Sparsity-promoting orthogonal dictionary updating for image reconstruction from highly undersampled magnetic resonance data.

PubMed

Huang, Jinhong; Guo, Li; Feng, Qianjin; Chen, Wufan; Feng, Yanqiu

2015-07-21

Image reconstruction from undersampled k-space data accelerates magnetic resonance imaging (MRI) by exploiting image sparseness in certain transform domains. Employing image patch representation over a learned dictionary has the advantage of being adaptive to local image structures and thus can better sparsify images than using fixed transforms (e.g. wavelets and total variations). Dictionary learning methods have recently been introduced to MRI reconstruction, and these methods demonstrate significantly reduced reconstruction errors compared to sparse MRI reconstruction using fixed transforms. However, the synthesis sparse coding problem in dictionary learning is NP-hard and computationally expensive. In this paper, we present a novel sparsity-promoting orthogonal dictionary updating method for efficient image reconstruction from highly undersampled MRI data. The orthogonality imposed on the learned dictionary enables the minimization problem in the reconstruction to be solved by an efficient optimization algorithm which alternately updates representation coefficients, orthogonal dictionary, and missing k-space data. Moreover, both sparsity level and sparse representation contribution using updated dictionaries gradually increase during iterations to recover more details, assuming the progressively improved quality of the dictionary. Simulation and real data experimental results both demonstrate that the proposed method is approximately 10 to 100 times faster than the K-SVD-based dictionary learning MRI method and simultaneously improves reconstruction accuracy.

Comparison of Orthogonal Transforms for Teleseismic Data

DTIC Science & Technology

1974-10-31

inverse transform Because the computations are done in-plaee( Y is both input and output arrays; X is a complex buffer array. The program generates...the forward transform the FFT is done first, then the array is phase-shifted; for the inverse transform the reverse procedure is followed. Each

Cayley transform on Stiefel manifolds

NASA Astrophysics Data System (ADS)

Macías-Virgós, Enrique; Pereira-Sáez, María José; Tanré, Daniel

2018-01-01

The Cayley transform for orthogonal groups is a well known construction with applications in real and complex analysis, linear algebra and computer science. In this work, we construct Cayley transforms on Stiefel manifolds. Applications to the Lusternik-Schnirelmann category and optimization problems are presented.

The 1980-81 AFOSR (Air Force Office of Scientific Research)-HTTM (Heat Transfer and Turbulence Mechanics)-Stanford Conference on Complex Turbulent Flows: Comparison of Computation and Experiment. Volume 3. Comparison of Computation with Experiment, and Computors’ Summary Report.

DTIC Science & Technology

1981-09-01

organized the paperwork system , including finances, travel, k, , f iling, and programs in a highly independent and responsible fashion. Thanks are also due...three-dimensional transformation procedure for arbitrary non-orthogonal coordinate systems , for the purpose of the three-dimensional turbulent...transformation procedure for arbitrary non-orthogonal coordinate systems so as to acquire the generality in the application for elliptic flows (for the square

An improved nearly-orthogonal structured mesh generation system with smoothness control functions

USDA-ARS?s Scientific Manuscript database

This paper presents an improved nearly-orthogonal structured mesh generation system with a set of smoothness control functions, which were derived based on the ratio between the Jacobian of the transformation matrix and the Jacobian of the metric tensor. The proposed smoothness control functions are...

Projective interpretation of some doubly special relativity theories

NASA Astrophysics Data System (ADS)

Jafari, N.; Shariati, A.

2011-09-01

A class of projective actions of the orthogonal group on the projective space is being studied. It is shown that the Fock-Lorentz and Magueijo-Smolin transformations known as doubly special relativity are such transformations. The formalism easily leads to new types of transformations.

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.

Local unitary equivalence of quantum states and simultaneous orthogonal equivalence

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

Jing, Naihuan, E-mail: jing@ncsu.edu; Yang, Min; Zhao, Hui, E-mail: zhaohui@bjut.edu.cn

2016-06-15

The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through simultaneous similarity under projective orthogonal transformations, and four parametrization independent algorithms are proposed to judge when two density matrices on ℂ{sup d{sub 1}} ⊗ ℂ{sup d{sub 2}} are locally unitary equivalent in connection with trace identities, Kronecker pencils, Albert determinants and Smith normal forms.

Entanglement bases and general structures of orthogonal complete bases

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

Zhong Zaizhe

2004-10-01

In quantum mechanics and quantum information, to establish the orthogonal bases is a useful means. The existence of unextendible product bases impels us to study the 'entanglement bases' problems. In this paper, the concepts of entanglement bases and exact-entanglement bases are defined, and a theorem about exact-entanglement bases is given. We discuss the general structures of the orthogonal complete bases. Two examples of applications are given. At last, we discuss the problem of transformation of the general structure forms.

Performance analysis of a finite radon transform in OFDM system under different channel models

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

Dawood, Sameer A.; Anuar, M. S.; Fayadh, Rashid A.

In this paper, a class of discrete Radon transforms namely Finite Radon Transform (FRAT) was proposed as a modulation technique in the realization of Orthogonal Frequency Division Multiplexing (OFDM). The proposed FRAT operates as a data mapper in the OFDM transceiver instead of the conventional phase shift mapping and quadrature amplitude mapping that are usually used with the standard OFDM based on Fast Fourier Transform (FFT), by the way that ensure increasing the orthogonality of the system. The Fourier domain approach was found here to be the more suitable way for obtaining the forward and inverse FRAT. This structure resultedmore » in a more suitable realization of conventional FFT- OFDM. It was shown that this application increases the orthogonality significantly in this case due to the use of Inverse Fast Fourier Transform (IFFT) twice, namely, in the data mapping and in the sub-carrier modulation also due to the use of an efficient algorithm in determining the FRAT coefficients called the optimal ordering method. The proposed approach was tested and compared with conventional OFDM, for additive white Gaussian noise (AWGN) channel, flat fading channel, and multi-path frequency selective fading channel. The obtained results showed that the proposed system has improved the bit error rate (BER) performance by reducing inter-symbol interference (ISI) and inter-carrier interference (ICI), comparing with conventional OFDM system.« less

Performance analysis of a finite radon transform in OFDM system under different channel models

NASA Astrophysics Data System (ADS)

Dawood, Sameer A.; Malek, F.; Anuar, M. S.; Fayadh, Rashid A.; Abdullah, Farrah Salwani

2015-05-01

In this paper, a class of discrete Radon transforms namely Finite Radon Transform (FRAT) was proposed as a modulation technique in the realization of Orthogonal Frequency Division Multiplexing (OFDM). The proposed FRAT operates as a data mapper in the OFDM transceiver instead of the conventional phase shift mapping and quadrature amplitude mapping that are usually used with the standard OFDM based on Fast Fourier Transform (FFT), by the way that ensure increasing the orthogonality of the system. The Fourier domain approach was found here to be the more suitable way for obtaining the forward and inverse FRAT. This structure resulted in a more suitable realization of conventional FFT- OFDM. It was shown that this application increases the orthogonality significantly in this case due to the use of Inverse Fast Fourier Transform (IFFT) twice, namely, in the data mapping and in the sub-carrier modulation also due to the use of an efficient algorithm in determining the FRAT coefficients called the optimal ordering method. The proposed approach was tested and compared with conventional OFDM, for additive white Gaussian noise (AWGN) channel, flat fading channel, and multi-path frequency selective fading channel. The obtained results showed that the proposed system has improved the bit error rate (BER) performance by reducing inter-symbol interference (ISI) and inter-carrier interference (ICI), comparing with conventional OFDM system.

A decentralized square root information filter/smoother

NASA Technical Reports Server (NTRS)

Bierman, G. J.; Belzer, M. R.

1985-01-01

A number of developments has recently led to a considerable interest in the decentralization of linear least squares estimators. The developments are partly related to the impending emergence of VLSI technology, the realization of parallel processing, and the need for algorithmic ways to speed the solution of dynamically decoupled, high dimensional estimation problems. A new method is presented for combining Square Root Information Filters (SRIF) estimates obtained from independent data sets. The new method involves an orthogonal transformation, and an information matrix filter 'homework' problem discussed by Schweppe (1973) is generalized. The employed SRIF orthogonal transformation methodology has been described by Bierman (1977).

Effective constitutive relations for large repetitive frame-like structures

NASA Technical Reports Server (NTRS)

Nayfeh, A. H.; Hefzy, M. S.

