction creates the momentum envelope (Chapter IV). The shape of the reaction wheel momentum envelope is a polyhedron [15...performance. This procedural limitation further reduces the operable reaction wheel momentum space polyhedron to the largest inscribed sphere, which...respective plane. These minima are also the global minima, each marked in magenta. The four-wheel polyhedron is again shown in three orthogonal views in

Test spaces and characterizations of quadratic spaces

NASA Astrophysics Data System (ADS)

Dvurečenskij, Anatolij

1996-10-01

We show that a test space consisting of nonzero vectors of a quadratic space E and of the set all maximal orthogonal systems in E is algebraic iff E is Dacey or, equivalently, iff E is orthomodular. In addition, we present another orthomodularity criteria of quadratic spaces, and using the result of Solèr, we show that they can imply that E is a real, complex, or quaternionic Hilbert space.

Development of Advanced Constitutive Models for Plain and Reinforced Concrete.

DTIC Science & Technology

1986-04-01

V * . . . . .. .. ,.*,*..~.*,..*.*.*..*.*..~...*.,*. - -. .. . . d .. . . . . . . . . . ~ --. % S ...surface, Figure D .5, be denoted as [ v ( s )]. Further, let ef (i = 1 to 3) denote the unit orthogonal base vectors of a rectangular Cartesian reference system...astic parts according to d .. = de. d ?. ( D -2) ij Ij I j one obtains d ? =1 n + S ni [ v ( ] ( D -3) where s i • e n, n 9 e ( D -4) In the case of

Reconstructing householder vectors from Tall-Skinny QR

DOE PAGES

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

2015-08-05

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

Tensor manifold-based extreme learning machine for 2.5-D face recognition

NASA Astrophysics Data System (ADS)

Chong, Lee Ying; Ong, Thian Song; Teoh, Andrew Beng Jin

2018-01-01

We explore the use of the Gabor regional covariance matrix (GRCM), a flexible matrix-based descriptor that embeds the Gabor features in the covariance matrix, as a 2.5-D facial descriptor and an effective means of feature fusion for 2.5-D face recognition problems. Despite its promise, matching is not a trivial problem for GRCM since it is a special instance of a symmetric positive definite (SPD) matrix that resides in non-Euclidean space as a tensor manifold. This implies that GRCM is incompatible with the existing vector-based classifiers and distance matchers. Therefore, we bridge the gap of the GRCM and extreme learning machine (ELM), a vector-based classifier for the 2.5-D face recognition problem. We put forward a tensor manifold-compliant ELM and its two variants by embedding the SPD matrix randomly into reproducing kernel Hilbert space (RKHS) via tensor kernel functions. To preserve the pair-wise distance of the embedded data, we orthogonalize the random-embedded SPD matrix. Hence, classification can be done using a simple ridge regressor, an integrated component of ELM, on the random orthogonal RKHS. Experimental results show that our proposed method is able to improve the recognition performance and further enhance the computational efficiency.

A 3D Ginibre Point Field

NASA Astrophysics Data System (ADS)

Kargin, Vladislav

2018-06-01

We introduce a family of three-dimensional random point fields using the concept of the quaternion determinant. The kernel of each field is an n-dimensional orthogonal projection on a linear space of quaternionic polynomials. We find explicit formulas for the basis of the orthogonal quaternion polynomials and for the kernel of the projection. For number of particles n → ∞, we calculate the scaling limits of the point field in the bulk and at the center of coordinates. We compare our construction with the previously introduced Fermi-sphere point field process.

A New and General Formulation of the Parametric HFGMC Micromechanical Method for Three-Dimensional Multi-Phase Composites

NASA Technical Reports Server (NTRS)

Haj-Ali, Rami; Aboudi, Jacob

2012-01-01

The recent two-dimensional (2-D) parametric formulation of the high fidelity generalized method of cells (HFGMC) reported by the authors is generalized for the micromechanical analysis of three-dimensional (3-D) multiphase composites with periodic microstructure. Arbitrary hexahedral subcell geometry is developed to discretize a triply periodic repeating unit-cell (RUC). Linear parametric-geometric mapping is employed to transform the arbitrary hexahedral subcell shapes from the physical space to an auxiliary orthogonal shape, where a complete quadratic displacement expansion is performed. Previously in the 2-D case, additional three equations are needed in the form of average moments of equilibrium as a result of the inclusion of the bilinear terms. However, the present 3-D parametric HFGMC formulation eliminates the need for such additional equations. This is achieved by expressing the coefficients of the full quadratic polynomial expansion of the subcell in terms of the side or face average-displacement vectors. The 2-D parametric and orthogonal HFGMC are special cases of the present 3-D formulation. The continuity of displacements and tractions, as well as the equilibrium equations, are imposed in the average (integral) sense as in the original HFGMC formulation. Each of the six sides (faces) of a subcell has an independent average displacement micro-variable vector which forms an energy-conjugate pair with the transformed average-traction vector. This allows generating symmetric stiffness matrices along with internal resisting vectors for the subcells which enhances the computational efficiency. The established new parametric 3-D HFGMC equations are formulated and solution implementations are addressed. Several applications for triply periodic 3-D composites are presented to demonstrate the general capability and varsity of the present parametric HFGMC method for refined micromechanical analysis by generating the spatial distributions of local stress fields. These applications include triply periodic composites with inclusions in the form of a cavity, spherical inclusion, ellipsoidal inclusion, discontinuous aligned short fiber. A 3-D repeating unit-cell for foam material composite is simulated.

Validation of a method to measure the vector fidelity of triaxial vector sensors

NASA Astrophysics Data System (ADS)

De Freitas, J. M.

2018-06-01

A method to measure the misalignment angles and vector fidelity of a mutually orthogonal arrangement of triaxial accelerometers has been validated by introducing known misalignments into the measurement procedure. The method is based on the excitation of all three accelerometers in equal measure and the determination of the second order responsivity tensor as a metric. The sensor axis misalignment angles measured using a sensor rotation technique as a reference were 1.49°  ±  0.05°, 0.63°  ±  0.02°, and 0.78°  ±  0.04°. The resolution of the new approach against the reference was 0.03° with an accuracy of 0.2° and maximum deviation of 0.4°. An ellipticity tensor β that characterises the extent to which a triaxial system preserves the input polarisation state purity was introduced. In a careful laboratory arrangement, up to 98% input polarisation state purity was shown to be maintained. It is recommended that documentation on commercial and research grade high-precision triaxial sensor systems should give the responsivity matrix . This technique will improve the range of vector fidelity measurement tools for triaxial accelerometers and other vector sensors such as magnetometers, gyroscopes and acoustic vector sensors.

On sufficient statistics of least-squares superposition of vector sets.

PubMed

Konagurthu, Arun S; Kasarapu, Parthan; Allison, Lloyd; Collier, James H; Lesk, Arthur M

2015-06-01

The problem of superposition of two corresponding vector sets by minimizing their sum-of-squares error under orthogonal transformation is a fundamental task in many areas of science, notably structural molecular biology. This problem can be solved exactly using an algorithm whose time complexity grows linearly with the number of correspondences. This efficient solution has facilitated the widespread use of the superposition task, particularly in studies involving macromolecular structures. This article formally derives a set of sufficient statistics for the least-squares superposition problem. These statistics are additive. This permits a highly efficient (constant time) computation of superpositions (and sufficient statistics) of vector sets that are composed from its constituent vector sets under addition or deletion operation, where the sufficient statistics of the constituent sets are already known (that is, the constituent vector sets have been previously superposed). This results in a drastic improvement in the run time of the methods that commonly superpose vector sets under addition or deletion operations, where previously these operations were carried out ab initio (ignoring the sufficient statistics). We experimentally demonstrate the improvement our work offers in the context of protein structural alignment programs that assemble a reliable structural alignment from well-fitting (substructural) fragment pairs. A C++ library for this task is available online under an open-source license.

Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. Part I. Application of the Huzinaga equation.

PubMed

Ferenczy, György G

2013-04-05

Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods. Copyright © 2012 Wiley Periodicals, Inc.

An orthogonal oriented quadrature hexagonal image pyramid

NASA Technical Reports Server (NTRS)

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

1987-01-01

An image pyramid has been developed with basis functions that are orthogonal, self-similar, and localized in space, spatial frequency, orientation, and phase. The pyramid operates on a hexagonal sample lattice. The set of seven basis functions consist of three even high-pass kernels, three odd high-pass kernels, and one low-pass kernel. The three even kernels are identified when rotated by 60 or 120 deg, and likewise for the odd. The seven basis functions occupy a point and a hexagon of six nearest neighbors on a hexagonal sample lattice. At the lowest level of the pyramid, the input lattice is the image sample lattice. At each higher level, the input lattice is provided by the low-pass coefficients computed at the previous level. At each level, the output is subsampled in such a way as to yield a new hexagonal lattice with a spacing sq rt 7 larger than the previous level, so that the number of coefficients is reduced by a factor of 7 at each level. The relationship between this image code and the processing architecture of the primate visual cortex is discussed.

Multidimensional signaling via wavelet packets

NASA Astrophysics Data System (ADS)

Lindsey, Alan R.

1995-04-01

This work presents a generalized signaling strategy for orthogonally multiplexed communication. Wavelet packet modulation (WPM) employs the basis functions from an arbitrary pruning of a full dyadic tree structured filter bank as orthogonal pulse shapes for conventional QAM symbols. The multi-scale modulation (MSM) and M-band wavelet modulation (MWM) schemes which have been recently introduced are handled as special cases, with the added benefit of an entire library of potentially superior sets of basis functions. The figures of merit are derived and it is shown that the power spectral density is equivalent to that for QAM (in fact, QAM is another special case) and hence directly applicable in existing systems employing this standard modulation. Two key advantages of this method are increased flexibility in time-frequency partitioning and an efficient all-digital filter bank implementation, making the WPM scheme more robust to a larger set of interferences (both temporal and sinusoidal) and computationally attractive as well.

Diffraction Theory for Polygonal Apertures

DTIC Science & Technology

1988-07-01

and utilized oblate spheroidal vector wave functions, and Nomura and Katsura (1955), who employed an expansion of the hypergeometric polynomial ...21 2 - 1 4, 2 - 1 3 4k3 - 3k 8 3 - 4 factor relates directly to the orthogonality relations for the Chebyshev polynomials given below. I T(Q TieQdk...convergence. 3.1.2.2 Gaussian Illuminated Corner In the sample calculation just discussed we discovered some of the basic characteristics of the GBE

Advances in Mixed Signal Processing for Regional and Teleseismic Arrays

DTIC Science & Technology

2006-08-15

1: Mixture of signals from two earthquakes from south of Africa and the Philippines observed at USAEDS long-period seismic array in Korea. Correct...window where the detector will miss valid signals . 2 Approaches to detecting signals on arrays all focus on the basic model that expresses the observed...possible use in detecting infrasound signals . The approach is based on orthogonal- ity properties of the eigen vectors of the spectral matrix under a

The parallel-antiparallel signal difference in double-wave-vector diffusion-weighted MR at short mixing times: A phase evolution perspective

NASA Astrophysics Data System (ADS)

Finsterbusch, Jürgen

2011-01-01

Experiments with two diffusion weightings applied in direct succession in a single acquisition, so-called double- or two-wave-vector diffusion-weighting (DWV) experiments at short mixing times, have been shown to be a promising tool to estimate cell or compartment sizes, e.g. in living tissue. The basic theory for such experiments predicts that the signal decays for parallel and antiparallel wave vector orientations differ by a factor of three for small wave vectors. This seems to be surprising because in standard, single-wave-vector experiments the polarity of the diffusion weighting has no influence on the signal attenuation. Thus, the question how this difference can be understood more pictorially is often raised. In this rather educational manuscript, the phase evolution during a DWV experiment for simple geometries, e.g. diffusion between parallel, impermeable planes oriented perpendicular to the wave vectors, is considered step-by-step and demonstrates how the signal difference develops. Considering the populations of the phase distributions obtained, the factor of three between the signal decays which is predicted by the theory can be reproduced. Furthermore, the intermediate signal decay for orthogonal wave vector orientations can be derived when investigating diffusion in a box. Thus, the presented “phase gymnastics” approach may help to understand the signal modulation observed in DWV experiments at short mixing times.

Fundamentals of Plasma Physics

NASA Astrophysics Data System (ADS)

Bellan, Paul M.

2008-07-01

Preface; 1. Basic concepts; 2. The Vlasov, two-fluid, and MHD models of plasma dynamics; 3. Motion of a single plasma particle; 4. Elementary plasma waves; 5. Streaming instabilities and the Landau problem; 6. Cold plasma waves in a magnetized plasma; 7. Waves in inhomogeneous plasmas and wave energy relations; 8. Vlasov theory of warm electrostatic waves in a magnetized plasma; 9. MHD equilibria; 10. Stability of static MHD equilibria; 11. Magnetic helicity interpreted and Woltjer-Taylor relaxation; 12. Magnetic reconnection; 13. Fokker-Planck theory of collisions; 14. Wave-particle nonlinearities; 15. Wave-wave nonlinearities; 16. Non-neutral plasmas; 17. Dusty plasmas; Appendix A. Intuitive method for vector calculus identities; Appendix B. Vector calculus in orthogonal curvilinear coordinates; Appendix C. Frequently used physical constants and formulae; Bibliography; References; Index.

Mathematical Theory of Generalized Duality Quantum Computers Acting on Vector-States

NASA Astrophysics Data System (ADS)

Cao, Huai-Xin; Long, Gui-Lu; Guo, Zhi-Hua; Chen, Zheng-Li

2013-06-01

Following the idea of duality quantum computation, a generalized duality quantum computer (GDQC) acting on vector-states is defined as a tuple consisting of a generalized quantum wave divider (GQWD) and a finite number of unitary operators as well as a generalized quantum wave combiner (GQWC). It is proved that the GQWD and GQWC of a GDQC are an isometry and a co-isometry, respectively, and mutually dual. It is also proved that every GDQC gives a contraction, called a generalized duality quantum gate (GDQG). A classification of GDQCs is given and the properties of GDQGs are discussed. Some applications are obtained, including two orthogonal duality quantum computer algorithms for unsorted database search and an understanding of the Mach-Zehnder interferometer.

Alignment of a vector magnetometer to an optical prism.

PubMed

Dietrich, M R; Bailey, K G; O'Connor, T P

2017-05-01

A method for alignment of a vector magnetometer to a rigidly attached prism is presented. This enables optical comparison of the magnetometer axes to physical surfaces in the apparatus, and thus an absolute determination of the magnetic field direction in space. This is in contrast with more common techniques, which focus on precise determination of the relative angles between magnetometer axes, and so are more suited to measuring differences in the direction of magnetic fields. Here we demonstrate precision better than 500 μrad on a fluxgate magnetometer, which also gives the coil orthogonality errors to a similar precision. The relative sensitivity of the three axes is also determined, with a precision of about 5 × 10 -4 .

A comparison of breeding and ensemble transform vectors for global ensemble generation

NASA Astrophysics Data System (ADS)

Deng, Guo; Tian, Hua; Li, Xiaoli; Chen, Jing; Gong, Jiandong; Jiao, Meiyan

2012-02-01

To compare the initial perturbation techniques using breeding vectors and ensemble transform vectors, three ensemble prediction systems using both initial perturbation methods but with different ensemble member sizes based on the spectral model T213/L31 are constructed at the National Meteorological Center, China Meteorological Administration (NMC/CMA). A series of ensemble verification scores such as forecast skill of the ensemble mean, ensemble resolution, and ensemble reliability are introduced to identify the most important attributes of ensemble forecast systems. The results indicate that the ensemble transform technique is superior to the breeding vector method in light of the evaluation of anomaly correlation coefficient (ACC), which is a deterministic character of the ensemble mean, the root-mean-square error (RMSE) and spread, which are of probabilistic attributes, and the continuous ranked probability score (CRPS) and its decomposition. The advantage of the ensemble transform approach is attributed to its orthogonality among ensemble perturbations as well as its consistence with the data assimilation system. Therefore, this study may serve as a reference for configuration of the best ensemble prediction system to be used in operation.

Polar decomposition for attitude determination from vector observations

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.

1993-01-01

This work treats the problem of weighted least squares fitting of a 3D Euclidean-coordinate transformation matrix to a set of unit vectors measured in the reference and transformed coordinates. A closed-form analytic solution to the problem is re-derived. The fact that the solution is the closest orthogonal matrix to some matrix defined on the measured vectors and their weights is clearly demonstrated. Several known algorithms for computing the analytic closed form solution are considered. An algorithm is discussed which is based on the polar decomposition of matrices into the closest unitary matrix to the decomposed matrix and a Hermitian matrix. A somewhat longer improved algorithm is suggested too. A comparison of several algorithms is carried out using simulated data as well as real data from the Upper Atmosphere Research Satellite. The comparison is based on accuracy and time consumption. It is concluded that the algorithms based on polar decomposition yield a simple although somewhat less accurate solution. The precision of the latter algorithms increase with the number of the measured vectors and with the accuracy of their measurement.

Quantum speed limit time in a magnetic resonance

NASA Astrophysics Data System (ADS)

Ivanchenko, E. A.

2017-12-01

A visualization for dynamics of a qudit spin vector in a time-dependent magnetic field is realized by means of mapping a solution for a spin vector on the three-dimensional spherical curve (vector hodograph). The obtained results obviously display the quantum interference of precessional and nutational effects on the spin vector in the magnetic resonance. For any spin the bottom bounds of the quantum speed limit time (QSL) are found. It is shown that the bottom bound goes down when using multilevel spin systems. Under certain conditions the non-nil minimal time, which is necessary to achieve the orthogonal state from the initial one, is attained at spin S = 2. An estimation of the product of two and three standard deviations of the spin components are presented. We discuss the dynamics of the mutual uncertainty, conditional uncertainty and conditional variance in terms of spin standard deviations. The study can find practical applications in the magnetic resonance, 3D visualization of computational data and in designing of optimized information processing devices for quantum computation and communication.

Blind separation of positive sources by globally convergent gradient search.

PubMed

Oja, Erkki; Plumbley, Mark

2004-09-01

The instantaneous noise-free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix. However, with some prior information on the sources, like positivity, new analysis and perhaps simplified solution methods may yet become possible. In this letter, we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded, which means that they have a nonzero pdf in the region of zero. It can be shown that in this case, the solution method is basically very simple: an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources. We propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint, under which the separating matrix is orthogonal. We further prove that in the Stiefel manifold of orthogonal matrices, the cost function is a Lyapunov function for the matrix gradient flow, implying global convergence. Thus, this algorithm is guaranteed to find the nonnegative well-grounded independent sources. The analysis is complemented by a numerical simulation, which illustrates the algorithm.

Patch-based image reconstruction for PET using prior-image derived dictionaries

NASA Astrophysics Data System (ADS)

Tahaei, Marzieh S.; Reader, Andrew J.

2016-09-01

In PET image reconstruction, regularization is often needed to reduce the noise in the resulting images. Patch-based image processing techniques have recently been successfully used for regularization in medical image reconstruction through a penalized likelihood framework. Re-parameterization within reconstruction is another powerful regularization technique in which the object in the scanner is re-parameterized using coefficients for spatially-extensive basis vectors. In this work, a method for extracting patch-based basis vectors from the subject’s MR image is proposed. The coefficients for these basis vectors are then estimated using the conventional MLEM algorithm. Furthermore, using the alternating direction method of multipliers, an algorithm for optimizing the Poisson log-likelihood while imposing sparsity on the parameters is also proposed. This novel method is then utilized to find sparse coefficients for the patch-based basis vectors extracted from the MR image. The results indicate the superiority of the proposed methods to patch-based regularization using the penalized likelihood framework.

Locally indistinguishable subspaces spanned by three-qubit unextendible product bases

NASA Astrophysics Data System (ADS)

Duan, Runyao; Xin, Yu; Ying, Mingsheng

2010-03-01

We study the local distinguishability of general multiqubit states and show that local projective measurements and classical communication are as powerful as the most general local measurements and classical communication. Remarkably, this indicates that the local distinguishability of multiqubit states can be decided efficiently. Another useful consequence is that a set of orthogonal n-qubit states is locally distinguishable only if the summation of their orthogonal Schmidt numbers is less than the total dimension 2n. Employing these results, we show that any orthonormal basis of a subspace spanned by arbitrary three-qubit orthogonal unextendible product bases (UPB) cannot be exactly distinguishable by local operations and classical communication. This not only reveals another intrinsic property of three-qubit orthogonal UPB but also provides a class of locally indistinguishable subspaces with dimension 4. We also explicitly construct locally indistinguishable subspaces with dimensions 3 and 5, respectively. Similar to the bipartite case, these results on multipartite locally indistinguishable subspaces can be used to estimate the one-shot environment-assisted classical capacity of a class of quantum broadcast channels.

Coherent vorticity extraction in resistive drift-wave turbulence: Comparison of orthogonal wavelets versus proper orthogonal decomposition

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

Futatani, S.; Bos, W.J.T.; Del-Castillo-Negrete, Diego B

2011-01-01

We assess two techniques for extracting coherent vortices out of turbulent flows: the wavelet based Coherent Vorticity Extraction (CVE) and the Proper Orthogonal Decomposition (POD). The former decomposes the flow field into an orthogonal wavelet representation and subsequent thresholding of the coefficients allows one to split the flow into organized coherent vortices with non-Gaussian statistics and an incoherent random part which is structureless. POD is based on the singular value decomposition and decomposes the flow into basis functions which are optimal with respect to the retained energy for the ensemble average. Both techniques are applied to direct numerical simulation datamore » of two-dimensional drift-wave turbulence governed by Hasegawa Wakatani equation, considering two limit cases: the quasi-hydrodynamic and the quasi-adiabatic regimes. The results are compared in terms of compression rate, retained energy, retained enstrophy and retained radial flux, together with the enstrophy spectrum and higher order statistics. (c) 2010 Published by Elsevier Masson SAS on behalf of Academie des sciences.« less

Observations on the Proper Orthogonal Decomposition

NASA Technical Reports Server (NTRS)

Berkooz, Gal

1992-01-01

The Proper Orthogonal Decomposition (P.O.D.), also known as the Karhunen-Loeve expansion, is a procedure for decomposing a stochastic field in an L(2) optimal sense. It is used in diverse disciplines from image processing to turbulence. Recently the P.O.D. is receiving much attention as a tool for studying dynamics of systems in infinite dimensional space. This paper reviews the mathematical fundamentals of this theory. Also included are results on the span of the eigenfunction basis, a geometric corollary due to Chebyshev's inequality and a relation between the P.O.D. symmetry and ergodicity.

Equivalent model of a dually-fed machine for electric drive control systems

NASA Astrophysics Data System (ADS)

Ostrovlyanchik, I. Yu; Popolzin, I. Yu

2018-05-01

The article shows that the mathematical model of a dually-fed machine is complicated because of the presence of a controlled voltage source in the rotor circuit. As a method of obtaining a mathematical model, the method of a generalized two-phase electric machine is applied and a rotating orthogonal coordinate system is chosen that is associated with the representing vector of a stator current. In the chosen coordinate system in the operator form the differential equations of electric equilibrium for the windings of the generalized machine (the Kirchhoff equation) are written together with the expression for the moment, which determines the electromechanical energy transformation in the machine. Equations are transformed so that they connect the currents of the windings, that determine the moment of the machine, and the voltages on these windings. The structural diagram of the machine is assigned to the written equations. Based on the written equations and accepted assumptions, expressions were obtained for the balancing the EMF of windings, and on the basis of these expressions an equivalent mathematical model of a dually-fed machine is proposed, convenient for use in electric drive control systems.

Identifying large scale structures at 1 AU using fluctuations and wavelets

NASA Astrophysics Data System (ADS)

Niembro, T.; Lara, A.

2016-12-01

The solar wind (SW) is inhomogeneous and it is dominated for two types of flows: one quasi-stationary and one related to large scale transients (such as coronal mass ejections and co-rotating interaction regions). The SW inhomogeneities can be study as fluctuations characterized by a wide range of length and time scales. We are interested in the study of the characteristic fluctuations caused by large scale transient events. To do so, we define the vector space F with the normalized moving monthly/annual deviations as the orthogonal basis. Then, we compute the norm in this space of the solar wind parameters (velocity, magnetic field, density and temperature) fluctuations using WIND data from August 1992 to August 2015. This norm gives important information about the presence of a large structure disturbance in the solar wind and by applying a wavelet transform to this norm, we are able to determine, without subjectivity, the duration of the compression regions of these large transient structures and, even more, to identify if the structure corresponds to a single or complex (or merged) event. With this method we have automatically detected most of the events identified and published by other authors.

Direct recovery of regional tracer kinetics from temporally inconsistent dynamic ECT projections using dimension-reduced time-activity basis

NASA Astrophysics Data System (ADS)

Maltz, Jonathan S.

2000-11-01

We present an algorithm of reduced computational cost which is able to estimate kinetic model parameters directly from dynamic ECT sinograms made up of temporally inconsistent projections. The algorithm exploits the extreme degree of parameter redundancy inherent in linear combinations of the exponential functions which represent the modes of first-order compartmental systems. The singular value decomposition is employed to find a small set of orthogonal functions, the linear combinations of which are able to accurately represent all modes within the physiologically anticipated range in a given study. The reduced-dimension basis is formed as the convolution of this orthogonal set with a measured input function. The Moore-Penrose pseudoinverse is used to find coefficients of this basis. Algorithm performance is evaluated at realistic count rates using MCAT phantom and clinical 99mTc-teboroxime myocardial study data. Phantom data are modelled as originating from a Poisson process. For estimates recovered from a single slice projection set containing 2.5×105 total counts, recovered tissue responses compare favourably with those obtained using more computationally intensive methods. The corresponding kinetic parameter estimates (coefficients of the new basis) exhibit negligible bias, while parameter variances are low, falling within 30% of the Cramér-Rao lower bound.

An evaluation of the accuracy of geomagnetic data obtained from an unattended, automated, quasi-absolute station

USGS Publications Warehouse

Herzog, D.C.

1990-01-01

A comparison is made of geomagnetic calibration data obtained from a high-sensitivity proton magnetometer enclosed within an orthogonal bias coil system, with data obtained from standard procedures at a mid-latitude U.S. Geological Survey magnetic observatory using a quartz horizontal magnetometer, a Ruska magnetometer, and a total field magnetometer. The orthogonal coil arrangement is used with the proton magnetometer to provide Deflected-Inclination-Deflected-Declination (DIDD) data from which quasi-absolute values of declination, horizontal intensity, and vertical intensity can be derived. Vector magnetometers provide the ordinate values to yield baseline calibrations for both the DIDD and standard observatory processes. Results obtained from a prototype system over a period of several months indicate that the DIDD unit can furnish adequate absolute field values for maintaining observatory calibration data, thus providing baseline control for unattended, remote stations. ?? 1990.

Knowledge Space: A Conceptual Basis for the Organization of Knowledge

ERIC Educational Resources Information Center

Meincke, Peter P. M.; Atherton, Pauline

1976-01-01

Proposes a new conceptual basis for visualizing the organization of information, or knowledge, which differentiates between the concept "vectors" for a field of knowledge represented in a multidimensional space, and the state "vectors" for a person based on his understanding of these concepts, and the representational…

High effective inverse dynamics modelling for dual-arm robot

NASA Astrophysics Data System (ADS)

Shen, Haoyu; Liu, Yanli; Wu, Hongtao

2018-05-01

To deal with the problem of inverse dynamics modelling for dual arm robot, a recursive inverse dynamics modelling method based on decoupled natural orthogonal complement is presented. In this model, the concepts and methods of Decoupled Natural Orthogonal Complement matrices are used to eliminate the constraint forces in the Newton-Euler kinematic equations, and the screws is used to express the kinematic and dynamics variables. On this basis, the paper has developed a special simulation program with symbol software of Mathematica and conducted a simulation research on the a dual-arm robot. Simulation results show that the proposed method based on decoupled natural orthogonal complement can save an enormous amount of CPU time that was spent in computing compared with the recursive Newton-Euler kinematic equations and the results is correct and reasonable, which can verify the reliability and efficiency of the method.

Bright-dark soliton pairs in a self-mode locking fiber laser

NASA Astrophysics Data System (ADS)

Meng, Yichang; Zhang, Shumin; Li, Hongfei; Du, Juan; Hao, Yanping; Li, Xingliang

2012-06-01

We have experimentally observed bright-dark soliton pairs in an erbium-doped fiber ring laser for the first time. This approach is different from the vector dark domain wall solitons which separate the two orthogonal linear polarization eigenstates of the laser emission. In our laser, the bright-dark soliton pairs can co-exist in any one polarization state. Numerical simulations based on the coupled complex Ginzburg-Landau equations have confirmed the experimental results.

Feasibility of Using the Space Shuttle to Conduct Global Geomagnetic Surveys (Phase I - Retrievable Probes)

DTIC Science & Technology

1985-07-01

Datatape Division 4-1 5.0 REFERENCES Acuna, M.H. et. al., The MAGSAT Vector Magnetometer - A Precision Fluxgate Magnetometer for the Measurement of the...charting would consist of a triaxial, mutually orthogonal fluxgate magnetometer and an absolute scalar magnetometer to check the flux- gates drift...While space-ready, triaxial fluxgate magnetometers are not an off-the-shelf item, their design concepts are well understood. Their resolution of less

Load cell having strain gauges of arbitrary location

DOEpatents

Spletzer, Barry [Albuquerque, NM

2007-03-13

A load cell utilizes a plurality of strain gauges mounted upon the load cell body such that there are six independent load-strain relations. Load is determined by applying the inverse of a load-strain sensitivity matrix to a measured strain vector. The sensitivity matrix is determined by performing a multivariate regression technique on a set of known loads correlated to the resulting strains. Temperature compensation is achieved by configuring the strain gauges as co-located orthogonal pairs.

Application of Linear Discriminant Analysis in Dimensionality Reduction for Hand Motion Classification

NASA Astrophysics Data System (ADS)

Phinyomark, A.; Hu, H.; Phukpattaranont, P.; Limsakul, C.

2012-01-01

The classification of upper-limb movements based on surface electromyography (EMG) signals is an important issue in the control of assistive devices and rehabilitation systems. Increasing the number of EMG channels and features in order to increase the number of control commands can yield a high dimensional feature vector. To cope with the accuracy and computation problems associated with high dimensionality, it is commonplace to apply a processing step that transforms the data to a space of significantly lower dimensions with only a limited loss of useful information. Linear discriminant analysis (LDA) has been successfully applied as an EMG feature projection method. Recently, a number of extended LDA-based algorithms have been proposed, which are more competitive in terms of both classification accuracy and computational costs/times with classical LDA. This paper presents the findings of a comparative study of classical LDA and five extended LDA methods. From a quantitative comparison based on seven multi-feature sets, three extended LDA-based algorithms, consisting of uncorrelated LDA, orthogonal LDA and orthogonal fuzzy neighborhood discriminant analysis, produce better class separability when compared with a baseline system (without feature projection), principle component analysis (PCA), and classical LDA. Based on a 7-dimension time domain and time-scale feature vectors, these methods achieved respectively 95.2% and 93.2% classification accuracy by using a linear discriminant classifier.

Sparse coded image super-resolution using K-SVD trained dictionary based on regularized orthogonal matching pursuit.

PubMed

Sajjad, Muhammad; Mehmood, Irfan; Baik, Sung Wook

2015-01-01

Image super-resolution (SR) plays a vital role in medical imaging that allows a more efficient and effective diagnosis process. Usually, diagnosing is difficult and inaccurate from low-resolution (LR) and noisy images. Resolution enhancement through conventional interpolation methods strongly affects the precision of consequent processing steps, such as segmentation and registration. Therefore, we propose an efficient sparse coded image SR reconstruction technique using a trained dictionary. We apply a simple and efficient regularized version of orthogonal matching pursuit (ROMP) to seek the coefficients of sparse representation. ROMP has the transparency and greediness of OMP and the robustness of the L1-minization that enhance the dictionary learning process to capture feature descriptors such as oriented edges and contours from complex images like brain MRIs. The sparse coding part of the K-SVD dictionary training procedure is modified by substituting OMP with ROMP. The dictionary update stage allows simultaneously updating an arbitrary number of atoms and vectors of sparse coefficients. In SR reconstruction, ROMP is used to determine the vector of sparse coefficients for the underlying patch. The recovered representations are then applied to the trained dictionary, and finally, an optimization leads to high-resolution output of high-quality. Experimental results demonstrate that the super-resolution reconstruction quality of the proposed scheme is comparatively better than other state-of-the-art schemes.

A high-sensitive static vector magnetometer based on two vibrating coils

NASA Astrophysics Data System (ADS)

Yin, Jing; Pan, Cheng Liang; Wang, Hong Bo; Feng, Zhi Hua

2011-12-01

A static vector magnetometer based on two-dimensional (2D) vibrating coils actuated by a piezoelectric cantilever is presented. Two individual sensing coils are orthogonally fastened at the tip of cantilever and piezoelectric sheets are used to excite the cantilever bending. Due to off-axis coupler on the tip, the cantilever generates bending and twisting vibrations simultaneously on their corresponding resonant frequencies, realizing the 2D rotating vibrations of the coils. According to Faraday-Lenz Law, output voltages are induced from the coils. They are amplified by a pre-amplifier circuit, decoupled by a phase-sensitive detector, and finally used to calculate the vector of magnetic field at the coil location. The coil head of a prototype magnetometer possesses a dc sensitivity of around 10 μV/Gs with a good linearity in the measuring range from 0 to 16 μT. The corresponding noise level is about 13.1 nT in the bandwidth from 0.01 Hz to 1 Hz.

Pu239 Cross-Section Variations Based on Experimental Uncertainties and Covariances

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

Sigeti, David Edward; Williams, Brian J.; Parsons, D. Kent

2016-10-18

Algorithms and software have been developed for producing variations in plutonium-239 neutron cross sections based on experimental uncertainties and covariances. The varied cross-section sets may be produced as random samples from the multi-variate normal distribution defined by an experimental mean vector and covariance matrix, or they may be produced as Latin-Hypercube/Orthogonal-Array samples (based on the same means and covariances) for use in parametrized studies. The variations obey two classes of constraints that are obligatory for cross-section sets and which put related constraints on the mean vector and covariance matrix that detemine the sampling. Because the experimental means and covariances domore » not obey some of these constraints to sufficient precision, imposing the constraints requires modifying the experimental mean vector and covariance matrix. Modification is done with an algorithm based on linear algebra that minimizes changes to the means and covariances while insuring that the operations that impose the different constraints do not conflict with each other.« less

Are Bred Vectors The Same As Lyapunov Vectors?