1981-01-01

Effective mechanical properties for large repetitive framelike structures are derived using combinations of strength of material and orthogonal transformation techniques. Symmetry considerations are used in order to identify independent property constants. The actual values of these constants are constructed according to a building block format which is carried out in the three consecutive steps: (1) all basic planar lattices are identified; (2) effective continuum properties are derived for each of these planar basic grids using matrix structural analysis methods; and (3) orthogonal transformations are used to determine the contribution of each basic set to the overall effective continuum properties of the structure.

Cell edge detection in JPEG2000 wavelet domain - analysis on sigmoid function edge model.

PubMed

Punys, Vytenis; Maknickas, Ramunas

2011-01-01

Big virtual microscopy images (80K x 60K pixels and larger) are usually stored using the JPEG2000 image compression scheme. Diagnostic quantification, based on image analysis, might be faster if performed on compressed data (approx. 20 times less the original amount), representing the coefficients of the wavelet transform. The analysis of possible edge detection without reverse wavelet transform is presented in the paper. Two edge detection methods, suitable for JPEG2000 bi-orthogonal wavelets, are proposed. The methods are adjusted according calculated parameters of sigmoid edge model. The results of model analysis indicate more suitable method for given bi-orthogonal wavelet.

Multilayer modal actuator-based piezoelectric transformers.

PubMed

Huang, Yao-Tien; Wu, Wen-Jong; Wang, Yen-Chieh; Lee, Chih-Kung

2007-02-01

An innovative, multilayer piezoelectric transformer equipped with a full modal filtering input electrode is reported herein. This modal-shaped electrode, based on the orthogonal property of structural vibration modes, is characterized by full modal filtering to ensure that only the desired vibration mode is excited during operation. The newly developed piezoelectric transformer is comprised of three layers: a multilayered input layer, an insulation layer, and a single output layer. The electrode shape of the input layer is derived from its structural vibration modal shape, which takes advantage of the orthogonal property of the vibration modes to achieve a full modal filtering effect. The insulation layer possesses two functions: first, to couple the mechanical vibration energy between the input and output, and second, to provide electrical insulation between the two layers. To meet the two functions, a low temperature, co-fired ceramic (LTCC) was used to provide the high mechanical rigidity and high electrical insulation. It can be shown that this newly developed piezoelectric transformer has the advantage of possessing a more efficient energy transfer and a wider optimal working frequency range when compared to traditional piezoelectric transformers. A multilayer piezoelectric, transformer-based inverter applicable for use in LCD monitors or portable displays is presented as well.

Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials

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

Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu; Department of Physics, Indiana University Northwest, 3400 Broadway, Gary IN 46408; Roy, Pinaki, E-mail: pinaki@isical.ac.in

We construct energy-dependent potentials for which the Schrödinger equations admit solutions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations of exceptional Hermite, Jacobi and Laguerre polynomials. We present several examples of boundary-value problems with energy-dependent potentials that admit a discrete spectrum and the corresponding normalizable solutions in closed form.

3-D discrete analytical ridgelet transform.

PubMed

Helbert, David; Carré, Philippe; Andres, Eric

2006-12-01

In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient.

Privacy Protection by Matrix Transformation

NASA Astrophysics Data System (ADS)

Yang, Weijia

Privacy preserving is indispensable in data mining. In this paper, we present a novel clustering method for distributed multi-party data sets using orthogonal transformation and data randomization techniques. Our method can not only protect privacy in face of collusion, but also achieve a higher level of accuracy compared to the existing methods.

Finite-mode analysis by means of intensity information in fractional optical systems.

PubMed

Alieva, Tatiana; Bastiaans, Martin J

2002-03-01

It is shown how a coherent optical signal that contains only a finite number of Hermite-Gauss modes can be reconstructed from the knowledge of its Radon-Wigner transform-associated with the intensity distribution in a fractional-Fourier-transform optical system-at only two transversal points. The proposed method can be generalized to any fractional system whose generator transform has a complete orthogonal set of eigenfunctions.

Mathematics of Computed Tomography

NASA Astrophysics Data System (ADS)

Hawkins, William Grant

A review of the applications of the Radon transform is presented, with emphasis on emission computed tomography and transmission computed tomography. The theory of the 2D and 3D Radon transforms, and the effects of attenuation for emission computed tomography are presented. The algebraic iterative methods, their importance and limitations are reviewed. Analytic solutions of the 2D problem the convolution and frequency filtering methods based on linear shift invariant theory, and the solution of the circular harmonic decomposition by integral transform theory--are reviewed. The relation between the invisible kernels, the inverse circular harmonic transform, and the consistency conditions are demonstrated. The discussion and review are extended to the 3D problem-convolution, frequency filtering, spherical harmonic transform solutions, and consistency conditions. The Cormack algorithm based on reconstruction with Zernike polynomials is reviewed. An analogous algorithm and set of reconstruction polynomials is developed for the spherical harmonic transform. The relations between the consistency conditions, boundary conditions and orthogonal basis functions for the 2D projection harmonics are delineated and extended to the 3D case. The equivalence of the inverse circular harmonic transform, the inverse Radon transform, and the inverse Cormack transform is presented. The use of the number of nodes of a projection harmonic as a filter is discussed. Numerical methods for the efficient implementation of angular harmonic algorithms based on orthogonal functions and stable recursion are presented. The derivation of a lower bound for the signal-to-noise ratio of the Cormack algorithm is derived.

Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations

NASA Astrophysics Data System (ADS)

Ariznabarreta, Gerardo; García-Ardila, Juan C.; Mañas, Manuel; Marcellán, Francisco

2018-05-01

In this paper, Geronimus–Uvarov perturbations for matrix orthogonal polynomials on the real line are studied and then applied to the analysis of non-Abelian integrable hierarchies. The orthogonality is understood in full generality, i.e. in terms of a nondegenerate continuous sesquilinear form, determined by a quasidefinite matrix of bivariate generalized functions with a well-defined support. We derive Christoffel-type formulas that give the perturbed matrix biorthogonal polynomials and their norms in terms of the original ones. The keystone for this finding is the Gauss–Borel factorization of the Gram matrix. Geronimus–Uvarov transformations are considered in the context of the 2D non-Abelian Toda lattice and noncommutative KP hierarchies. The interplay between transformations and integrable flows is discussed. Miwa shifts, τ-ratio matrix functions and Sato formulas are given. Bilinear identities, involving Geronimus–Uvarov transformations, first for the Baker functions, then secondly for the biorthogonal polynomials and its second kind functions, and finally for the τ-ratio matrix functions, are found.

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

Development of a multipurpose hand controller for JEMRMS

NASA Technical Reports Server (NTRS)

Matsuhira, Nobuto; Iikura, Shoichi; Asakura, Makoto; Shinomiya, Yasuo

1990-01-01

A prototype multipurpose hand controller for the JEMRMS (Japanese Experiment Module Remote Manipulator System) was developed. The hand controller (H/C) is an orthogonal type, with 6 degrees of freedom (DOF) and small size. The orthogonal type H/C is very simple for coordinate transformations and can easily control any type of manipulators. In fact, the JEMRMS is planned to have two manipulators controlled by a common H/C at this stage. The H/C was able to be used as a rate control joystick and a force reflection master arm, using an experimental 6 DOF manipulator. Good maneuverability was confirmed in the verification test. The orthogonal type H/C is suitable for use as a common H/C for the two manipulators of the JEMRMS.

Wavelet transforms with discrete-time continuous-dilation wavelets

NASA Astrophysics Data System (ADS)

Zhao, Wei; Rao, Raghuveer M.

1999-03-01

Wavelet constructions and transforms have been confined principally to the continuous-time domain. Even the discrete wavelet transform implemented through multirate filter banks is based on continuous-time wavelet functions that provide orthogonal or biorthogonal decompositions. This paper provides a novel wavelet transform construction based on the definition of discrete-time wavelets that can undergo continuous parameter dilations. The result is a transformation that has the advantage of discrete-time or digital implementation while circumventing the problem of inadequate scaling resolution seen with conventional dyadic or M-channel constructions. Examples of constructing such wavelets are presented.

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.

Structural Technology Evaluation and Analysis Program (STEAP). Delivery Order 0046: Multiscale Modeling of Composite Structures Subjected to Cyclic Loading

DTIC Science & Technology

2012-09-01

on transformation field analysis [19], proper orthogonal decomposition [63], eigenstrains [23], and others [1, 29, 39] have brought significant...commercial finite element software (Abaqus) along with the user material subroutine utility ( UMAT ) is employed to solve these problems. In this section...Symmetric Coefficients TFA: Transformation Field Analysis UMAT : User Material Subroutine

Information security using multiple reference-based optical joint transform correlation and orthogonal code

NASA Astrophysics Data System (ADS)

Nazrul Islam, Mohammed; Karim, Mohammad A.; Vijayan Asari, K.

2013-09-01

Protecting and processing of confidential information, such as personal identification, biometrics, remains a challenging task for further research and development. A new methodology to ensure enhanced security of information in images through the use of encryption and multiplexing is proposed in this paper. We use orthogonal encoding scheme to encode multiple information independently and then combine them together to save storage space and transmission bandwidth. The encoded and multiplexed image is encrypted employing multiple reference-based joint transform correlation. The encryption key is fed into four channels which are relatively phase shifted by different amounts. The input image is introduced to all the channels and then Fourier transformed to obtain joint power spectra (JPS) signals. The resultant JPS signals are again phase-shifted and then combined to form a modified JPS signal which yields the encrypted image after having performed an inverse Fourier transformation. The proposed cryptographic system makes the confidential information absolutely inaccessible to any unauthorized intruder, while allows for the retrieval of the information to the respective authorized recipient without any distortion. The proposed technique is investigated through computer simulations under different practical conditions in order to verify its overall robustness.

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.

Measurement of the temperature coefficient of ratio transformers

NASA Technical Reports Server (NTRS)

Briggs, Matthew E.; Gammon, Robert W.; Shaumeyer, J. N.

1993-01-01

We have measured the temperature coefficient of the output of several ratio transformers at ratios near 0.500,000 using an ac bridge and a dual-phase, lock-in amplifier. The two orthogonal output components were each resolved to +/- ppb of the bridge drive signal. The results for three commercial ratio transformers between 20 and 50 C range from 0.5 to 100 ppb/K for the signal component in phase with the bridge drive, and from 4 to 300 ppb/K for the quadrature component.

CCD filter and transform techniques for interference excision

NASA Technical Reports Server (NTRS)

Borsuk, G. M.; Dewitt, R. N.

1976-01-01

The theoretical and some experimental results of a study aimed at applying CCD filter and transform techniques to the problem of interference excision within communications channels were presented. Adaptive noise (interference) suppression was achieved by the modification of received signals such that they were orthogonal to the recently measured noise field. CCD techniques were examined to develop real-time noise excision processing. They were recursive filters, circulating filter banks, transversal filter banks, an optical implementation of the chirp Z transform, and a CCD analog FFT.

Theory and operational rules for the discrete Hankel transform.

PubMed

Baddour, Natalie; Chouinard, Ugo

2015-04-01

Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.

The spectral expansion of the elasticity random field

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

Malyarenko, Anatoliy; Ostoja-Starzewski, Martin

2014-12-10

We consider a deformable body that occupies a region D in the plane. In our model, the body’s elasticity tensor H(x) is the restriction to D of a second-order mean-square continuous random field. Under translation, the expected value and the correlation tensor of the field H(x) do not change. Under action of an arbitrary element k of the orthogonal group O(2), they transform according to the reducible orthogonal representation k ⟼ S{sup 2}(S{sup 2}(k)) of the above group. We find the spectral expansion of the correlation tensor R(x) of the elasticity field as well as the expansion of the fieldmore » itself in terms of stochastic integrals with respect to a family of orthogonal scattered random measures.« less

A channel estimation scheme for MIMO-OFDM systems

NASA Astrophysics Data System (ADS)

He, Chunlong; Tian, Chu; Li, Xingquan; Zhang, Ce; Zhang, Shiqi; Liu, Chaowen

2017-08-01

In view of the contradiction of the time-domain least squares (LS) channel estimation performance and the practical realization complexity, a reduced complexity channel estimation method for multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) based on pilot is obtained. This approach can transform the complexity of MIMO-OFDM channel estimation problem into a simple single input single output-orthogonal frequency division multiplexing (SISO-OFDM) channel estimation problem and therefore there is no need for large matrix pseudo-inverse, which greatly reduces the complexity of algorithms. Simulation results show that the bit error rate (BER) performance of the obtained method with time orthogonal training sequences and linear minimum mean square error (LMMSE) criteria is better than that of time-domain LS estimator and nearly optimal performance.

LiFi: transforming fibre into wireless

NASA Astrophysics Data System (ADS)

Yin, Liang; Islim, Mohamed Sufyan; Haas, Harald

2017-01-01

Light-fidelity (LiFi) uses energy-efficient light-emitting diodes (LEDs) for high-speed wireless communication, and it has a great potential to be integrated with fibre communication for future gigabit networks. However, by making fibre communication wireless, multiuser interference arises. Traditional methods use orthogonal multiple access (OMA) for interference avoidance. In this paper, multiuser interference is exploited with the use of non-orthogonal multiple access (NOMA) relying on successive interference cancellation (SIC). The residual interference due to imperfect SIC in practical scenarios is characterized with a proportional model. Results show that NOMA offers 5 -10 dB gain on the equivalent signal-to-interference-plus-noise ratio (SINR) over OMA. The bit error rate (BER) performance of direct current optical orthogonal frequency division multiplexing (DCO-OFDM) is shown to be significantly improved when SIC is used.

Operational method of solution of linear non-integer ordinary and partial differential equations.

PubMed

Zhukovsky, K V

2016-01-01

We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.

On differential transformations between Cartesian and curvilinear (geodetic) coordinates

NASA Technical Reports Server (NTRS)

Soler, T.

1976-01-01

Differential transformations are developed between Cartesian and curvilinear orthogonal coordinates. Only matrix algebra is used for the presentation of the basic concepts. After defining the reference systems used the rotation (R), metric (H), and Jacobian (J) matrices of the transformations between cartesian and curvilinear coordinate systems are introduced. A value of R as a function of H and J is presented. Likewise an analytical expression for J(-1) as a function of H(-2) and R is obtained. Emphasis is placed on showing that differential equations are equivalent to conventional similarity transformations. Scaling methods are discussed along with ellipsoidal coordinates. Differential transformations between elipsoidal and geodetic coordinates are established.

Image secure transmission for optical orthogonal frequency-division multiplexing visible light communication systems using chaotic discrete cosine transform

NASA Astrophysics Data System (ADS)

Wang, Zhongpeng; Zhang, Shaozhong; Chen, Fangni; Wu, Ming-Wei; Qiu, Weiwei

2017-11-01

A physical encryption scheme for orthogonal frequency-division multiplexing (OFDM) visible light communication (VLC) systems using chaotic discrete cosine transform (DCT) is proposed. In the scheme, the row of the DCT matrix is permutated by a scrambling sequence generated by a three-dimensional (3-D) Arnold chaos map. Furthermore, two scrambling sequences, which are also generated from a 3-D Arnold map, are employed to encrypt the real and imaginary parts of the transmitted OFDM signal before the chaotic DCT operation. The proposed scheme enhances the physical layer security and improves the bit error rate (BER) performance for OFDM-based VLC. The simulation results prove the efficiency of the proposed encryption method. The experimental results show that the proposed security scheme not only protects image data from eavesdroppers but also keeps the good BER and peak-to-average power ratio performances for image-based OFDM-VLC systems.

Model predictive control system and method for integrated gasification combined cycle power generation

DOEpatents

Kumar, Aditya; Shi, Ruijie; Kumar, Rajeeva; Dokucu, Mustafa

2013-04-09

Control system and method for controlling an integrated gasification combined cycle (IGCC) plant are provided. The system may include a controller coupled to a dynamic model of the plant to process a prediction of plant performance and determine a control strategy for the IGCC plant over a time horizon subject to plant constraints. The control strategy may include control functionality to meet a tracking objective and control functionality to meet an optimization objective. The control strategy may be configured to prioritize the tracking objective over the optimization objective based on a coordinate transformation, such as an orthogonal or quasi-orthogonal projection. A plurality of plant control knobs may be set in accordance with the control strategy to generate a sequence of coordinated multivariable control inputs to meet the tracking objective and the optimization objective subject to the prioritization resulting from the coordinate transformation.

A technique for measuring vertically and horizontally polarized microwave brightness temperatures using electronic polarization-basis rotation

NASA Technical Reports Server (NTRS)

Gasiewski, Albin J.

1992-01-01

This technique for electronically rotating the polarization basis of an orthogonal-linear polarization radiometer is based on the measurement of the first three feedhorn Stokes parameters, along with the subsequent transformation of this measured Stokes vector into a rotated coordinate frame. The technique requires an accurate measurement of the cross-correlation between the two orthogonal feedhorn modes, for which an innovative polarized calibration load was developed. The experimental portion of this investigation consisted of a proof of concept demonstration of the technique of electronic polarization basis rotation (EPBR) using a ground based 90-GHz dual orthogonal-linear polarization radiometer. Practical calibration algorithms for ground-, aircraft-, and space-based instruments were identified and tested. The theoretical effort consisted of radiative transfer modeling using the planar-stratified numerical model described in Gasiewski and Staelin (1990).