NASA Astrophysics Data System (ADS)

Kalnay, E.; Corazza, M.; Cai, M.

Regional loss of predictability is an indication of the instability of the underlying flow, where small errors in the initial conditions (or imperfections in the model) grow to large amplitudes in finite times. The stability properties of evolving flows have been studied using Lyapunov vectors (e.g., Alligood et al, 1996, Ott, 1993, Kalnay, 2002), singular vectors (e.g., Lorenz, 1965, Farrell, 1988, Molteni and Palmer, 1993), and, more recently, with bred vectors (e.g., Szunyogh et al, 1997, Cai et al, 2001). Bred vectors (BVs) are, by construction, closely related to Lyapunov vectors (LVs). In fact, after an infinitely long breeding time, and with the use of infinitesimal ampli- tudes, bred vectors are identical to leading Lyapunov vectors. In practical applications, however, bred vectors are different from Lyapunov vectors in two important ways: a) bred vectors are never globally orthogonalized and are intrinsically local in space and time, and b) they are finite-amplitude, finite-time vectors. These two differences are very significant in a dynamical system whose size is very large. For example, the at- mosphere is large enough to have "room" for several synoptic scale instabilities (e.g., storms) to develop independently in different regions (say, North America and Aus- tralia), and it is complex enough to have several different possible types of instabilities (such as barotropic, baroclinic, convective, and even Brownian motion). Bred vectors share some of their properties with leading LVs (Corazza et al, 2001a, 2001b, Toth and Kalnay, 1993, 1997, Cai et al, 2001). For example, 1) Bred vectors are independent of the norm used to define the size of the perturba- tion. Corazza et al. (2001) showed that bred vectors obtained using a potential enstro- phy norm were indistinguishable from bred vectors obtained using a streamfunction squared norm, in contrast with singular vectors. 2) Bred vectors are independent of the length of the rescaling period as long as the perturbations remain approximately linear (for example, for atmospheric models the interval for rescaling could be varied between a single time step and 1 day without affecting qualitatively the characteristics of the bred vectors. However, the finite-amplitude, finite-time, and lack of orthogonalization of the BVs introduces important differences with LVs: 1) In regions that undergo strong instabilities, the bred vectors tend to be locally domi- 1 nated by simple, low-dimensional structures. Patil et al (2001) showed that the BV-dim (appendix) gives a good estimate of the number of dominant directions (shapes) of the local k bred vectors. For example, if half of them are aligned in one direction, and half in a different direction, the BV-dim is about two. If the majority of the bred vectors are aligned predominantly in one direction and only a few are aligned in a second direction, then the BV-dim is between 1 and 2. Patil et al., (2001) showed that the regions with low dimensionality cover about 20% of the atmosphere. They also found that these low-dimensionality regions have a very well defined vertical structure, and a typical lifetime of 3-7 days. The low dimensionality identifies regions where the in- stability of the basic flow has manifested itself in a low number of preferred directions of perturbation growth. 2) Using a Quasi-Geostrophic simulation system of data assimilation developed by Morss (1999), Corazza et al (2001a, b) found that bred vectors have structures that closely resemble the background (short forecasts used as first guess) errors, which in turn dominate the local analysis errors. This is especially true in regions of low dimensionality, which is not surprising if these are unstable regions where errors grow in preferred shapes. 3) The number of bred vectors needed to represent the unstable subspace in the QG system is small (about 6-10). This was shown by computing the local BV-dim as a function of the number of independent bred vectors. Convergence in the local dimen- sion starts to occur at about 6 BVs, and is essentially complete when the number of vectors is about 10-15 (Corazza et al, 2001a). This should be contrasted with the re- sults of Snyder and Joly (1998) and Palmer et al (1998) who showed that hundreds of Lyapunov vectors with positive Lyapunov exponents are needed to represent the attractor of the system in quasi-geostrophic models. 4) Since only a few bred vectors are needed, and background errors project strongly in the subspace of bred vectors, Corazza et al (2001b) were able to develop cost-efficient methods to improve the 3D-Var data assimilation by adding to the background error covariance terms proportional to the outer product of the bred vectors, thus represent- ing the "errors of the day". This approach led to a reduction of analysis error variance of about 40% at very low cost. 5) The fact that BVs have finite amplitude provides a natural way to filter out instabil- ities present in the system that have fast growth, but saturate nonlinearly at such small amplitudes that they are irrelevant for ensemble perturbations. As shown by Lorenz (1996) Lyapunov vectors (and singular vectors) of models including these physical phenomena would be dominated by the fast but small amplitude instabilities, unless they are explicitly excluded from the linearized models. Bred vectors, on the other 2 hand, through the choice of an appropriate size for the perturbation, provide a natural filter based on nonlinear saturation of fast but irrelevant instabilities. 6) Every bred vector is qualitatively similar to the *leading* LV. LVs beyond the leading LV are obtained by orthogonalization after each time step with respect to the previous LVs subspace. The orthogonalization requires the introduction of a norm. With an enstrophy norm, the successive LVs have larger and larger horizontal scales, and a choice of a stream function norm would lead to successively smaller scales in the LVs. Beyond the first few LVs, there is little qualitative similarity between the background errors and the LVs. In summary, in a system like the atmosphere with enough physical space for several independent local instabilities, BVs and LVs share some properties but they also have significant differences. BV are finite-amplitude, finite-time, and because they are not globally orthogonalized, they have local properties in space. Bred vectors are akin to the leading LV, but bred vectors derived from different arbitrary initial perturba- tions remain distinct from each other, instead of collapsing into a single leading vec- tor, presumably because the nonlinear terms and physical parameterizations introduce sufficient stochastic forcing to avoid such convergence. As a result, there is no need for global orthogonalization, and the number of bred vectors required to describe the natural instabilities in an atmospheric system (from a local point of view) is much smaller than the number of Lyapunov vectors with positive Lyapunov exponents. The BVs are independent of the norm, whereas the LVs beyond the first one do depend on the choice of norm: for example, they become larger in scale with a vorticity norm, and smaller with a stream function norm. These properties of BVs result in significant advantages for data assimilation and en- semble forecasting for the atmosphere. Errors in the analysis have structures very similar to bred vectors, and it is found that they project very strongly on the subspace of a few bred vectors. This is not true for either Lyapunov vectors beyond the lead- ing LVs, or for singular vectors unless they are constructed with a norm based on the analysis error covariance matrix (or a bred vector covariance). The similarity between bred vectors and analysis errors leads to the ability to include "errors of the day" in the background error covariance and a significant improvement of the analysis beyond 3D-Var at a very low cost (Corazza, 2001b). References Alligood K. T., T. D. Sauer and J. A. Yorke, 1996: Chaos: an introduction to dynamical systems. Springer-Verlag, New York. Buizza R., J. Tribbia, F. Molteni and T. Palmer, 1993: Computation of optimal unstable 3 structures for numerical weather prediction models. Tellus, 45A, 388-407. Cai, M., E. Kalnay and Z. Toth, 2001: Potential impact of bred vectors on ensemble forecasting and data assimilation in the Zebiak-Cane model. Submitted to J of Climate. Corazza, M., E. Kalnay, D. J. Patil, R. Morss, M. Cai, I. Szunyogh, B. R. Hunt, E. Ott and J. Yorke, 2001: Use of the breeding technique to determine the structure of the "errors of the day". Submitted to Nonlinear Processes in Geophysics. Corazza, M., E. Kalnay, DJ Patil, E. Ott, J. Yorke, I Szunyogh and M. Cai, 2001: Use of the breeding technique in the estimation of the background error covariance matrix for a quasigeostrophic model. AMS Symposium on Observations, Data Assimilation and Predictability, Preprints volume, Orlando, FA, 14-17 January 2002. Farrell, B., 1988: Small error dynamics and the predictability of atmospheric flow, J. Atmos. Sciences, 45, 163-172. Kalnay, E 2002: Atmospheric modeling, data assimilation and predictability. Chapter 6. Cambridge University Press, UK. In press. Kalnay E and Z Toth 1994: Removing growing errors in the analysis. Preprints, Tenth Conference on Numerical Weather Prediction, pp 212-215. Amer. Meteor. Soc., July 18-22, 1994. Lorenz, E.N., 1965: A study of the predictability of a 28-variable atmospheric model. Tellus, 21, 289-307. Lorenz, E.N., 1996: Predictability- A problem partly solved. Proceedings of the ECMWF Seminar on Predictability, Reading, England, Vol. 1 1-18. Molteni F. and TN Palmer, 1993: Predictability and finite-time instability of the north- ern winter circulation. Q. J. Roy. Meteorol. Soc. 119, 269-298. Morss, R.E.: 1999: Adaptive observations: Idealized sampling strategies for improving numerical weather prediction. Ph.D. Thesis, Massachussetts Institute of Technology, 225pp. Ott, E., 1993: Chaos in Dynamical Systems. Cambridge University Press. New York. Palmer, TN, R. Gelaro, J. Barkmeijer and R. Buizza, 1998: Singular vectors, metrics and adaptive observations. J. Atmos Sciences, 55, 633-653. Patil, DJ, BR Hunt, E Kalnay, J. Yorke, and E. Ott, 2001: Local low dimensionality of atmospheric dynamics. Phys. Rev. Lett., 86, 5878. Patil, DJ, I. Szunyogh, BR Hunt, E Kalnay, E Ott, and J. Yorke, 2001: Using large 4 member ensembles to isolate local low dimensionality of atmospheric dynamics. AMS Symposium on Observations, Data Assimilation and Predictability, Preprints volume, Orlando, FA, 14-17 January 2002. Snyder, C. and A. Joly, 1998: Development of perturbations within growing baroclinic waves. Q. J. Roy. Meteor. Soc., 124, pp 1961. Szunyogh, I, E. Kalnay and Z. Toth, 1997: A comparison of Lyapunov and Singular vectors in a low resolution GCM. Tellus, 49A, 200-227. Toth, Z and E Kalnay 1993: Ensemble forecasting at NMC - the generation of pertur- bations. Bull. Amer. Meteorol. Soc., 74, 2317-2330. Toth, Z and E Kalnay 1997: Ensemble forecasting at NCEP and the breeding method. Mon Wea Rev, 125, 3297-3319. * Corresponding author address: Eugenia Kalnay, Meteorology Depart- ment, University of Maryland, College Park, MD 20742-2425, USA; email: ekalnay@atmos.umd.edu Appendix: BV-dimension Patil et al., (2001) defined local bred vectors around a point in the 3-dimensional grid of the model by taking the 24 closest horizontal neighbors. If there are k bred vectors available, and N model variables for each grid point, the k local bred vectors form the columns of a 25Nxk matrix B. The kxk covariance matrix is C=B^T B. Its eigen- values are positive, and its eigenvectors v(i) are the singular vectors of the local bred vector subspace. The Bred Vector dimension (BV-dim) measures the local effective dimension: BV-dim[s,s,...,s(k)]={SUM[s(i)]}^2/SUM[s(i)]^2 where s(i) are the square roots of the eigenvalues of the covariance matrix. 5

Research of facial feature extraction based on MMC

NASA Astrophysics Data System (ADS)

Xue, Donglin; Zhao, Jiufen; Tang, Qinhong; Shi, Shaokun

2017-07-01

Based on the maximum margin criterion (MMC), a new algorithm of statistically uncorrelated optimal discriminant vectors and a new algorithm of orthogonal optimal discriminant vectors for feature extraction were proposed. The purpose of the maximum margin criterion is to maximize the inter-class scatter while simultaneously minimizing the intra-class scatter after the projection. Compared with original MMC method and principal component analysis (PCA) method, the proposed methods are better in terms of reducing or eliminating the statistically correlation between features and improving recognition rate. The experiment results on Olivetti Research Laboratory (ORL) face database shows that the new feature extraction method of statistically uncorrelated maximum margin criterion (SUMMC) are better in terms of recognition rate and stability. Besides, the relations between maximum margin criterion and Fisher criterion for feature extraction were revealed.

Implementation of biological tissue Mueller matrix for polarization-sensitive optical coherence tomography based on LabVIEW

NASA Astrophysics Data System (ADS)

Lin, Yongping; Zhang, Xiyang; He, Youwu; Cai, Jianyong; Li, Hui

2018-02-01

The Jones matrix and the Mueller matrix are main tools to study polarization devices. The Mueller matrix can also be used for biological tissue research to get complete tissue properties, while the commercial optical coherence tomography system does not give relevant analysis function. Based on the LabVIEW, a near real time display method of Mueller matrix image of biological tissue is developed and it gives the corresponding phase retardant image simultaneously. A quarter-wave plate was placed at 45 in the sample arm. Experimental results of the two orthogonal channels show that the phase retardance based on incident light vector fixed mode and the Mueller matrix based on incident light vector dynamic mode can provide an effective analysis method of the existing system.

Alignment of a vector magnetometer to an optical prism

DOE PAGES

Dietrich, M. R.; Bailey, K. G.; O’Connor, T. P.

2017-05-12

A method for alignment of a vector magnetometer to a rigidly attached prism is presented. This enables optical comparison of the magnetometer axes to physical surfaces in the apparatus, and thus an absolute determination of the magnetic field direction in space. This is in contrast with more common techniques, which focus on precise determination of the relative angles between magnetometer axes, and so are more suited to measuring differences in the direction of magnetic fields. Here we demonstrate precision better than 500 μrad on a fluxgate magnetometer, which also gives the coil orthogonality errors to a similar precision. As amore » result, the relative sensitivity of the three axes is also determined, with a precision of about 5 ×10 –4.« less

Tracking sperm whales with a towed acoustic vector sensor.

PubMed

Thode, Aaron; Skinner, Jeff; Scott, Pam; Roswell, Jeremy; Straley, Janice; Folkert, Kendall

2010-11-01

Passive acoustic towed linear arrays are increasingly used to detect marine mammal sounds during mobile anthropogenic activities. However, these arrays cannot resolve between signals arriving from the port or starboard without vessel course changes or multiple cable deployments, and their performance is degraded by vessel self-noise and non-acoustic mechanical vibration. In principle acoustic vector sensors can resolve these directional ambiguities, as well as flag the presence of non-acoustic contamination, provided that the vibration-sensitive sensors can be successfully integrated into compact tow modules. Here a vector sensor module attached to the end of a 800 m towed array is used to detect and localize 1813 sperm whale "clicks" off the coast of Sitka, AK. Three methods were used to identify frequency regimes relatively free of non-acoustic noise contamination, and then the active intensity (propagating energy) of the signal was computed between 4-10 kHz along three orthogonal directions, providing unambiguous bearing estimates of two sperm whales over time. These bearing estimates are consistent with those obtained via conventional methods, but the standard deviations of the vector sensor bearing estimates are twice those of the conventionally-derived bearings. The resolved ambiguities of the bearings deduced from vessel course changes match the vector sensor predictions.

Method of Conjugate Radii for Solving Linear and Nonlinear Systems

NASA Technical Reports Server (NTRS)

Nachtsheim, Philip R.

1999-01-01

This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.

Quantum secret sharing using the d-dimensional GHZ state

NASA Astrophysics Data System (ADS)

Bai, Chen-Ming; Li, Zhi-Hui; Xu, Ting-Ting; Li, Yong-Ming

2017-03-01

We propose a quantum secret sharing scheme that uses an orthogonal pair of n-qudit GHZ states and local distinguishability. In the proposed protocol, the participants use an X-basis measurement and classical communication to distinguish between the two orthogonal states and reconstruct the original secret. We also present (2, n)-threshold and generalized restricted (2, n)-threshold schemes that enable any two cooperating players from two disjoint groups to always reconstruct the secret. Compared to the existing scheme by Rahaman and Parker (Phys Rev A 91:022330, 2015), the proposed scheme is more general and the access structure contains more authorized sets.

Horizontal vectorization of electron repulsion integrals.

PubMed

Pritchard, Benjamin P; Chow, Edmond

2016-10-30

We present an efficient implementation of the Obara-Saika algorithm for the computation of electron repulsion integrals that utilizes vector intrinsics to calculate several primitive integrals concurrently in a SIMD vector. Initial benchmarks display a 2-4 times speedup with AVX instructions over comparable scalar code, depending on the basis set. Speedup over scalar code is found to be sensitive to the level of contraction of the basis set, and is best for (lAlB|lClD) quartets when lD  = 0 or lB=lD=0, which makes such a vectorization scheme particularly suitable for density fitting. The basic Obara-Saika algorithm, how it is vectorized, and the performance bottlenecks are analyzed and discussed. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Surrogate models for sheet metal stamping problem based on the combination of proper orthogonal decomposition and radial basis function

NASA Astrophysics Data System (ADS)

Dang, Van Tuan; Lafon, Pascal; Labergere, Carl

2017-10-01

In this work, a combination of Proper Orthogonal Decomposition (POD) and Radial Basis Function (RBF) is proposed to build a surrogate model based on the Benchmark Springback 3D bending from the Numisheet2011 congress. The influence of the two design parameters, the geometrical parameter of the die radius and the process parameter of the blank holder force, on the springback of the sheet after a stamping operation is analyzed. The classical Design of Experience (DoE) uses Full Factorial to design the parameter space with sample points as input data for finite element method (FEM) numerical simulation of the sheet metal stamping process. The basic idea is to consider the design parameters as additional dimensions for the solution of the displacement fields. The order of the resultant high-fidelity model is reduced through the use of POD method which performs model space reduction and results in the basis functions of the low order model. Specifically, the snapshot method is used in our work, in which the basis functions is derived from snapshot deviation of the matrix of the final displacements fields of the FEM numerical simulation. The obtained basis functions are then used to determine the POD coefficients and RBF is used for the interpolation of these POD coefficients over the parameter space. Finally, the presented POD-RBF approach which is used for shape optimization can be performed with high accuracy.

Useful lower limits to polarization contributions to intermolecular interactions using a minimal basis of localized orthogonal orbitals: theory and analysis of the water dimer.

PubMed

Azar, R Julian; Horn, Paul Richard; Sundstrom, Eric Jon; Head-Gordon, Martin

2013-02-28

The problem of describing the energy-lowering associated with polarization of interacting molecules is considered in the overlapping regime for self-consistent field wavefunctions. The existing approach of solving for absolutely localized molecular orbital (ALMO) coefficients that are block-diagonal in the fragments is shown based on formal grounds and practical calculations to often overestimate the strength of polarization effects. A new approach using a minimal basis of polarized orthogonal local MOs (polMOs) is developed as an alternative. The polMO basis is minimal in the sense that one polarization function is provided for each unpolarized orbital that is occupied; such an approach is exact in second-order perturbation theory. Based on formal grounds and practical calculations, the polMO approach is shown to underestimate the strength of polarization effects. In contrast to the ALMO method, however, the polMO approach yields results that are very stable to improvements in the underlying AO basis expansion. Combining the ALMO and polMO approaches allows an estimate of the range of energy-lowering due to polarization. Extensive numerical calculations on the water dimer using a large range of basis sets with Hartree-Fock theory and a variety of different density functionals illustrate the key considerations. Results are also presented for the polarization-dominated Na(+)CH4 complex. Implications for energy decomposition analysis of intermolecular interactions are discussed.

An implementation of the QMR method based on coupled two-term recurrences

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noeel M.

1992-01-01

The authors have proposed a new Krylov subspace iteration, the quasi-minimal residual algorithm (QMR), for solving non-Hermitian linear systems. In the original implementation of the QMR method, the Lanczos process with look-ahead is used to generate basis vectors for the underlying Krylov subspaces. In the Lanczos algorithm, these basis vectors are computed by means of three-term recurrences. It has been observed that, in finite precision arithmetic, vector iterations based on three-term recursions are usually less robust than mathematically equivalent coupled two-term vector recurrences. This paper presents a look-ahead algorithm that constructs the Lanczos basis vectors by means of coupled two-term recursions. Implementation details are given, and the look-ahead strategy is described. A new implementation of the QMR method, based on this coupled two-term algorithm, is described. A simplified version of the QMR algorithm without look-ahead is also presented, and the special case of QMR for complex symmetric linear systems is considered. Results of numerical experiments comparing the original and the new implementations of the QMR method are reported.

Theory and Applications of Elliptically Contoured and Related Distributions

DTIC Science & Technology

1990-09-01

is invariant under n x n orthogonal transfor- mations. When the parent distribution is more generally ECp(pA, X, 4), the c.f. of X is n E(eitrTIX...those properties to some wider class than that of SD? 18 A largest characterization of SD is a demonstration that there is no generating vector Y...Takemura’s Generalizations of Cochran’s Theorem," George P.H. Styan, September 1982. 3. " Some Further Applications of Finite Difference Operators," Kai

Shear free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism

NASA Technical Reports Server (NTRS)

Lind, R. W.

1972-01-01

The problem of finding algebraically special solutions to the vacuum Einstein-Maxwell equations was investigated using a spin coefficient formalism. The general case in which the degenerate null vectors are not hypersurface orthogonal is reduced to a problem of solving five coupled differential equations that are no longer dependent on the affine parameter along the degenerate null directions. It is shown that the most general regular, shear-free, nonradiating solution to these equations is the Kerr-Newman metric.

IEEE International Symposium Information Theory, held at Santa Monica California, February 9-12, 1981.

DTIC Science & Technology

1981-01-01

Channel and study permutation codes as a special case. ,uch a code is generated by an initial vector x, a group G of orthogonal n by n matrices, and a...random-access components, is introduced and studied . Under this scheme, the network stations are divided into groups , each of which is assigned a...IEEE INFORMATION THEORY GROUP CO-SPONSORED BY: UNION RADIO SCIENTIFIQUE INTERNATIONALE IEEE Catalog Number 81 CH 1609-7 IT 𔃻. 81 ~20 04Q SECURITY

Coordination-Assisted Bioorthogonal Chemistry: Orthogonal Tetrazine Ligation with Vinylboronic Acid and a Strained Alkene.

PubMed

Eising, Selma; Xin, Bo-Tao; Kleinpenning, Fleur; Heming, Juriaan; Florea, Bogdan; Overkleeft, Herman; Bonger, Kimberly Michelle

2018-05-28

Bioorthogonal chemistry can be used for the selective modification of biomolecules without interfering with any other functionality present. Recent developments in the field provided orthogonal bioorthogonal reactions for modification of multiple biomolecules simultaneously. During our research, we have observed exceptional high reaction rates in the bioorthogonal inverse electron-demand Diels-Alder (iEDDA) reaction between non-strained vinylboronic acids (VBAs) and dipyridyl-s-tetrazines relative to that of tetrazines bearing a methyl or phenyl substituent. As VBAs are mild Lewis acids, we hypothesize that coordination of the pyridyl nitrogen to the boronic acid promotes the tetrazine ligation. Here, we explore the molecular basis and scope of the VBA-tetrazine ligation in more detail and benefit from its unique reactivity in the simultaneous orthogonal tetrazine labelling of two proteins modified with VBA and norbornene, a widely used strained alkene. We further show that the two orthogonal iEDDA reactions can be carried out in living cells by labelling of the proteasome using a non-selective probe equipped with a VBA and a subunit-selective one bearing a norbornene. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Analysis and interpretation of satellite fragmentation data

NASA Technical Reports Server (NTRS)

Tan, Arjun

1987-01-01

The velocity perturbations of the fragments of a satellite can shed valuable information regarding the nature and intensity of the fragmentation. A feasibility study on calculating the velocity perturbations from existing equations was carried out by analyzing 23 major documented fragmentation events. It was found that whereas the calculated values of the radial components of the velocity change were often unusually high, those in the two other orthogonal directions were mostly reasonable. Since the uncertainties in the radial component necessarily translate into uncertainties in the total velocity change, it is suggested that alternative expressions for the radial component of velocity be sought for the purpose of determining the cause of the fragmentation from the total velocity change. The calculated variances in the velocity perturbations in the two directions orthogonal to the radial vector indicate that they have the smallest values for collision induced breakups and the largest values for low-intensity explosion induced breakups. The corresponding variances for high-intensity explosion induced breakups generally have values intermediate between those of the two extreme categories. A three-dimensional plot of the variances in the two orthogonal velocity perturbations and the plane change angle shows a clear separation between the three major types of breakups. This information is used to reclassify a number of satellite fragmentation events of unknown category.

Spectral-element Method for 3D Marine Controlled-source EM Modeling

NASA Astrophysics Data System (ADS)

Liu, L.; Yin, C.; Zhang, B., Sr.; Liu, Y.; Qiu, C.; Huang, X.; Zhu, J.

2017-12-01

As one of the predrill reservoir appraisal methods, marine controlled-source EM (MCSEM) has been widely used in mapping oil reservoirs to reduce risk of deep water exploration. With the technical development of MCSEM, the need for improved forward modeling tools has become evident. We introduce in this paper spectral element method (SEM) for 3D MCSEM modeling. It combines the flexibility of finite-element and high accuracy of spectral method. We use Galerkin weighted residual method to discretize the vector Helmholtz equation, where the curl-conforming Gauss-Lobatto-Chebyshev (GLC) polynomials are chosen as vector basis functions. As a kind of high-order complete orthogonal polynomials, the GLC have the characteristic of exponential convergence. This helps derive the matrix elements analytically and improves the modeling accuracy. Numerical 1D models using SEM with different orders show that SEM method delivers accurate results. With increasing SEM orders, the modeling accuracy improves largely. Further we compare our SEM with finite-difference (FD) method for a 3D reservoir model (Figure 1). The results show that SEM method is more effective than FD method. Only when the mesh is fine enough, can FD achieve the same accuracy of SEM. Therefore, to obtain the same precision, SEM greatly reduces the degrees of freedom and cost. Numerical experiments with different models (not shown here) demonstrate that SEM is an efficient and effective tool for MSCEM modeling that has significant advantages over traditional numerical methods.This research is supported by Key Program of National Natural Science Foundation of China (41530320), China Natural Science Foundation for Young Scientists (41404093), and Key National Research Project of China (2016YFC0303100, 2017YFC0601900).

Proceedings of the Conference on Joint Problem Solving and Microcomputers.

DTIC Science & Technology

1983-08-01

socio - cultural norm, not as "truth" about the domain, nor on the basis of formal properties attributed to the expert’s mental model. According to Grif...the basis of the task studied or on the grounds of abstract hypotheses about . the domain. Socio - cultural domain representations cannot rely on these...orthogonal to concrete vs. abstract. The con- crete specific acts (some, genetically primary examples) occupy the top left cell. The set of socio - cultural

Study of Equatorial Ionospheric irregularities and Mapping of Electron Density Profiles and Ionograms

DTIC Science & Technology

2012-03-09

equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the...wave function arguments from complex scalars to complex vectors . This conversion allows us to separate the electric field vector and the imaginary...magnetic field vector , because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while ex- ponentials of imaginary

Velocity field calculation for non-orthogonal numerical grids

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

Flach, G. P.

2015-03-01

Computational grids containing cell faces that do not align with an orthogonal (e.g. Cartesian, cylindrical) coordinate system are routinely encountered in porous-medium numerical simulations. Such grids are referred to in this study as non-orthogonal grids because some cell faces are not orthogonal to a coordinate system plane (e.g. xy, yz or xz plane in Cartesian coordinates). Non-orthogonal grids are routinely encountered at the Savannah River Site in porous-medium flow simulations for Performance Assessments and groundwater flow modeling. Examples include grid lines that conform to the sloping roof of a waste tank or disposal unit in a 2D Performance Assessment simulation,more » and grid surfaces that conform to undulating stratigraphic surfaces in a 3D groundwater flow model. Particle tracking is routinely performed after a porous-medium numerical flow simulation to better understand the dynamics of the flow field and/or as an approximate indication of the trajectory and timing of advective solute transport. Particle tracks are computed by integrating the velocity field from cell to cell starting from designated seed (starting) positions. An accurate velocity field is required to attain accurate particle tracks. However, many numerical simulation codes report only the volumetric flowrate (e.g. PORFLOW) and/or flux (flowrate divided by area) crossing cell faces. For an orthogonal grid, the normal flux at a cell face is a component of the Darcy velocity vector in the coordinate system, and the pore velocity for particle tracking is attained by dividing by water content. For a non-orthogonal grid, the flux normal to a cell face that lies outside a coordinate plane is not a true component of velocity with respect to the coordinate system. Nonetheless, normal fluxes are often taken as Darcy velocity components, either naively or with accepted approximation. To enable accurate particle tracking or otherwise present an accurate depiction of the velocity field for a non-orthogonal grid, Darcy velocity components are rigorously derived in this study from normal fluxes to cell faces, which are assumed to be provided by or readily computed from porous-medium simulation code output. The normal fluxes are presumed to satisfy mass balances for every computational cell, and if so, the derived velocity fields are consistent with these mass balances. Derivations are provided for general two-dimensional quadrilateral and three-dimensional hexagonal systems, and for the commonly encountered special cases of perfectly vertical side faces in 2D and 3D and a rectangular footprint in 3D.« less

Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices.

PubMed

Leclerc, Arnaud; Carrington, Tucker

2014-05-07

We propose an iterative method for computing vibrational spectra that significantly reduces the memory cost of calculations. It uses a direct product primitive basis, but does not require storing vectors with as many components as there are product basis functions. Wavefunctions are represented in a basis each of whose functions is a sum of products (SOP) and the factorizable structure of the Hamiltonian is exploited. If the factors of the SOP basis functions are properly chosen, wavefunctions are linear combinations of a small number of SOP basis functions. The SOP basis functions are generated using a shifted block power method. The factors are refined with a rank reduction algorithm to cap the number of terms in a SOP basis function. The ideas are tested on a 20-D model Hamiltonian and a realistic CH3CN (12 dimensional) potential. For the 20-D problem, to use a standard direct product iterative approach one would need to store vectors with about 10(20) components and would hence require about 8 × 10(11) GB. With the approach of this paper only 1 GB of memory is necessary. Results for CH3CN agree well with those of a previous calculation on the same potential.

Orthogonal bases of invariants in tensor models

NASA Astrophysics Data System (ADS)

Diaz, Pablo; Rey, Soo-Jong

2018-02-01

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

A POD reduced order model for resolving angular direction in neutron/photon transport problems

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

Buchan, A.G., E-mail: andrew.buchan@imperial.ac.uk; Calloo, A.A.; Goffin, M.G.

2015-09-01

This article presents the first Reduced Order Model (ROM) that efficiently resolves the angular dimension of the time independent, mono-energetic Boltzmann Transport Equation (BTE). It is based on Proper Orthogonal Decomposition (POD) and uses the method of snapshots to form optimal basis functions for resolving the direction of particle travel in neutron/photon transport problems. A unique element of this work is that the snapshots are formed from the vector of angular coefficients relating to a high resolution expansion of the BTE's angular dimension. In addition, the individual snapshots are not recorded through time, as in standard POD, but instead theymore » are recorded through space. In essence this work swaps the roles of the dimensions space and time in standard POD methods, with angle and space respectively. It is shown here how the POD model can be formed from the POD basis functions in a highly efficient manner. The model is then applied to two radiation problems; one involving the transport of radiation through a shield and the other through an infinite array of pins. Both problems are selected for their complex angular flux solutions in order to provide an appropriate demonstration of the model's capabilities. It is shown that the POD model can resolve these fluxes efficiently and accurately. In comparison to high resolution models this POD model can reduce the size of a problem by up to two orders of magnitude without compromising accuracy. Solving times are also reduced by similar factors.« less

Large deformation analysis of axisymmetric inhomogeneities including coupled elastic and plastic anisotropy

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

Brannon, R.M.

1996-12-31

A mathematical framework is developed for the study of materials containing axisymmetric inclusions or flaws such as ellipsoidal voids, penny-shaped cracks, or fibers of circular cross-section. The general case of nonuniform statistical distributions of such heterogeneities is attacked by first considering a spatially uniform distribution of flaws that are all oriented in the same direction. Assuming an isotropic substrate, the macroscopic material properties of this simpler microstructure naturally should be transversely isotropic. An orthogonal basis for the linear subspace consisting of all double-symmetric transversely-isotropic fourth-order tensors associated with a given material vector is applied to deduce the explicit functional dependencemore » of the material properties of these aligned materials on the shared symmetry axis. The aligned and uniform microstructure seems geometrically simple enough that the macroscopic transversely isotropic properties could be derived in closed form. Since the resulting properties are transversely isotropic, the analyst must therefore be able to identify the appropriate coefficients of the transverse basis. Once these functions are identified, a principle of superposition of strain rates ay be applied to define an expectation integral for the composite properties of a material containing arbitrary anisotropic distributions of axisymmetric inhomogeneities. A proposal for coupling plastic anisotropy to the elastic anisotropy is presented in which the composite yield surface is interpreted as a distortion of the isotropic substrate yield surface; the distortion directions are coupled to the elastic anisotropy directions. Finally, some commonly assumed properties (such as major symmetry) of the Cauchy tangent stiffness tensor are shown to be inappropriate for large distortions of anisotropic materials.« less

An Alternate Set of Basis Functions for the Electromagnetic Solution of Arbitrarily-Shaped, Three-Dimensional, Closed, Conducting Bodies Using Method of Moments

NASA Technical Reports Server (NTRS)

Mackenzie, Anne I.; Baginski, Michael E.; Rao, Sadasiva M.

2008-01-01

In this work, we present an alternate set of basis functions, each defined over a pair of planar triangular patches, for the method of moments solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped, closed, conducting surfaces. The present basis functions are point-wise orthogonal to the pulse basis functions previously defined. The prime motivation to develop the present set of basis functions is to utilize them for the electromagnetic solution of dielectric bodies using a surface integral equation formulation which involves both electric and magnetic cur- rents. However, in the present work, only the conducting body solution is presented and compared with other data.

Visualizing vector field topology in fluid flows

NASA Technical Reports Server (NTRS)

Helman, James L.; Hesselink, Lambertus

1991-01-01

Methods of automating the analysis and display of vector field topology in general and flow topology in particular are discussed. Two-dimensional vector field topology is reviewed as the basis for the examination of topology in three-dimensional separated flows. The use of tangent surfaces and clipping in visualizing vector field topology in fluid flows is addressed.

SIC-POVMS and MUBS: Geometrical Relationships in Prime Dimension

NASA Astrophysics Data System (ADS)

Appleby, D. M.