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

NASA Technical Reports Server (NTRS)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

Coherent orthogonal polynomials

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

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

2013-08-15

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

Physiological variation in left atrial transverse orientation does not influence orthogonal P-wave morphology.

PubMed

Petersson, Richard; Mosén, Henrik; Steding-Ehrenborg, Katarina; Carlson, Jonas; Faxén, Lisa; Mohtadi, Alan; Platonov, Pyotr G; Holmqvist, Fredrik

2017-03-01

It has previously been demonstrated that orthogonal P-wave morphology in healthy athletes does not depend on atrial size, but the possible impact of left atrial orientation on P-wave morphology remains unknown. In this study, we investigated if left atrial transverse orientation affects P-wave morphology in different populations. Forty-seven patients with atrial fibrillation, 21 patients with arrhythmogenic right ventricular cardiomyopathy, 67 healthy athletes, and 56 healthy volunteers were included. All underwent cardiac magnetic resonance imaging or computed tomography and the orientation of the left atrium was determined. All had 12-lead electrocardiographic recordings, which were transformed into orthogonal leads and orthogonal P-wave morphology was obtained. The median left atrial transverse orientation was 87 (83, 91) degrees (lower and upper quartiles) in the total study population. There was no difference in left atrial transverse orientation between individuals with different orthogonal P-wave morphologies. The physiological variation in left atrial orientation was small within as well as between the different populations. There was no difference in left atrial transverse orientation between subjects with type 1 and type 2 P-wave morphology, implying that in this setting the P-wave morphology was more dependent on atrial conduction than orientation. © 2016 Wiley Periodicals, Inc.

MUFACT: An Algorithm for Multiple Factor Analyses of Singular and Nonsingular Data with Orthogonal and Oblique Transformation Solutions

ERIC Educational Resources Information Center

Hofmann, Richard J.

1978-01-01

A general factor analysis computer algorithm is briefly discussed. The algorithm is highly transportable with minimum limitations on the number of observations. Both singular and non-singular data can be analyzed. (Author/JKS)

Orthogonal tandem catalysis

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

Lohr, Tracy L.; Marks, Tobin J.

2015-05-20

Tandem catalysis is a growing field that is beginning to yield important scientific and technological advances toward new and more efficient catalytic processes. 'One-pot' tandem reactions, where multiple catalysts and reagents, combined in a single reaction vessel undergo a sequence of precisely staged catalytic steps, are highly attractive from the standpoint of reducing both waste and time. Orthogonal tandem catalysis is a subset of one-pot reactions in which more than one catalyst is used to promote two or more mechanistically distinct reaction steps. This Perspective summarizes and analyses some of the recent developments and successes in orthogonal tandem catalysis, withmore » particular focus on recent strategies to address catalyst incompatibility. We also highlight the concept of thermodynamic leveraging by coupling multiple catalyst cycles to effect challenging transformations not observed in single-step processes, and to encourage application of this technique to energetically unfavourable or demanding reactions.« less

Video-based depression detection using local Curvelet binary patterns in pairwise orthogonal planes.

PubMed

Pampouchidou, Anastasia; Marias, Kostas; Tsiknakis, Manolis; Simos, Panagiotis; Fan Yang; Lemaitre, Guillaume; Meriaudeau, Fabrice

2016-08-01

Depression is an increasingly prevalent mood disorder. This is the reason why the field of computer-based depression assessment has been gaining the attention of the research community during the past couple of years. The present work proposes two algorithms for depression detection, one Frame-based and the second Video-based, both employing Curvelet transform and Local Binary Patterns. The main advantage of these methods is that they have significantly lower computational requirements, as the extracted features are of very low dimensionality. This is achieved by modifying the previously proposed algorithm which considers Three-Orthogonal-Planes, to only Pairwise-Orthogonal-Planes. Performance of the algorithms was tested on the benchmark dataset provided by the Audio/Visual Emotion Challenge 2014, with the person-specific system achieving 97.6% classification accuracy, and the person-independed one yielding promising preliminary results of 74.5% accuracy. The paper concludes with open issues, proposed solutions, and future plans.

Mathematical approach to recover EEG brain signals with artifacts by means of Gram-Schmidt transform

NASA Astrophysics Data System (ADS)

Runnova, A. E.; Zhuravlev, M. O.; Koronovskiy, A. A.; Hramov, A. E.

2017-04-01

A novel method for removing oculomotor artifacts on electroencephalographical signals is proposed and based on the orthogonal Gram-Schmidt transform using electrooculography data. The method has shown high efficiency removal of artifacts caused by spontaneous movements of the eyeballs (about 95-97% correct remote oculomotor artifacts). This method may be recommended for multi-channel electroencephalography data processing in an automatic on-line in a variety of psycho-physiological experiments.

Is Fourier analysis performed by the visual system or by the visual investigator.

PubMed

Ochs, A L

1979-01-01

A numerical Fourier transform was made of the pincushion grid illusion and the spectral components orthogonal to the illusory lines were isolated. Their inverse transform creates a picture of the illusion. The spatial-frequency response of cortical, simple receptive field neurons similarly filters the grid. A complete set of these neurons thus approximates a two-dimensional Fourier analyzer. One cannot conclude, however, that the brain actually uses frequency-domain information to interpret visual images.

Multivariate Multiscale Analysis

DTIC Science & Technology

1990-11-08

The conditions on k in the second half of the statement of the proposition can be somewhat relaxed. In the cases n = 2 and n = 3 the details are given...of Mathematical Func- lions, Dover, New York, N.Y., 1965. [2] Bray and D. C. Solmon, The horocycle transform and harmonic analysis on the Poincare disk...H. Izen, Inversion of the k- plane transform by orthogonal function series expansions, Inverse Problems, 5 (1989), 181-202. [20] J. V. Leahy, K. T

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

Gorbachev, D V; Ivanov, V I

Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles.

Image processing to optimize wave energy converters

NASA Astrophysics Data System (ADS)

Bailey, Kyle Marc-Anthony

The world is turning to renewable energies as a means of ensuring the planet's future and well-being. There have been a few attempts in the past to utilize wave power as a means of generating electricity through the use of Wave Energy Converters (WEC), but only recently are they becoming a focal point in the renewable energy field. Over the past few years there has been a global drive to advance the efficiency of WEC. Placing a mechanical device either onshore or offshore that captures the energy within ocean surface waves to drive a mechanical device is how wave power is produced. This paper seeks to provide a novel and innovative way to estimate ocean wave frequency through the use of image processing. This will be achieved by applying a complex modulated lapped orthogonal transform filter bank to satellite images of ocean waves. The complex modulated lapped orthogonal transform filterbank provides an equal subband decomposition of the Nyquist bounded discrete time Fourier Transform spectrum. The maximum energy of the 2D complex modulated lapped transform subband is used to determine the horizontal and vertical frequency, which subsequently can be used to determine the wave frequency in the direction of the WEC by a simple trigonometric scaling. The robustness of the proposed method is provided by the applications to simulated and real satellite images where the frequency is known.

Wavelet analysis applied to the IRAS cirrus

NASA Technical Reports Server (NTRS)

Langer, William D.; Wilson, Robert W.; Anderson, Charles H.

1994-01-01

The structure of infrared cirrus clouds is analyzed with Laplacian pyramid transforms, a form of non-orthogonal wavelets. Pyramid and wavelet transforms provide a means to decompose images into their spatial frequency components such that all spatial scales are treated in an equivalent manner. The multiscale transform analysis is applied to IRAS 100 micrometer maps of cirrus emission in the north Galactic pole region to extract features on different scales. In the maps we identify filaments, fragments and clumps by separating all connected regions. These structures are analyzed with respect to their Hausdorff dimension for evidence of the scaling relationships in the cirrus clouds.

Coloured computational imaging with single-pixel detectors based on a 2D discrete cosine transform

NASA Astrophysics Data System (ADS)

Liu, Bao-Lei; Yang, Zhao-Hua; Liu, Xia; Wu, Ling-An

2017-02-01

We propose and demonstrate a computational imaging technique that uses structured illumination based on a two-dimensional discrete cosine transform to perform imaging with a single-pixel detector. A scene is illuminated by a projector with two sets of orthogonal patterns, then by applying an inverse cosine transform to the spectra obtained from the single-pixel detector a full-colour image is retrieved. This technique can retrieve an image from sub-Nyquist measurements, and the background noise is easily cancelled to give excellent image quality. Moreover, the experimental set-up is very simple.