2009-03-01

The paper concerns Weyl-Heisenberg covariant SIC-POVMs (symmetric informationally complete positive operator valued measures) and full sets of MUBs (mutually unbiased bases) in prime dimension. When represented as vectors in generalized Bloch space a SIC-POVM forms a d2-1 dimensional regular simplex (d being the Hilbert space dimension). By contrast, the generalized Bloch vectors representing a full set of MUBs form d+1 mutually orthogonal d-1 dimensional regular simplices. In this paper we show that, in the Weyl-Heisenberg case, there are some simple geometrical relationships between the single SIC-POVM simplex and the d+1 MUB simplices. We go on to give geometrical interpretations of the minimum uncertainty states introduced by Wootters and Sussman, and by Appleby, Dang and Fuchs, and of the fiduciality condition given by Appleby, Dang and Fuchs.

New vibration-rotation code for tetraatomic molecules exhibiting wide-amplitude motion: WAVR4

NASA Astrophysics Data System (ADS)

Kozin, Igor N.; Law, Mark M.; Tennyson, Jonathan; Hutson, Jeremy M.

2004-11-01

A general computational method for the accurate calculation of rotationally and vibrationally excited states of tetraatomic molecules is developed. The resulting program is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. The program offers a choice of coordinate systems based on Radau, Jacobi, diatom-diatom and orthogonal satellite vectors. The method includes all six vibrational dimensions plus three rotational dimensions. Vibration-rotation calculations with reduced dimensionality in the radial degrees of freedom are easily tackled via constraints imposed on the radial coordinates via the input file. Program summaryTitle of program: WAVR4 Catalogue number: ADUN Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUN Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: Persons requesting the program must sign the standard CPC nonprofit use license Computer: Developed under Tru64 UNIX, ported to Microsoft Windows and Sun Unix Operating systems under which the program has been tested: Tru64 Unix, Microsoft Windows, Sun Unix Programming language used: Fortran 90 Memory required to execute with typical data: case dependent No. of lines in distributed program, including test data, etc.: 11 937 No. of bytes in distributed program, including test data, etc.: 84 770 Distribution format: tar.gz Nature of physical problem: WAVR4 calculates the bound ro-vibrational levels and wavefunctions of a tetraatomic system using body-fixed coordinates based on generalised orthogonal vectors. Method of solution: The angular coordinates are treated using a finite basis representation (FBR) based on products of spherical harmonics. A discrete variable representation (DVR) [1] based on either Morse-oscillator-like or spherical-oscillator functions [2] is used for the radial coordinates. Matrix elements are computed using an efficient Gaussian quadrature in the angular coordinates and the DVR approximation in the radial coordinates. The solution of the secular problem is carried through a series of intermediate diagonalisations and truncations. Restrictions on the complexity of the problem: (1) The size of the final Hamiltonian matrix that can be practically diagonalised; (2) The DVR approximation for a radial coordinate fails for values of the coordinate near zero—this is remedied only for one radial coordinate by using analytical integration. Typical running time: problem-dependent Unusual features of the program: A user-supplied subroutine to evaluate the potential energy is a program requirement. External routines: BLAS and LAPACK are required. References: [1] J.C. Light, I.P. Hamilton, J.V. Lill, J. Chem. Phys. 92 (1985) 1400. [2] J.R. Henderson, C.R. Le Sueur, J. Tennyson, Comp. Phys. Comm. 75 (1993) 379.

Electronic energy transfer through non-adiabatic vibrational-electronic resonance. I. Theory for a dimer

NASA Astrophysics Data System (ADS)

Tiwari, Vivek; Peters, William K.; Jonas, David M.

2017-10-01

Non-adiabatic vibrational-electronic resonance in the excited electronic states of natural photosynthetic antennas drastically alters the adiabatic framework, in which electronic energy transfer has been conventionally studied, and suggests the possibility of exploiting non-adiabatic dynamics for directed energy transfer. Here, a generalized dimer model incorporates asymmetries between pigments, coupling to the environment, and the doubly excited state relevant for nonlinear spectroscopy. For this generalized dimer model, the vibrational tuning vector that drives energy transfer is derived and connected to decoherence between singly excited states. A correlation vector is connected to decoherence between the ground state and the doubly excited state. Optical decoherence between the ground and singly excited states involves linear combinations of the correlation and tuning vectors. Excitonic coupling modifies the tuning vector. The correlation and tuning vectors are not always orthogonal, and both can be asymmetric under pigment exchange, which affects energy transfer. For equal pigment vibrational frequencies, the nonadiabatic tuning vector becomes an anti-correlated delocalized linear combination of intramolecular vibrations of the two pigments, and the nonadiabatic energy transfer dynamics become separable. With exchange symmetry, the correlation and tuning vectors become delocalized intramolecular vibrations that are symmetric and antisymmetric under pigment exchange. Diabatic criteria for vibrational-excitonic resonance demonstrate that anti-correlated vibrations increase the range and speed of vibronically resonant energy transfer (the Golden Rule rate is a factor of 2 faster). A partial trace analysis shows that vibronic decoherence for a vibrational-excitonic resonance between two excitons is slower than their purely excitonic decoherence.

Electronic energy transfer through non-adiabatic vibrational-electronic resonance. I. Theory for a dimer.

PubMed

Tiwari, Vivek; Peters, William K; Jonas, David M

2017-10-21

Non-adiabatic vibrational-electronic resonance in the excited electronic states of natural photosynthetic antennas drastically alters the adiabatic framework, in which electronic energy transfer has been conventionally studied, and suggests the possibility of exploiting non-adiabatic dynamics for directed energy transfer. Here, a generalized dimer model incorporates asymmetries between pigments, coupling to the environment, and the doubly excited state relevant for nonlinear spectroscopy. For this generalized dimer model, the vibrational tuning vector that drives energy transfer is derived and connected to decoherence between singly excited states. A correlation vector is connected to decoherence between the ground state and the doubly excited state. Optical decoherence between the ground and singly excited states involves linear combinations of the correlation and tuning vectors. Excitonic coupling modifies the tuning vector. The correlation and tuning vectors are not always orthogonal, and both can be asymmetric under pigment exchange, which affects energy transfer. For equal pigment vibrational frequencies, the nonadiabatic tuning vector becomes an anti-correlated delocalized linear combination of intramolecular vibrations of the two pigments, and the nonadiabatic energy transfer dynamics become separable. With exchange symmetry, the correlation and tuning vectors become delocalized intramolecular vibrations that are symmetric and antisymmetric under pigment exchange. Diabatic criteria for vibrational-excitonic resonance demonstrate that anti-correlated vibrations increase the range and speed of vibronically resonant energy transfer (the Golden Rule rate is a factor of 2 faster). A partial trace analysis shows that vibronic decoherence for a vibrational-excitonic resonance between two excitons is slower than their purely excitonic decoherence.

New separated polynomial solutions to the Zernike system on the unit disk and interbasis expansion.

PubMed

Pogosyan, George S; Wolf, Kurt Bernardo; Yakhno, Alexander

2017-10-01

The differential equation proposed by Frits Zernike to obtain a basis of polynomial orthogonal solutions on the unit disk to classify wavefront aberrations in circular pupils is shown to have a set of new orthonormal solution bases involving Legendre and Gegenbauer polynomials in nonorthogonal coordinates, close to Cartesian ones. We find the overlaps between the original Zernike basis and a representative of the new set, which turn out to be Clebsch-Gordan coefficients.

A linear polarization converter with near unity efficiency in microwave regime

NASA Astrophysics Data System (ADS)

Xu, Peng; Wang, Shen-Yun; Geyi, Wen

2017-04-01

In this paper, we present a linear polarization converter in the reflective mode with near unity conversion efficiency. The converter is designed in an array form on the basis of a pair of orthogonally arranged three-dimensional split-loop resonators sharing a common terminal coaxial port and a continuous metallic ground slab. It converts the linearly polarized incident electromagnetic wave at resonance to its orthogonal counterpart upon the reflection mode. The conversion mechanism is explained by an equivalent circuit model, and the conversion efficiency can be tuned by changing the impedance of the terminal port. Such a scheme of the linear polarization converter has potential applications in microwave communications, remote sensing, and imaging.

Geometric convex cone volume analysis

NASA Astrophysics Data System (ADS)

Li, Hsiao-Chi; Chang, Chein-I.

2016-05-01

Convexity is a major concept used to design and develop endmember finding algorithms (EFAs). For abundance unconstrained techniques, Pixel Purity Index (PPI) and Automatic Target Generation Process (ATGP) which use Orthogonal Projection (OP) as a criterion, are commonly used method. For abundance partially constrained techniques, Convex Cone Analysis is generally preferred which makes use of convex cones to impose Abundance Non-negativity Constraint (ANC). For abundance fully constrained N-FINDR and Simplex Growing Algorithm (SGA) are most popular methods which use simplex volume as a criterion to impose ANC and Abundance Sum-to-one Constraint (ASC). This paper analyze an issue encountered in volume calculation with a hyperplane introduced to illustrate an idea of bounded convex cone. Geometric Convex Cone Volume Analysis (GCCVA) projects the boundary vectors of a convex cone orthogonally on a hyperplane to reduce the effect of background signatures and a geometric volume approach is applied to address the issue arose from calculating volume and further improve the performance of convex cone-based EFAs.

Characterising dark matter searches at colliders and direct detection experiments: Vector mediators

DOE PAGES

Buchmueller, Oliver; Dolan, Matthew J.; Malik, Sarah A.; ...

2015-01-09

We introduce a Minimal Simplified Dark Matter (MSDM) framework to quantitatively characterise dark matter (DM) searches at the LHC. We study two MSDM models where the DM is a Dirac fermion which interacts with a vector and axial-vector mediator. The models are characterised by four parameters: m DM, M med , g DM and g q, the DM and mediator masses, and the mediator couplings to DM and quarks respectively. The MSDM models accurately capture the full event kinematics, and the dependence on all masses and couplings can be systematically studied. The interpretation of mono-jet searches in this framework canmore » be used to establish an equal-footing comparison with direct detection experiments. For theories with a vector mediator, LHC mono-jet searches possess better sensitivity than direct detection searches for light DM masses (≲5 GeV). For axial-vector mediators, LHC and direct detection searches generally probe orthogonal directions in the parameter space. We explore the projected limits of these searches from the ultimate reach of the LHC and multi-ton xenon direct detection experiments, and find that the complementarity of the searches remains. In conclusion, we provide a comparison of limits in the MSDM and effective field theory (EFT) frameworks to highlight the deficiencies of the EFT framework, particularly when exploring the complementarity of mono-jet and direct detection searches.« less

A Removal of Eye Movement and Blink Artifacts from EEG Data Using Morphological Component Analysis

PubMed Central

Wagatsuma, Hiroaki

2017-01-01

EEG signals contain a large amount of ocular artifacts with different time-frequency properties mixing together in EEGs of interest. The artifact removal has been substantially dealt with by existing decomposition methods known as PCA and ICA based on the orthogonality of signal vectors or statistical independence of signal components. We focused on the signal morphology and proposed a systematic decomposition method to identify the type of signal components on the basis of sparsity in the time-frequency domain based on Morphological Component Analysis (MCA), which provides a way of reconstruction that guarantees accuracy in reconstruction by using multiple bases in accordance with the concept of “dictionary.” MCA was applied to decompose the real EEG signal and clarified the best combination of dictionaries for this purpose. In our proposed semirealistic biological signal analysis with iEEGs recorded from the brain intracranially, those signals were successfully decomposed into original types by a linear expansion of waveforms, such as redundant transforms: UDWT, DCT, LDCT, DST, and DIRAC. Our result demonstrated that the most suitable combination for EEG data analysis was UDWT, DST, and DIRAC to represent the baseline envelope, multifrequency wave-forms, and spiking activities individually as representative types of EEG morphologies. PMID:28194221

Very high order discontinuous Galerkin method in elliptic problems

NASA Astrophysics Data System (ADS)

Jaśkowiec, Jan

2017-09-01

The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

Very high order discontinuous Galerkin method in elliptic problems

NASA Astrophysics Data System (ADS)

Jaśkowiec, Jan

2018-07-01

The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

The Vector Electric Field Instrument on the C/NOFS Satellite

NASA Technical Reports Server (NTRS)

Pfaff, R.; Kujawski, J.; Uribe, P.; Bromund, K.; Fourre, R.; Acuna, M.; Le, G.; Farrell, W.; Holzworth, R.; McCarthy, M.;

New Basis Functions for the Electromagnetic Solution of Arbitrarily-shaped, Three Dimensional Conducting Bodies Using Method of Moments

NASA Technical Reports Server (NTRS)

Mackenzie, Anne I.; Baginski, Michael E.; Rao, Sadasiva M.

2007-01-01

In this work, we present a new set of basis functions, de ned over a pair of planar triangular patches, for the solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped surfaces using the method of moments solution procedure. The basis functions are constant over the function subdomain and resemble pulse functions for one and two dimensional problems. Further, another set of basis functions, point-wise orthogonal to the first set, is also de ned over the same function space. The primary objective of developing these basis functions is to utilize them for the electromagnetic solution involving conducting, dielectric, and composite bodies. However, in the present work, only the conducting body solution is presented and compared with other data.

New Basis Functions for the Electromagnetic Solution of Arbitrarily-shaped, Three Dimensional Conducting Bodies using Method of Moments

NASA Technical Reports Server (NTRS)

Mackenzie, Anne I.; Baginski, Michael E.; Rao, Sadasiva M.

2008-01-01

In this work, we present a new set of basis functions, defined over a pair of planar triangular patches, for the solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped surfaces using the method of moments solution procedure. The basis functions are constant over the function subdomain and resemble pulse functions for one and two dimensional problems. Further, another set of basis functions, point-wise orthogonal to the first set, is also defined over the same function space. The primary objective of developing these basis functions is to utilize them for the electromagnetic solution involving conducting, dielectric, and composite bodies. However, in the present work, only the conducting body solution is presented and compared with other data.

Practical auxiliary basis implementation of Rung 3.5 functionals

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

Janesko, Benjamin G., E-mail: b.janesko@tcu.edu; Scalmani, Giovanni; Frisch, Michael J.

2014-07-21

Approximate exchange-correlation functionals for Kohn-Sham density functional theory often benefit from incorporating exact exchange. Exact exchange is constructed from the noninteracting reference system's nonlocal one-particle density matrix γ(r{sup -vector},r{sup -vector}′). Rung 3.5 functionals attempt to balance the strengths and limitations of exact exchange using a new ingredient, a projection of γ(r{sup -vector},r{sup -vector} ′) onto a semilocal model density matrix γ{sub SL}(ρ(r{sup -vector}),∇ρ(r{sup -vector}),r{sup -vector}−r{sup -vector} ′). γ{sub SL} depends on the electron density ρ(r{sup -vector}) at reference point r{sup -vector}, and is closely related to semilocal model exchange holes. We present a practical implementation of Rung 3.5 functionals, expandingmore » the r{sup -vector}−r{sup -vector} ′ dependence of γ{sub SL} in an auxiliary basis set. Energies and energy derivatives are obtained from 3D numerical integration as in standard semilocal functionals. We also present numerical tests of a range of properties, including molecular thermochemistry and kinetics, geometries and vibrational frequencies, and bandgaps and excitation energies. Rung 3.5 functionals typically provide accuracy intermediate between semilocal and hybrid approximations. Nonlocal potential contributions from γ{sub SL} yield interesting successes and failures for band structures and excitation energies. The results enable and motivate continued exploration of Rung 3.5 functional forms.« less

Optical rogue waves associated with the negative coherent coupling in an isotropic medium.

PubMed

Sun, Wen-Rong; Tian, Bo; Jiang, Yan; Zhen, Hui-Ling

2015-02-01

Optical rogue waves of the coupled nonlinear Schrödinger equations with negative coherent coupling, which describe the propagation of orthogonally polarized optical waves in an isotropic medium, are reported. We construct and discuss a family of the vector rogue-wave solutions, including the bright rogue waves, four-petaled rogue waves, and dark rogue waves. A bright rogue wave without a valley can split up, giving birth to two bright rogue waves, and an eye-shaped rogue wave can split up, giving birth to two dark rogue waves.

Multi-Body Dynamics Including the Effects of Flexibility and Compliance.

DTIC Science & Technology

1980-04-01

SJIs k (3) where SJK is a 3 x 3 orthogonal transformation matrix defined as [47]: SJK - ji ! i (4) (Regarding notation, the J and K in SJK and the...indicates that the derivative is computed in R. However, since the nkj are fixed in Bk, their derivatives may be written as k x nk where .k is the angular...single rotation about an appropriate axis. If X k is a unit vector along this axis and if 1 is the rotation angle, the four Euler parameters describing

Singular value description of a digital radiographic detector: Theory and measurements

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

Kyprianou, Iacovos S.; Badano, Aldo; Gallas, Brandon D.

The H operator represents the deterministic performance of any imaging system. For a linear, digital imaging system, this system operator can be written in terms of a matrix, H, that describes the deterministic response of the system to a set of point objects. A singular value decomposition of this matrix results in a set of orthogonal functions (singular vectors) that form the system basis. A linear combination of these vectors completely describes the transfer of objects through the linear system, where the respective singular values associated with each singular vector describe the magnitude with which that contribution to the objectmore » is transferred through the system. This paper is focused on the measurement, analysis, and interpretation of the H matrix for digital x-ray detectors. A key ingredient in the measurement of the H matrix is the detector response to a single x ray (or infinitestimal x-ray beam). The authors have developed a method to estimate the 2D detector shift-variant, asymmetric ray response function (RRF) from multiple measured line response functions (LRFs) using a modified edge technique. The RRF measurements cover a range of x-ray incident angles from 0 deg. (equivalent location at the detector center) to 30 deg. (equivalent location at the detector edge) for a standard radiographic or cone-beam CT geometric setup. To demonstrate the method, three beam qualities were tested using the inherent, Lu/Er, and Yb beam filtration. The authors show that measures using the LRF, derived from an edge measurement, underestimate the system's performance when compared with the H matrix derived using the RRF. Furthermore, the authors show that edge measurements must be performed at multiple directions in order to capture rotational asymmetries of the RRF. The authors interpret the results of the H matrix SVD and provide correlations with the familiar MTF methodology. Discussion is made about the benefits of the H matrix technique with regards to signal detection theory, and the characterization of shift-variant imaging systems.« less

A vector fetal magnetocardiogram system with high sensitivity

NASA Astrophysics Data System (ADS)

Kandori, Akihiko; Miyashita, Tsuyoshi; Tsukada, Keiji; Horigome, Hitoshi; Asaka, Mitsuhiro; Shigemitsu, Sadahiko; Takahashi, Miho; Terada, Yasushi; Mitsui, Toshio; Chiba, Yoshihide

1999-12-01

The vector fetal magnetocardiogram (V-FMCG) system that measures the three orthogonal components of the magnetic field from a fetal heart has been developed to clearly observe fetal cardiac activity during pregnancy by using the superconducting quantum interference device. To detect a clear V-FMCG signal, the bottom of the cryostat was made of thin glass-fiber-reinforced plastic and the total length between the pickup coil to the outer surface is 12 mm. Because the cryostat bottom was made thinner, the area of the cryostat's top and bottom could be made smaller, thus a low evaporation loss (<1.2 l per day) and a long refilling interval (>10 days) were obtained. The gantry was able to tilt the cryostat and the bed could move in three axis directions, which made it possible to easily locate the vector pickup coil at an optimum position to obtain the maximum magnetic field from a fetal heart. We obtained V-FMCGs from 21 normal fetuses with gestation periods of 27-38 weeks. Using these vector signals, the dipoles were estimated and the relationship between the strength of the dipole moments and the number of gestation weeks could be obtained. Thus, V-FMCG seems to represent a new noninvasive tool for clearly detecting the electrophysiological activity of a fetal heart.

Noise-induced drift in two-dimensional anisotropic systems

NASA Astrophysics Data System (ADS)

Farago, Oded

2017-10-01

We study the isothermal Brownian dynamics of a particle in a system with spatially varying diffusivity. Due to the heterogeneity of the system, the particle's mean displacement does not vanish even if it does not experience any physical force. This phenomenon has been termed "noise-induced drift," and has been extensively studied for one-dimensional systems. Here, we examine the noise-induced drift in a two-dimensional anisotropic system, characterized by a symmetric diffusion tensor with unequal diagonal elements. A general expression for the mean displacement vector is derived and presented as a sum of two vectors, depicting two distinct drifting effects. The first vector describes the tendency of the particle to drift toward the high diffusivity side in each orthogonal principal diffusion direction. This is a generalization of the well-known expression for the noise-induced drift in one-dimensional systems. The second vector represents a novel drifting effect, not found in one-dimensional systems, originating from the spatial rotation in the directions of the principal axes. The validity of the derived expressions is verified by using Langevin dynamics simulations. As a specific example, we consider the relative diffusion of two transmembrane proteins, and demonstrate that the average distance between them increases at a surprisingly fast rate of several tens of micrometers per second.

Vector control of wind turbine on the basis of the fuzzy selective neural net*

NASA Astrophysics Data System (ADS)

Engel, E. A.; Kovalev, I. V.; Engel, N. E.

2016-04-01

An article describes vector control of wind turbine based on fuzzy selective neural net. Based on the wind turbine system’s state, the fuzzy selective neural net tracks an maximum power point under random perturbations. Numerical simulations are accomplished to clarify the applicability and advantages of the proposed vector wind turbine’s control on the basis of the fuzzy selective neuronet. The simulation results show that the proposed intelligent control of wind turbine achieves real-time control speed and competitive performance, as compared to a classical control model with PID controllers based on traditional maximum torque control strategy.

Rigidly rotating zero-angular-momentum observer surfaces in the Kerr spacetime

NASA Astrophysics Data System (ADS)

Frolov, Andrei V.; Frolov, Valeri P.

2014-12-01

A stationary observer in the Kerr spacetime has zero angular momentum if their angular velocity ω has a particular value, which depends on the position of the observer. Worldlines of such zero-angular-momentum observers (ZAMOs) with the same value of the angular velocity ω form a three-dimensional surface, which has the property that the Killing vectors generating time translation and rotation are tangent to it. We call such a surface a rigidly rotating ZAMO surface. This definition allows for a natural generalization to the surfaces inside the black hole, where ZAMO trajectories formally become spacelike. A general property of such a surface is that there exist linear combinations of the Killing vectors with constant coefficients which make them orthogonal on it. In this paper we discuss properties of the rigidly rotating ZAMO surfaces both outside and inside the black hole and the relevance of these objects to a couple of interesting physical problems.

Truncated feature representation for automatic target detection using transformed data-based decomposition

NASA Astrophysics Data System (ADS)

Riasati, Vahid R.

2016-05-01

In this work, the data covariance matrix is diagonalized to provide an orthogonal bases set using the eigen vectors of the data. The eigen-vector decomposition of the data is transformed and filtered in the transform domain to truncate the data for robust features related to a specified set of targets. These truncated eigen features are then combined and reconstructed to utilize in a composite filter and consequently utilized for the automatic target detection of the same class of targets. The results associated with the testing of the current technique are evaluated using the peak-correlation and peak-correlation energy metrics and are presented in this work. The inverse transformed eigen-bases of the current technique may be thought of as an injected sparsity to minimize data in representing the skeletal data structure information associated with the set of targets under consideration.

Intertwining solutions for magnetic relativistic Hartree type equations

NASA Astrophysics Data System (ADS)

Cingolani, Silvia; Secchi, Simone

2018-05-01

We consider the magnetic pseudo-relativistic Schrödinger equation where , m  >  0, is an external continuous scalar potential, is a continuous vector potential and is a convolution kernel, is a constant, , . We assume that A and V are symmetric with respect to a closed subgroup G of the group of orthogonal linear transformations of . If for any , the cardinality of the G-orbit of x is infinite, then we prove the existence of infinitely many intertwining solutions assuming that is either linear in x or uniformly bounded. The results are proved by means of a new local realization of the square root of the magnetic laplacian to a local elliptic operator with Neumann boundary condition on a half-space. Moreover we derive an existence result of a ground state intertwining solution for bounded vector potentials, if G admits a finite orbit.

Simultaneously frequency down-conversion, independent multichannel phase shifting and zero-IF receiving using a phase modulator in a sagnac loop and balanced detection

NASA Astrophysics Data System (ADS)

Zhu, Zihang; Zhao, Shanghong; Li, Xuan; Lin, Tao; Hu, Dapeng

2018-03-01

Photonic microwave frequency down-conversion with independent multichannel phase shifting and zero-intermediate frequency (IF) receiving is proposed and demonstrated by simulation. By combined use of a phase modulator (PM) in a sagnac loop and an optical bandpass filter (OBPF), orthogonal polarized carrier suppression single sideband (CS-SSB) signals are obtained. By adjusting the polarization controllers (PCs) to introduce the phase difference in the optical domain and using balanced detection to eliminate the direct current components, the phase of the generated IF signal can be arbitrarily tuned. Besides, the radio frequency (RF) vector signal can be also frequency down-converted to baseband directly by choosing two quadrature channels. In the simulation, high gain and continuously tunable phase shifts over the 360 degree range are verified. Furthermore, 2.5 Gbit/s RF vector signals centered at 10 GHz with different modulation formats are successfully demodulated.

An introduction to tensor calculus, relativity and cosmology /3rd edition/

NASA Astrophysics Data System (ADS)

Lawden, D. F.

This textbook introduction to the principles of special relativity proceeds within the context of cartesian tensors. Newton's laws of motion are reviewed, as are the Lorentz transformations, Minkowski space-time, and the Fitzgerald contraction. Orthogonal transformations are described, and invariants, gradients, tensor derivatives, contraction, scalar products, divergence, pseudotensors, vector products, and curl are defined. Special relativity mechanics are explored in terms of mass, momentum, the force vector, the Lorentz transformation equations for force, calculations for photons and neutrinos, the development of the Lagrange and Hamilton equations, and the energy-momentum tensor. Electrodynamics is investigated, together with general tensor calculus and Riemmanian space. The General Theory of Relativity is presented, along with applications to astrophysical phenomena such as black holes and gravitational waves. Finally, analytical discussions of cosmological problems are reviewed, particularly Einstein, de Sitter, and Friedmann universes, redshifts, event horizons, and the redshift.

Improvements in Block-Krylov Ritz Vectors and the Boundary Flexibility Method of Component Synthesis

NASA Technical Reports Server (NTRS)

Carney, Kelly Scott

1997-01-01

A method of dynamic substructuring is presented which utilizes a set of static Ritz vectors as a replacement for normal eigenvectors in component mode synthesis. This set of Ritz vectors is generated in a recurrence relationship, proposed by Wilson, which has the form of a block-Krylov subspace. The initial seed to the recurrence algorithm is based upon the boundary flexibility vectors of the component. Improvements have been made in the formulation of the initial seed to the Krylov sequence, through the use of block-filtering. A method to shift the Krylov sequence to create Ritz vectors that will represent the dynamic behavior of the component at target frequencies, the target frequency being determined by the applied forcing functions, has been developed. A method to terminate the Krylov sequence has also been developed. Various orthonormalization schemes have been developed and evaluated, including the Cholesky/QR method. Several auxiliary theorems and proofs which illustrate issues in component mode synthesis and loss of orthogonality in the Krylov sequence have also been presented. The resulting methodology is applicable to both fixed and free- interface boundary components, and results in a general component model appropriate for any type of dynamic analysis. The accuracy is found to be comparable to that of component synthesis based upon normal modes, using fewer generalized coordinates. In addition, the block-Krylov recurrence algorithm is a series of static solutions and so requires significantly less computation than solving the normal eigenspace problem. The requirement for less vectors to form the component, coupled with the lower computational expense of calculating these Ritz vectors, combine to create a method more efficient than traditional component mode synthesis.

A Galerkin Approach to Define Measured Terrain Surfaces with Analytic Basis Vectors to Produce a Compact Representation

DTIC Science & Technology

2010-11-01

defined herein as terrain whose surface deformation due to a single vehicle traversing the surface is negligible, such as paved roads (both asphalt ...ground vehicle reliability predictions. Current application of this work is limited to the analysis of U.S. Highways, comprised of both asphalt and...Highways that are consistent between asphalt and concrete roads b. The principle terrain characteristics are defined with analytic basis vectors

Approximate techniques of structural reanalysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Lowder, H. E.

1974-01-01

A study is made of two approximate techniques for structural reanalysis. These include Taylor series expansions for response variables in terms of design variables and the reduced-basis method. In addition, modifications to these techniques are proposed to overcome some of their major drawbacks. The modifications include a rational approach to the selection of the reduced-basis vectors and the use of Taylor series approximation in an iterative process. For the reduced basis a normalized set of vectors is chosen which consists of the original analyzed design and the first-order sensitivity analysis vectors. The use of the Taylor series approximation as a first (initial) estimate in an iterative process, can lead to significant improvements in accuracy, even with one iteration cycle. Therefore, the range of applicability of the reanalysis technique can be extended. Numerical examples are presented which demonstrate the gain in accuracy obtained by using the proposed modification techniques, for a wide range of variations in the design variables.

Semistochastic approach to many electron systems

NASA Astrophysics Data System (ADS)

Grossjean, M. K.; Grossjean, M. F.; Schulten, K.; Tavan, P.

1992-08-01

A Pariser-Parr-Pople (PPP) Hamiltonian of an 8π electron system of the molecule octatetraene, represented in a configuration-interaction basis (CI basis), is analyzed with respect to the statistical properties of its matrix elements. Based on this analysis we develop an effective Hamiltonian, which represents virtual excitations by a Gaussian orthogonal ensemble (GOE). We also examine numerical approaches which replace the original Hamiltonian by a semistochastically generated CI matrix. In that CI matrix, the matrix elements of high energy excitations are choosen randomly according to distributions reflecting the statistics of the original CI matrix.

Cross-Sectional and Longitudinal Investigation of the Power Vector in Astigmatism: The Yamagata Study (Funagata).

PubMed

Namba, Hiroyuki; Kawasaki, Ryo; Sugano, Akira; Nishi, Katsuhiro; Murakami, Takanori; Nishitsuka, Koichi; Kato, Takeo; Kayama, Takamasa; Yamashita, Hidetoshi

2018-01-01

To investigate how age and other factors affect astigmatism in Japanese adults over a period of 5 years. We included 512 Japanese participants who had undergone systemic and ophthalmological examinations both in 2005-2007 and in 2010-2012 in Funagata town, Yamagata, Japan. Astigmatism was evaluated using power vector analyses, where J0 represents the power of orthogonal astigmatism. Positive values of J0 indicate with-the-rule astigmatism, whereas negative values indicate against-the-rule (ATR). In this cross-sectional investigation, J0 represented the power of orthogonal astigmatism, and multivariate regression revealed that both J0 and corneal J0 (cJ0) declined with increasing age (both P < 0.001). In a longitudinal investigation spanning 5 years, the mean amounts of change (Δ) in J0 and ΔcJ0 were -0.045 ± 0.308 and -0.072 ± 0.278, respectively. This confirmed an ATR shift with increasing age in most individuals. The age-divided distribution of the magnitude of differences indicated that older age was associated with a larger astigmatic change over a 5-year period in both the cornea and the entire eye. Using multivariate logistic regression, we observed that older age at baseline was a risk factor for low ΔJ0, indicating a large shift toward ATR astigmatism. We confirmed that a refractive and keratometric shift toward ATR astigmatism occurs with aging. Older age at baseline was also associated with a larger magnitude of astigmatic changes over the subsequent 5 years.

Representation of the equatorial stratospheric quasi-biennial oscillation in EOF phase space. [EOF (empirical orthogonal function)

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

Wallace, J.M.; Panetta, R.L.; Estberg, J.

1993-06-15

A 35-year record of monthly mean zonal wind data for the equatorial stratosphere is represented in terms of a vector (radius and phase angle) in a two-dimensional phase space defined by the normalized expansion coefficients of the two leading empirical orthogonal functions (EOFs) of the vertical structure. The tip of the vector completes one nearly circular loop during each cycle of the quasi-biennial oscillation (QBO). Hence, its position and rate of progress along the orbit of the point provide a measure of the instantaneous amplitude and rate of phase progression of the QBO. Although the phase of the QBO bearsmore » little if any relation to calendar month, the rate of phase progression is strongly modulated by the first and second harmonics of the annual cycle, with a primary maximum in April/May, in agreement with previous studies based on the descent rates of easterly and westerly regimes. A simple linear prediction model is developed for the rate of phase progression, based on the phase of the QBO and the phase of the annual cycle. The model is capable of hindcasting the phase of the QBO to within a specified degree of accuracy approximately 50% longer than a default scheme based on the mean observed rate of phase progression of the QBO (1 cycle per 28.1 months). If the seasonal dependence is ignored, the prediction equation corresponds to the [open quotes]circle map,[close quotes] for which an extensive literature exists in dynamical systems theory. 17 refs., 14 figs., 2 tabs.« less

One-Channel Surface Electromyography Decomposition for Muscle Force Estimation.

PubMed

Sun, Wentao; Zhu, Jinying; Jiang, Yinlai; Yokoi, Hiroshi; Huang, Qiang

2018-01-01

Estimating muscle force by surface electromyography (sEMG) is a non-invasive and flexible way to diagnose biomechanical diseases and control assistive devices such as prosthetic hands. To estimate muscle force using sEMG, a supervised method is commonly adopted. This requires simultaneous recording of sEMG signals and muscle force measured by additional devices to tune the variables involved. However, recording the muscle force of the lost limb of an amputee is challenging, and the supervised method has limitations in this regard. Although the unsupervised method does not require muscle force recording, it suffers from low accuracy due to a lack of reference data. To achieve accurate and easy estimation of muscle force by the unsupervised method, we propose a decomposition of one-channel sEMG signals into constituent motor unit action potentials (MUAPs) in two steps: (1) learning an orthogonal basis of sEMG signals through reconstruction independent component analysis; (2) extracting spike-like MUAPs from the basis vectors. Nine healthy subjects were recruited to evaluate the accuracy of the proposed approach in estimating muscle force of the biceps brachii. The results demonstrated that the proposed approach based on decomposed MUAPs explains more than 80% of the muscle force variability recorded at an arbitrary force level, while the conventional amplitude-based approach explains only 62.3% of this variability. With the proposed approach, we were also able to achieve grip force control of a prosthetic hand, which is one of the most important clinical applications of the unsupervised method. Experiments on two trans-radial amputees indicated that the proposed approach improves the performance of the prosthetic hand in grasping everyday objects.