The transformation of aerodynamic stability derivatives by symbolic mathematical computation

NASA Technical Reports Server (NTRS)

Howard, J. C.

1975-01-01

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

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.

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.

General optical discrete z transform: design and application.

PubMed

Ngo, Nam Quoc

2016-12-20

This paper presents a generalization of the discrete z transform algorithm. It is shown that the GOD-ZT algorithm is a generalization of several important conventional discrete transforms. Based on the GOD-ZT algorithm, a tunable general optical discrete z transform (GOD-ZT) processor is synthesized using the silica-based finite impulse response transversal filter. To demonstrate the effectiveness of the method, the design and simulation of a tunable optical discrete Fourier transform (ODFT) processor as a special case of the synthesized GOD-ZT processor is presented. It is also shown that the ODFT processor can function as a real-time optical spectrum analyzer. The tunable ODFT has an important potential application as a tunable optical demultiplexer at the receiver end of an optical orthogonal frequency-division multiplexing transmission system.

Optical chirp z-transform processor with a simplified architecture.

PubMed

Ngo, Nam Quoc

2014-12-29

Using a simplified chirp z-transform (CZT) algorithm based on the discrete-time convolution method, this paper presents the synthesis of a simplified architecture of a reconfigurable optical chirp z-transform (OCZT) processor based on the silica-based planar lightwave circuit (PLC) technology. In the simplified architecture of the reconfigurable OCZT, the required number of optical components is small and there are no waveguide crossings which make fabrication easy. The design of a novel type of optical discrete Fourier transform (ODFT) processor as a special case of the synthesized OCZT is then presented to demonstrate its effectiveness. The designed ODFT can be potentially used as an optical demultiplexer at the receiver of an optical fiber orthogonal frequency division multiplexing (OFDM) transmission system.

Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes.

PubMed

Wen, Yuanhui; Chremmos, Ioannis; Chen, Yujie; Zhu, Jiangbo; Zhang, Yanfeng; Yu, Siyuan

2018-05-11

Mode sorting is an essential function for optical multiplexing systems that exploit the orthogonality of the orbital angular momentum mode space. The familiar log-polar optical transformation provides a simple yet efficient approach whose resolution is, however, restricted by a considerable overlap between adjacent modes resulting from the limited excursion of the phase along a complete circle around the optical vortex axis. We propose and experimentally verify a new optical transformation that maps spirals (instead of concentric circles) to parallel lines. As the phase excursion along a spiral in the wave front of an optical vortex is theoretically unlimited, this new optical transformation can separate orbital angular momentum modes with superior resolution while maintaining unity efficiency.

Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes

NASA Astrophysics Data System (ADS)

Wen, Yuanhui; Chremmos, Ioannis; Chen, Yujie; Zhu, Jiangbo; Zhang, Yanfeng; Yu, Siyuan

2018-05-01

Mode sorting is an essential function for optical multiplexing systems that exploit the orthogonality of the orbital angular momentum mode space. The familiar log-polar optical transformation provides a simple yet efficient approach whose resolution is, however, restricted by a considerable overlap between adjacent modes resulting from the limited excursion of the phase along a complete circle around the optical vortex axis. We propose and experimentally verify a new optical transformation that maps spirals (instead of concentric circles) to parallel lines. As the phase excursion along a spiral in the wave front of an optical vortex is theoretically unlimited, this new optical transformation can separate orbital angular momentum modes with superior resolution while maintaining unity efficiency.

New approach to isometric transformations in oblique local coordinate systems of reference

NASA Astrophysics Data System (ADS)

Stępień, Grzegorz; Zalas, Ewa; Ziębka, Tomasz

2017-12-01

The research article describes a method of isometric transformation and determining an exterior orientation of a measurement instrument. The method is based on a designation of a "virtual" translation of two relative oblique orthogonal systems to a common, known in the both systems, point. The relative angle orientation of the systems does not change as each of the systems is moved along its axis. The next step is the designation of the three rotation angles (e.g. Tait-Bryan or Euler angles), transformation of the system convoluted at the calculated angles and moving the system to the initial position where the primary coordinate system was. This way eliminates movements of the systems from the calculations and makes it possible to calculate angles of mutual rotation angles of two orthogonal systems primarily involved in the movement. The research article covers laboratory calculations for simulated data. The accuracy of the results is 10-6 m (10-3 regarding the accuracy of the input data). This confi rmed the correctness of the assumed calculation method. In the following step the method was verifi ed under fi eld conditions, where the accuracy of the method raised to 0.003 m. The proposed method enabled to make the measurements with the oblique and uncentered instrument, e.g. total station instrument set over an unknown point. This is the reason why the method was named by the authors as Total Free Station - TFS. The method may be also used for isometric transformations for photogrammetric purposes.

Orthogonal Discrimination among Functional Groups in Ullmann-Type C-O and C-N Couplings.

PubMed

Rovira, Mireia; Soler, Marta; Güell, Imma; Wang, Ming-Zheng; Gómez, Laura; Ribas, Xavi

2016-09-02

The copper-catalyzed arylation of nucleophiles has been established as an efficient methodology for the formation of C-C and C-heteroatom bonds. Considering the advances during the last two decades, the ligand choice plays a key role in such transformations and can strongly influence the catalytic efficiency. The applicability of these Ullmann-type coupling reactions regarding the orthogonal selectivity of different functional groups constitutes a challenging subject for current synthetic strategies. Herein, we report a useful toolkit of Cu-based catalysts for the chemoselective arylation of a wide-range of nucleophiles in competitive reactions using aryl iodides and bromides. We show in this work that the arylation of all kinds of amides can be orthogonal to that of amines (aliphatic or aromatic) and phenol derivatives. This high chemoselectivity can be governed by the use of different ligands, yielding the desired coupling products under mild conditions. The selectivity trends are maintained for electronically biased iodobenzene and bromobenzene electrophiles. Radical clock experiments discard the occurrence of radical-based mechanisms.

Simulation of multivariate stationary stochastic processes using dimension-reduction representation methods

NASA Astrophysics Data System (ADS)

Liu, Zhangjun; Liu, Zenghui; Peng, Yongbo

2018-03-01

In view of the Fourier-Stieltjes integral formula of multivariate stationary stochastic processes, a unified formulation accommodating spectral representation method (SRM) and proper orthogonal decomposition (POD) is deduced. By introducing random functions as constraints correlating the orthogonal random variables involved in the unified formulation, the dimension-reduction spectral representation method (DR-SRM) and the dimension-reduction proper orthogonal decomposition (DR-POD) are addressed. The proposed schemes are capable of representing the multivariate stationary stochastic process with a few elementary random variables, bypassing the challenges of high-dimensional random variables inherent in the conventional Monte Carlo methods. In order to accelerate the numerical simulation, the technique of Fast Fourier Transform (FFT) is integrated with the proposed schemes. For illustrative purposes, the simulation of horizontal wind velocity field along the deck of a large-span bridge is proceeded using the proposed methods containing 2 and 3 elementary random variables. Numerical simulation reveals the usefulness of the dimension-reduction representation methods.

Oceanic ridges and transform faults: Their intersection angles and resistance to plate motion

USGS Publications Warehouse

Lachenbruch, A.H.; Thompson, G.A.

1972-01-01

The persistent near-orthogonal pattern formed by oceanic ridges and transform faults defies explanation in terms of rigid plates because it probably depends on the energy associated with deformation. For passive spreading, it is likely that the ridges and transforms adjust to a configuration offering minimum resistance to plate separation. This leads to a simple geometric model which yields conditions for the occurrence of transform faults and an aid to interpretation of structural patterns in the sea floor. Under reasonable assumptions, it is much more difficult for diverging plates to spread a kilometer of ridge than to slip a kilometer of transform fault, and the patterns observed at spreading centers might extend to lithospheric depths. Under these conditions, the resisting force at spreading centers could play a significant role in the dynamics of plate-tectonic systems. ?? 1972.

A Ramanujan-type measure for the Askey-Wilson polynomials

NASA Technical Reports Server (NTRS)

Atakishiyev, Natig M.

1995-01-01

A Ramanujan-type representation for the Askey-Wilson q-beta integral, admitting the transformation q to q(exp -1), is obtained. Orthogonality of the Askey-Wilson polynomials with respect to a measure, entering into this representation, is proved. A simple way of evaluating the Askey-Wilson q-beta integral is also given.