Artificial Vector Calibration Method for Differencing Magnetic Gradient Tensor Systems

PubMed Central

Li, Zhining; Zhang, Yingtang; Yin, Gang

2018-01-01

The measurement error of the differencing (i.e., using two homogenous field sensors at a known baseline distance) magnetic gradient tensor system includes the biases, scale factors, nonorthogonality of the single magnetic sensor, and the misalignment error between the sensor arrays, all of which can severely affect the measurement accuracy. In this paper, we propose a low-cost artificial vector calibration method for the tensor system. Firstly, the error parameter linear equations are constructed based on the single-sensor’s system error model to obtain the artificial ideal vector output of the platform, with the total magnetic intensity (TMI) scalar as a reference by two nonlinear conversions, without any mathematical simplification. Secondly, the Levenberg–Marquardt algorithm is used to compute the integrated model of the 12 error parameters by nonlinear least-squares fitting method with the artificial vector output as a reference, and a total of 48 parameters of the system is estimated simultaneously. The calibrated system outputs along the reference platform-orthogonal coordinate system. The analysis results show that the artificial vector calibrated output can track the orientation fluctuations of TMI accurately, effectively avoiding the “overcalibration” problem. The accuracy of the error parameters’ estimation in the simulation is close to 100%. The experimental root-mean-square error (RMSE) of the TMI and tensor components is less than 3 nT and 20 nT/m, respectively, and the estimation of the parameters is highly robust. PMID:29373544

On the theoretical link between LLL-reduction and Lambda-decorrelation

NASA Astrophysics Data System (ADS)

Lannes, A.

2013-04-01

The LLL algorithm, introduced by Lenstra et al. (Math Ann 261:515-534, 1982), plays a key role in many fields of applied mathematics. In particular, it is used as an effective numerical tool for preconditioning the integer least-squares problems arising in high-precision geodetic positioning and Global Navigation Satellite Systems (GNSS). In 1992, Teunissen developed a method for solving these nearest-lattice point (NLP) problems. This method is referred to as Lambda (for Least-squares AMBiguity Decorrelation Adjustment). The preconditioning stage of Lambda corresponds to its decorrelation algorithm. From an epistemological point of view, the latter was devised through an innovative statistical approach completely independent of the LLL algorithm. Recent papers pointed out some similarities between the LLL algorithm and the Lambda-decorrelation algorithm. We try to clarify this point in the paper. We first introduce a parameter measuring the orthogonality defect of the integer basis in which the NLP problem is solved, the LLL-reduced basis of the LLL algorithm, or the Λ -basis of the Lambda method. With regard to this problem, the potential qualities of these bases can then be compared. The Λ -basis is built by working at the level of the variance-covariance matrix of the float solution, while the LLL-reduced basis is built by working at the level of its inverse. As a general rule, the orthogonality defect of the Λ -basis is greater than that of the corresponding LLL-reduced basis; these bases are however very close to one another. To specify this tight relationship, we present a method that provides the dual LLL-reduced basis of a given Λ -basis. As a consequence of this basic link, all the recent developments made on the LLL algorithm can be applied to the Lambda-decorrelation algorithm. This point is illustrated in a concrete manner: we present a parallel Λ -type decorrelation algorithm derived from the parallel LLL algorithm of Luo and Qiao (Proceedings of the fourth international C^* conference on computer science and software engineering. ACM Int Conf P Series. ACM Press, pp 93-101, 2012).

Modeling of mass transfer of Phospholipids in separation process with supercritical CO2 fluid by RBF artificial neural networks

USDA-ARS?s Scientific Manuscript database

An artificial Radial Basis Function (RBF) neural network model was developed for the prediction of mass transfer of the phospholipids from canola meal in supercritical CO2 fluid. The RBF kind of artificial neural networks (ANN) with orthogonal least squares (OLS) learning algorithm were used for mod...

The Unevenness and Non-orthogonal State of Distribution of Corneal Thickness and the Influence on Correction of Myopic Astigmatism by LASEK.

PubMed

Wang, Shulin; Wang, Xin; Liu, Mingna; Wang, Haiying; Li, Jing; Shi, Weiyun

2015-09-01

To observe and calculate the unevenness and the non-orthogonal state of distribution of corneal thickness and the relationship between them using Pentacam and to investigate the influence of unevenness and the non-orthogonal state on correction of myopic astigmatism by laser subepithelial keratomileusis (LASEK). 230 eyes with myopic astigmatism treated with LASEK were divided into two groups: 114 eyes as the low astigmatism group (-0.25 to -0.75 DC) and 116 eyes as the midrange-high astigmatism group (-1.00 to -4.50 DC). With the help of the diagram of keratoconus evaluation program of the Pentacam, the D 3.0 and D 6.5 were calculated for the index of distribution of unevenness of the corneal thickness, and the absolute value of the angle between the maximum and minimum progression-index orientation (M 90) for the index of non-orthogonal states. The correction of myopic astigmatism by LASEK was based on standard vector analysis and power vector analysis. The follow-up period was for 3 months. The preoperative M 90 was 22.14° ± 20.87°, D 6.5 was 58.66 ± 21.32 μm, and D 3.0 was 16.11 ± 4.28 μm for the 230 eyes that were tested. The D 6.5 of low astigmatism group (55.62 ± 20.81) μm was significantly lower than that of midrange-high astigmatism group (61.65 ± 21.48) μm (P < 0.05). Of the 230 eyes, the M 90 was positively correlated with D 6.5 (r = 0.37, P < 0.001), and D 6.5 was positively correlated with D 3.0 (r = 0.56, P < 0.001). 3 months postoperatively, the absolute error vector (|EV|) of low astigmatism group (0.46 ± 0.34) was significantly lower than that of midrange-high astigmatism group (0.53 ± 0.29) (P < 0.01). The error of magnitude of low astigmatism group (-0.10 ± 0.31) was significantly lower than that of midrange-high astigmatism group (0.08 ± 0.41) (P < 0.001). The absolute error of angle (|EA|) of low astigmatism group (26.10 ± 27.24) was significantly higher than that of midrange-high astigmatism group (9.99 ± 17.32) (P < 0.001). The correction ratio of low astigmatism group (1.45 ± 1.21) was significantly higher than that of midrange-high astigmatism group (0.94 ± 0.33) (P < 0.01). The error ratio (ER) of low astigmatism group (1.34 ± 1.40) was significantly higher than that of midrange-high astigmatism group (0.42 ± 0.27) (P < 0.001). In low astigmatism group, M 90 was positively correlated with |EV| (r = 0.30, P < 0.001). In midrange-high astigmatism group, M 90 was positively correlated with ER (r = 0.31, P < 0.001) and D 6.5 was positively correlated with |EV| and B, respectively (r = 0.34, 0.33, P < 0.001). The relationship between unevenness and non-orthogonal state of distribution of corneal thickness could influence the correction of astigmatism by LASEK. Therefore, more attention should be paid to the correction of midrange-high astigmatism group by excimer surgery.

Excited states from quantum Monte Carlo in the basis of Slater determinants

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

Humeniuk, Alexander; Mitrić, Roland, E-mail: roland.mitric@uni-wuerzburg.de

2014-11-21

Building on the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm introduced recently by Booth et al. [J. Chem. Phys. 131, 054106 (2009)] to compute the ground state of correlated many-electron systems, an extension to the computation of excited states (exFCIQMC) is presented. The Hilbert space is divided into a large part consisting of pure Slater determinants and a much smaller orthogonal part (the size of which is controlled by a cut-off threshold), from which the lowest eigenstates can be removed efficiently. In this way, the quantum Monte Carlo algorithm is restricted to the orthogonal complement of the lower excitedmore » states and projects out the next highest excited state. Starting from the ground state, higher excited states can be found one after the other. The Schrödinger equation in imaginary time is solved by the same population dynamics as in the ground state algorithm with modified probabilities and matrix elements, for which working formulae are provided. As a proof of principle, the method is applied to lithium hydride in the 3-21G basis set and to the helium dimer in the aug-cc-pVDZ basis set. It is shown to give the correct electronic structure for all bond lengths. Much more testing will be required before the applicability of this method to electron correlation problems of interesting size can be assessed.« less

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

Zhu, Xiaojun; Lei, Guangtsai; Pan, Guangwen

In this paper, the continuous operator is discretized into matrix forms by Galerkin`s procedure, using periodic Battle-Lemarie wavelets as basis/testing functions. The polynomial decomposition of wavelets is applied to the evaluation of matrix elements, which makes the computational effort of the matrix elements no more expensive than that of method of moments (MoM) with conventional piecewise basis/testing functions. A new algorithm is developed employing the fast wavelet transform (FWT). Owing to localization, cancellation, and orthogonal properties of wavelets, very sparse matrices have been obtained, which are then solved by the LSQR iterative method. This algorithm is also adaptive in thatmore » one can add at will finer wavelet bases in the regions where fields vary rapidly, without any damage to the system orthogonality of the wavelet basis functions. To demonstrate the effectiveness of the new algorithm, we applied it to the evaluation of frequency-dependent resistance and inductance matrices of multiple lossy transmission lines. Numerical results agree with previously published data and laboratory measurements. The valid frequency range of the boundary integral equation results has been extended two to three decades in comparison with the traditional MoM approach. The new algorithm has been integrated into the computer aided design tool, MagiCAD, which is used for the design and simulation of high-speed digital systems and multichip modules Pan et al. 29 refs., 7 figs., 6 tabs.« less

A novel orthogonal transmission-virtual grating method and its applications in measuring micro 3-D shape of deformed liquid surface

NASA Astrophysics Data System (ADS)

Liu, Zhanwei; Huang, Xianfu; Xie, Huimin

2013-02-01

Deformed liquid surface directly involves the surface tension, which can always be used to account for the kinematics of aquatic insects in gas-liquid interface and the light metal floating on the water surface. In this paper a novel method based upon deformed transmission-virtual grating is proposed for determination of deformed liquid surface. By addressing an orthogonal grating (1-5 line/mm) under the transparent water groove and then capturing images from upset of the deformed water surface, a displacement vector of full-field which directly associates the 3-D deformed liquid surface then can be evaluated by processing the recorded deformed fringe pattern in the two directions (x- and y-direction). Theories and equations for the method are thoroughly delivered. Validation test to measure the deformed water surface caused by a Chinese 1-cent coin has been conducted to demonstrate the ability of the developed method. The obtained results show that the method is robust in determination of micro 3-D surface of deformed liquid with a submicron scale resolution and with a wide range application scope.

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

Regularization of Mickelsson generators for nonexceptional quantum groups

NASA Astrophysics Data System (ADS)

Mudrov, A. I.

2017-08-01

Let g' ⊂ g be a pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces C N-2 ⊂ C N and U q (g') ⊂ U q (g) be a pair of quantum groups with a triangular decomposition U q (g) = U q (g-) U q (g+) U q (h). Let Z q (g, g') be the corresponding step algebra. We assume that its generators are rational trigonometric functions h ∗ → U q (g±). We describe their regularization such that the resulting generators do not vanish for any choice of the weight.

Functional Materials from Polymeric Ionic Liquids

NASA Astrophysics Data System (ADS)

Segalman, Rachel; Sanoja, Gabriel; Michenfelder-Schauser, Nicole; Mitragotri, Samir; Seshadri, Ram

Ionic liquids (IL's) have been suggested for applications as diverse as solubilizing cellulose, antimicrobial treatments, and electrolytes in batteries due to their molten salt properties. A polymeric cation (such as imidazolium) is an excellent host for any associated anion. As a result, polymerized ionic liquids are not just solid counterparts to IL's, but are shown to be vectors for the inclusion of a wide variety of functionalities ranging from multi-valent ions to magnetic anions. Moreover, PIL block copolymers allow orthogonal control over mechanical and morphological properties, ultimately leading to a conceptual framework for processable, tunable, multifunctional materials.

The Big-Five factor structure as an integrative framework: an analysis of Clarke's AVA model.

PubMed

Goldberg, L R; Sweeney, D; Merenda, P F; Hughes, J E

1996-06-01

Using a large (N = 3,629) sample of participants selected to be representative of U.S. working adults in the year 2,000, we provide links between the constructs in 2 personality models that have been derived from quite different rationales. We demonstrate the use of a novel procedure for providing orthogonal Big-Five factor scores and use those scores to analyze the scales of the Activity Vector Analysis (AVA). We discuss the implications of our many findings both for the science of personality assessment and for future research using the AVA model.

Two fast approximate wavelet algorithms for image processing, classification, and recognition

NASA Astrophysics Data System (ADS)

Wickerhauser, Mladen V.

1994-07-01

We use large libraries of template waveforms with remarkable orthogonality properties to recast the relatively complex principal orthogonal decomposition (POD) into an optimization problem with a fast solution algorithm. Then it becomes practical to use POD to solve two related problems: recognizing or classifying images, and inverting a complicated map from a low-dimensional configuration space to a high-dimensional measurement space. In the case where the number N of pixels or measurements is more than 1000 or so, the classical O(N3) POD algorithms becomes very costly, but it can be replaced with an approximate best-basis method that has complexity O(N2logN). A variation of POD can also be used to compute an approximate Jacobian for the complicated map.

Mixed models and reduction method for dynamic analysis of anisotropic shells

NASA Technical Reports Server (NTRS)

Noor, A. K.; Peters, J. M.

1985-01-01

A time-domain computational procedure is presented for predicting the dynamic response of laminated anisotropic shells. The two key elements of the procedure are: (1) use of mixed finite element models having independent interpolation (shape) functions for stress resultants and generalized displacements for the spatial discretization of the shell, with the stress resultants allowed to be discontinuous at interelement boundaries; and (2) use of a dynamic reduction method, with the global approximation vectors consisting of the static solution and an orthogonal set of Lanczos vectors. The dynamic reduction is accomplished by means of successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate the global approximation vectors. Then the Rayleigh-Ritz technique is used to generate a reduced system of ordinary differential equations in the amplitudes of these modes. The temporal integration of the reduced differential equations is performed by using an explicit half-station central difference scheme (Leap-frog method). The effectiveness of the proposed procedure is demonstrated by means of a numerical example and its advantages over reduction methods used with the displacement formulation are discussed.

Solving large-scale dynamic systems using band Lanczos method in Rockwell NASTRAN on CRAY X-MP

NASA Technical Reports Server (NTRS)

Gupta, V. K.; Zillmer, S. D.; Allison, R. E.

1986-01-01

The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix.

Simple automatic strategy for background drift correction in chromatographic data analysis.

PubMed

Fu, Hai-Yan; Li, He-Dong; Yu, Yong-Jie; Wang, Bing; Lu, Peng; Cui, Hua-Peng; Liu, Ping-Ping; She, Yuan-Bin

2016-06-03

Chromatographic background drift correction, which influences peak detection and time shift alignment results, is a critical stage in chromatographic data analysis. In this study, an automatic background drift correction methodology was developed. Local minimum values in a chromatogram were initially detected and organized as a new baseline vector. Iterative optimization was then employed to recognize outliers, which belong to the chromatographic peaks, in this vector, and update the outliers in the baseline until convergence. The optimized baseline vector was finally expanded into the original chromatogram, and linear interpolation was employed to estimate background drift in the chromatogram. The principle underlying the proposed method was confirmed using a complex gas chromatographic dataset. Finally, the proposed approach was applied to eliminate background drift in liquid chromatography quadrupole time-of-flight samples used in the metabolic study of Escherichia coli samples. The proposed method was comparable with three classical techniques: morphological weighted penalized least squares, moving window minimum value strategy and background drift correction by orthogonal subspace projection. The proposed method allows almost automatic implementation of background drift correction, which is convenient for practical use. Copyright © 2016 Elsevier B.V. All rights reserved.

Chemoselective ligation and antigen vectorization.

PubMed

Gras-Masse, H

2001-01-01

The interest in cocktail-lipopeptide vaccines has now been confirmed by phase I clinical trials: highly diversified B-, T-helper or cytotoxic T-cell epitopes can be combined with a lipophilic vector for the induction of B- and T-cell responses of predetermined specificity. With the goal of producing an improved vaccine that should ideally induce a multispecific response in non-selected populations, increasing the diversity of the immunizing mixture represents one of the most obvious strategies.The selective delivery of antigens to professional antigen-presenting cells represents another promising approach for the improvement of vaccine efficacy. In this context, the mannose-receptor represents an attractive entry point for the targeting to dendritic cells of antigens linked to clustered glycosides or glycomimetics. In all cases, highly complex but fully characterized molecules must be produced. To develop a modular and flexible strategy which could be generally applicable to a large set of peptide antigens, we elected to explore the potentialities of chemoselective ligation methods. The hydrazone bond was found particularly reliable and fully compatible with sulphide ligation. Hydrazone/thioether orthogonal ligation systems could be developed to account for the nature of the antigens and the solubility of the vector systems. Copyright 2001 The International Association for Biologicals.

Balanced Centrality of Networks.

PubMed

Debono, Mark; Lauri, Josef; Sciriha, Irene

2014-01-01

There is an age-old question in all branches of network analysis. What makes an actor in a network important, courted, or sought? Both Crossley and Bonacich contend that rather than its intrinsic wealth or value, an actor's status lies in the structures of its interactions with other actors. Since pairwise relation data in a network can be stored in a two-dimensional array or matrix, graph theory and linear algebra lend themselves as great tools to gauge the centrality (interpreted as importance, power, or popularity, depending on the purpose of the network) of each actor. We express known and new centralities in terms of only two matrices associated with the network. We show that derivations of these expressions can be handled exclusively through the main eigenvectors (not orthogonal to the all-one vector) associated with the adjacency matrix. We also propose a centrality vector (SWIPD) which is a linear combination of the square, walk, power, and degree centrality vectors with weightings of the various centralities depending on the purpose of the network. By comparing actors' scores for various weightings, a clear understanding of which actors are most central is obtained. Moreover, for threshold networks, the (SWIPD) measure turns out to be independent of the weightings.

Computing energy levels of CH4, CHD3, CH3D, and CH3F with a direct product basis and coordinates based on the methyl subsystem.

PubMed

Zhao, Zhiqiang; Chen, Jun; Zhang, Zhaojun; Zhang, Dong H; Wang, Xiao-Gang; Carrington, Tucker; Gatti, Fabien

2018-02-21

Quantum mechanical calculations of ro-vibrational energies of CH 4 , CHD 3 , CH 3 D, and CH 3 F were made with two different numerical approaches. Both use polyspherical coordinates. The computed energy levels agree, confirming the accuracy of the methods. In the first approach, for all the molecules, the coordinates are defined using three Radau vectors for the CH 3 subsystem and a Jacobi vector between the remaining atom and the centre of mass of CH 3 . Euler angles specifying the orientation of a frame attached to CH 3 with respect to a frame attached to the Jacobi vector are used as vibrational coordinates. A direct product potential-optimized discrete variable vibrational basis is used to build a Hamiltonian matrix. Ro-vibrational energies are computed using a re-started Arnoldi eigensolver. In the second approach, the coordinates are the spherical coordinates associated with four Radau vectors or three Radau vectors and a Jacobi vector, and the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions, and eigenvalues are computed with the Lanczos algorithm. For CH 4 , CHD 3 , and CH 3 D, we report the first J > 0 energy levels computed on the Wang-Carrington potential energy surface [X.-G. Wang and T. Carrington, J. Chem. Phys. 141(15), 154106 (2014)]. For CH 3 F, the potential energy surface of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.

Computing energy levels of CH4, CHD3, CH3D, and CH3F with a direct product basis and coordinates based on the methyl subsystem

NASA Astrophysics Data System (ADS)

Zhao, Zhiqiang; Chen, Jun; Zhang, Zhaojun; Zhang, Dong H.; Wang, Xiao-Gang; Carrington, Tucker; Gatti, Fabien

2018-02-01

Quantum mechanical calculations of ro-vibrational energies of CH4, CHD3, CH3D, and CH3F were made with two different numerical approaches. Both use polyspherical coordinates. The computed energy levels agree, confirming the accuracy of the methods. In the first approach, for all the molecules, the coordinates are defined using three Radau vectors for the CH3 subsystem and a Jacobi vector between the remaining atom and the centre of mass of CH3. Euler angles specifying the orientation of a frame attached to CH3 with respect to a frame attached to the Jacobi vector are used as vibrational coordinates. A direct product potential-optimized discrete variable vibrational basis is used to build a Hamiltonian matrix. Ro-vibrational energies are computed using a re-started Arnoldi eigensolver. In the second approach, the coordinates are the spherical coordinates associated with four Radau vectors or three Radau vectors and a Jacobi vector, and the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions, and eigenvalues are computed with the Lanczos algorithm. For CH4, CHD3, and CH3D, we report the first J > 0 energy levels computed on the Wang-Carrington potential energy surface [X.-G. Wang and T. Carrington, J. Chem. Phys. 141(15), 154106 (2014)]. For CH3F, the potential energy surface of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.

A force vector and surface orientation sensor for intelligent grasping

NASA Technical Reports Server (NTRS)

Mcglasson, W. D.; Lorenz, R. D.; Duffie, N. A.; Gale, K. L.

1991-01-01

The paper discusses a force vector and surface orientation sensor suitable for intelligent grasping. The use of a novel four degree-of-freedom force vector robotic fingertip sensor allows efficient, real time intelligent grasping operations. The basis of sensing for intelligent grasping operations is presented and experimental results demonstrate the accuracy and ease of implementation of this approach.

Dynamics and Synchronization of Nonlinear Oscillators with Time Delays: A Study with Fiber Lasers

DTIC Science & Technology

2007-07-19

or coupling lines PC Polarization Controller PD Photodetector VA Variable Attenuator WDM Wavelength Division Multiplexer x Chapter 1 Introduction 1.1...lasers and detectors. Injection locking of lasers is a common practice that can be used to lock the frequency and phase of a laser to an injected signal...finding a basis vector that maximizes the mean squared projection of the data. Succeeding basis vectors are found that max- imize the projection with the

Balanced multiwavelets with interpolatory property.

PubMed

Li, Baobin; Peng, Lizhong

2011-05-01

Balanced multiwavelets with interpolatory property are discussed in this paper. This kind of multiwavelets can have a sampling property like Shannon's sampling theorem. It has been shown that the corresponding matrix-valued refinable mask has special structure, and an orthogonal multifilter bank {H(z),G(z)} can be reduced to a scalar valued conjugate quadrature filter (CQF) a(z) . But it does not mean that any scalar CQF can form a "good" multifilter bank which can generate a vector-valued refinable function with some degree of smoothness. In the context of balanced multiwavelets, we give the definition of transferring balance order, which a scalar CQF a(z) satisfies, to guarantee that the multiwavelet Ψ generated is balanced. On the basis of the parametrization of a scalar CQF with any length and conditions of transferring balance order, parametrization of multifilter banks which can generate interpolatory multiwavelet and interpolatory scaling function, is gotten. Moreover, some balanced interpolatory multiwavelets have been constructed. Interpolatory analysis-ready multiwavelets (armlets) are also discussed in this paper. It is known that conditions of armlets are easy to validate, compared with balanced multiwavelets. But it will be present that if the corresponding scaling function Φ is interpolatory, the multiwavelet Ψ is balanced of order n if and only if it is an armlet of order n. Finally, the application of balanced multiwavelets with interpolatory property in image processing is also discussed.

Wavelet-like bases for thin-wire integral equations in electromagnetics

NASA Astrophysics Data System (ADS)

Francomano, E.; Tortorici, A.; Toscano, E.; Ala, G.; Viola, F.

2005-03-01

In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.

Target detection using the background model from the topological anomaly detection algorithm

NASA Astrophysics Data System (ADS)

Dorado Munoz, Leidy P.; Messinger, David W.; Ziemann, Amanda K.

2013-05-01

The Topological Anomaly Detection (TAD) algorithm has been used as an anomaly detector in hyperspectral and multispectral images. TAD is an algorithm based on graph theory that constructs a topological model of the background in a scene, and computes an anomalousness ranking for all of the pixels in the image with respect to the background in order to identify pixels with uncommon or strange spectral signatures. The pixels that are modeled as background are clustered into groups or connected components, which could be representative of spectral signatures of materials present in the background. Therefore, the idea of using the background components given by TAD in target detection is explored in this paper. In this way, these connected components are characterized in three different approaches, where the mean signature and endmembers for each component are calculated and used as background basis vectors in Orthogonal Subspace Projection (OSP) and Adaptive Subspace Detector (ASD). Likewise, the covariance matrix of those connected components is estimated and used in detectors: Constrained Energy Minimization (CEM) and Adaptive Coherence Estimator (ACE). The performance of these approaches and the different detectors is compared with a global approach, where the background characterization is derived directly from the image. Experiments and results using self-test data set provided as part of the RIT blind test target detection project are shown.

Proper Orthogonal Decomposition in Optimal Control of Fluids

NASA Technical Reports Server (NTRS)

Ravindran, S. S.

1999-01-01

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

A T Matrix Method Based upon Scalar Basis Functions

NASA Technical Reports Server (NTRS)

Mackowski, D.W.; Kahnert, F. M.; Mishchenko, Michael I.

2013-01-01

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

Application of information-retrieval methods to the classification of physical data

NASA Technical Reports Server (NTRS)

Mamotko, Z. N.; Khorolskaya, S. K.; Shatrovskiy, L. I.

1975-01-01

Scientific data received from satellites are characterized as a multi-dimensional time series, whose terms are vector functions of a vector of measurement conditions. Information retrieval methods are used to construct lower dimensional samples on the basis of the condition vector, in order to obtain these data and to construct partial relations. The methods are applied to the joint Soviet-French Arkad project.

The simple procedure for the fluxgate magnetometers calibration

NASA Astrophysics Data System (ADS)

Marusenkov, Andriy

2014-05-01

The fluxgate magnetometers are widely used in geophysics investigations including the geomagnetic field monitoring at the global network of geomagnetic observatories as well as for electromagnetic sounding of the Earth's crust conductivity. For solving these tasks the magnetometers have to be calibrated with an appropriate level of accuracy. As a particular case, the ways to satisfy the recent requirements to the scaling and orientation errors of 1-second INTERNAGNET magnetometers are considered in the work. The goal of the present study was to choose a simple and reliable calibration method for estimation of scale factors and angular errors of the three-axis magnetometers in the field. There are a large number of the scalar calibration methods, which use a free rotation of the sensor in the calibration field followed by complicated data processing procedures for numerical solution of the high-order equations set. The chosen approach also exploits the Earth's magnetic field as a calibrating signal, but, in contrast to other methods, the sensor has to be oriented in some particular positions in respect to the total field vector, instead of the sensor free rotation. This allows to use very simple and straightforward linear computation formulas and, as a result, to achieve more reliable estimations of the calibrated parameters. The estimation of the scale factors is performed by the sequential aligning of each component of the sensor in two positions: parallel and anti-parallel to the Earth's magnetic field vector. The estimation of non-orthogonality angles between each pair of components is performed after sequential aligning of the components at the angles +/- 45 and +/- 135 degrees of arc in respect to the total field vector. Due to such four positions approach the estimations of the non-orthogonality angles are invariant to the zero offsets and non-linearity of transfer functions of the components. The experimental justifying of the proposed method by means of the Coil Calibration system reveals, that the achieved accuracy (<0.04 % for scale factors and 0.03 degrees of arc for angle errors) is sufficient for many applications, particularly for satisfying the INTERMAGNET requirements to 1-second instruments.

A hierarchical preconditioner for the electric field integral equation on unstructured meshes based on primal and dual Haar bases

NASA Astrophysics Data System (ADS)

Adrian, S. B.; Andriulli, F. P.; Eibert, T. F.

2017-02-01

A new hierarchical basis preconditioner for the electric field integral equation (EFIE) operator is introduced. In contrast to existing hierarchical basis preconditioners, it works on arbitrary meshes and preconditions both the vector and the scalar potential within the EFIE operator. This is obtained by taking into account that the vector and the scalar potential discretized with loop-star basis functions are related to the hypersingular and the single layer operator (i.e., the well known integral operators from acoustics). For the single layer operator discretized with piecewise constant functions, a hierarchical preconditioner can easily be constructed. Thus the strategy we propose in this work for preconditioning the EFIE is the transformation of the scalar and the vector potential into operators equivalent to the single layer operator and to its inverse. More specifically, when the scalar potential is discretized with star functions as source and testing functions, the resulting matrix is a single layer operator discretized with piecewise constant functions and multiplied left and right with two additional graph Laplacian matrices. By inverting these graph Laplacian matrices, the discretized single layer operator is obtained, which can be preconditioned with the hierarchical basis. Dually, when the vector potential is discretized with loop functions, the resulting matrix can be interpreted as a hypersingular operator discretized with piecewise linear functions. By leveraging on a scalar Calderón identity, we can interpret this operator as spectrally equivalent to the inverse single layer operator. Then we use a linear-in-complexity, closed-form inverse of the dual hierarchical basis to precondition the hypersingular operator. The numerical results show the effectiveness of the proposed preconditioner and the practical impact of theoretical developments in real case scenarios.

3D Magnetization Vector Inversion of Magnetic Data: Improving and Comparing Methods

NASA Astrophysics Data System (ADS)

Liu, Shuang; Hu, Xiangyun; Zhang, Henglei; Geng, Meixia; Zuo, Boxin

2017-12-01

Magnetization vector inversion is an useful approach to invert for magnetic anomaly in the presence of significant remanent magnetization and self-demagnetization. However, magnetizations are usually obtained in many different directions under the influences of geophysical non-uniqueness. We propose an iteration algorithm of magnetization vector inversion (M-IDI) that one couple of magnetization direction is iteratively computed after the magnetization intensity is recovered from the magnitude magnetic anomaly. And we compare it with previous methods of (1) three orthogonal components inversion of total magnetization vector at Cartesian framework (MMM), (2) intensity, inclination and declination inversion at spherical framework (MID), (3) directly recovering the magnetization inclination and declination (M-IDCG) and (4) estimating the magnetization direction using correlation method (M-IDC) at the sequential inversion frameworks. The synthetic examples indicate that MMM returns multiply magnetization directions and MID results are strongly dependent on initial model and parameter weights. M-IDI computes faster than M-IDC and achieves a constant magnetization direction compared with M-IDCG. Additional priori information constraints can improve the results of MMM, MID and M-IDCG. Obtaining one magnetization direction, M-IDC and M-IDI are suitable for single and isolated anomaly. Finally, M-IDI and M-IDC are used to invert and interpret the magnetic anomaly of the Galinge iron-ore deposit (NW China) and the results are verified by information from drillholes and physical properties measurements of ore and rock samples. Magnetization vector inversion provides a comprehensive way to evaluate and investigate the remanent magnetization and self-demagnetization.

Prediction of protein structural classes by Chou's pseudo amino acid composition: approached using continuous wavelet transform and principal component analysis.

PubMed

Li, Zhan-Chao; Zhou, Xi-Bin; Dai, Zong; Zou, Xiao-Yong

2009-07-01

A prior knowledge of protein structural classes can provide useful information about its overall structure, so it is very important for quick and accurate determination of protein structural class with computation method in protein science. One of the key for computation method is accurate protein sample representation. Here, based on the concept of Chou's pseudo-amino acid composition (AAC, Chou, Proteins: structure, function, and genetics, 43:246-255, 2001), a novel method of feature extraction that combined continuous wavelet transform (CWT) with principal component analysis (PCA) was introduced for the prediction of protein structural classes. Firstly, the digital signal was obtained by mapping each amino acid according to various physicochemical properties. Secondly, CWT was utilized to extract new feature vector based on wavelet power spectrum (WPS), which contains more abundant information of sequence order in frequency domain and time domain, and PCA was then used to reorganize the feature vector to decrease information redundancy and computational complexity. Finally, a pseudo-amino acid composition feature vector was further formed to represent primary sequence by coupling AAC vector with a set of new feature vector of WPS in an orthogonal space by PCA. As a showcase, the rigorous jackknife cross-validation test was performed on the working datasets. The results indicated that prediction quality has been improved, and the current approach of protein representation may serve as a useful complementary vehicle in classifying other attributes of proteins, such as enzyme family class, subcellular localization, membrane protein types and protein secondary structure, etc.

Nonlinear polarization rotation and orthogonal polarization generation experienced in a single-beam configuration

NASA Astrophysics Data System (ADS)

Minkovski, N.; Petrov, G. I.; Saltiel, S. M.; Albert, O.; Etchepare, J.

2004-09-01

Nonlinear polarization rotation and generation of a polarization component orthogonal to the input beam were observed along fourfold axes of YVO4 and BaF2 crystals. We demonstrate experimentally that in both crystals the angle of rotation is proportional, at low intensities, to the square of the product of the input intensity and the crystal length and is the result of simultaneous action of two third-order processes. This type of nonlinear polarization rotation is driven by the real part of the cubic susceptibility. The recorded energy exchange between the two orthogonal components can exceed 10%. It is to our knowledge the highest energy-conversion efficiency achieved in a single beam nonresonant χ(3) interaction. A simple theoretical model is elaborated to describe the dependence of nonlinear polarization rotation and orthogonal polarization generation on the intensity of the input beam at both low- and high-intensity levels. It reveals the potential contributions from the real and the imaginary parts of the susceptibility tensor. Moreover, this kind of measurement is designed to permit the determination of the magnitude and the sign of the anisotropy of the real part of third-order nonlinearity in crystals with cubic or tetragonal symmetry on the basis of polarization-rotation measurements. The χxxxx(3) component of the third-order susceptibility tensor and its anisotropy sign and amplitude value for BaF2 and YVO4 crystals are estimated and discussed.

Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer

NASA Astrophysics Data System (ADS)

Wang, Xiao-Gang; Carrington, Tucker

2018-02-01

We compute numerically exact rovibrational levels of water dimer, with 12 vibrational coordinates, on the accurate CCpol-8sf ab initio flexible monomer potential energy surface [C. Leforestier et al., J. Chem. Phys. 137, 014305 (2012)]. It does not have a sum-of-products or multimode form and therefore quadrature in some form must be used. To do the calculation, it is necessary to use an efficient basis set and to develop computational tools, for evaluating the matrix-vector products required to calculate the spectrum, that obviate the need to store the potential on a 12D quadrature grid. The basis functions we use are products of monomer vibrational wavefunctions and standard rigid-monomer basis functions (which involve products of three Wigner functions). Potential matrix-vector products are evaluated using the F matrix idea previously used to compute rovibrational levels of 5-atom and 6-atom molecules. When the coupling between inter- and intra-monomer coordinates is weak, this crude adiabatic type basis is efficient (only a few monomer vibrational wavefunctions are necessary), although the calculation of matrix elements is straightforward. It is much easier to use than an adiabatic basis. The product structure of the basis is compatible with the product structure of the kinetic energy operator and this facilitates computation of matrix-vector products. Compared with the results obtained using a [6 + 6]D adiabatic approach, we find good agreement for the inter-molecular levels and larger differences for the intra-molecular water bend levels.

Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer.

PubMed

Wang, Xiao-Gang; Carrington, Tucker

2018-02-21

We compute numerically exact rovibrational levels of water dimer, with 12 vibrational coordinates, on the accurate CCpol-8sf ab initio flexible monomer potential energy surface [C. Leforestier et al., J. Chem. Phys. 137, 014305 (2012)]. It does not have a sum-of-products or multimode form and therefore quadrature in some form must be used. To do the calculation, it is necessary to use an efficient basis set and to develop computational tools, for evaluating the matrix-vector products required to calculate the spectrum, that obviate the need to store the potential on a 12D quadrature grid. The basis functions we use are products of monomer vibrational wavefunctions and standard rigid-monomer basis functions (which involve products of three Wigner functions). Potential matrix-vector products are evaluated using the F matrix idea previously used to compute rovibrational levels of 5-atom and 6-atom molecules. When the coupling between inter- and intra-monomer coordinates is weak, this crude adiabatic type basis is efficient (only a few monomer vibrational wavefunctions are necessary), although the calculation of matrix elements is straightforward. It is much easier to use than an adiabatic basis. The product structure of the basis is compatible with the product structure of the kinetic energy operator and this facilitates computation of matrix-vector products. Compared with the results obtained using a [6 + 6]D adiabatic approach, we find good agreement for the inter-molecular levels and larger differences for the intra-molecular water bend levels.

Search for the Higgs boson in lepton, tau, and jets final states

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

Abazov, V. M.; Abbott, B.; Acharya, B. S.

2013-09-01

We present a search for the standard model Higgs boson in final states with an electron or muon and a hadronically decaying tau lepton in association with two or more jets using 9.7 fb-1 of Run II Fermilab Tevatron Collider data collected with the D0 detector. The analysis is sensitive to Higgs boson production via gluon fusion, associated vector boson production, and vector boson fusion, followed by the Higgs boson decay to tau lepton pairs or to W boson pairs. The ratios of 95% C.L. upper limits on the cross section times branching ratio to those predicted by the standardmore » model are obtained for orthogonal subsamples that are enriched in either H → τ τ decays or H → WW decays, and for the combination of these subsample limits. The observed and expected limit ratios for the combined subsamples at a Higgs boson mass of 125 GeV are 11.3 and 9.0 respectively.« less

Spin-reorientation transitions in the Cairo pentagonal magnet Bi 4 Fe 5 O 13 F

DOE PAGES

Tsirlin, Alexander A.; Rousochatzakis, Ioannis; Filimonov, Dmitry; ...

2017-09-19

Here, we show that interlayer spins play a dual role in the Cairo pentagonal magnet Bi 4Fe 5O 13F, on one hand mediating the three-dimensional magnetic order, and on the other driving spin-reorientation transitions both within and between the planes. The corresponding sequence of magnetic orders unraveled by neutron diffraction and Mössbauer spectroscopy features two orthogonal magnetic structures described by opposite local vector chiralities, and an intermediate, partly disordered phase with nearly collinear spins. A similar collinear phase has been predicted theoretically to be stabilized by quantum fluctuations, but Bi 4Fe 5O 13F is very far from the relevant parametermore » regime. While the observed in-plane reorientation cannot be explained by any standard frustration mechanism, our ab initio band-structure calculations reveal strong single-ion anisotropy of the interlayer Fe 3+ spins that turns out to be instrumental in controlling the local vector chirality and the associated interlayer order.« less

Spin-reorientation transitions in the Cairo pentagonal magnet Bi4Fe5O13F

NASA Astrophysics Data System (ADS)

Tsirlin, Alexander A.; Rousochatzakis, Ioannis; Filimonov, Dmitry; Batuk, Dmitry; Frontzek, Matthias; Abakumov, Artem M.

2017-09-01

We show that interlayer spins play a dual role in the Cairo pentagonal magnet Bi4Fe5O13F , on one hand mediating the three-dimensional magnetic order, and on the other driving spin-reorientation transitions both within and between the planes. The corresponding sequence of magnetic orders unraveled by neutron diffraction and Mössbauer spectroscopy features two orthogonal magnetic structures described by opposite local vector chiralities, and an intermediate, partly disordered phase with nearly collinear spins. A similar collinear phase has been predicted theoretically to be stabilized by quantum fluctuations, but Bi4Fe5O13F is very far from the relevant parameter regime. While the observed in-plane reorientation cannot be explained by any standard frustration mechanism, our ab initio band-structure calculations reveal strong single-ion anisotropy of the interlayer Fe3 + spins that turns out to be instrumental in controlling the local vector chirality and the associated interlayer order.

Teaching Vectors Through an Interactive Game Based Laboratory

NASA Astrophysics Data System (ADS)

O'Brien, James; Sirokman, Gergely

2014-03-01

In recent years, science and particularly physics education has been furthered by the use of project based interactive learning [1]. There is a tremendous amount of evidence [2] that use of these techniques in a college learning environment leads to a deeper appreciation and understanding of fundamental concepts. Since vectors are the basis for any advancement in physics and engineering courses the cornerstone of any physics regimen is a concrete and comprehensive introduction to vectors. Here, we introduce a new turn based vector game that we have developed to help supplement traditional vector learning practices, which allows students to be creative, work together as a team, and accomplish a goal through the understanding of basic vector concepts.

Electrically switchable photonic liquid crystal devices for routing of a polarized light wave

NASA Astrophysics Data System (ADS)

Rushnova, Irina I.; Melnikova, Elena A.; Tolstik, Alexei L.; Muravsky, Alexander A.

2018-04-01

The new mode of LC alignment based on photoalignment AtA-2 azo dye where the refractive interface between orthogonal orientations of the LC director exists without voltage and disappeared or changed with critical voltage has been proposed. The technology to fabricate electrically controlled liquid crystal elements for spatial separation and switching of linearly polarized light beams on the basis of the total internal reflection effect has been significantly improved. Its distinctive feature is the application of a composite alignment material comprising two sublayers of Nylon-6 and AtA-2 photoalignment azo dye offering patterned liquid crystal director orientation with high alignment quality value q = 0 . 998. The fabricated electrically controlled spatially structured liquid crystal devices enable implementation of propagation directions separation for orthogonally polarized light beams and their switching with minimal crosstalk.

Investigation of effects of process parameters on properties of friction stir welded joints

NASA Astrophysics Data System (ADS)

Chauhan, Atul; Soota, Tarun; Rajput, S. K.

2018-03-01

This work deals with application of friction stir welding (FSW) using application of Taguchi orthogonal array. FSW procedure is used for joining the aluminium alloy AA6063-T0 plates in butt configuration with orthogonal combination of factors and their levels. The combination of factors involving tool rotation speed, tool travel speed and tool pin profile are used in three levels. Grey relational analysis (GRA) has been applied to select optimum level of factors for optimising UTS, ductility and hardness of joint. Experiments have been conducted with two different tool materials (HSS and HCHCr steel) with various factors level combinations for joining AA6063-T0. On the basis of grey relational grades at different levels of factors and analysis of variance (ANOVA) ideal combination of factors are determined. The influence of tool material is also studied.

Recognition and Classification of Road Condition on the Basis of Friction Force by Using a Mobile Robot

NASA Astrophysics Data System (ADS)

Watanabe, Tatsuhito; Katsura, Seiichiro

A person operating a mobile robot in a remote environment receives realistic visual feedback about the condition of the road on which the robot is moving. The categorization of the road condition is necessary to evaluate the conditions for safe and comfortable driving. For this purpose, the mobile robot should be capable of recognizing and classifying the condition of the road surfaces. This paper proposes a method for recognizing the type of road surfaces on the basis of the friction between the mobile robot and the road surfaces. This friction is estimated by a disturbance observer, and a support vector machine is used to classify the surfaces. The support vector machine identifies the type of the road surface using feature vector, which is determined using the arithmetic average and variance derived from the torque values. Further, these feature vectors are mapped onto a higher dimensional space by using a kernel function. The validity of the proposed method is confirmed by experimental results.

Third International Kharkov Symposium "Physics and Engineering of Millimeter and Submillimeter Waves" MSMW󈨦 Symposium Proceedings, Volume 1,

DTIC Science & Technology

1998-09-01

potential of the surface wave electromagnetic field; ea is the unit of the polarization vectors : ex = ela. = e2x= (qx/\\q\\)\\/L\\q\\/(ei + e0), ely... polarization basis of the incident wave: EB°=eB^(/kr), (1) where e„ is the cyclic unit vector , n = ±1, k is the wave vector . The equation describing...rectangular grid. From the direction determined by wave vector k0, the plane electromagnetic wave of linear polarization incidents onto the array. It

Tunable positive and negative refraction of infrared radiation in graphene-dielectric multilayers

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

Zhang, R. Z.; Zhang, Z. M., E-mail: zhuomin.zhang@me.gatech.edu

2015-11-09

Graphene-dielectric multilayers consisting of alternating layers of atom-thick graphene and nanometer-scale dielectric films exhibit characteristics of hyperbolic metamaterials, in which one positive and one negative permittivity are defined for orthogonal directions. Negative permittivity for electric field polarized in the direction parallel to the conductive graphene sheets gives rise to a negative angle of refraction and low-loss transmission for the side-incidence perspective proposed in this work. The Poynting vector tracing demonstrates the switching between positive and negative refraction in the mid-infrared region by tuning the chemical potential of graphene. This adjustable dual-mode metamaterial holds promise for infrared imaging applications.

Pattern recognition invariant under changes of scale and orientation

NASA Astrophysics Data System (ADS)

Arsenault, Henri H.; Parent, Sebastien; Moisan, Sylvain

1997-08-01

We have used a modified method proposed by neiberg and Casasent to successfully classify five kinds of military vehicles. The method uses a wedge filter to achieve scale invariance, and lines in a multi-dimensional feature space correspond to each target with out-of-plane orientations over 360 degrees around a vertical axis. The images were not binarized, but were filtered in a preprocessing step to reduce aliasing. The feature vectors were normalized and orthogonalized by means of a neural network. Out-of-plane rotations of 360 degrees and scale changes of a factor of four were considered. Error-free classification was achieved.

Distributed measurement of polarization mode coupling in fiber ring based on P-OTDR complete polarization state detection.

PubMed

Huang, Zejia; Wu, Chongqing; Wang, Zhi; Wang, Jian; Liu, Lanlan

2018-02-19

Using a quaternion method, the polarization mode-coupling coefficient can be derived from three components of the Stokes vectors at three adjacent points along a fiber. A complete polarization optical time-domain reflectometry scheme for polarization mode coupling distributed measurement in polarization-maintaining fiber ring is proposed based on the above theoretical derivations. By comparing the measurement results of two opposite incident directions and two orthogonal polarization axes of polarization-maintaining fiber rings with different lengths, the feasibility and repeatability of the measurement scheme are verified experimentally with a positioning spatial resolution of 1 meter.

A polarization-division multiplexing SSB-OFDM system with beat interference cancellation receivers

NASA Astrophysics Data System (ADS)

Yang, Peiling; Ma, Jianxin; Zhang, Junyi

2018-06-01

In this paper, we have proposed a polarization-division multiplexing (PDM) single-sideband optical orthogonal frequency division multiplexing (SSB-OOFDM) scheme with signal-signal beat interference cancellation receivers with balanced detection (ICRBD). This system can double channel capacity and improve spectrum efficiency (SE) with the reduced guard band (GB) due to the PDM. Multiple input multiple output (MIMO) technique is used to solve polarization mode dispersion (PMD) associated with channel estimation and equalization. By simulation, we demonstrate the efficacy of the proposed technique for a 2 ×40 Gbit/s 16-QAM SSB-PDM-OOFDM system according to the error vector magnitude (EVM) and the constellation diagrams.

Young—Capelli symmetrizers in superalgebras†

PubMed Central

Brini, Andrea; Teolis, Antonio G. B.

1989-01-01

Let Supern[U [unk] V] be the nth homogeneous subspace of the supersymmetric algebra of U [unk] V, where U and V are Z2-graded vector spaces over a field K of characteristic zero. The actions of the general linear Lie superalgebras pl(U) and pl(V) span two finite-dimensional K-subalgebras B and [unk] of EndK(Supern[U [unk] V]) that are the centralizers of each other. Young—Capelli symmetrizers and Young—Capelli *-symmetrizers give rise to K-linear bases of B and [unk] containing orthogonal systems of idempotents; thus they yield complete decompositions of B and [unk] into minimal left and right ideals, respectively. PMID:16594014

A wave shaping approach of ferrite inductors exhibiting hysteresis using orthogonal field bias

NASA Astrophysics Data System (ADS)

Adly, A. A.; Abd-El-Hafiz, S. K.; Mahgoub, A. O.

2018-05-01

Advances in power electronic systems have considerably contributed to a wide spectrum of applications. In most power electronic circuits, inductors play crucial functions. Utilization of ferrite cores becomes a must when large inductances are required. Nevertheless, this results in an additional complexity due to their hysteresis nature. Recently, an efficient approach for modeling vector hysteresis using tri-node Hopfield neural networks (HNNs) has been introduced. This paper presents a wave shaping approach using hollow cylindrical ferrite core inductors having axial and toroidal windings. The approach investigates the possibility of tuning the inductor permeability to minimize circuit harmonics. Details of the approach are given in the paper.

Coherent states for the relativistic harmonic oscillator

NASA Technical Reports Server (NTRS)

Aldaya, Victor; Guerrero, J.

1995-01-01

Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

A 3-Axis Miniature Magnetic Sensor Based on a Planar Fluxgate Magnetometer with an Orthogonal Fluxguide.

PubMed

Lu, Chih-Cheng; Huang, Jeff

2015-06-19

A new class of tri-axial miniature magnetometer consisting of a planar fluxgate structure with an orthogonal ferromagnetic fluxguide centrally situated over the magnetic cores is presented. The magnetic sensor possesses a cruciform ferromagnetic core placed diagonally upon the square excitation coil under which two pairs of pick-up coils for in-plane field detection are allocated. Effective principles and analysis of the magnetometer for 3-D field vectors are described and verified by numerically electromagnetic simulation for the excitation and magnetization of the ferromagnetic cores. The sensor is operated by applying the second-harmonic detection technique that can verify V-B relationship and device responsivity. Experimental characterization of the miniature fluxgate device demonstrates satisfactory spatial magnetic field detection results in terms of responsivity and noise spectrum. As a result, at an excitation frequency of 50 kHz, a maximum in-plane responsivity of 122.4 V/T appears and a maximum out-of-plane responsivity of 11.6 V/T is obtained as well. The minimum field noise spectra are found to be 0.11 nT/√Hz and 6.29 nT/√Hz, respectively, in X- and Z-axis at 1 Hz under the same excitation frequency. Compared with the previous tri-axis fluxgate devices, this planar magnetic sensor with an orthogonal fluxguide provides beneficial enhancement in both sensory functionality and manufacturing simplicity. More importantly, this novel device concept is considered highly suitable for the extension to a silicon sensor made by the current CMOS-MEMS technologies, thus emphasizing its emerging applications of field detection in portable industrial electronics.

Predictive Sampling of Rare Conformational Events in Aqueous Solution: Designing a Generalized Orthogonal Space Tempering Method.

PubMed

Lu, Chao; Li, Xubin; Wu, Dongsheng; Zheng, Lianqing; Yang, Wei

2016-01-12

In aqueous solution, solute conformational transitions are governed by intimate interplays of the fluctuations of solute-solute, solute-water, and water-water interactions. To promote molecular fluctuations to enhance sampling of essential conformational changes, a common strategy is to construct an expanded Hamiltonian through a series of Hamiltonian perturbations and thereby broaden the distribution of certain interactions of focus. Due to a lack of active sampling of configuration response to Hamiltonian transitions, it is challenging for common expanded Hamiltonian methods to robustly explore solvent mediated rare conformational events. The orthogonal space sampling (OSS) scheme, as exemplified by the orthogonal space random walk and orthogonal space tempering methods, provides a general framework for synchronous acceleration of slow configuration responses. To more effectively sample conformational transitions in aqueous solution, in this work, we devised a generalized orthogonal space tempering (gOST) algorithm. Specifically, in the Hamiltonian perturbation part, a solvent-accessible-surface-area-dependent term is introduced to implicitly perturb near-solute water-water fluctuations; more importantly in the orthogonal space response part, the generalized force order parameter is generalized as a two-dimension order parameter set, in which essential solute-solvent and solute-solute components are separately treated. The gOST algorithm is evaluated through a molecular dynamics simulation study on the explicitly solvated deca-alanine (Ala10) peptide. On the basis of a fully automated sampling protocol, the gOST simulation enabled repetitive folding and unfolding of the solvated peptide within a single continuous trajectory and allowed for detailed constructions of Ala10 folding/unfolding free energy surfaces. The gOST result reveals that solvent cooperative fluctuations play a pivotal role in Ala10 folding/unfolding transitions. In addition, our assessment analysis suggests that because essential conformational events are mainly driven by the compensating fluctuations of essential solute-solvent and solute-solute interactions, commonly employed "predictive" sampling methods are unlikely to be effective on this seemingly "simple" system. The gOST development presented in this paper illustrates how to employ the OSS scheme for physics-based sampling method designs.

On bipartite pure-state entanglement structure in terms of disentanglement

NASA Astrophysics Data System (ADS)

Herbut, Fedor

2006-12-01

Schrödinger's disentanglement [E. Schrödinger, Proc. Cambridge Philos. Soc. 31, 555 (1935)], i.e., remote state decomposition, as a physical way to study entanglement, is carried one step further with respect to previous work in investigating the qualitative side of entanglement in any bipartite state vector. Remote measurement (or, equivalently, remote orthogonal state decomposition) from previous work is generalized to remote linearly independent complete state decomposition both in the nonselective and the selective versions. The results are displayed in terms of commutative square diagrams, which show the power and beauty of the physical meaning of the (antiunitary) correlation operator inherent in the given bipartite state vector. This operator, together with the subsystem states (reduced density operators), constitutes the so-called correlated subsystem picture. It is the central part of the antilinear representation of a bipartite state vector, and it is a kind of core of its entanglement structure. The generalization of previously elaborated disentanglement expounded in this article is a synthesis of the antilinear representation of bipartite state vectors, which is reviewed, and the relevant results of [Cassinelli et al., J. Math. Anal. Appl. 210, 472 (1997)] in mathematical analysis, which are summed up. Linearly independent bases (finite or infinite) are shown to be almost as useful in some quantum mechanical studies as orthonormal ones. Finally, it is shown that linearly independent remote pure-state preparation carries the highest probability of occurrence. This singles out linearly independent remote influence from all possible ones.

Vector sensor for scanning SQUID microscopy

NASA Astrophysics Data System (ADS)

Dang, Vu The; Toji, Masaki; Thanh Huy, Ho; Miyajima, Shigeyuki; Shishido, Hiroaki; Hidaka, Mutsuo; Hayashi, Masahiko; Ishida, Takekazu

2017-07-01

We plan to build a novel 3-dimensional (3D) scanning SQUID microscope with high sensitivity and high spatial resolution. In the system, a vector sensor consists of three SQUID sensors and three pick-up coils realized on a single chip. Three pick-up coils are configured in orthogonal with each other to measure the magnetic field vector of X, Y, Z components. We fabricated some SQUID chips with one uniaxial pick-up coil or three vector pick-up coils and carried out fundamental measurements to reveal the basic characteristics. Josephson junctions (JJs) of sensors are designed to have the critical current density J c of 320 A/cm2, and the critical current I c becomes 12.5 μA for the 2.2μm × 2.2μm JJ. We carefully positioned the three pickup coils so as to keep them at the same height at the centers of all three X, Y and Z coils. This can be done by arranging them along single line parallel to a sample surface. With the aid of multilayer technology of Nb-based fabrication, we attempted to reduce an inner diameter of the pickup coils to enhance both sensitivity and spatial resolution. The method for improving a spatial resolution of a local magnetic field image is to employ an XYZ piezo-driven scanner for controlling the positions of the pick-up coils. The fundamental characteristics of our SQUID sensors confirmed the proper operation of our SQUID sensors and found a good agreement with our design parameters.

Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models

DOE PAGES

Carlberg, Kevin T.

2014-11-05

Our work presents a method to adaptively refine reduced-order models a posteriori without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive h-refinement: it enriches the reduced-basis space online by ‘splitting’ a given basis vector into several vectors with disjoint support. The splitting scheme is defined by a tree structure constructed offline via recursive k-means clustering of the state variables using snapshot data. This method identifies the vectors to split online using a dual-weighted-residual approach that aims to reduce error in an output quantity of interest. The resulting method generates a hierarchy of subspaces online without requiring large-scale operationsmore » or full-order-model solves. Furthermore, it enables the reduced-order model to satisfy any prescribed error tolerance regardless of its original fidelity, as a completely refined reduced-order model is mathematically equivalent to the original full-order model. Experiments on a parameterized inviscid Burgers equation highlight the ability of the method to capture phenomena (e.g., moving shocks) not contained in the span of the original reduced basis.« less

Eight cm technology thruster development. [structurally integrated ion thruster for attitude control and stationkeeping of synchronous satellites

NASA Technical Reports Server (NTRS)

Hyman, J., Jr.

1974-01-01

A structural integrated ion thruster with 8-cm beam diameter (SIT-8) was developed for attitude control and stationkeeping of synchronous satellites. As optimized, the system demonstrates a thrust T=1.14 mlb (not corrected for beam V sub B = 1200 V (I sub sp = 2200 sec) total propellant utilization efficiency nu sub u = 59.8% (is approximately 72% without auxiliary pulse-igniter electrode), and electrical efficiency n sub E 61.9%. The thruster incorporates a wire-mesh anode and tantalum cover surfaces to control discharge chamber flake formation and employs an auxiliary pulse-igniter electrode for hollow-cathode ignition. When the SIT-8 is integrated with the compatible SIT-5 propellant tankage, the system envelope is 35 cm long by 13 cm flange bolt circle with a mass of 9.8 kg including 6.8 kg of mercury propellant. Two thrust vectoring systems which generate beam deflections in two orthogonal directions were also developed under the program and tested with the 8-cm thruster. One system vectors the beam over + or - 10 degrees by gimbaling of the entire thruster (not including tankage), while the other system vectors the beam over + or - 7 degrees by translating the accel electrode relative to the screen electrode.

Fluorescent nanodiamonds embedded in biocompatible translucent shells.

PubMed

Rehor, Ivan; Slegerova, Jitka; Kucka, Jan; Proks, Vladimir; Petrakova, Vladimira; Adam, Marie-Pierre; Treussart, François; Turner, Stuart; Bals, Sara; Sacha, Pavel; Ledvina, Miroslav; Wen, Amy M; Steinmetz, Nicole F; Cigler, Petr

2014-03-26

High pressure high temperature (HPHT) nanodiamonds (NDs) represent extremely promising materials for construction of fluorescent nanoprobes and nanosensors. However, some properties of bare NDs limit their direct use in these applications: they precipitate in biological solutions, only a limited set of bio-orthogonal conjugation techniques is available and the accessible material is greatly polydisperse in shape. In this work, we encapsulate bright 30-nm fluorescent nanodiamonds (FNDs) in 10-20-nm thick translucent (i.e., not altering FND fluorescence) silica shells, yielding monodisperse near-spherical particles of mean diameter 66 nm. High yield modification of the shells with PEG chains stabilizes the particles in ionic solutions, making them applicable in biological environments. We further modify the opposite ends of PEG chains with fluorescent dyes or vectoring peptide using click chemistry. High conversion of this bio-orthogonal coupling yielded circa 2000 dye or peptide molecules on a single FND. We demonstrate the superior properties of these particles by in vitro interaction with human prostate cancer cells: while bare nanodiamonds strongly aggregate in the buffer and adsorb onto the cell membrane, the shell encapsulated NDs do not adsorb nonspecifically and they penetrate inside the cells. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Fluorescent Nanodiamonds Embedded in Biocompatible Translucent Shells

PubMed Central

Rehor, Ivan; Slegerova, Jitka; Kucka, Jan; Proks, Vladimir; Petrakova, Vladimira; Adam, Marie-Pierre; Treussart, François; Turner, Stuart; Bals, Sara; Sacha, Pavel; Ledvina, Miroslav; Wen, Amy M.; Steinmetz, Nicole F.; Cigler, Petr

2016-01-01

High pressure high temperature (HPHT) nanodiamonds (NDs) represent extremely promising materials for construction of fluorescent nanoprobes and nanosensors. However, some properties of bare NDs limit their direct use in these applications: they precipitate in biological solutions, only a limited set of bio-orthogonal conjugation techniques is available and the accessible material is greatly polydisperse in shape. In this work, we encapsulate bright 30-nm fluorescent nanodiamonds (FNDs) in 10–20-nm thick translucent (i.e., not altering FND fluorescence) silica shells, yielding monodisperse near-spherical particles of mean diameter 66 nm. High yield modification of the shells with PEG chains stabilizes the particles in ionic solutions, making them applicable in biological environments. We further modify the opposite ends of PEG chains with fluorescent dyes or vectoring peptide using click chemistry. High conversion of this bio-orthogonal coupling yielded circa 2000 dye or peptide molecules on a single FND. We demonstrate the superior properties of these particles by in vitro interaction with human prostate cancer cells: while bare nanodiamonds strongly aggregate in the buffer and adsorb onto the cell membrane, the shell encapsulated NDs do not adsorb nonspecifically and they penetrate inside the cells. PMID:24500945

Impairment assessment of orthogonal frequency division multiplexing over dispersion-managed links in backbone and backhaul networks

NASA Astrophysics Data System (ADS)

Tamilarasan, Ilavarasan; Saminathan, Brindha; Murugappan, Meenakshi

2016-04-01

The past decade has seen the phenomenal usage of orthogonal frequency division multiplexing (OFDM) in the wired as well as wireless communication domains, and it is also proposed in the literature as a future proof technique for the implementation of flexible resource allocation in cognitive optical networks. Fiber impairment assessment and adaptive compensation becomes critical in such implementations. A comprehensive analytical model for impairments in OFDM-based fiber links is developed. The proposed model includes the combined impact of laser phase fluctuations, fiber dispersion, self phase modulation, cross phase modulation, four-wave mixing, the nonlinear phase noise due to the interaction of amplified spontaneous emission with fiber nonlinearities, and the photodetector noises. The bit error rate expression for the proposed model is derived based on error vector magnitude estimation. The performance analysis of the proposed model is presented and compared for dispersion compensated and uncompensated backbone/backhaul links. The results suggest that OFDM would perform better for uncompensated links than the compensated links due to the negligible FWM effects and there is a need for flexible compensation. The proposed model can be employed in cognitive optical networks for accurate assessment of fiber-related impairments.

Comment on “Rethinking first-principles electron transport theories with projection operators: The problems caused by partitioning the basis set” [J. Chem. Phys. 139, 114104 (2013)

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

Brandbyge, Mads, E-mail: mads.brandbyge@nanotech.dtu.dk

2014-05-07

In a recent paper Reuter and Harrison [J. Chem. Phys. 139, 114104 (2013)] question the widely used mean-field electron transport theories, which employ nonorthogonal localized basis sets. They claim these can violate an “implicit decoupling assumption,” leading to wrong results for the current, different from what would be obtained by using an orthogonal basis, and dividing surfaces defined in real-space. We argue that this assumption is not required to be fulfilled to get exact results. We show how the current/transmission calculated by the standard Greens function method is independent of whether or not the chosen basis set is nonorthogonal, andmore » that the current for a given basis set is consistent with divisions in real space. The ambiguity known from charge population analysis for nonorthogonal bases does not carry over to calculations of charge flux.« less

Genetic modification of hematopoietic cells using retroviral and lentiviral vectors: safety considerations for vector design and delivery into target cells.

PubMed

Dropulic, Boro

2005-07-01

The recent development of leukemia in three patients following retroviral vector gene transfer in hematopoietic stem cells, resulting in the death of one patient, has raised safety concerns for the use of integrating gene transfer vectors for human gene therapy. This review discusses these serious adverse events from the perspective of whether restrictions on vector design and vector-modified target cells are warranted at this time. A case is made against presently establishing specific restrictions for vector design and transduced cells; rather, their safety should be ascertained by empiric evaluation in appropriate preclinical models on a case-by-case basis. Such preclinical data, coupled with proper informed patient consent and a risk-benefit ratio analysis, provide the best available prospective evaluation of gene transfer vectors prior to their translation into the clinic.

Simultaneous determination of penicillin G salts by infrared spectroscopy: Evaluation of combining orthogonal signal correction with radial basis function-partial least squares regression

NASA Astrophysics Data System (ADS)

Talebpour, Zahra; Tavallaie, Roya; Ahmadi, Seyyed Hamid; Abdollahpour, Assem

2010-09-01

In this study, a new method for the simultaneous determination of penicillin G salts in pharmaceutical mixture via FT-IR spectroscopy combined with chemometrics was investigated. The mixture of penicillin G salts is a complex system due to similar analytical characteristics of components. Partial least squares (PLS) and radial basis function-partial least squares (RBF-PLS) were used to develop the linear and nonlinear relation between spectra and components, respectively. The orthogonal signal correction (OSC) preprocessing method was used to correct unexpected information, such as spectral overlapping and scattering effects. In order to compare the influence of OSC on PLS and RBF-PLS models, the optimal linear (PLS) and nonlinear (RBF-PLS) models based on conventional and OSC preprocessed spectra were established and compared. The obtained results demonstrated that OSC clearly enhanced the performance of both RBF-PLS and PLS calibration models. Also in the case of some nonlinear relation between spectra and component, OSC-RBF-PLS gave satisfactory results than OSC-PLS model which indicated that the OSC was helpful to remove extrinsic deviations from linearity without elimination of nonlinear information related to component. The chemometric models were tested on an external dataset and finally applied to the analysis commercialized injection product of penicillin G salts.

Spatially orthogonal chemical functionalization of a hierarchical pore network for catalytic cascade reactions

NASA Astrophysics Data System (ADS)

Parlett, Christopher M. A.; Isaacs, Mark A.; Beaumont, Simon K.; Bingham, Laura M.; Hondow, Nicole S.; Wilson, Karen; Lee, Adam F.

2016-02-01

The chemical functionality within porous architectures dictates their performance as heterogeneous catalysts; however, synthetic routes to control the spatial distribution of individual functions within porous solids are limited. Here we report the fabrication of spatially orthogonal bifunctional porous catalysts, through the stepwise template removal and chemical functionalization of an interconnected silica framework. Selective removal of polystyrene nanosphere templates from a lyotropic liquid crystal-templated silica sol-gel matrix, followed by extraction of the liquid crystal template, affords a hierarchical macroporous-mesoporous architecture. Decoupling of the individual template extractions allows independent functionalization of macropore and mesopore networks on the basis of chemical and/or size specificity. Spatial compartmentalization of, and directed molecular transport between, chemical functionalities affords control over the reaction sequence in catalytic cascades; herein illustrated by the Pd/Pt-catalysed oxidation of cinnamyl alcohol to cinnamic acid. We anticipate that our methodology will prompt further design of multifunctional materials comprising spatially compartmentalized functions.

Programmable molecular recognition based on the geometry of DNA nanostructures.

PubMed

Woo, Sungwook; Rothemund, Paul W K

2011-07-10

From ligand-receptor binding to DNA hybridization, molecular recognition plays a central role in biology. Over the past several decades, chemists have successfully reproduced the exquisite specificity of biomolecular interactions. However, engineering multiple specific interactions in synthetic systems remains difficult. DNA retains its position as the best medium with which to create orthogonal, isoenergetic interactions, based on the complementarity of Watson-Crick binding. Here we show that DNA can be used to create diverse bonds using an entirely different principle: the geometric arrangement of blunt-end stacking interactions. We show that both binary codes and shape complementarity can serve as a basis for such stacking bonds, and explore their specificity, thermodynamics and binding rules. Orthogonal stacking bonds were used to connect five distinct DNA origami. This work, which demonstrates how a single attractive interaction can be developed to create diverse bonds, may guide strategies for molecular recognition in systems beyond DNA nanostructures.

Conical refraction of elastic waves in absorbing crystals

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

Alshits, V. I., E-mail: alshits@ns.crys.ras.ru; Lyubimov, V. N.

2011-10-15

The absorption-induced acoustic-axis splitting in a viscoelastic crystal with an arbitrary anisotropy is considered. It is shown that after 'switching on' absorption, the linear vector polarization field in the vicinity of the initial degeneracy point having an orientation singularity with the Poincare index n = {+-}1/2, transforms to a planar distribution of ellipses with two singularities n = {+-}1/4 corresponding to new axes. The local geometry of the slowness surface of elastic waves is studied in the vicinity of new degeneracy points and a self-intersection line connecting them. The absorption-induced transformation of the classical picture of conical refraction is studied.more » The ellipticity of waves at the edge of the self-intersection wedge in a narrow interval of propagation directions drastically changes from circular at the wedge ends to linear in the middle of the wedge. For the wave normal directed to an arbitrary point of this wedge, during movement of the displacement vector over the corresponding polarization ellipse, the wave ray velocity s runs over the same cone describing refraction in a crystal without absorption. In this case, the end of the vector moves along a universal ellipse whose plane is orthogonal to the acoustic axis for zero absorption. The areal velocity of this movement differs from the angular velocity of the displacement vector on the polarization ellipse only by a constant factor, being delayed by {pi}/2 in phase. When the wave normal is localized at the edge of the wedge in its central region, the movement of vector s along the universal ellipse becomes drastically nonuniform and the refraction transforms from conical to wedge-like.« less

Polarized object detection in crabs: a two-channel system.