Experimental research of adaptive OFDM and OCT precoding with a high SE for VLLC system

NASA Astrophysics Data System (ADS)

Liu, Shuang-ao; He, Jing; Chen, Qinghui; Deng, Rui; Zhou, Zhihua; Chen, Shenghai; Chen, Lin

2017-09-01

In this paper, an adaptive orthogonal frequency division multiplexing (OFDM) modulation scheme with 128/64/32/16-quadrature amplitude modulation (QAM) and orthogonal circulant matrix transform (OCT) precoding is proposed and experimentally demonstrated for a visible laser light communication (VLLC) system with a cost-effective 450-nm blue-light laser diode (LD). The performance of OCT precoding is compared with conventional the adaptive Discrete Fourier Transform-spread (DFT-spread) OFDM scheme, 32 QAM OCT precoding OFDM scheme, 64 QAM OCT precoding OFDM scheme and adaptive OCT precoding OFDM scheme. The experimental results show that OCT precoding can achieve a relatively flat signal-to-noise ratio (SNR) curve, and it can provide performance improvement in bit error rate (BER). Furthermore, the BER of the proposed OFDM signal with a raw bit rate 5.04 Gb/s after 5-m free space transmission is less than 20% of soft-decision forward error correlation (SD-FEC) threshold of 2.4 × 10-2, and the spectral efficiency (SE) of 4.2 bit/s/Hz can be successfully achieved.

Extraction of object skeletons in multispectral imagery by the orthogonal regression fitting

NASA Astrophysics Data System (ADS)

Palenichka, Roman M.; Zaremba, Marek B.

2003-03-01

Accurate and automatic extraction of skeletal shape of objects of interest from satellite images provides an efficient solution to such image analysis tasks as object detection, object identification, and shape description. The problem of skeletal shape extraction can be effectively solved in three basic steps: intensity clustering (i.e. segmentation) of objects, extraction of a structural graph of the object shape, and refinement of structural graph by the orthogonal regression fitting. The objects of interest are segmented from the background by a clustering transformation of primary features (spectral components) with respect to each pixel. The structural graph is composed of connected skeleton vertices and represents the topology of the skeleton. In the general case, it is a quite rough piecewise-linear representation of object skeletons. The positions of skeleton vertices on the image plane are adjusted by means of the orthogonal regression fitting. It consists of changing positions of existing vertices according to the minimum of the mean orthogonal distances and, eventually, adding new vertices in-between if a given accuracy if not yet satisfied. Vertices of initial piecewise-linear skeletons are extracted by using a multi-scale image relevance function. The relevance function is an image local operator that has local maximums at the centers of the objects of interest.

A comparison of orthogonal transformations for digital speech processing.

NASA Technical Reports Server (NTRS)

Campanella, S. J.; Robinson, G. S.

1971-01-01

Discrete forms of the Fourier, Hadamard, and Karhunen-Loeve transforms are examined for their capacity to reduce the bit rate necessary to transmit speech signals. To rate their effectiveness in accomplishing this goal the quantizing error (or noise) resulting for each transformation method at various bit rates is computed and compared with that for conventional companded PCM processing. Based on this comparison, it is found that Karhunen-Loeve provides a reduction in bit rate of 13.5 kbits/s, Fourier 10 kbits/s, and Hadamard 7.5 kbits/s as compared with the bit rate required for companded PCM. These bit-rate reductions are shown to be somewhat independent of the transmission bit rate.

On E-discretization of tori of compact simple Lie groups. II

NASA Astrophysics Data System (ADS)

Hrivnák, Jiří; Juránek, Michal

2017-10-01

Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.

Orthogonal-blendshape-based editing system for facial motion capture data.

PubMed

Li, Qing; Deng, Zhigang

2008-01-01

The authors present a novel data-driven 3D facial motion capture data editing system using automated construction of an orthogonal blendshape face model and constrained weight propagation, aiming to bridge the popular facial motion capture technique and blendshape approach. In this work, a 3D facial-motion-capture-editing problem is transformed to a blendshape-animation-editing problem. Given a collected facial motion capture data set, we construct a truncated PCA space spanned by the greatest retained eigenvectors and a corresponding blendshape face model for each anatomical region of the human face. As such, modifying blendshape weights (PCA coefficients) is equivalent to editing their corresponding motion capture sequence. In addition, a constrained weight propagation technique allows animators to balance automation and flexible controls.

Quantum state matching of qubits via measurement-induced nonlinear transformations

NASA Astrophysics Data System (ADS)

Kálmán, Orsolya; Kiss, Tamás

2018-03-01

We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined with a postselection scheme conditioned on the measurement result obtained on one of the qubits of the pair. The resulting transformation is a deterministic, nonlinear, chaotic map in the Hilbert space. We derive a class of these transformations capable of orthogonalizing nonorthogonal qubit states after a few iterations. These nonlinear maps orthogonalize states which correspond to the two different convergence regions of the nonlinear map. Based on the analysis of the border (the so-called Julia set) between the two regions of convergence, we show that it is always possible to find a map capable of deciding whether an unknown state is within a neighborhood of fixed radius around a desired quantum state. We analyze which one- and two-qubit operations would physically realize the scheme. It is possible to find a single two-qubit unitary gate for each map or, alternatively, a universal special two-qubit gate together with single-qubit gates in order to carry out the task. We note that it is enough to have a single physical realization of the required gates due to the iterative nature of the scheme.

Sparse Representation of Smooth Linear Operators

DTIC Science & Technology

1990-08-01

8217,ns, m = 0,2 ,...,I where Sm is defined by Eq. (2.3). We further define Rk, 2 to be the orthogonal n k,2complement of S, 2 in S,+ 1, smk EDR ,2 Sk,2 1...1987. [9] L. Greengard and J. Strain . The fast Gauss transform. Technical report, Department of Computer Science, Yale University, 1989. [10] A

A new fractional wavelet transform

NASA Astrophysics Data System (ADS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-03-01

The fractional Fourier transform (FRFT) is a potent tool to analyze the time-varying signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. A novel fractional wavelet transform (FRWT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the time-FRFD-frequency plane. The definition, basic properties, inverse transform and reproducing kernel of the proposed FRWT are considered. It has been shown that an FRWT with proper order corresponds to the classical wavelet transform (WT). The multiresolution analysis (MRA) associated with the developed FRWT, together with the construction of the orthogonal fractional wavelets are also presented. Three applications are discussed: the analysis of signal with time-varying frequency content, the FRFD spectrum estimation of signals that involving noise, and the construction of fractional Harr wavelet. Simulations verify the validity of the proposed FRWT.

Linear-algebraic bath transformation for simulating complex open quantum systems

DOE PAGES

Huh, Joonsuk; Mostame, Sarah; Fujita, Takatoshi; ...

2014-12-02

In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly coupled multiple parallelmore » chains. Furthermore, the transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics.« less

Bayesian estimation of Karhunen–Loève expansions; A random subspace approach

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

Chowdhary, Kenny; Najm, Habib N.

One of the most widely-used statistical procedures for dimensionality reduction of high dimensional random fields is Principal Component Analysis (PCA), which is based on the Karhunen-Lo eve expansion (KLE) of a stochastic process with finite variance. The KLE is analogous to a Fourier series expansion for a random process, where the goal is to find an orthogonal transformation for the data such that the projection of the data onto this orthogonal subspace is optimal in the L 2 sense, i.e, which minimizes the mean square error. In practice, this orthogonal transformation is determined by performing an SVD (Singular Value Decomposition)more » on the sample covariance matrix or on the data matrix itself. Sampling error is typically ignored when quantifying the principal components, or, equivalently, basis functions of the KLE. Furthermore, it is exacerbated when the sample size is much smaller than the dimension of the random field. In this paper, we introduce a Bayesian KLE procedure, allowing one to obtain a probabilistic model on the principal components, which can account for inaccuracies due to limited sample size. The probabilistic model is built via Bayesian inference, from which the posterior becomes the matrix Bingham density over the space of orthonormal matrices. We use a modified Gibbs sampling procedure to sample on this space and then build a probabilistic Karhunen-Lo eve expansions over random subspaces to obtain a set of low-dimensional surrogates of the stochastic process. We illustrate this probabilistic procedure with a finite dimensional stochastic process inspired by Brownian motion.« less

Bayesian estimation of Karhunen–Loève expansions; A random subspace approach

DOE PAGES

Chowdhary, Kenny; Najm, Habib N.