PubMed

Basnak, Melanie Ailín; Pérez-Schuster, Verónica; Hermitte, Gabriela; Berón de Astrada, Martín

2018-05-25

Many animal species take advantage of polarization vision for vital tasks such as orientation, communication and contrast enhancement. Previous studies have suggested that decapod crustaceans use a two-channel polarization system for contrast enhancement. Here, we characterize the polarization contrast sensitivity in a grapsid crab . We estimated the polarization contrast sensitivity of the animals by quantifying both their escape response and changes in heart rate when presented with polarized motion stimuli. The motion stimulus consisted of an expanding disk with an 82 deg polarization difference between the object and the background. More than 90% of animals responded by freezing or trying to avoid the polarized stimulus. In addition, we co-rotated the electric vector (e-vector) orientation of the light from the object and background by increments of 30 deg and found that the animals' escape response varied periodically with a 90 deg period. Maximum escape responses were obtained for object and background e-vectors near the vertical and horizontal orientations. Changes in cardiac response showed parallel results but also a minimum response when e-vectors of object and background were shifted by 45 deg with respect to the maxima. These results are consistent with an orthogonal receptor arrangement for the detection of polarized light, in which two channels are aligned with the vertical and horizontal orientations. It has been hypothesized that animals with object-based polarization vision rely on a two-channel detection system analogous to that of color processing in dichromats. Our results, obtained by systematically varying the e-vectors of object and background, provide strong empirical support for this theoretical model of polarized object detection. © 2018. Published by The Company of Biologists Ltd.

"Analytical" vector-functions I

NASA Astrophysics Data System (ADS)

Todorov, Vladimir Todorov

2017-12-01

In this note we try to give a new (or different) approach to the investigation of analytical vector functions. More precisely a notion of a power xn; n ∈ ℕ+ of a vector x ∈ ℝ3 is introduced which allows to define an "analytical" function f : ℝ3 → ℝ3. Let furthermore f (ξ )= ∑n =0 ∞ anξn be an analytical function of the real variable ξ. Here we replace the power ξn of the number ξ with the power of a vector x ∈ ℝ3 to obtain a vector "power series" f (x )= ∑n =0 ∞ anxn . We research some properties of the vector series as well as some applications of this idea. Note that an "analytical" vector function does not depend of any basis, which may be used in research into some problems in physics.

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES

PubMed Central

GILLETTE, ANDREW; RAND, ALEXANDER; BAJAJ, CHANDRAJIT

2016-01-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties. PMID:28077939

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES.

PubMed

Gillette, Andrew; Rand, Alexander; Bajaj, Chandrajit

2016-10-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties.

Construction of promoter-probe shuttle vectors for Escherichia coli and corynebacteria on the basis of promoterless alpha-amylase gene.

PubMed

Ugorcáková, J; Bukovská, G; Timko, J

2000-01-01

We constructed new promoter-probe vectors for E. coli and corynebacteria based on the promoterless alpha-amylase gene originating from Bacillus subtilis. Vectors pJUPAE1 and pJUPAE2 are suitable for isolation of transcriptionally active fragments from plasmids, phages or genomic DNA. alpha-Amylase activity can be easily visually detected on agar plates containing a chromogenic substrate, or by direct measurement of alpha-amylase activity.

Manifolds for pose tracking from monocular video

NASA Astrophysics Data System (ADS)

Basu, Saurav; Poulin, Joshua; Acton, Scott T.

2015-03-01

We formulate a simple human-pose tracking theory from monocular video based on the fundamental relationship between changes in pose and image motion vectors. We investigate the natural embedding of the low-dimensional body pose space into a high-dimensional space of body configurations that behaves locally in a linear manner. The embedded manifold facilitates the decomposition of the image motion vectors into basis motion vector fields of the tangent space to the manifold. This approach benefits from the style invariance of image motion flow vectors, and experiments to validate the fundamental theory show reasonable accuracy (within 4.9 deg of the ground truth).

Signal detection using support vector machines in the presence of ultrasonic speckle

NASA Astrophysics Data System (ADS)

Kotropoulos, Constantine L.; Pitas, Ioannis

2002-04-01

Support Vector Machines are a general algorithm based on guaranteed risk bounds of statistical learning theory. They have found numerous applications, such as in classification of brain PET images, optical character recognition, object detection, face verification, text categorization and so on. In this paper we propose the use of support vector machines to segment lesions in ultrasound images and we assess thoroughly their lesion detection ability. We demonstrate that trained support vector machines with a Radial Basis Function kernel segment satisfactorily (unseen) ultrasound B-mode images as well as clinical ultrasonic images.

Subgrid-scale physical parameterization in atmospheric modeling: How can we make it consistent?

NASA Astrophysics Data System (ADS)

Yano, Jun-Ichi

2016-07-01

Approaches to subgrid-scale physical parameterization in atmospheric modeling are reviewed by taking turbulent combustion flow research as a point of reference. Three major general approaches are considered for its consistent development: moment, distribution density function (DDF), and mode decomposition. The moment expansion is a standard method for describing the subgrid-scale turbulent flows both in geophysics and engineering. The DDF (commonly called PDF) approach is intuitively appealing as it deals with a distribution of variables in subgrid scale in a more direct manner. Mode decomposition was originally applied by Aubry et al (1988 J. Fluid Mech. 192 115-73) in the context of wall boundary-layer turbulence. It is specifically designed to represent coherencies in compact manner by a low-dimensional dynamical system. Their original proposal adopts the proper orthogonal decomposition (empirical orthogonal functions) as their mode-decomposition basis. However, the methodology can easily be generalized into any decomposition basis. Among those, wavelet is a particularly attractive alternative. The mass-flux formulation that is currently adopted in the majority of atmospheric models for parameterizing convection can also be considered a special case of mode decomposition, adopting segmentally constant modes for the expansion basis. This perspective further identifies a very basic but also general geometrical constraint imposed on the massflux formulation: the segmentally-constant approximation. Mode decomposition can, furthermore, be understood by analogy with a Galerkin method in numerically modeling. This analogy suggests that the subgrid parameterization may be re-interpreted as a type of mesh-refinement in numerical modeling. A link between the subgrid parameterization and downscaling problems is also pointed out.

Bidirectional segmentation of prostate capsule from ultrasound volumes: an improved strategy

NASA Astrophysics Data System (ADS)

Wei, Liyang; Narayanan, Ramkrishnan; Kumar, Dinesh; Fenster, Aaron; Barqawi, Albaha; Werahera, Priya; Crawford, E. David; Suri, Jasjit S.

2008-03-01

Prostate volume is an indirect indicator for several prostate diseases. Volume estimation is a desired requirement during prostate biopsy, therapy and clinical follow up. Image segmentation is thus necessary. Previously, discrete dynamic contour (DDC) was implemented in orthogonal unidirectional on the slice-by-slice basis for prostate boundary estimation. This suffered from the glitch that it needed stopping criteria during the propagation of segmentation procedure from slice-to-slice. To overcome this glitch, axial DDC was implemented and this suffered from the fact that central axis never remains fixed and wobbles during propagation of segmentation from slice-to-slice. The effect of this was a multi-fold reconstructed surface. This paper presents a bidirectional DDC approach, thereby removing the two glitches. Our bidirectional DDC protocol was tested on a clinical dataset on 28 3-D ultrasound image volumes acquired using side fire Philips transrectal ultrasound. We demonstrate the orthogonal bidirectional DDC strategy achieved the most accurate volume estimation compared with previously published orthogonal unidirectional DDC and axial DDC methods. Compared to the ground truth, we show that the mean volume estimation errors were: 18.48%, 9.21% and 7.82% for unidirectional, axial and bidirectional DDC methods, respectively. The segmentation architecture is implemented in Visual C++ in Windows environment.

Motion streaks in fast motion rivalry cause orientation-selective suppression.

PubMed

Apthorp, Deborah; Wenderoth, Peter; Alais, David

2009-05-14

We studied binocular rivalry between orthogonally translating arrays of random Gaussian blobs and measured the strength of rivalry suppression for static oriented probes. Suppression depth was quantified by expressing monocular probe thresholds during dominance relative to thresholds during suppression. Rivalry between two fast motions or two slow motions was compared in order to test the suggestion that fast-moving objects leave oriented "motion streaks" due to temporal integration (W. S. Geisler, 1999). If fast motions do produce motion streaks, then fast motion rivalry might also entail rivalry between the orthogonal streak orientations. We tested this using a static oriented probe that was aligned either parallel to the motion trajectory (hence collinear with the "streaks") or was orthogonal to the trajectory, predicting that rivalry suppression would be greater for parallel probes, and only for rivalry between fast motions. Results confirmed that suppression depth did depend on probe orientation for fast motion but not for slow motion. Further experiments showed that threshold elevations for the oriented probe during suppression exhibited clear orientation tuning. However, orientation-tuned elevations were also present during dominance, suggesting within-channel masking as the basis of the extra-deep suppression. In sum, the presence of orientation-dependent suppression in fast motion rivalry is consistent with the "motion streaks" hypothesis.

Bethe vectors for XXX-spin chain

NASA Astrophysics Data System (ADS)

Burdík, Čestmír; Fuksa, Jan; Isaev, Alexei

2014-11-01

The paper deals with algebraic Bethe ansatz for XXX-spin chain. Generators of Yang-Baxter algebra are expressed in basis of free fermions and used to calculate explicit form of Bethe vectors. Their relation to N-component models is used to prove conjecture about their form in general. Some remarks on inhomogeneous XXX-spin chain are included.

Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra

NASA Astrophysics Data System (ADS)

Ohkubo, Yusuke

2018-05-01

In this paper, we obtain the formula for the Kac determinant of the algebra arising from the level N representation of the Ding-Iohara-Miki algebra. It is also discovered that its singular vectors correspond to generalized Macdonald functions (the q-deformed version of the AFLT basis).

Polarization ellipse and Stokes parameters in geometric algebra.

PubMed

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

2012-01-01

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

New QCD sum rules based on canonical commutation relations

NASA Astrophysics Data System (ADS)

Hayata, Tomoya

2012-04-01

New derivation of QCD sum rules by canonical commutators is developed. It is the simple and straightforward generalization of Thomas-Reiche-Kuhn sum rule on the basis of Kugo-Ojima operator formalism of a non-abelian gauge theory and a suitable subtraction of UV divergences. By applying the method to the vector and axial vector current in QCD, the exact Weinberg’s sum rules are examined. Vector current sum rules and new fractional power sum rules are also discussed.

[Cloning and gene expression in lactic acid bacteria].

PubMed

Bondarenko, V M; Beliavskaia, V A

2000-01-01

The possibility of using the genera Lactobacillus and Lactococcus as vector representatives is widely discussed at present. The prospects of the construction of recombinant bacteria are closely connected with the solution of a number of problems: the level of the transcription of cloned genes, the effectiveness of the translation of heterologous mRNA, the stability of protein with respect to bacterial intracellular proteases, the method by protein molecules leave the cell (by secretion or as the result of lysis). To prevent segregation instability, the construction of vector molecules on the basis of stable cryptic plasmids found in wild strains of lactic acid bacteria was proposed. High copying plasmids with low molecular weight were detected in L. plantarum and L. pentosus strains. Several plasmids with molecular weights of 1.7, 1.8 and 2.3 kb were isolated from bacterial cells to be used as the basis for the construction of vector molecules. Genes of chloramphenicol- and erythromycin-resistance from Staphylococcus aureus plasmids were used as marker genes ensuring cell transformation. The vector plasmids thus constructed exhibited high transformation activity in the electroporation of different strains, including L. casei, L. plantarum, L. acidophilus, L. fermentum and L. brevis which could be classified with the replicons of a wide circle of hosts. But the use of these plasmids was limited due to the risk of the uncontrolled dissemination of recombinant plasmids. L. acidophilus were also found to have strictly specific plasmids with good prospects of being used as the basis for the creation of vectors, incapable of dissemination. In addition to the search of strain-specific plasmids, incapable of uncontrolled gene transmission, the use of chromosome-integrated heterologous genes is recommended in cloning to ensure the maximum safety.

On the Application of Time-Reversed Space-Time Block Code to Aeronautical Telemetry

DTIC Science & Technology

2014-06-01

Keying (SOQPSK), bit error rate (BER), Orthogonal Frequency Division Multiplexing ( OFDM ), Generalized time-reversed space-time block codes (GTR-STBC) 16...Alamouti code [4]) is optimum [2]. Although OFDM is generally applied on a per subcarrier basis in frequency selective fading, it is not a viable...Calderbank, “Finite-length MIMO decision feedback equal- ization for space-time block-coded signals over multipath-fading channels,” IEEE Transac- tions on

Ultrasound beam transmission using a discretely orthogonal Gaussian aperture basis

NASA Astrophysics Data System (ADS)

Roberts, R. A.

2018-04-01

Work is reported on development of a computational model for ultrasound beam transmission at an arbitrary geometry transmission interface for generally anisotropic materials. The work addresses problems encountered when the fundamental assumptions of ray theory do not hold, thereby introducing errors into ray-theory-based transmission models. Specifically, problems occur when the asymptotic integral analysis underlying ray theory encounters multiple stationary phase points in close proximity, due to focusing caused by concavity on either the entry surface or a material slowness surface. The approach presented here projects integrands over both the transducer aperture and the entry surface beam footprint onto a Gaussian-derived basis set, thereby distributing the integral over a summation of second-order phase integrals which are amenable to single stationary phase point analysis. Significantly, convergence is assured provided a sufficiently fine distribution of basis functions is used.

Gram-Schmidt algorithms for covariance propagation

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1977-01-01

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UD(transpose of U), where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and coloured process noise parameters increase mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Gram-Schmidt algorithms for covariance propagation

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1975-01-01

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UDU/T/, where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and colored process noise parameters increases mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Negative values of quasidistributions and quantum wave and number statistics

NASA Astrophysics Data System (ADS)

Peřina, J.; Křepelka, J.

2018-04-01

We consider nonclassical wave and number quantum statistics, and perform a decomposition of quasidistributions for nonlinear optical down-conversion processes using Bessel functions. We show that negative values of the quasidistribution do not directly represent probabilities; however, they directly influence measurable number statistics. Negative terms in the decomposition related to the nonclassical behavior with negative amplitudes of probability can be interpreted as positive amplitudes of probability in the negative orthogonal Bessel basis, whereas positive amplitudes of probability in the positive basis describe classical cases. However, probabilities are positive in all cases, including negative values of quasidistributions. Negative and positive contributions of decompositions to quasidistributions are estimated. The approach can be adapted to quantum coherence functions.

Dictionary Approaches to Image Compression and Reconstruction

NASA Technical Reports Server (NTRS)

Ziyad, Nigel A.; Gilmore, Erwin T.; Chouikha, Mohamed F.

1998-01-01

This paper proposes using a collection of parameterized waveforms, known as a dictionary, for the purpose of medical image compression. These waveforms, denoted as phi(sub gamma), are discrete time signals, where gamma represents the dictionary index. A dictionary with a collection of these waveforms is typically complete or overcomplete. Given such a dictionary, the goal is to obtain a representation image based on the dictionary. We examine the effectiveness of applying Basis Pursuit (BP), Best Orthogonal Basis (BOB), Matching Pursuits (MP), and the Method of Frames (MOF) methods for the compression of digitized radiological images with a wavelet-packet dictionary. The performance of these algorithms is studied for medical images with and without additive noise.

Dictionary Approaches to Image Compression and Reconstruction

NASA Technical Reports Server (NTRS)

Ziyad, Nigel A.; Gilmore, Erwin T.; Chouikha, Mohamed F.

1998-01-01

This paper proposes using a collection of parameterized waveforms, known as a dictionary, for the purpose of medical image compression. These waveforms, denoted as lambda, are discrete time signals, where y represents the dictionary index. A dictionary with a collection of these waveforms Is typically complete or over complete. Given such a dictionary, the goal is to obtain a representation Image based on the dictionary. We examine the effectiveness of applying Basis Pursuit (BP), Best Orthogonal Basis (BOB), Matching Pursuits (MP), and the Method of Frames (MOF) methods for the compression of digitized radiological images with a wavelet-packet dictionary. The performance of these algorithms is studied for medical images with and without additive noise.

Polarization and propagation characteristics of switchable first-order azimuthally asymmetric beam generated in dual-mode fiber.

PubMed

Khan, Saba N; Chatterjee, Sudip K; Chaudhuri, Partha Roy

2015-02-20

We report here the controlled generation of a linearly polarized first-order azimuthally asymmetric beam (F-AAB) in a dual-mode fiber (DMF) by appropriate superposition of selectively excited zeroth-order vector modes that are doughnut-shaped azimuthally symmetric beams (D-ASBs). We first demonstrate continually switching polarization mode structures having an identical two-lobe intensity profile (i.e., intra-F-AAB conversion). Then, under a distinct launching state, we generate mode structures progressively toggling between the doughnut-shaped profile and two-lobe pattern having dissimilar polarization orientations (i.e., F-AAB to D-ASB conversion). Interestingly, a decentralized elliptical Gaussian beam possessing homogenous spatial polarization is obtained by enhancing the contribution of the fundamental mode (HE₁₁/LP₀₁) in selectively excited F-AAB. A smoothly varying azimuth of the input beam in this situation resulted in redistribution of transverse energy procuring a unique and exciting unconventional two-grain T-polarized beam having mutually orthogonal state of polarization (SOP). All of the above three were achieved under a given set of launching conditions (tilt/offset) of a Gaussian mode (TEM₀₀) devised with changing SOP of the input beam. A strong modulation in the output beam characteristics was also observed with the variation in propagation distance (for a fixed input SOP) owing to the large difference in propagation constants of the participating modes (LP₀₁ and one of the F-AABs). Finally, this particular study led to a design for a low-cost highly sensitive strain measuring device based on tracking the centroid movement of the output intensity pattern. Each of our experimentally observed intensity/polarization distributions is theoretically mapped on a one-to-one basis considering a linear superposition of appropriately excited LP basis modes of the waveguide toward a complete understanding of the polarization and mode propagation in the dual-mode structure.

Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space.

PubMed

Stępień, Grzegorz

2018-03-17

The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems-interior and exterior orientation of sensors-to a common, known in both systems, point. Each of the systems is translated along its axis (the systems have common origins) and at the same time the angular relative orientation of both coordinate systems is constant. The translation of both coordinate systems is defined by the spatial norm determining the length of vectors in the new Hilbert type space. As such, the displacement of two relative oblique orthogonal systems is reduced to zero. This makes it possible to directly calculate the rotation matrix of the sensor. The next and final step is the return translation of the system along an already known track. The method can be used for big rotation angles. The method was verified in laboratory conditions for the test data set and measurement data (field data). The accuracy of the results in the laboratory test is on the level of 10 -6 of the input data. This confirmed the correctness of the assumed calculation method. The method is a further development of the author's 2017 Total Free Station (TFS) transformation to several centroids in Hilbert type space. This is the reason why the method is called Multi-Centroid Isometric Transformation-MCIT. MCIT is very fast and enables, by reducing to zero the translation of two relative oblique orthogonal coordinate systems, direct calculation of the exterior orientation of the sensors.

A 3-Axis Miniature Magnetic Sensor Based on a Planar Fluxgate Magnetometer with an Orthogonal Fluxguide

PubMed Central

Lu, Chih-Cheng; Huang, Jeff

2015-01-01

A new class of tri-axial miniature magnetometer consisting of a planar fluxgate structure with an orthogonal ferromagnetic fluxguide centrally situated over the magnetic cores is presented. The magnetic sensor possesses a cruciform ferromagnetic core placed diagonally upon the square excitation coil under which two pairs of pick-up coils for in-plane field detection are allocated. Effective principles and analysis of the magnetometer for 3-D field vectors are described and verified by numerically electromagnetic simulation for the excitation and magnetization of the ferromagnetic cores. The sensor is operated by applying the second-harmonic detection technique that can verify V-B relationship and device responsivity. Experimental characterization of the miniature fluxgate device demonstrates satisfactory spatial magnetic field detection results in terms of responsivity and noise spectrum. As a result, at an excitation frequency of 50 kHz, a maximum in-plane responsivity of 122.4 V/T appears and a maximum out-of-plane responsivity of 11.6 V/T is obtained as well. The minimum field noise spectra are found to be 0.11 nT/√Hz and 6.29 nT/√Hz, respectively, in X- and Z-axis at 1 Hz under the same excitation frequency. Compared with the previous tri-axis fluxgate devices, this planar magnetic sensor with an orthogonal fluxguide provides beneficial enhancement in both sensory functionality and manufacturing simplicity. More importantly, this novel device concept is considered highly suitable for the extension to a silicon sensor made by the current CMOS-MEMS technologies, thus emphasizing its emerging applications of field detection in portable industrial electronics. PMID:26102496

Gibbsian Stationary Non-equilibrium States

NASA Astrophysics Data System (ADS)

De Carlo, Leonardo; Gabrielli, Davide

2017-09-01

We study the structure of stationary non-equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non reversible transition rates corresponding to a fixed invariant measure. The first one uses the equivalence of this problem with the construction of divergence free flows on the transition graph. Since divergence free flows are characterized by cyclic decompositions we can generate families of models from elementary cycles on the configuration space. The second construction is a functional discrete Hodge decomposition for translational covariant discrete vector fields. According to this, for example, the instantaneous current of any interacting particle system on a finite torus can be canonically decomposed in a gradient part, a circulation term and an harmonic component. All the three components are associated with functions on the configuration space. This decomposition is unique and constructive. The stationary condition can be interpreted as an orthogonality condition with respect to an harmonic discrete vector field and we use this decomposition to construct models having a fixed invariant measure.

Vector solitons in coupled nonlinear Schrödinger equations with spatial stimulated scattering and inhomogeneous dispersion

NASA Astrophysics Data System (ADS)

Gromov, E. M.; Malomed, B. A.; Tyutin, V. V.

2018-01-01

The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schrödinger equations, which incorporate the cross-phase modulation, pseudo-stimulated-Raman-scattering (pseudo-SRS), cross-pseudo-SRS, and spatially inhomogeneous second-order dispersion (SOD). The system models co-propagation of electromagnetic waves with orthogonal polarizations in plasmas. It is shown that the soliton's wavenumber downshift, caused by pseudo-SRS, may be compensated by an upshift, induced by the inhomogeneous SOD, to produce stable stationary two-component solitons. The corresponding approximate analytical solutions for stable solitons are found. Analytical results are well confirmed by their numerical counterparts. Further, the evolution of inputs composed of spatially even and odd components is investigated by means of systematic simulations, which reveal three different outcomes: formation of a breather which keeps opposite parities of the components; splitting into a pair of separating vector solitons; and spreading of the weak odd component into a small-amplitude pedestal with an embedded dark soliton.

String theory origin of constrained multiplets

NASA Astrophysics Data System (ADS)

Kallosh, Renata; Vercnocke, Bert; Wrase, Timm

2016-09-01

We study the non-linearly realized spontaneously broken supersymmetry of the (anti-)D3-brane action in type IIB string theory. The worldvolume fields are one vector A μ , three complex scalars ϕ i and four 4d fermions λ 0, λ i. These transform, in addition to the more familiar {N}=4 linear supersymmetry, also under 16 spontaneously broken, non-linearly realized supersymmetries. We argue that the worldvolume fields can be packaged into the following constrained 4d non-linear {N}=1 multiplets: four chiral multiplets S, Y i that satisfy S 2 = SY i =0 and contain the worldvolume fermions λ 0 and λ i ; and four chiral multiplets W α , H i that satisfy S{W}_{α }=S{overline{D}}_{overset{\\cdotp }{α }}{overline{H}}^{overline{imath}}=0 and contain the vector A μ and the scalars ϕ i . We also discuss how placing an anti-D3-brane on top of intersecting O7-planes can lead to an orthogonal multiplet Φ that satisfies S(Φ -overline{Φ})=0 , which is particularly interesting for inflationary cosmology.

Field-effect transistor having a superlattice channel and high carrier velocities at high applied fields

DOEpatents

Chaffin, deceased, Roger J.; Dawson, Ralph; Fritz, Ian J.; Osbourn, Gordon C.; Zipperian, Thomas E.

1989-01-01

A field effect transistor comprises a semiconductor having a source, a drain, a channel and a gate in operational relationship. The semiconductor is a strained layer superlattice comprising alternating quantum well and barrier layers, the quantum well layers and barrier layers being selected from the group of layer pairs consisting of InGaAs/AlGaAs, InAs/InAlGaAs, and InAs/InAlAsP. The layer thicknesses of the quantum well and barrier layers are sufficiently thin that the alternating layers constitute a superlattice which has a superlattice conduction band energy level structure in k-vector space which includes a lowest energy .GAMMA.-valley and a next lowest energy L-valley, each k-vector corresponding to one of the orthogonal directions defined by the planes of said layers and the directions perpendicular thereto. The layer thicknesses of the quantum well layers are selected to provide a superlattice L.sub.2D -valley which has a shape which is substantially more two-dimensional than that of said bulk L-valley.

Spacecraft attitude and velocity control system

NASA Technical Reports Server (NTRS)

Paluszek, Michael A. (Inventor); Piper, Jr., George E. (Inventor)

1992-01-01

A spacecraft attitude and/or velocity control system includes a controller which responds to at least attitude errors to produce command signals representing a force vector F and a torque vector T, each having three orthogonal components, which represent the forces and torques which are to be generated by the thrusters. The thrusters may include magnetic torquer or reaction wheels. Six difference equations are generated, three having the form ##EQU1## where a.sub.j is the maximum torque which the j.sup.th thruster can produce, b.sub.j is the maximum force which the j.sup.th thruster can produce, and .alpha..sub.j is a variable representing the throttling factor of the j.sup.th thruster, which may range from zero to unity. The six equations are summed to produce a single scalar equation relating variables .alpha..sub.j to a performance index Z: ##EQU2## Those values of .alpha. which maximize the value of Z are determined by a method for solving linear equations, such as a linear programming method. The Simplex method may be used. The values of .alpha..sub.j are applied to control the corresponding thrusters.

On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states

NASA Astrophysics Data System (ADS)

Klappenecker, Andreas; Rötteler, Martin; Shparlinski, Igor E.; Winterhof, Arne

2005-08-01

We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension n consisting of n2 operators of rank one which have an inner product close to uniform. This is motivated by the related question of constructing symmetric informationally complete POVMs (SIC-POVMs) for which the inner products are perfectly uniform. However, SIC-POVMs are notoriously hard to construct and, despite some success of constructing them numerically, there is no analytic construction known. We present two constructions of approximate versions of SIC-POVMs, where a small deviation from uniformity of the inner products is allowed. The first construction is based on selecting vectors from a maximal collection of mutually unbiased bases and works whenever the dimension of the system is a prime power. The second construction is based on perturbing the matrix elements of a subset of mutually unbiased bases. Moreover, we construct vector systems in Cn which are almost orthogonal and which might turn out to be useful for quantum computation. Our constructions are based on results of analytic number theory.

Self-similar motion of a Nambu-Goto string

NASA Astrophysics Data System (ADS)

Igata, Takahisa; Houri, Tsuyoshi; Harada, Tomohiro

2016-09-01

We study the self-similar motion of a string in a self-similar spacetime by introducing the concept of a self-similar string, which is defined as the world sheet to which a homothetic vector field is tangent. It is shown that in Nambu-Goto theory, the equations of motion for a self-similar string reduce to those for a particle. Moreover, under certain conditions such as the hypersurface orthogonality of the homothetic vector field, the equations of motion for a self-similar string simplify to the geodesic equations on a (pseudo)Riemannian space. As a concrete example, we investigate a self-similar Nambu-Goto string in a spatially flat Friedmann-Lemaître-Robertson-Walker expanding universe with self-similarity and obtain solutions of open and closed strings, which have various nontrivial configurations depending on the rate of the cosmic expansion. For instance, we obtain a circular solution that evolves linearly in the cosmic time while keeping its configuration by the balance between the effects of the cosmic expansion and string tension. We also show the instability for linear radial perturbation of the circular solutions.

A Quasioptical Vector Interferometer for Polarization Control

NASA Technical Reports Server (NTRS)

Chuss, David T.; Wollack, Edward J.; Moseley, Harvey S.; Novak, Giles

2005-01-01

We present a mathematical description of a Quasioptical Vector Interferometer (QVI), a device that maps an input polarization state to an output polarization state by introducing a phase delay between two linear orthogonal components of the input polarization. The advantages of such a device over a spinning wave-plate modulator for measuring astronomical polarization in the far-infrared through millimeter are: 1. The use of small, linear motions eliminates the need for cryogenic rotational bearings, 2. The phase flexibility allows measurement of Stokes V as well as Q and U, and 3. The QVI allows for both multi-wavelength and broadband modulation. We suggest two implementations of this device as an astronomical polarization modulator. The first involves two such modulators placed in series. By adjusting the two phase delays, it is possible to use such a modulator to measure Stokes Q, U, and V for passbands that are not too large. Conversely, a single QVI may be used to measure Q and V independent of frequency. In this implementation, Stokes U must be measured by rotating the instrument. We conclude this paper by presenting initial laboratory results.

Practical somewhat-secure quantum somewhat-homomorphic encryption with coherent states

NASA Astrophysics Data System (ADS)

Tan, Si-Hui; Ouyang, Yingkai; Rohde, Peter P.

2018-04-01

We present a scheme for implementing homomorphic encryption on coherent states encoded using phase-shift keys. The encryption operations require only rotations in phase space, which commute with computations in the code space performed via passive linear optics, and with generalized nonlinear phase operations that are polynomials of the photon-number operator in the code space. This encoding scheme can thus be applied to any computation with coherent-state inputs, and the computation proceeds via a combination of passive linear optics and generalized nonlinear phase operations. An example of such a computation is matrix multiplication, whereby a vector representing coherent-state amplitudes is multiplied by a matrix representing a linear optics network, yielding a new vector of coherent-state amplitudes. By finding an orthogonal partitioning of the support of our encoded states, we quantify the security of our scheme via the indistinguishability of the encrypted code words. While we focus on coherent-state encodings, we expect that this phase-key encoding technique could apply to any continuous-variable computation scheme where the phase-shift operator commutes with the computation.

Geometry of generalized depolarizing channels

NASA Astrophysics Data System (ADS)

Burrell, Christian K.

2009-10-01

A generalized depolarizing channel acts on an N -dimensional quantum system to compress the “Bloch ball” in N2-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2d (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.

Geometry of generalized depolarizing channels

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

Burrell, Christian K.

2009-10-15

A generalized depolarizing channel acts on an N-dimensional quantum system to compress the 'Bloch ball' in N{sup 2}-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2{sup d} (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors formsmore » a simplex.« less

The Role of Innate Immunity in Conditioning Mosquito Susceptibility to West Nile Virus

PubMed Central

Prasad, Abhishek N.; Brackney, Doug. E.; Ebel, Gregory D.

2013-01-01

Arthropod-borne viruses (arboviruses) represent an emerging threat to human and livestock health globally. In particular, those transmitted by mosquitoes present the greatest challenges to disease control efforts. An understanding of the molecular basis for mosquito innate immunity to arbovirus infection is therefore critical to investigations regarding arbovirus evolution, virus-vector ecology, and mosquito vector competence. In this review, we discuss the current state of understanding regarding mosquito innate immunity to West Nile virus. We draw from the literature with respect to other virus-vector pairings to attempt to draw inferences to gaps in our knowledge about West Nile virus and relevant vectors. PMID:24351797

Vector Potential, Electromagnetic Induction and "Physical Meaning"

ERIC Educational Resources Information Center

Giuliani, G.

2010-01-01

A forgotten experiment by Andre Blondel (1914) proves, as held on the basis of theoretical arguments in a previous paper, that the time variation of the magnetic flux is not the cause of the induced emf; the physical agent is instead the vector potential through the term [equation omitted] (when the induced circuit is at rest). The "good…

Automated classification of maxillofacial cysts in cone beam CT images using contourlet transformation and Spherical Harmonics.

PubMed

Abdolali, Fatemeh; Zoroofi, Reza Aghaeizadeh; Otake, Yoshito; Sato, Yoshinobu

2017-02-01

Accurate detection of maxillofacial cysts is an essential step for diagnosis, monitoring and planning therapeutic intervention. Cysts can be of various sizes and shapes and existing detection methods lead to poor results. Customizing automatic detection systems to gain sufficient accuracy in clinical practice is highly challenging. For this purpose, integrating the engineering knowledge in efficient feature extraction is essential. This paper presents a novel framework for maxillofacial cysts detection. A hybrid methodology based on surface and texture information is introduced. The proposed approach consists of three main steps as follows: At first, each cystic lesion is segmented with high accuracy. Then, in the second and third steps, feature extraction and classification are performed. Contourlet and SPHARM coefficients are utilized as texture and shape features which are fed into the classifier. Two different classifiers are used in this study, i.e. support vector machine and sparse discriminant analysis. Generally SPHARM coefficients are estimated by the iterative residual fitting (IRF) algorithm which is based on stepwise regression method. In order to improve the accuracy of IRF estimation, a method based on extra orthogonalization is employed to reduce linear dependency. We have utilized a ground-truth dataset consisting of cone beam CT images of 96 patients, belonging to three maxillofacial cyst categories: radicular cyst, dentigerous cyst and keratocystic odontogenic tumor. Using orthogonalized SPHARM, residual sum of squares is decreased which leads to a more accurate estimation. Analysis of the results based on statistical measures such as specificity, sensitivity, positive predictive value and negative predictive value is reported. The classification rate of 96.48% is achieved using sparse discriminant analysis and orthogonalized SPHARM features. Classification accuracy at least improved by 8.94% with respect to conventional features. This study demonstrated that our proposed methodology can improve the computer assisted diagnosis (CAD) performance by incorporating more discriminative features. Using orthogonalized SPHARM is promising in computerized cyst detection and may have a significant impact in future CAD systems. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Time Domain Propagation of Quantum and Classical Systems using a Wavelet Basis Set Method

NASA Astrophysics Data System (ADS)

Lombardini, Richard; Nowara, Ewa; Johnson, Bruce

2015-03-01

The use of an orthogonal wavelet basis set (Optimized Maximum-N Generalized Coiflets) to effectively model physical systems in the time domain, in particular the electromagnetic (EM) pulse and quantum mechanical (QM) wavefunction, is examined in this work. Although past research has demonstrated the benefits of wavelet basis sets to handle computationally expensive problems due to their multiresolution properties, the overlapping supports of neighboring wavelet basis functions poses problems when dealing with boundary conditions, especially with material interfaces in the EM case. Specifically, this talk addresses this issue using the idea of derivative matching creating fictitious grid points (T.A. Driscoll and B. Fornberg), but replaces the latter element with fictitious wavelet projections in conjunction with wavelet reconstruction filters. Two-dimensional (2D) systems are analyzed, EM pulse incident on silver cylinders and the QM electron wave packet circling the proton in a hydrogen atom system (reduced to 2D), and the new wavelet method is compared to the popular finite-difference time-domain technique.

Four classes of interactions for evolutionary games.