2016-04-13

One of the most widely-used statistical procedures for dimensionality reduction of high dimensional random fields is Principal Component Analysis (PCA), which is based on the Karhunen-Lo eve expansion (KLE) of a stochastic process with finite variance. The KLE is analogous to a Fourier series expansion for a random process, where the goal is to find an orthogonal transformation for the data such that the projection of the data onto this orthogonal subspace is optimal in the L 2 sense, i.e, which minimizes the mean square error. In practice, this orthogonal transformation is determined by performing an SVD (Singular Value Decomposition)more » on the sample covariance matrix or on the data matrix itself. Sampling error is typically ignored when quantifying the principal components, or, equivalently, basis functions of the KLE. Furthermore, it is exacerbated when the sample size is much smaller than the dimension of the random field. In this paper, we introduce a Bayesian KLE procedure, allowing one to obtain a probabilistic model on the principal components, which can account for inaccuracies due to limited sample size. The probabilistic model is built via Bayesian inference, from which the posterior becomes the matrix Bingham density over the space of orthonormal matrices. We use a modified Gibbs sampling procedure to sample on this space and then build a probabilistic Karhunen-Lo eve expansions over random subspaces to obtain a set of low-dimensional surrogates of the stochastic process. We illustrate this probabilistic procedure with a finite dimensional stochastic process inspired by Brownian motion.« less

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.

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,

Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials

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

Ho, Choon-Lin, E-mail: hcl@mail.tku.edu.tw

2011-04-15

Research Highlights: > Physical examples involving exceptional orthogonal polynomials. > Exceptional polynomials as deformations of classical orthogonal polynomials. > Exceptional polynomials from Darboux-Crum transformation. - Abstract: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X{sub l} Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree l = 1, 2, and ..., and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new X{sub l} polynomials deserve further analysis, it ismore » also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.« less

Power system frequency estimation based on an orthogonal decomposition method

NASA Astrophysics Data System (ADS)

Lee, Chih-Hung; Tsai, Men-Shen

2018-06-01

In recent years, several frequency estimation techniques have been proposed by which to estimate the frequency variations in power systems. In order to properly identify power quality issues under asynchronously-sampled signals that are contaminated with noise, flicker, and harmonic and inter-harmonic components, a good frequency estimator that is able to estimate the frequency as well as the rate of frequency changes precisely is needed. However, accurately estimating the fundamental frequency becomes a very difficult task without a priori information about the sampling frequency. In this paper, a better frequency evaluation scheme for power systems is proposed. This method employs a reconstruction technique in combination with orthogonal filters, which may maintain the required frequency characteristics of the orthogonal filters and improve the overall efficiency of power system monitoring through two-stage sliding discrete Fourier transforms. The results showed that this method can accurately estimate the power system frequency under different conditions, including asynchronously sampled signals contaminated by noise, flicker, and harmonic and inter-harmonic components. The proposed approach also provides high computational efficiency.

Lithosperic rheology controls on oceanic spreading patterns

NASA Astrophysics Data System (ADS)

Gerya, T.

2012-04-01

Mid-ocean ridges sectioned by transform faults represent one of the most prominent surface expressions of terrestrial plate tectonics. A fundamental long standing problem of plate tectonics is how and why ridge-transform spreading patterns are formed and maintained. On the one hand, geometrical correspondence between mid-ocean ridges and respective rifted margins apparently suggests that many oceanic transform faults are inherited structures that persisted throughout the entire history of oceanic spreading. On the other hand, data from incipient oceanic spreading regions show that transform faults are not directly inherited from transverse rift structures and start to develop as or after oceanic spreading nucleate. Based on self-consistent 3D thermomechanical numerical model of oceanic spreading we demonstrate that only limited range of oceanic lithosphere rheologies can reproduce natural spreading patterns. In particular, spontaneous formation and long-term stability of orthogonal ridge-transform spreading pattern requires visco-brittle/plastic rheology of plates with strong dynamic weakening of spontaneously forming faults. Our, numerical models of incipient oceanic spreading demonstrate that one or several oceanic transform faults can form gradually within broad non-transform accommodation zones connecting initially offset spreading centers. Orientation of transform faults and spreading centers changes exponentially with time as the result of new oceanic crust growth. The resulting orthogonal ridge-transform system is established within few millions of years after the beginning of oceanic spreading. By its fundamental physical origin, this system is a crustal growth pattern governed by space accommodation and not a plate breakup pattern governed by stress distribution. It is demonstrated that the characteristic extension-parallel orientation of oceanic transform faults can be obtained from space accommodation criteria as a steady state orientation of a strike-slip fault sustaining in between simultaneously growing offset crustal segments. Numerical models also suggest that transform faults can develop at single straight ridge as the result of dynamical instability of constructive plate boundaries caused by weakening of forming brittle/plastic fractures. Boundary instability from asymmetric plate growth can spontaneously start in alternate directions along successive ridge sections; the resultant curved ridges become transform faults within a few million years. Offsets along the transform faults change continuously with time by asymmetric plate growth and discontinuously by ridge jumps. Degree of asymmetric plate accretion increases with increasing degree of brittle/plastic weakening. It is also strongly dependent on the brittle/plastic yielding criterion and is notably reduced in models with pressure-dependent brittle/plastic plate strength compared to models with pressure-independent strength.

Mathieu Progressive Waves

NASA Astrophysics Data System (ADS)

Andrei, B. Utkin

2011-10-01

A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal curvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.

Implementing the sine transform of fermionic modes as a tensor network

NASA Astrophysics Data System (ADS)

Epple, Hannes; Fries, Pascal; Hinrichsen, Haye

2017-09-01

Based on the algebraic theory of signal processing, we recursively decompose the discrete sine transform of the first kind (DST-I) into small orthogonal block operations. Using a diagrammatic language, we then second-quantize this decomposition to construct a tensor network implementing the DST-I for fermionic modes on a lattice. The complexity of the resulting network is shown to scale as 5/4 n logn (not considering swap gates), where n is the number of lattice sites. Our method provides a systematic approach of generalizing Ferris' spectral tensor network for nontrivial boundary conditions.

A complex guided spectral transform Lanczos method for studying quantum resonance states

DOE PAGES

Yu, Hua-Gen

2014-12-28

A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos (cFOL) polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the originalmore » Hamiltonian in the spectral range of interest. Therefore the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO₂, and compared to previous calculations.« less

Combined invariants to similarity transformation and to blur using orthogonal Zernike moments

PubMed Central

Beijing, Chen; Shu, Huazhong; Zhang, Hui; Coatrieux, Gouenou; Luo, Limin; Coatrieux, Jean-Louis

2011-01-01

The derivation of moment invariants has been extensively investigated in the past decades. In this paper, we construct a set of invariants derived from Zernike moments which is simultaneously invariant to similarity transformation and to convolution with circularly symmetric point spread function (PSF). Two main contributions are provided: the theoretical framework for deriving the Zernike moments of a blurred image and the way to construct the combined geometric-blur invariants. The performance of the proposed descriptors is evaluated with various PSFs and similarity transformations. The comparison of the proposed method with the existing ones is also provided in terms of pattern recognition accuracy, template matching and robustness to noise. Experimental results show that the proposed descriptors perform on the overall better. PMID:20679028

Axial 3D region of interest reconstruction using weighted cone beam BPF/DBPF algorithm cascaded with adequately oriented orthogonal butterfly filtering

NASA Astrophysics Data System (ADS)

Tang, Shaojie; Tang, Xiangyang

2016-03-01

Axial cone beam (CB) computed tomography (CT) reconstruction is still the most desirable in clinical applications. As the potential candidates with analytic form for the task, the back projection-filtration (BPF) and the derivative backprojection filtered (DBPF) algorithms, in which Hilbert filtering is the common algorithmic feature, are originally derived for exact helical and axial reconstruction from CB and fan beam projection data, respectively. These two algorithms have been heuristically extended for axial CB reconstruction via adoption of virtual PI-line segments. Unfortunately, however, streak artifacts are induced along the Hilbert filtering direction, since these algorithms are no longer accurate on the virtual PI-line segments. We have proposed to cascade the extended BPF/DBPF algorithm with orthogonal butterfly filtering for image reconstruction (namely axial CB-BPP/DBPF cascaded with orthogonal butterfly filtering), in which the orientation-specific artifacts caused by post-BP Hilbert transform can be eliminated, at a possible expense of losing the BPF/DBPF's capability of dealing with projection data truncation. Our preliminary results have shown that this is not the case in practice. Hence, in this work, we carry out an algorithmic analysis and experimental study to investigate the performance of the axial CB-BPP/DBPF cascaded with adequately oriented orthogonal butterfly filtering for three-dimensional (3D) reconstruction in region of interest (ROI).

Real-time interactive 3D manipulation of particles viewed in two orthogonal observation planes.