PubMed

Szabó, György; Bodó, Kinga S; Allen, Benjamin; Nowak, Martin A

2015-08-01

The symmetric four-strategy games are decomposed into a linear combination of 16 basis games represented by orthogonal matrices. Among these basis games four classes can be distinguished as it is already found for the three-strategy games. The games with self-dependent (cross-dependent) payoffs are characterized by matrices consisting of uniform rows (columns). Six of 16 basis games describe coordination-type interactions among the strategy pairs and three basis games span the parameter space of the cyclic components that are analogous to the rock-paper-scissors games. In the absence of cyclic components the game is a potential game and the potential matrix is evaluated. The main features of the four classes of games are discussed separately and we illustrate some characteristic strategy distributions on a square lattice in the low noise limit if logit rule controls the strategy evolution. Analysis of the general properties indicates similar types of interactions at larger number of strategies for the symmetric matrix games.

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

PubMed

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

2010-08-01

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

Use of Multi-class Empirical Orthogonal Function for Identification of Hydrogeological Parameters and Spatiotemporal Pattern of Multiple Recharges in Groundwater Modeling

NASA Astrophysics Data System (ADS)

Huang, C. L.; Hsu, N. S.; Yeh, W. W. G.; Hsieh, I. H.

2017-12-01

This study develops an innovative calibration method for regional groundwater modeling by using multi-class empirical orthogonal functions (EOFs). The developed method is an iterative approach. Prior to carrying out the iterative procedures, the groundwater storage hydrographs associated with the observation wells are calculated. The combined multi-class EOF amplitudes and EOF expansion coefficients of the storage hydrographs are then used to compute the initial gauss of the temporal and spatial pattern of multiple recharges. The initial guess of the hydrogeological parameters are also assigned according to in-situ pumping experiment. The recharges include net rainfall recharge and boundary recharge, and the hydrogeological parameters are riverbed leakage conductivity, horizontal hydraulic conductivity, vertical hydraulic conductivity, storage coefficient, and specific yield. The first step of the iterative algorithm is to conduct the numerical model (i.e. MODFLOW) by the initial guess / adjusted values of the recharges and parameters. Second, in order to determine the best EOF combination of the error storage hydrographs for determining the correction vectors, the objective function is devised as minimizing the root mean square error (RMSE) of the simulated storage hydrographs. The error storage hydrograph are the differences between the storage hydrographs computed from observed and simulated groundwater level fluctuations. Third, adjust the values of recharges and parameters and repeat the iterative procedures until the stopping criterion is reached. The established methodology was applied to the groundwater system of Ming-Chu Basin, Taiwan. The study period is from January 1st to December 2ed in 2012. Results showed that the optimal EOF combination for the multiple recharges and hydrogeological parameters can decrease the RMSE of the simulated storage hydrographs dramatically within three calibration iterations. It represents that the iterative approach that using EOF techniques can capture the groundwater flow tendency and detects the correction vector of the simulated error sources. Hence, the established EOF-based methodology can effectively and accurately identify the multiple recharges and hydrogeological parameters.

Fault-tolerant corrector/detector chip for high-speed data processing

DOEpatents

Andaleon, David D.; Napolitano, Jr., Leonard M.; Redinbo, G. Robert; Shreeve, William O.

1994-01-01

An internally fault-tolerant data error detection and correction integrated circuit device (10) and a method of operating same. The device functions as a bidirectional data buffer between a 32-bit data processor and the remainder of a data processing system and provides a 32-bit datum is provided with a relatively short eight bits of data-protecting parity. The 32-bits of data by eight bits of parity is partitioned into eight 4-bit nibbles and two 4-bit nibbles, respectively. For data flowing towards the processor the data and parity nibbles are checked in parallel and in a single operation employing a dual orthogonal basis technique. The dual orthogonal basis increase the efficiency of the implementation. Any one of ten (eight data, two parity) nibbles are correctable if erroneous, or two different erroneous nibbles are detectable. For data flowing away from the processor the appropriate parity nibble values are calculated and transmitted to the system along with the data. The device regenerates parity values for data flowing in either direction and compares regenerated to generated parity with a totally self-checking equality checker. As such, the device is self-validating and enabled to both detect and indicate an occurrence of an internal failure. A generalization of the device to protect 64-bit data with 16-bit parity to protect against byte-wide errors is also presented.

Fault-tolerant corrector/detector chip for high-speed data processing

DOEpatents

Andaleon, D.D.; Napolitano, L.M. Jr.; Redinbo, G.R.; Shreeve, W.O.

1994-03-01

An internally fault-tolerant data error detection and correction integrated circuit device and a method of operating same is described. The device functions as a bidirectional data buffer between a 32-bit data processor and the remainder of a data processing system and provides a 32-bit datum with a relatively short eight bits of data-protecting parity. The 32-bits of data by eight bits of parity is partitioned into eight 4-bit nibbles and two 4-bit nibbles, respectively. For data flowing towards the processor the data and parity nibbles are checked in parallel and in a single operation employing a dual orthogonal basis technique. The dual orthogonal basis increase the efficiency of the implementation. Any one of ten (eight data, two parity) nibbles are correctable if erroneous, or two different erroneous nibbles are detectable. For data flowing away from the processor the appropriate parity nibble values are calculated and transmitted to the system along with the data. The device regenerates parity values for data flowing in either direction and compares regenerated to generated parity with a totally self-checking equality checker. As such, the device is self-validating and enabled to both detect and indicate an occurrence of an internal failure. A generalization of the device to protect 64-bit data with 16-bit parity to protect against byte-wide errors is also presented. 8 figures.

Nonlinear Reduced-Order Analysis with Time-Varying Spatial Loading Distributions

NASA Technical Reports Server (NTRS)

Prezekop, Adam

2008-01-01

Oscillating shocks acting in combination with high-intensity acoustic loadings present a challenge to the design of resilient hypersonic flight vehicle structures. This paper addresses some features of this loading condition and certain aspects of a nonlinear reduced-order analysis with emphasis on system identification leading to formation of a robust modal basis. The nonlinear dynamic response of a composite structure subject to the simultaneous action of locally strong oscillating pressure gradients and high-intensity acoustic loadings is considered. The reduced-order analysis used in this work has been previously demonstrated to be both computationally efficient and accurate for time-invariant spatial loading distributions, provided that an appropriate modal basis is used. The challenge of the present study is to identify a suitable basis for loadings with time-varying spatial distributions. Using a proper orthogonal decomposition and modal expansion, it is shown that such a basis can be developed. The basis is made more robust by incrementally expanding it to account for changes in the location, frequency and span of the oscillating pressure gradient.

Involution and Difference Schemes for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.

In the present paper we consider the Navier-Stokes equations for the two-dimensional viscous incompressible fluid flows and apply to these equations our earlier designed general algorithmic approach to generation of finite-difference schemes. In doing so, we complete first the Navier-Stokes equations to involution by computing their Janet basis and discretize this basis by its conversion into the integral conservation law form. Then we again complete the obtained difference system to involution with eliminating the partial derivatives and extracting the minimal Gröbner basis from the Janet basis. The elements in the obtained difference Gröbner basis that do not contain partial derivatives of the dependent variables compose a conservative difference scheme. By exploiting arbitrariness in the numerical integration approximation we derive two finite-difference schemes that are similar to the classical scheme by Harlow and Welch. Each of the two schemes is characterized by a 5×5 stencil on an orthogonal and uniform grid. We also demonstrate how an inconsistent difference scheme with a 3×3 stencil is generated by an inappropriate numerical approximation of the underlying integrals.

Reduced-order model for underwater target identification using proper orthogonal decomposition

NASA Astrophysics Data System (ADS)

Ramesh, Sai Sudha; Lim, Kian Meng

2017-03-01

Research on underwater acoustics has seen major development over the past decade due to its widespread applications in domains such as underwater communication/navigation (SONAR), seismic exploration and oceanography. In particular, acoustic signatures from partially or fully buried targets can be used in the identification of buried mines for mine counter measures (MCM). Although there exist several techniques to identify target properties based on SONAR images and acoustic signatures, these methods first employ a feature extraction method to represent the dominant characteristics of a data set, followed by the use of an appropriate classifier based on neural networks or the relevance vector machine. The aim of the present study is to demonstrate the applications of proper orthogonal decomposition (POD) technique in capturing dominant features of a set of scattered pressure signals, and subsequent use of the POD modes and coefficients in the identification of partially buried underwater target parameters such as its location, size and material density. Several numerical examples are presented to demonstrate the performance of the system identification method based on POD. Although the present study is based on 2D acoustic model, the method can be easily extended to 3D models and thereby enables cost-effective representations of large-scale data.

CIG-P: Circular Interaction Graph for Proteomics.

PubMed

Hobbs, Christopher K; Leung, Michelle; Tsang, Herbert H; Ebhardt, H Alexander

2014-10-31

A typical affinity purification coupled to mass spectrometry (AP-MS) experiment includes the purification of a target protein (bait) using an antibody and subsequent mass spectrometry analysis of all proteins co-purifying with the bait (aka prey proteins). Like any other systems biology approach, AP-MS experiments generate a lot of data and visualization has been challenging, especially when integrating AP-MS experiments with orthogonal datasets. We present Circular Interaction Graph for Proteomics (CIG-P), which generates circular diagrams for visually appealing final representation of AP-MS data. Through a Java based GUI, the user inputs experimental and reference data as file in csv format. The resulting circular representation can be manipulated live within the GUI before exporting the diagram as vector graphic in pdf format. The strength of CIG-P is the ability to integrate orthogonal datasets with each other, e.g. affinity purification data of kinase PRPF4B in relation to the functional components of the spliceosome. Further, various AP-MS experiments can be compared to each other. CIG-P aids to present AP-MS data to a wider audience and we envision that the tool finds other applications too, e.g. kinase - substrate relationships as a function of perturbation. CIG-P is available under: http://sourceforge.net/projects/cig-p/

Einstein-Cartan Theory of Gravitation: Kinematical Parameters and Maxwell Equations

NASA Astrophysics Data System (ADS)

Katkar, L. N.

2015-03-01

In the space-time manifold of Einstein-Cartan Theory (ECT) of gravitation, the expressions for the time-like kinematical parameters are derived and the propagation equation for expansion is obtained.It has been observed that when the spin tensor is u-orthogonal the spin of the gravitating matter has no influence on the propagation equation of expansion while it has influence when it is not u-orthogonal. The usual formula for the curl of gradient of a scalar function is not zero in ECT. So is the case with the divergence of the curl of a vector.Their expressions on the space-time manifold of ECT are derived. A new derivative operator d ∗ is introduced to develop the calculus on space-time manifold of ECT. It is obtained by taking the covariant derivative of an associated tensor of a form with respect to an asymmetric connections. We have used this differential operator to obtain the form of the Maxwell's equations in the ECT of gravitation. Cartan's equations of structure are also derived through the new derivative operator. It has been shown that unlike the consequences of exterior derivative in Einstein space-time, the repetition of d ∗ on a form of any degree is not zero.

A Method to Recognize Anatomical Site and Image Acquisition View in X-ray Images.

PubMed

Chang, Xiao; Mazur, Thomas; Li, H Harold; Yang, Deshan

2017-12-01

A method was developed to recognize anatomical site and image acquisition view automatically in 2D X-ray images that are used in image-guided radiation therapy. The purpose is to enable site and view dependent automation and optimization in the image processing tasks including 2D-2D image registration, 2D image contrast enhancement, and independent treatment site confirmation. The X-ray images for 180 patients of six disease sites (the brain, head-neck, breast, lung, abdomen, and pelvis) were included in this study with 30 patients each site and two images of orthogonal views each patient. A hierarchical multiclass recognition model was developed to recognize general site first and then specific site. Each node of the hierarchical model recognized the images using a feature extraction step based on principal component analysis followed by a binary classification step based on support vector machine. Given two images in known orthogonal views, the site recognition model achieved a 99% average F1 score across the six sites. If the views were unknown in the images, the average F1 score was 97%. If only one image was taken either with or without view information, the average F1 score was 94%. The accuracy of the site-specific view recognition models was 100%.

Genetic algorithm based feature selection combined with dual classification for the automated detection of proliferative diabetic retinopathy.

PubMed

Welikala, R A; Fraz, M M; Dehmeshki, J; Hoppe, A; Tah, V; Mann, S; Williamson, T H; Barman, S A

2015-07-01

Proliferative diabetic retinopathy (PDR) is a condition that carries a high risk of severe visual impairment. The hallmark of PDR is the growth of abnormal new vessels. In this paper, an automated method for the detection of new vessels from retinal images is presented. This method is based on a dual classification approach. Two vessel segmentation approaches are applied to create two separate binary vessel map which each hold vital information. Local morphology features are measured from each binary vessel map to produce two separate 4-D feature vectors. Independent classification is performed for each feature vector using a support vector machine (SVM) classifier. The system then combines these individual outcomes to produce a final decision. This is followed by the creation of additional features to generate 21-D feature vectors, which feed into a genetic algorithm based feature selection approach with the objective of finding feature subsets that improve the performance of the classification. Sensitivity and specificity results using a dataset of 60 images are 0.9138 and 0.9600, respectively, on a per patch basis and 1.000 and 0.975, respectively, on a per image basis. Copyright © 2015 Elsevier Ltd. All rights reserved.

On the Prognostic Efficiency of Topological Descriptors for Magnetograms of Active Regions

NASA Astrophysics Data System (ADS)

Knyazeva, I. S.; Urtiev, F. A.; Makarenko, N. G.

2017-12-01

Solar flare prediction remains an important practical task of space weather. An increase in the amount and quality of observational data and the development of machine-learning methods has led to an improvement in prediction techniques. Additional information has been retrieved from the vector magnetograms; these have been recently supplemented by traditional line-of-sight (LOS) magnetograms. In this work, the problem of the comparative prognostic efficiency of features obtained on the basis of vector data and LOS magnetograms is discussed. Invariants obtained from a topological analysis of LOS magnetograms are used as complexity characteristics of magnetic patterns. Alternatively, the so-called SHARP parameters were used; they were calculated by the data analysis group of the Stanford University Laboratory on the basis of HMI/SDO vector magnetograms and are available online at the website (http://jsoc.stanford.edu/) with the solar dynamics observatory (SDO) database for the entire history of SDO observations. It has been found that the efficiency of large-flare prediction based on topological descriptors of LOS magnetograms in epignosis mode is at least s no worse than the results of prognostic schemes based on vector features. The advantages of the use of topological invariants based on LOS data are discussed.

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

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

Improved MODIS aerosol retrieval in urban areas using a land classification approach and empirical orthogonal functions

NASA Astrophysics Data System (ADS)

Levitan, Nathaniel; Gross, Barry

2016-10-01

New, high-resolution aerosol products are required in urban areas to improve the spatial coverage of the products, in terms of both resolution and retrieval frequency. These new products will improve our understanding of the spatial variability of aerosols in urban areas and will be useful in the detection of localized aerosol emissions. Urban aerosol retrieval is challenging for existing algorithms because of the high spatial variability of the surface reflectance, indicating the need for improved urban surface reflectance models. This problem can be stated in the language of novelty detection as the problem of selecting aerosol parameters whose effective surface reflectance spectrum is not an outlier in some space. In this paper, empirical orthogonal functions, a reconstruction-based novelty detection technique, is used to perform single-pixel aerosol retrieval using the single angular and temporal sample provided by the MODIS sensor. The empirical orthogonal basis functions are trained for different land classes using the MODIS BRDF MCD43 product. Existing land classification products are used in training and aerosol retrieval. The retrieval is compared against the existing operational MODIS 3 KM Dark Target (DT) aerosol product and co-located AERONET data. Based on the comparison, our method allows for a significant increase in retrieval frequency and a moderate decrease in the known biases of MODIS urban aerosol retrievals.

Seismotectonics of the Hindukush and Baluchistan arc

NASA Astrophysics Data System (ADS)

Verma, R. K.; Mukhopadhyay, M.; Bhanja, A. K.

1980-07-01

A seismicity map of that part of the Pakistan-Afghanistan region lying between the latitudes 28° to 38°N and longitudes 66° to 75°E is given using all available data for the period 1890-1970. The earthquakes of magnitude 4.5 and above were considered in the preparation of this map. On the basis of this map, it is observed that the seismicity pattern over the well-known Hindukush region is quite complex. Two prominent, mutually orthogonal, seismicity lineaments, namely the northvestern and the north-eastern trends, characterize the Hindukush area. The northwestern trend appears to extend from the Main Boundary Fault of the Kashmir Himalaya on the southeast to the plains of the Amu Darya in Uzbekistan on the northwest beyond the Hindukush. The Sulaiman and Kirthar ranges of Pakistan are well-defined zones of intermontane seismicity exhibiting north-south alignment. Thirty-two new focal-mechanism solutions for the above-mentioned region have been determined. These, together with the results obtained by earlier workers, suggest the pre-dominance of strike-slip faulting in the area. The Hazara Mountains, the Sulaiman wrench zone and the Kirthar wrench zone, as well as the supposed extension of the Murray ridge up to the Karachi coast, appear to be mostly undergoing strike-slip movements. In the Hindukush region, thrust and strike-slip faulting are found to be equally prevalent. Almost all the thrust-type mechanisms belonging to the Hindukush area have both the nodal planes in the NW-SE direction for shallow as well as intermediate depth earthquakes. The dip of P-axes for the events indicating thrust type mechanisms rarely exceeds 35°. The direction of the seismic slip vector obtained through thrust type solutions is always directed towards the northeast. The epicentral pattern together with these results suggest a deep-seated fault zone paralleling the northwesterly seismic zone underneath the Hindukush. This NW-lineament has a preference for thrust faulting, and it appears to extend from the vicinity of the Main Boundary Fault of the Kashmir Himalaya on the southeast of Uzbekistan on the northwest through Hindukush. Almost orthogonal to this NW-seismic zone, there is a NE-seismic lineament in which there is a preference for strike-slip faulting. The above results are discussed from the point of view of convergence of the Indian and Eurasian plates in the light of plate tectonics theory.

Lumley's PODT definition of large eddies and a trio of numerical procedures. [Proper Orthogonal Decomposition Theorem

NASA Technical Reports Server (NTRS)

Payne, Fred R.

1992-01-01

Lumley's 1967 Moscow paper provided, for the first time, a completely rational definition of the physically-useful term 'large eddy', popular for a half-century. The numerical procedures based upon his results are: (1) PODT (Proper Orthogonal Decomposition Theorem), which extracts the Large Eddy structure of stochastic processes from physical or computer simulation two-point covariances, and 2) LEIM (Large-Eddy Interaction Model), a predictive scheme for the dynamical large eddies based upon higher order turbulence modeling. Earlier Lumley's work (1964) forms the basis for the final member of the triad of numerical procedures: this predicts the global neutral modes of turbulence which have surprising agreement with both structural eigenmodes and those obtained from the dynamical equations. The ultimate goal of improved engineering design tools for turbulence may be near at hand, partly due to the power and storage of 'supermicrocomputer' workstations finally becoming adequate for the demanding numerics of these procedures.

Orthogonal polynomial projectors for the Projector Augmented Wave (PAW) formalism.

NASA Astrophysics Data System (ADS)

Holzwarth, N. A. W.; Matthews, G. E.; Tackett, A. R.; Dunning, R. B.

1998-03-01

The PAW method for density functional electronic structure calculations developed by Blöchl(Phys. Rev. B 50), 17953 (1994) and also used by our group(Phys. Rev. B 55), 2005 (1997) has numerical advantages of a pseudopotential technique while retaining the physics of an all-electron formalism. We describe a new method for generating the necessary set of atom-centered projector and basis functions, based on choosing the projector functions from a set of orthogonal polynomials multiplied by a localizing weight factor. Numerical benefits of the new scheme result from having direct control of the shape of the projector functions and from the use of a simple repulsive local potential term to eliminate ``ghost state" problems, which can haunt calculations of this kind. We demonstrate the method by calculating the cohesive energies of CaF2 and Mo and the density of states of CaMoO4 which shows detailed agreement with LAPW results over a 66 eV range of energy including upper core, valence, and conduction band states.

PSD-95 is required to sustain the molecular organization of the postsynaptic density

PubMed Central

Chen, Xiaobing; Nelson, Christopher D; Li, Xiang; Winters, Christine A.; Azzam, Rita; Sousa, Alioscka A.; Leapman, Richard D.; Gainer, Harold; Sheng, Morgan; Reese, Thomas S.

2011-01-01

PSD-95, a membrane-associated guanylate kinase (MAGUK), is the major scaffolding protein in the excitatory postsynaptic density (PSD) and a potent regulator of synaptic strength. Here we show that PSD-95 is in an extended configuration and positioned into regular arrays of vertical filaments that contact both glutamate receptors and orthogonal horizontal elements layered deep inside the PSD in rat hippocampal spine synapses. RNAi knockdown of PSD-95 leads to loss of entire patches of PSD material, and EM tomography shows that the patchy loss correlates with loss of PSD-95-containing vertical filaments, horizontal elements associated with the vertical filaments, and putative AMPA, but not NMDA receptor type structures. These observations show that the orthogonal molecular scaffold constructed from PSD-95-containing vertical filaments and their associated horizontal elements is essential for sustaining the three dimensional molecular organization of the PSD. Our findings provide a structural basis for understanding the functional role of PSD-95 at the PSD. PMID:21525273

Forebody and afterbody solutions of the Navier-Stokes equations for supersonic flow over blunt bodies in a generalized orthogonal coordinate system

NASA Technical Reports Server (NTRS)

Gnoffo, P. A.

1978-01-01

A coordinate transformation, which can approximate many different two-dimensional and axisymmetric body shapes with an analytic function, is used as a basis for solving the Navier-Stokes equations for the purpose of predicting 0 deg angle of attack supersonic flow fields. The transformation defines a curvilinear, orthogonal coordinate system in which coordinate lines are perpendicular to the body and the body is defined by one coordinate line. This system is mapped in to a rectangular computational domain in which the governing flow field equations are solved numerically. Advantages of this technique are that the specification of boundary conditions are simplified and, most importantly, the entire flow field can be obtained, including flow in the wake. Good agreement has been obtained with experimental data for pressure distributions, density distributions, and heat transfer over spheres and cylinders in supersonic flow. Approximations to the Viking aeroshell and to a candidate Jupiter probe are presented and flow fields over these shapes are calculated.

Orthogonal sparse linear discriminant analysis

NASA Astrophysics Data System (ADS)

Liu, Zhonghua; Liu, Gang; Pu, Jiexin; Wang, Xiaohong; Wang, Haijun

2018-03-01

Linear discriminant analysis (LDA) is a linear feature extraction approach, and it has received much attention. On the basis of LDA, researchers have done a lot of research work on it, and many variant versions of LDA were proposed. However, the inherent problem of LDA cannot be solved very well by the variant methods. The major disadvantages of the classical LDA are as follows. First, it is sensitive to outliers and noises. Second, only the global discriminant structure is preserved, while the local discriminant information is ignored. In this paper, we present a new orthogonal sparse linear discriminant analysis (OSLDA) algorithm. The k nearest neighbour graph is first constructed to preserve the locality discriminant information of sample points. Then, L2,1-norm constraint on the projection matrix is used to act as loss function, which can make the proposed method robust to outliers in data points. Extensive experiments have been performed on several standard public image databases, and the experiment results demonstrate the performance of the proposed OSLDA algorithm.

Study on energy saving of subway station based on orthogonal experimental method

NASA Astrophysics Data System (ADS)

Guo, Lei

2017-05-01

With the characteristics of quick, efficient and large amount transport, the subway has become an important way to solve urban traffic congestion. As the subway environment will follow the change of external environment factors such as temperature and load of personnel changes, three-dimensional numerical simulations study is conducted by using CFD software for air distribution of subway platform. The influence of different loads (the supply air temperature and velocity of air condition, personnel load, heat flux of the wall) on the subway platform flow field are also analysed. The orthogonal experiment method is applied to the numerical simulation analysis for human comfort under different parameters. Based on those results, the functional relationship between human comfort and the boundary conditions of the platform is produced by multiple linear regression fitting method, the order of major boundary conditions which affect human comfort is obtained. The above study provides a theoretical basis for the final energy-saving strategies.

Spectral likelihood expansions for Bayesian inference

NASA Astrophysics Data System (ADS)

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.

Nonnormal operators in physics, a singular-vectors approach: illustration in polarization optics.

PubMed

Tudor, Tiberiu

2016-04-20

The singular-vectors analysis of a general nonnormal operator defined on a finite-dimensional complex vector space is given in the frame of a pure operatorial ("nonmatrix," "coordinate-free") approach, performed in a Dirac language. The general results are applied in the field of polarization optics, where the nonnormal operators are widespread as operators of various polarization devices. Two nonnormal polarization devices representative for the class of nonnormal and even pathological operators-the standard two-layer elliptical ideal polarizer (singular operator) and the three-layer ambidextrous ideal polarizer (singular and defective operator)-are analyzed in detail. It is pointed out that the unitary polar component of the operator exists and preserves, in such pathological case too, its role of converting the input singular basis of the operator in its output singular basis. It is shown that for any nonnormal ideal polarizer a complementary one exists, so that the tandem of their operators uniquely determines their (common) unitary polar component.

Calibration Errors in Interferometric Radio Polarimetry

NASA Astrophysics Data System (ADS)

Hales, Christopher A.

2017-08-01

Residual calibration errors are difficult to predict in interferometric radio polarimetry because they depend on the observational calibration strategy employed, encompassing the Stokes vector of the calibrator and parallactic angle coverage. This work presents analytic derivations and simulations that enable examination of residual on-axis instrumental leakage and position-angle errors for a suite of calibration strategies. The focus is on arrays comprising alt-azimuth antennas with common feeds over which parallactic angle is approximately uniform. The results indicate that calibration schemes requiring parallactic angle coverage in the linear feed basis (e.g., the Atacama Large Millimeter/submillimeter Array) need only observe over 30°, beyond which no significant improvements in calibration accuracy are obtained. In the circular feed basis (e.g., the Very Large Array above 1 GHz), 30° is also appropriate when the Stokes vector of the leakage calibrator is known a priori, but this rises to 90° when the Stokes vector is unknown. These findings illustrate and quantify concepts that were previously obscure rules of thumb.

New method for solving inductive electric fields in the non-uniformly conducting ionosphere

NASA Astrophysics Data System (ADS)

Vanhamäki, H.; Amm, O.; Viljanen, A.

2006-10-01

We present a new calculation method for solving inductive electric fields in the ionosphere. The time series of the potential part of the ionospheric electric field, together with the Hall and Pedersen conductances serves as the input to this method. The output is the time series of the induced rotational part of the ionospheric electric field. The calculation method works in the time-domain and can be used with non-uniform, time-dependent conductances. In addition, no particular symmetry requirements are imposed on the input potential electric field. The presented method makes use of special non-local vector basis functions called the Cartesian Elementary Current Systems (CECS). This vector basis offers a convenient way of representing curl-free and divergence-free parts of 2-dimensional vector fields and makes it possible to solve the induction problem using simple linear algebra. The new calculation method is validated by comparing it with previously published results for Alfvén wave reflection from a uniformly conducting ionosphere.

The underlying pathway structure of biochemical reaction networks

PubMed Central

Schilling, Christophe H.; Palsson, Bernhard O.

1998-01-01

Bioinformatics is yielding extensive, and in some cases complete, genetic and biochemical information about individual cell types and cellular processes, providing the composition of living cells and the molecular structure of its components. These components together perform integrated cellular functions that now need to be analyzed. In particular, the functional definition of biochemical pathways and their role in the context of the whole cell is lacking. In this study, we show how the mass balance constraints that govern the function of biochemical reaction networks lead to the translation of this problem into the realm of linear algebra. The functional capabilities of biochemical reaction networks, and thus the choices that cells can make, are reflected in the null space of their stoichiometric matrix. The null space is spanned by a finite number of basis vectors. We present an algorithm for the synthesis of a set of basis vectors for spanning the null space of the stoichiometric matrix, in which these basis vectors represent the underlying biochemical pathways that are fundamental to the corresponding biochemical reaction network. In other words, all possible flux distributions achievable by a defined set of biochemical reactions are represented by a linear combination of these basis pathways. These basis pathways thus represent the underlying pathway structure of the defined biochemical reaction network. This development is significant from a fundamental and conceptual standpoint because it yields a holistic definition of biochemical pathways in contrast to definitions that have arisen from the historical development of our knowledge about biochemical processes. Additionally, this new conceptual framework will be important in defining, characterizing, and studying biochemical pathways from the rapidly growing information on cellular function. PMID:9539712

Vowel Imagery Decoding toward Silent Speech BCI Using Extreme Learning Machine with Electroencephalogram

PubMed Central

Kim, Jongin; Park, Hyeong-jun

2016-01-01

The purpose of this study is to classify EEG data on imagined speech in a single trial. We recorded EEG data while five subjects imagined different vowels, /a/, /e/, /i/, /o/, and /u/. We divided each single trial dataset into thirty segments and extracted features (mean, variance, standard deviation, and skewness) from all segments. To reduce the dimension of the feature vector, we applied a feature selection algorithm based on the sparse regression model. These features were classified using a support vector machine with a radial basis function kernel, an extreme learning machine, and two variants of an extreme learning machine with different kernels. Because each single trial consisted of thirty segments, our algorithm decided the label of the single trial by selecting the most frequent output among the outputs of the thirty segments. As a result, we observed that the extreme learning machine and its variants achieved better classification rates than the support vector machine with a radial basis function kernel and linear discrimination analysis. Thus, our results suggested that EEG responses to imagined speech could be successfully classified in a single trial using an extreme learning machine with a radial basis function and linear kernel. This study with classification of imagined speech might contribute to the development of silent speech BCI systems. PMID:28097128

Scale-invariant streamline equations and strings of singular vorticity for perturbed anisotropic solutions of the Navier-Stokes equation

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

Libin, A., E-mail: a_libin@netvision.net.il

2012-12-15

A linear combination of a pair of dual anisotropic decaying Beltrami flows with spatially constant amplitudes (the Trkal solutions) with the same eigenvalue of the curl operator and of a constant velocity orthogonal vector to the Beltrami pair yields a triplet solution of the force-free Navier-Stokes equation. The amplitudes slightly variable in space (large scale perturbations) yield the emergence of a time-dependent phase between the dual Beltrami flows and of the upward velocity, which are unstable at large values of the Reynolds number. They also lead to the formation of large-scale curved prisms of streamlines with edges being the stringsmore » of singular vorticity.« less

Genotoxicity of retroviral hematopoietic stem cell gene therapy

PubMed Central

Trobridge, Grant D

2012-01-01

Introduction Retroviral vectors have been developed for hematopoietic stem cell (HSC) gene therapy and have successfully cured X-linked severe combined immunodeficiency (SCID-X1), adenosine deaminase deficiency (ADA-SCID), adrenoleukodystrophy, and Wiskott-Aldrich syndrome. However, in HSC gene therapy clinical trials, genotoxicity mediated by integrated vector proviruses has led to clonal expansion, and in some cases frank leukemia. Numerous studies have been performed to understand the molecular basis of vector-mediated genotoxicity with the aim of developing safer vectors and safer gene therapy protocols. These genotoxicity studies are critical to advancing HSC gene therapy. Areas covered This review provides an introduction to the mechanisms of retroviral vector genotoxicity. It also covers advances over the last 20 years in designing safer gene therapy vectors, and in integration site analysis in clinical trials and large animal models. Mechanisms of retroviral-mediated genotoxicity, and the risk factors that contribute to clonal expansion and leukemia in HSC gene therapy are introduced. Expert opinion Continued research on virus–host interactions and next-generation vectors should further improve the safety of future HSC gene therapy vectors and protocols. PMID:21375467

New Mechanism for Toughening Ceramic Materials

DTIC Science & Technology

1994-02-01

Ferroelastic toughening, twinning, domain switching 1 17. 340.TY Q .Al MD0 .I SOWL&Nrv CLO.ASS1RC M SIS . W CASSWCAMlS 9: j"hTAfCm Of AMTLACT OF AD...crystal (Cubefaces orthogonal to (IM()) on the basis of the pseudocubic si mmetry X-ray diffraction traces using CuKa radiation were obtained show ing...Metastable Te- observed on ground or fracture surfaces of single crystals an- tragonal Zirconia Crystals." J. MAter Si . 18. 2619-28 (1983) ’T. C. Yuan

An intertwined method for making low-rank, sum-of-product basis functions that makes it possible to compute vibrational spectra of molecules with more than 10 atoms

PubMed Central

Thomas, Phillip S.

2017-01-01

We propose a method for solving the vibrational Schrödinger equation with which one can compute spectra for molecules with more than ten atoms. It uses sum-of-product (SOP) basis functions stored in a canonical polyadic tensor format and generated by evaluating matrix-vector products. By doing a sequence of partial optimizations, in each of which the factors in a SOP basis function for a single coordinate are optimized, the rank of the basis functions is reduced as matrix-vector products are computed. This is better than using an alternating least squares method to reduce the rank, as is done in the reduced-rank block power method. Partial optimization is better because it speeds up the calculation by about an order of magnitude and allows one to significantly reduce the memory cost. We demonstrate the effectiveness of the new method by computing vibrational spectra of two molecules, ethylene oxide (C2H4O) and cyclopentadiene (C5H6), with 7 and 11 atoms, respectively. PMID:28571348

An intertwined method for making low-rank, sum-of-product basis functions that makes it possible to compute vibrational spectra of molecules with more than 10 atoms.

PubMed

Thomas, Phillip S; Carrington, Tucker

2017-05-28

We propose a method for solving the vibrational Schrödinger equation with which one can compute spectra for molecules with more than ten atoms. It uses sum-of-product (SOP) basis functions stored in a canonical polyadic tensor format and generated by evaluating matrix-vector products. By doing a sequence of partial optimizations, in each of which the factors in a SOP basis function for a single coordinate are optimized, the rank of the basis functions is reduced as matrix-vector products are computed. This is better than using an alternating least squares method to reduce the rank, as is done in the reduced-rank block power method. Partial optimization is better because it speeds up the calculation by about an order of magnitude and allows one to significantly reduce the memory cost. We demonstrate the effectiveness of the new method by computing vibrational spectra of two molecules, ethylene oxide (C 2 H 4 O) and cyclopentadiene (C 5 H 6 ), with 7 and 11 atoms, respectively.

SU-E-T-422: Fast Analytical Beamlet Optimization for Volumetric Intensity-Modulated Arc Therapy

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

Chan, Kenny S K; Lee, Louis K Y; Xing, L

2015-06-15

Purpose: To implement a fast optimization algorithm on CPU/GPU heterogeneous computing platform and to obtain an optimal fluence for a given target dose distribution from the pre-calculated beamlets in an analytical approach. Methods: The 2D target dose distribution was modeled as an n-dimensional vector and estimated by a linear combination of independent basis vectors. The basis set was composed of the pre-calculated beamlet dose distributions at every 6 degrees of gantry angle and the cost function was set as the magnitude square of the vector difference between the target and the estimated dose distribution. The optimal weighting of the basis,more » which corresponds to the optimal fluence, was obtained analytically by the least square method. Those basis vectors with a positive weighting were selected for entering into the next level of optimization. Totally, 7 levels of optimization were implemented in the study.Ten head-and-neck and ten prostate carcinoma cases were selected for the study and mapped to a round water phantom with a diameter of 20cm. The Matlab computation was performed in a heterogeneous programming environment with Intel i7 CPU and NVIDIA Geforce 840M GPU. Results: In all selected cases, the estimated dose distribution was in a good agreement with the given target dose distribution and their correlation coefficients were found to be in the range of 0.9992 to 0.9997. Their root-mean-square error was monotonically decreasing and converging after 7 cycles of optimization. The computation took only about 10 seconds and the optimal fluence maps at each gantry angle throughout an arc were quickly obtained. Conclusion: An analytical approach is derived for finding the optimal fluence for a given target dose distribution and a fast optimization algorithm implemented on the CPU/GPU heterogeneous computing environment greatly reduces the optimization time.« less

Balancing aggregation and smoothing errors in inverse models

DOE PAGES

Turner, A. J.; Jacob, D. J.

2015-06-30

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function ofmore » state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.« less

Balancing aggregation and smoothing errors in inverse models

NASA Astrophysics Data System (ADS)

Turner, A. J.; Jacob, D. J.

2015-01-01

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function of state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.

Balancing aggregation and smoothing errors in inverse models

NASA Astrophysics Data System (ADS)

Turner, A. J.; Jacob, D. J.

2015-06-01

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function of state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.

Computational and experimental analysis of TMS-induced electric field vectors critical to neuronal activation

NASA Astrophysics Data System (ADS)

Krieg, Todd D.; Salinas, Felipe S.; Narayana, Shalini; Fox, Peter T.; Mogul, David J.

2015-08-01

Objective. Transcranial magnetic stimulation (TMS) represents a powerful technique to noninvasively modulate cortical neurophysiology in the brain. However, the relationship between the magnetic fields created by TMS coils and neuronal activation in the cortex is still not well-understood, making predictable cortical activation by TMS difficult to achieve. Our goal in this study was to investigate the relationship between induced electric fields and cortical activation measured by blood flow response. Particularly, we sought to discover the E-field characteristics that lead to cortical activation. Approach. Subject-specific finite element models (FEMs) of the head and brain were constructed for each of six subjects using magnetic resonance image scans. Positron emission tomography (PET) measured each subject’s cortical response to image-guided robotically-positioned TMS to the primary motor cortex. FEM models that employed the given coil position, orientation, and stimulus intensity in experimental applications of TMS were used to calculate the electric field (E-field) vectors within a region of interest for each subject. TMS-induced E-fields were analyzed to better understand what vector components led to regional cerebral blood flow (CBF) responses recorded by PET. Main results. This study found that decomposing the E-field into orthogonal vector components based on the cortical surface geometry (and hence, cortical neuron directions) led to significant differences between the regions of cortex that were active and nonactive. Specifically, active regions had significantly higher E-field components in the normal inward direction (i.e., parallel to pyramidal neurons in the dendrite-to-axon orientation) and in the tangential direction (i.e., parallel to interneurons) at high gradient. In contrast, nonactive regions had higher E-field vectors in the outward normal direction suggesting inhibitory responses. Significance. These results provide critical new understanding of the factors by which TMS induces cortical activation necessary for predictive and repeatable use of this noninvasive stimulation modality.

Time and Space in Tzeltal: Is the Future Uphill?

PubMed Central

Brown, Penelope

2012-01-01

Linguistic expressions of time often draw on spatial language, which raises the question of whether cultural specificity in spatial language and cognition is reflected in thinking about time. In the Mayan language Tzeltal, spatial language relies heavily on an absolute frame of reference utilizing the overall slope of the land, distinguishing an “uphill/downhill” axis oriented from south to north, and an orthogonal “crossways” axis (sunrise-set) on the basis of which objects at all scales are located. Does this absolute system for calculating spatial relations carry over into construals of temporal relations? This question was explored in a study where Tzeltal consultants produced temporal expressions and performed two different non-linguistic temporal ordering tasks. The results show that at least five distinct schemata for conceptualizing time underlie Tzeltal linguistic expressions: (i) deictic ego-centered time, (ii) time as an ordered sequence (e.g., “first”/“later”), (iii) cyclic time (times of the day, seasons), (iv) time as spatial extension or location (e.g., “entering/exiting July”), and (v) a time vector extending uphillwards into the future. The non-linguistic task results showed that the “time moves uphillwards” metaphor, based on the absolute frame of reference prevalent in Tzeltal spatial language and thinking and important as well in the linguistic expressions for time, is not strongly reflected in responses on these tasks. It is argued that systematic and consistent use of spatial language in an absolute frame of reference does not necessarily transfer to consistent absolute time conceptualization in non-linguistic tasks; time appears to be more open to alternative construals. PMID:22787451

Generation of vector beams using a double-wedge depolarizer: Non-quantum entanglement

NASA Astrophysics Data System (ADS)

Samlan, C. T.; Viswanathan, Nirmal K.

2016-07-01

Propagation of horizontally polarized Gaussian beam through a double-wedge depolarizer generates vector beams with spatially varying state of polarization. Jones calculus is used to show that such beams are maximally nonseparable on the basis of even (Gaussian)-odd (Hermite-Gaussian) mode parity and horizontal-vertical polarization state. The maximum nonseparability in the two degrees of freedom of the vector beam at the double wedge depolarizer output is verified experimentally using a modified Sagnac interferometer and linear analyser projected interferograms to measure the concurrence 0.94±0.002 and violation of Clauser-Horne-Shimony-Holt form of Bell-like inequality 2.704±0.024. The investigation is carried out in the context of the use of vector beams for metrological applications.

Performance Comparison of Orthogonal and Quasi-orthogonal Codes in Quasi-Synchronous Cellular CDMA Communication

NASA Astrophysics Data System (ADS)

Jos, Sujit; Kumar, Preetam; Chakrabarti, Saswat

Orthogonal and quasi-orthogonal codes are integral part of any DS-CDMA based cellular systems. Orthogonal codes are ideal for use in perfectly synchronous scenario like downlink cellular communication. Quasi-orthogonal codes are preferred over orthogonal codes in the uplink communication where perfect synchronization cannot be achieved. In this paper, we attempt to compare orthogonal and quasi-orthogonal codes in presence of timing synchronization error. This will give insight into the synchronization demands in DS-CDMA systems employing the two classes of sequences. The synchronization error considered is smaller than chip duration. Monte-Carlo simulations have been carried out to verify the analytical and numerical results.

Nontraditional method for determining unperturbed orbits of unknown space objects using incomplete optical observational data

NASA Astrophysics Data System (ADS)

Perov, N. I.

1985-02-01

A physical-geometrical method for computing the orbits of earth satellites on the basis of an inadequate number of angular observations (N3) was developed. Specifically, a new method has been developed for calculating the elements of Keplerian orbits of unidentified artificial satellites using two angular observations (alpha sub k, S sub k, k = 1). The first section gives procedures for determining the topocentric distance to AES on the basis of one optical observation. This is followed by description of a very simple method for determining unperturbed orbits using two satellite position vectors and a time interval which is applicable even in the case of antiparallel AED position vectors, a method designated the R sub 2 iterations method.

Reducing the cost of using collocation to compute vibrational energy levels: Results for CH2NH.

PubMed

Avila, Gustavo; Carrington, Tucker

2017-08-14

In this paper, we improve the collocation method for computing vibrational spectra that was presented in the work of Avila and Carrington, Jr. [J. Chem. Phys. 143, 214108 (2015)]. Known quadrature and collocation methods using a Smolyak grid require storing intermediate vectors with more elements than points on the Smolyak grid. This is due to the fact that grid labels are constrained among themselves and basis labels are constrained among themselves. We show that by using the so-called hierarchical basis functions, one can significantly reduce the memory required. In this paper, the intermediate vectors have only as many elements as the Smolyak grid. The ideas are tested by computing energy levels of CH 2 NH.

A partitioned correlation function interaction approach for describing electron correlation in atoms

NASA Astrophysics Data System (ADS)

Verdebout, S.; Rynkun, P.; Jönsson, P.; Gaigalas, G.; Froese Fischer, C.; Godefroid, M.

2013-04-01

The traditional multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis. For atoms with many closed core shells, or complicated shell structures, a large orbital basis is needed to saturate the different electron correlation effects such as valence, core-valence and correlation within the core shells. The large orbital basis leads to massive configuration state function (CSF) expansions that are difficult to handle, even on large computer systems. We show that it is possible to relax the orthonormality restriction on the orbital basis and break down the originally very large calculations into a series of smaller calculations that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The expansion coefficients of the PCFs are determined from a low dimensional generalized eigenvalue problem. The interaction and overlap matrices are computed using a biorthonormal transformation technique (Verdebout et al 2010 J. Phys. B: At. Mol. Phys. 43 074017). The new method, called partitioned correlation function interaction (PCFI), converges rapidly with respect to the orbital basis and gives total energies that are lower than the ones from ordinary MCHF and CI calculations. The PCFI method is also very flexible when it comes to targeting different electron correlation effects. Focusing our attention on neutral lithium, we show that by dedicating a PCF to the single excitations from the core, spin- and orbital-polarization effects can be captured very efficiently, leading to highly improved convergence patterns for hyperfine parameters compared with MCHF calculations based on a single orthogonal radial orbital basis. By collecting separately optimized PCFs to correct the MR function, the variational degrees of freedom in the relative mixing coefficients of the CSFs building the PCFs are inhibited. The constraints on the mixing coefficients lead to small off-sets in computed properties such as hyperfine structure, isotope shift and transition rates, with respect to the correct values. By (partially) deconstraining the mixing coefficients one converges to the correct limits and keeps the tremendous advantage of improved convergence rates that comes from the use of several orbital sets. Reducing ultimately each PCF to a single CSF with its own orbital basis leads to a non-orthogonal CI approach. Various perspectives of the new method are given.

Black light - How sensors filter spectral variation of the illuminant

NASA Technical Reports Server (NTRS)

Brainard, David H.; Wandell, Brian A.; Cowan, William B.

1989-01-01

Visual sensor responses may be used to classify objects on the basis of their surface reflectance functions. In a color image, the image data are represented as a vector of sensor responses at each point in the image. This vector depends both on the surface reflectance functions and on the spectral power distribution of the ambient illumination. Algorithms designed to classify objects on the basis of their surface reflectance functions typically attempt to overcome the dependence of the sensor responses on the illuminant by integrating sensor data collected from multiple surfaces. In machine vision applications, it is shown that it is often possible to design the sensor spectral responsivities so that the vector direction of the sensor responses does not depend upon the illuminant. The conditions under which this is possible are given and an illustrative calculation is performed. In biological systems, where the sensor responsivities are fixed, it is shown that some changes in the illumination cause no change in the sensor responses. Such changes in illuminant are called black illuminants. It is possible to express any illuminant as the sum of two unique components. One component is a black illuminant. The second component is called the visible component. The visible component of an illuminant completely characterizes the effect of the illuminant on the vector of sensor responses.

Nonlinear optical cryptosystem based on joint Fresnel transform correlator under vector wave illumination

NASA Astrophysics Data System (ADS)

Xueju, Shen; Chao, Lin; Xiao, Zou; Jianjun, Cai

2015-05-01

We present a nonlinear optical cryptosystem with multi-dimensional keys including phase, polarization and diffraction distance. To make full use of the degrees of freedom that optical processing offers, an elaborately designed vector wave with both a space-variant phase and locally linear polarization is generated with a common-path interferometer for illumination. The joint transform correlator in the Fresnel domain, implemented with a double optical wedge, is utilized as the encryption framework which provides an additional key known as the Fresnel diffraction distance. Two nonlinear operations imposed on the recorded joint Fresnel power distribution (JFPD) by a charge coupled device (CCD) are adopted. The first one is the division of power distribution of the reference window random function which is previously proposed by researchers and can improve the quality of the decrypted image. The second one is the recording of a hybrid JFPD using a micro-polarizers array with orthogonal and random transmissive axes attached to the CCD. Then the hybrid JFPD is further scrambled by substituting random noise for partial power distribution. The two nonlinear operations break the linearity of this cryptosystem and provide ultra security. We verify our proposal using a quick response code for noise-free recovery.

An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation

NASA Technical Reports Server (NTRS)

Litt, Jonathan S.

2007-01-01

A new linear point design technique is presented for the determination of tuning parameters that enable the optimal estimation of unmeasured engine outputs, such as thrust. The engine's performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters related to each major engine component. Accurate thrust reconstruction depends on knowledge of these health parameters, but there are usually too few sensors to be able to estimate their values. In this new technique, a set of tuning parameters is determined that accounts for degradation by representing the overall effect of the larger set of health parameters as closely as possible in a least squares sense. The technique takes advantage of the properties of the singular value decomposition of a matrix to generate a tuning parameter vector of low enough dimension that it can be estimated by a Kalman filter. A concise design procedure to generate a tuning vector that specifically takes into account the variables of interest is presented. An example demonstrates the tuning parameters ability to facilitate matching of both measured and unmeasured engine outputs, as well as state variables. Additional properties of the formulation are shown to lend themselves well to diagnostics.

An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation

NASA Technical Reports Server (NTRS)

Litt, Jonathan S.

2007-01-01

A new linear point design technique is presented for the determination of tuning parameters that enable the optimal estimation of unmeasured engine outputs, such as thrust. The engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters related to each major engine component. Accurate thrust reconstruction depends on knowledge of these health parameters, but there are usually too few sensors to be able to estimate their values. In this new technique, a set of tuning parameters is determined that accounts for degradation by representing the overall effect of the larger set of health parameters as closely as possible in a least-squares sense. The technique takes advantage of the properties of the singular value decomposition of a matrix to generate a tuning parameter vector of low enough dimension that it can be estimated by a Kalman filter. A concise design procedure to generate a tuning vector that specifically takes into account the variables of interest is presented. An example demonstrates the tuning parameters ability to facilitate matching of both measured and unmeasured engine outputs, as well as state variables. Additional properties of the formulation are shown to lend themselves well to diagnostics.

An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation

NASA Technical Reports Server (NTRS)

Litt, Jonathan S.

2005-01-01

A new linear point design technique is presented for the determination of tuning parameters that enable the optimal estimation of unmeasured engine outputs such as thrust. The engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters related to each major engine component. Accurate thrust reconstruction depends upon knowledge of these health parameters, but there are usually too few sensors to be able to estimate their values. In this new technique, a set of tuning parameters is determined which accounts for degradation by representing the overall effect of the larger set of health parameters as closely as possible in a least squares sense. The technique takes advantage of the properties of the singular value decomposition of a matrix to generate a tuning parameter vector of low enough dimension that it can be estimated by a Kalman filter. A concise design procedure to generate a tuning vector that specifically takes into account the variables of interest is presented. An example demonstrates the tuning parameters ability to facilitate matching of both measured and unmeasured engine outputs, as well as state variables. Additional properties of the formulation are shown to lend themselves well to diagnostics.

Spectrally efficient digitized radio-over-fiber system with k-means clustering-based multidimensional quantization.

PubMed

Zhang, Lu; Pang, Xiaodan; Ozolins, Oskars; Udalcovs, Aleksejs; Popov, Sergei; Xiao, Shilin; Hu, Weisheng; Chen, Jiajia

2018-04-01

We propose a spectrally efficient digitized radio-over-fiber (D-RoF) system by grouping highly correlated neighboring samples of the analog signals into multidimensional vectors, where the k-means clustering algorithm is adopted for adaptive quantization. A 30  Gbit/s D-RoF system is experimentally demonstrated to validate the proposed scheme, reporting a carrier aggregation of up to 40 100 MHz orthogonal frequency division multiplexing (OFDM) channels with quadrate amplitude modulation (QAM) order of 4 and an aggregation of 10 100 MHz OFDM channels with a QAM order of 16384. The equivalent common public radio interface rates from 37 to 150  Gbit/s are supported. Besides, the error vector magnitude (EVM) of 8% is achieved with the number of quantization bits of 4, and the EVM can be further reduced to 1% by increasing the number of quantization bits to 7. Compared with conventional pulse coding modulation-based D-RoF systems, the proposed D-RoF system improves the signal-to-noise-ratio up to ∼9  dB and greatly reduces the EVM, given the same number of quantization bits.

Maximal compression of the redshift-space galaxy power spectrum and bispectrum

NASA Astrophysics Data System (ADS)

Gualdi, Davide; Manera, Marc; Joachimi, Benjamin; Lahav, Ofer

2018-05-01

We explore two methods of compressing the redshift-space galaxy power spectrum and bispectrum with respect to a chosen set of cosmological parameters. Both methods involve reducing the dimension of the original data vector (e.g. 1000 elements) to the number of cosmological parameters considered (e.g. seven ) using the Karhunen-Loève algorithm. In the first case, we run MCMC sampling on the compressed data vector in order to recover the 1D and 2D posterior distributions. The second option, approximately 2000 times faster, works by orthogonalizing the parameter space through diagonalization of the Fisher information matrix before the compression, obtaining the posterior distributions without the need of MCMC sampling. Using these methods for future spectroscopic redshift surveys like DESI, Euclid, and PFS would drastically reduce the number of simulations needed to compute accurate covariance matrices with minimal loss of constraining power. We consider a redshift bin of a DESI-like experiment. Using the power spectrum combined with the bispectrum as a data vector, both compression methods on average recover the 68 {per cent} credible regions to within 0.7 {per cent} and 2 {per cent} of those resulting from standard MCMC sampling, respectively. These confidence intervals are also smaller than the ones obtained using only the power spectrum by 81 per cent, 80 per cent, and 82 per cent respectively, for the bias parameter b1, the growth rate f, and the scalar amplitude parameter As.

Compositions of orthogonal glutamyl-tRNA and aminoacyl-tRNA synthetase pairs and uses thereof

DOEpatents

Anderson, J Christopher [San Francisco, CA; Schultz, Peter G [La Jolla, CA; Santoro, Stephen [Cambridge, MA

2009-05-05

Compositions and methods of producing components of protein biosynthetic machinery that include glutamyl orthogonal tRNAs, glutamyl orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of glutamyl tRNAs/synthetases are provided. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins using these orthogonal pairs.

Blazed vector grating liquid crystal cells with photocrosslinkable polymeric alignment films fabricated by one-step polarizer rotation method

NASA Astrophysics Data System (ADS)

Kawai, Kotaro; Kuzuwata, Mitsuru; Sasaki, Tomoyuki; Noda, Kohei; Kawatsuki, Nobuhiro; Ono, Hiroshi

2014-12-01

Blazed vector grating liquid crystal (LC) cells, in which the directors of low-molar-mass LCs are antisymmetrically distributed, were fabricated by one-step exposure of an empty glass cell inner-coated with a photocrosslinkable polymer LC (PCLC) to UV light. By adopting a LC cell structure, twisted nematic (TN) and homogeneous (HOMO) alignments were obtained in the blazed vector grating LC cells. Moreover, the diffraction efficiency of the blazed vector grating LC cells was greatly improved by increasing the thickness of the device in comparison with that of a blazed vector grating with a thin film structure obtained in our previous study. In addition, the diffraction efficiency and polarization states of ±1st-order diffracted beams from the resultant blazed vector grating LC cells were controlled by designing a blazed pattern in the alignment films, and these diffraction properties were well explained on the basis of Jones calculus and the elastic continuum theory of nematic LCs.

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

NASA Astrophysics Data System (ADS)

Yu, Hua-Gen

2016-08-01

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using a multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH4 and H2CO are given, together with a comparison with previous results.

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

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

Yu, Hua-Gen, E-mail: hgy@bnl.gov

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using amore » multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH{sub 4} and H{sub 2}CO are given, together with a comparison with previous results.« less

Larvicidal activity of few select indigenous plants of North East India against disease vector mosquitoes (Diptera: Culicidae).

PubMed

Dohutia, C; Bhattacharyya, D R; Sharma, S K; Mohapatra, P K; Bhattacharjee, K; Gogoi, K; Gogoi, P; Mahanta, J; Prakash, A

2015-03-01

Mosquitoes are the vectors of several life threatening diseases like dengue, malaria, Japanese encephalitis and lymphatic filariasis, which are widely present in the north-eastern states of India. Investigations on five local plants of north-east India, selected on the basis of their use by indigenous communities as fish poison, were carried out to study their mosquito larvicidal potential against Anopheles stephensi (malaria vector), Stegomyia aegypti (dengue vector) and Culex quinquefasciatus (lymphatic filariasis vector) mosquitoes. Crude Petroleum ether extracts of the roots of three plants viz. Derris elliptica, Linostoma decandrum and Croton tiglium were found to have remarkable larvicidal activity; D. elliptica extract was the most effective and with LC50 value of 0.307 μg/ml its activity was superior to propoxur, the standard synthetic larvicide. Half-life of larvicidal activity of D. elliptica and L. decandrum extracts ranged from 2-4 days.

Composite fermion basis for two-component Bose gases

NASA Astrophysics Data System (ADS)

Meyer, Marius; Liabotro, Ola

The composite fermion (CF) construction is known to produce wave functions that are not necessarily orthogonal, or even linearly independent, after projection. While usually not a practical issue in the quantum Hall regime, we have previously shown that it presents a technical challenge for rotating Bose gases with low angular momentum. These are systems where the CF approach yield surprisingly good approximations to the exact eigenstates of weak short-range interactions, and so solving the problem of linearly dependent wave functions is of interest. It can also be useful for studying CF excitations for fermions. Here we present several ways of constructing a basis for the space of ``simple CF states'' for two-component rotating Bose gases in the lowest Landau level, and prove that they all give a basis. Using the basis, we study the structure of the lowest-lying state using so-called restricted wave functions. We also examine the scaling of the overlap between the exact and CF wave functions at the maximal possible angular momentum for simple states. This work was financially supported by the Research Council of Norway.

On the "Optimal" Choice of Trial Functions for Modelling Potential Fields

NASA Astrophysics Data System (ADS)

Michel, Volker

2015-04-01

There are many trial functions (e.g. on the sphere) available which can be used for the modelling of a potential field. Among them are orthogonal polynomials such as spherical harmonics and radial basis functions such as spline or wavelet basis functions. Their pros and cons have been widely discussed in the last decades. We present an algorithm, the Regularized Functional Matching Pursuit (RFMP), which is able to choose trial functions of different kinds in order to combine them to a stable approximation of a potential field. One main advantage of the RFMP is that the constructed approximation inherits the advantages of the different basis systems. By including spherical harmonics, coarse global structures can be represented in a sparse way. However, the additional use of spline basis functions allows a stable handling of scattered data grids. Furthermore, the inclusion of wavelets and scaling functions yields a multiscale analysis of the potential. In addition, ill-posed inverse problems (like a downward continuation or the inverse gravimetric problem) can be regularized with the algorithm. We show some numerical examples to demonstrate the possibilities which the RFMP provides.

Basis set study of classical rotor lattice dynamics.

PubMed

Witkoskie, James B; Wu, Jianlan; Cao, Jianshu

2004-03-22

The reorientational relaxation of molecular systems is important in many phenomenon and applications. In this paper, we explore the reorientational relaxation of a model Brownian rotor lattice system with short range interactions in both the high and low temperature regimes. In this study, we use a basis set expansion to capture collective motions of the system. The single particle basis set is used in the high temperature regime, while the spin wave basis is used in the low temperature regime. The equations of motion derived in this approach are analogous to the generalized Langevin equation, but the equations render flexibility by allowing nonequilibrium initial conditions. This calculation shows that the choice of projection operators in the generalized Langevin equation (GLE) approach corresponds to defining a specific inner-product space, and this inner-product space should be chosen to reveal the important physics of the problem. The basis set approach corresponds to an inner-product and projection operator that maintain the orthogonality of the spherical harmonics and provide a convenient platform for analyzing GLE expansions. The results compare favorably with numerical simulations, and the formalism is easily extended to more complex systems. (c) 2004 American Institute of Physics

Accurate wavelengths for X-ray spectroscopy and the NIST hydrogen-like ion database

NASA Astrophysics Data System (ADS)

Kotochigova, S. A.; Kirby, K. P.; Brickhouse, N. S.; Mohr, P. J.; Tupitsyn, I. I.

2005-06-01

We have developed an ab initio multi-configuration Dirac-Fock-Sturm method for the precise calculation of X-ray emission spectra, including energies, transition wavelengths and transition probabilities. The calculations are based on non-orthogonal basis sets, generated by solving the Dirac-Fock and Dirac-Fock-Sturm equations. Inclusion of Sturm functions into the basis set provides an efficient description of correlation effects in highly charged ions and fast convergence of the configuration interaction procedure. A second part of our study is devoted to developing a theoretical procedure and creating an interactive database to generate energies and transition frequencies for hydrogen-like ions. This procedure is highly accurate and based on current knowledge of the relevant theory, which includes relativistic, quantum electrodynamic, recoil, and nuclear size effects.

[What makes an insect a vector?].

PubMed

Kampen, Helge

2009-01-01

Blood-feeding insects transmit numerous viruses, bacteria, protozoans and helminths to vertebrates. The developmental cycles of the microorganisms in their vectors and the mechanisms of transmission are generally extremely complex and the result of a long-lasting coevolution of vector and vectored pathogen based on mutual adaptation. The conditions necessary for an insect to become a vector are multiple but require an innate vector competence as a genetic basis. Next to the vector competence plenty of entomological, ecological and pathogen-related factors are decisive, given the availability of infection sources. The various modes of pathogen transmission by vectors are connected to the developmental routes of the microorganisms in their vectors. In particular, pathogens transmitted by saliva encounter a lot of cellular and acellular barriers during their migration from the insect's midgut through the hemocele into the salivary fluid, including components of the insect's immune system. With regard to intracellular development, receptor-mediated invasion mechanisms are of relevance. As an environmental factor, the temperature has a paramount impact on the vectorial roles of hematophagous insects. Not only has it a considerable influence on the duration of a pathogen's development in its vector (extrinsic incubation period) but it can render putatively vector-incompetent insects to vectors ("leaky gut" phenomenon). Equally crucial are behavioural aspects of both the insect and the pathogen such as blood host preferences, seasonal appearance and circadian biting activity on the vector's side and diurnal/nocturnal periodicity on the pathogen's side which facilitate a contact in the first place.

Single-Vector Calibration of Wind-Tunnel Force Balances

NASA Technical Reports Server (NTRS)

Parker, P. A.; DeLoach, R.

2003-01-01

An improved method of calibrating a wind-tunnel force balance involves the use of a unique load application system integrated with formal experimental design methodology. The Single-Vector Force Balance Calibration System (SVS) overcomes the productivity and accuracy limitations of prior calibration methods. A force balance is a complex structural spring element instrumented with strain gauges for measuring three orthogonal components of aerodynamic force (normal, axial, and side force) and three orthogonal components of aerodynamic torque (rolling, pitching, and yawing moments). Force balances remain as the state-of-the-art instrument that provide these measurements on a scale model of an aircraft during wind tunnel testing. Ideally, each electrical channel of the balance would respond only to its respective component of load, and it would have no response to other components of load. This is not entirely possible even though balance designs are optimized to minimize these undesirable interaction effects. Ultimately, a calibration experiment is performed to obtain the necessary data to generate a mathematical model and determine the force measurement accuracy. In order to set the independent variables of applied load for the calibration 24 NASA Tech Briefs, October 2003 experiment, a high-precision mechanical system is required. Manual deadweight systems have been in use at Langley Research Center (LaRC) since the 1940s. These simple methodologies produce high confidence results, but the process is mechanically complex and labor-intensive, requiring three to four weeks to complete. Over the past decade, automated balance calibration systems have been developed. In general, these systems were designed to automate the tedious manual calibration process resulting in an even more complex system which deteriorates load application quality. The current calibration approach relies on a one-factor-at-a-time (OFAT) methodology, where each independent variable is incremented individually throughout its full-scale range, while all other variables are held at a constant magnitude. This OFAT approach has been widely accepted because of its inherent simplicity and intuitive appeal to the balance engineer. LaRC has been conducting research in a "modern design of experiments" (MDOE) approach to force balance calibration. Formal experimental design techniques provide an integrated view to the entire calibration process covering all three major aspects of an experiment; the design of the experiment, the execution of the experiment, and the statistical analyses of the data. In order to overcome the weaknesses in the available mechanical systems and to apply formal experimental techniques, a new mechanical system was required. The SVS enables the complete calibration of a six-component force balance with a series of single force vectors.

Universal modal radiation laws for all thermal emitters

PubMed Central

Zhu, Linxiao; Fan, Shanhui

2017-01-01

We derive four laws relating the absorptivity and emissivity of thermal emitters. Unlike the original Kirchhoff radiation law derivations, these derivations include diffraction, and so are valid also for small objects, and can also cover nonreciprocal objects. The proofs exploit two recent approaches. First, we express all fields in terms of the mode-converter basis sets of beams; these sets, which can be uniquely established for any linear optical object, give orthogonal input beams that are coupled one-by-one to orthogonal output beams. Second, we consider thought experiments using universal linear optical machines, which allow us to couple appropriate beams and black bodies. Two of these laws can be regarded as rigorous extensions of previously known laws: One gives a modal version of a radiation law for reciprocal objects—the absorptivity of any input beam equals the emissivity into the “backward” (i.e., phase-conjugated) version of that beam; another gives the overall equality of the sums of the emissivities and the absorptivities for any object, including nonreciprocal ones. The other two laws, valid for reciprocal and nonreciprocal objects, are quite different from previous relations. One shows universal equivalence of the absorptivity of each mode-converter input beam and the emissivity into its corresponding scattered output beam. The other gives unexpected equivalences of absorptivity and emissivity for broad classes of beams. Additionally, we prove these orthogonal mode-converter sets of input and output beams are the ones that maximize absorptivities and emissivities, respectively, giving these beams surprising additional physical meaning. PMID:28396436

3D shape recovery of a newborn skull using thin-plate splines.

PubMed

Lapeer, R J; Prager, R W

2000-01-01

The objective of this paper is to construct a mesh-model of a newborn skull for finite element analysis to study its deformation when subjected to the forces present during labour. The current state of medical imaging technology has reached a level which allows accurate visualisation and shape recovery of biological organs and body-parts. However, a sufficiently large set of medical images cannot always be obtained, often because of practical or ethical reasons, and the requirement to recover the shape of the biological object of interest has to be met by other means. Such is the case for a newborn skull. A method to recover the three-dimensional (3D) shape from (minimum) two orthogonal atlas images of the object of interest and a homologous object is described. This method is based on matching landmarks and curves on the orthogonal images of the object of interest with corresponding landmarks and curves on the homologous or 'master'-object which is fully defined in 3D space. On the basis of this set of corresponding landmarks, a thin-plate spline function can be derived to warp from the 'master'-object space to the 'slave'-object space. This method is applied to recover the 3D shape of a newborn skull. Images from orthogonal view-planes are obtained from an atlas. The homologous object is an adult skull, obtained from CT-images made available by the Visible Human Project. After shape recovery, a mesh-model of the newborn skull is generated.

High-speed polarization sensitive optical coherence tomography for retinal diagnostics

NASA Astrophysics Data System (ADS)

Yin, Biwei; Wang, Bingqing; Vemishetty, Kalyanramu; Nagle, Jim; Liu, Shuang; Wang, Tianyi; Rylander, Henry G., III; Milner, Thomas E.

2012-01-01

We report design and construction of an FPGA-based high-speed swept-source polarization-sensitive optical coherence tomography (SS-PS-OCT) system for clinical retinal imaging. Clinical application of the SS-PS-OCT system is accurate measurement and display of thickness, phase retardation and birefringence maps of the retinal nerve fiber layer (RNFL) in human subjects for early detection of glaucoma. The FPGA-based SS-PS-OCT system provides three incident polarization states on the eye and uses a bulk-optic polarization sensitive balanced detection module to record two orthogonal interference fringe signals. Interference fringe signals and relative phase retardation between two orthogonal polarization states are used to obtain Stokes vectors of light returning from each RNFL depth. We implement a Levenberg-Marquardt algorithm on a Field Programmable Gate Array (FPGA) to compute accurate phase retardation and birefringence maps. For each retinal scan, a three-state Levenberg-Marquardt nonlinear algorithm is applied to 360 clusters each consisting of 100 A-scans to determine accurate maps of phase retardation and birefringence in less than 1 second after patient measurement allowing real-time clinical imaging-a speedup of more than 300 times over previous implementations. We report application of the FPGA-based SS-PS-OCT system for real-time clinical imaging of patients enrolled in a clinical study at the Eye Institute of Austin and Duke Eye Center.

Binocular eye movement control and motion perception: what is being tracked?

PubMed

van der Steen, Johannes; Dits, Joyce

2012-10-19

We investigated under what conditions humans can make independent slow phase eye movements. The ability to make independent movements of the two eyes generally is attributed to few specialized lateral eyed animal species, for example chameleons. In our study, we showed that humans also can move the eyes in different directions. To maintain binocular retinal correspondence independent slow phase movements of each eye are produced. We used the scleral search coil method to measure binocular eye movements in response to dichoptically viewed visual stimuli oscillating in orthogonal direction. Correlated stimuli led to orthogonal slow eye movements, while the binocularly perceived motion was the vector sum of the motion presented to each eye. The importance of binocular fusion on independency of the movements of the two eyes was investigated with anti-correlated stimuli. The perceived global motion pattern of anti-correlated dichoptic stimuli was perceived as an oblique oscillatory motion, as well as resulted in a conjugate oblique motion of the eyes. We propose that the ability to make independent slow phase eye movements in humans is used to maintain binocular retinal correspondence. Eye-of-origin and binocular information are used during the processing of binocular visual information, and it is decided at an early stage whether binocular or monocular motion information and independent slow phase eye movements of each eye are produced during binocular tracking.