PubMed

Perch-Nielsen, Ivan; Rodrigo, Peter; Glückstad, Jesper

2005-04-18

The generalized phase contrast (GPC) method has been applied to transform a single TEM00 beam into a manifold of counterpropagating-beam traps capable of real-time interactive manipulation of multiple microparticles in three dimensions (3D). This paper reports on the use of low numerical aperture (NA), non-immersion, objective lenses in an implementation of the GPC-based 3D trapping system. Contrary to high-NA based optical tweezers, the GPC trapping system demonstrated here operates with long working distance (>10 mm), and offers a wider manipulation region and a larger field of view for imaging through each of the two opposing objective lenses. As a consequence of the large working distance, simultaneous monitoring of the trapped particles in a second orthogonal observation plane is demonstrated.

Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force

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

Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external “observer.” Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Thus, even a possibility to describe physical reality by means of non-Hermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. We show that non-Hermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Further, we propose a quantum canonical transformation that maps Hermitian systems ontomore » non-Hermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.« less

Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force

DOE PAGES

Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

2016-08-26

A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external “observer.” Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Thus, even a possibility to describe physical reality by means of non-Hermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. We show that non-Hermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Further, we propose a quantum canonical transformation that maps Hermitian systems ontomore » non-Hermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.« less

Imagining physically impossible self-rotations: geometry is more important than gravity.

PubMed

Creem, S H; Wraga, M; Proffitt, D R

2001-08-01

Previous studies found that it is easier for observers to spatially update displays during imagined self-rotation versus array rotation. The present study examined whether either the physics of gravity or the geometric relationship between the viewer and array guided this self-rotation advantage. Experiments 1-3 preserved a real or imagined orthogonal relationship between the viewer and the array, requiring a rotation in the observer's transverse plane. Despite imagined self-rotations that defied gravity, a viewer advantage remained. Without this orthogonal relationship (Experiment 4), the viewer advantage was lost. We suggest that efficient transformation of the egocentric reference frame relies on the representation of body-environment relations that allow rotation around the observer's principal axis. This efficiency persists across different and conflicting physical and imagined postures.

Imagining physically impossible self-rotations: geometry is more important than gravity

NASA Technical Reports Server (NTRS)

Creem, S. H.; Wraga, M.; Proffitt, D. R.; Kaiser, M. K. (Principal Investigator)

2001-01-01

Previous studies found that it is easier for observers to spatially update displays during imagined self-rotation versus array rotation. The present study examined whether either the physics of gravity or the geometric relationship between the viewer and array guided this self-rotation advantage. Experiments 1-3 preserved a real or imagined orthogonal relationship between the viewer and the array, requiring a rotation in the observer's transverse plane. Despite imagined self-rotations that defied gravity, a viewer advantage remained. Without this orthogonal relationship (Experiment 4), the viewer advantage was lost. We suggest that efficient transformation of the egocentric reference frame relies on the representation of body-environment relations that allow rotation around the observer's principal axis. This efficiency persists across different and conflicting physical and imagined postures.

The multifacet graphically contracted function method. II. A general procedure for the parameterization of orthogonal matrices and its application to arc factors

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

Shepard, Ron; Brozell, Scott R.; Gidofalvi, Gergely

2014-08-14

Practical algorithms are presented for the parameterization of orthogonal matrices Q ∈ R {sup m×n} in terms of the minimal number of essential parameters (φ). Both square n = m and rectangular n < m situations are examined. Two separate kinds of parameterizations are considered, one in which the individual columns of Q are distinct, and the other in which only Span(Q) is significant. The latter is relevant to chemical applications such as the representation of the arc factors in the multifacet graphically contracted function method and the representation of orbital coefficients in SCF and DFT methods. The parameterizations aremore » represented formally using products of elementary Householder reflector matrices. Standard mathematical libraries, such as LAPACK, may be used to perform the basic low-level factorization, reduction, and other algebraic operations. Some care must be taken with the choice of phase factors in order to ensure stability and continuity. The transformation of gradient arrays between the Q and (φ) parameterizations is also considered. Operation counts for all factorizations and transformations are determined. Numerical results are presented which demonstrate the robustness, stability, and accuracy of these algorithms.« less

Understanding Antipsychotic Drug Treatment Effects: A Novel Method to Reduce Pseudospecificity of the Positive and Negative Syndrome Scale (PANSS) Factors.

PubMed

Hopkins, Seth C; Ogirala, Ajay; Loebel, Antony; Koblan, Kenneth S

2017-12-01

The Positive and Negative Syndrome Scale (PANSS) is the most widely used efficacy measure in acute treatment studies of schizophrenia. However, interpretation of the efficacy of antipsychotics in improving specific symptom domains is confounded by moderate-to-high correlations among standard (Marder) PANSS factors. The authors review the results of an uncorrelated PANSS score matrix (UPSM) transform designed to reduce pseudospecificity in assessment of symptom change in patients with schizophrenia. Based on a factor analysis of five pooled, placebo-controlled lurasidone clinical trials (N=1,710 patients), a UPSM transform was identified that generated PANSS factors with high face validity (good correlation with standard Marder PANSS factors), and high specificity/orthogonality (low levels of between-factor correlation measuring change during treatment). Between-factor correlations were low at baseline for both standard (Marder) PANSS factors and transformed PANSS factors. However, when measured change in symptom severity was measured during treatment (in a pooled 5-study analysis), there was a notable difference for standard PANSS factors, where changes across factors were found to be highly correlated (factors exhibited pseudospecificity), compared to transformed PANSS factors, where factor change scores exhibited the same low levels of between-factor correlation observed at baseline. At Week 6-endpoint, correlations among PANSS factor severity scores were moderate-to-high for standard factors (0.34-0.68), but continued to be low for the transformed factors (-0.22-0.20). As an additional validity check, we analyzed data from one of the original five pooled clinical trials that included other well-validated assessment scales (MADRS, Negative Symptom Assessment scale [NSA]). In this baseline analysis, UPSM-transformed PANSS factor severity scores (negative and depression factors) were found to correlate well with the MADRS and NSA. The availability of transformed PANSS factors with a high degree of orthogonality/specificity, but which retain a high degree of concurrent and face validity, can reduce pseudospecificity as a measurement confound, and should facilitate the drug development process, permitting a more accurate characterization of the efficacy of putative new agents in targeting specific symptom domains in patients with psychotic illness.

Spectral resolution enhancement of Fourier-transform spectrometer based on orthogonal shear interference using Wollaston prism

NASA Astrophysics Data System (ADS)

Cong, Lin-xiao; Huang, Min; Cai, Qi-sheng

2017-10-01

In this paper, a multi-line interferogram stitching method based on orthogonal shear using the Wollaston prism(WP) was proposed with a 2D projection interferogram recorded through the rotation of CCD, making the spectral resolution of Fourier-Transform spectrometer(FTS) of a limited spatial size increase by at least three times. The fringes on multi-lines were linked with the pixels of equal optical path difference (OPD). Ideally, the error of sampled phase within one pixel was less than half the wavelength, ensuring consecutive values in the over-sampled dimension while aliasing in another. In the simulation, with the calibration of 1.064μm, spectral lines at 1.31μm and 1.56μm of equal intensity were tested and observed. The result showed a bias of 0.13% at 1.31μm and 1.15% at 1.56μm in amplitude, and the FWHM at 1.31μm reduced from 25nm to 8nm after the sample points increased from 320 to 960. In the comparison of reflectance spectrum of carnauba wax within near infrared(NIR) band, the absorption peak at 1.2μm was more obvious and zoom of the band 1.38 1.43μm closer to the reference, although some fluctuation was in the short-wavelength region arousing the spectral crosstalk. In conclusion, with orthogonal shear based on the rotation of the CCD relative to the axis of WP, the spectral resolution of static FTS was enhanced by the projection of fringes to the grid coordinates and stitching the interferograms into a larger OPD, which showed the advantages of cost and miniaturization in the space-constrained NIR applications.

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

Kim, M; Suh, T; Cho, W

Purpose: A potential validation tool for compensating patient positioning error was developed using 2D/3D and 3D/3D image registration. Methods: For 2D/3D registration, digitally reconstructed radiography (DRR) and three-dimensional computed tomography (3D-CT) images were applied. The ray-casting algorithm is the most straightforward method for generating DRR. We adopted the traditional ray-casting method, which finds the intersections of a ray with all objects, voxels of the 3D-CT volume in the scene. The similarity between the extracted DRR and orthogonal image was measured by using a normalized mutual information method. Two orthogonal images were acquired from a Cyber-Knife system from the anterior-posterior (AP)more » and right lateral (RL) views. The 3D-CT and two orthogonal images of an anthropomorphic phantom and head and neck cancer patient were used in this study. For 3D/3D registration, planning CT and in-room CT image were applied. After registration, the translation and rotation factors were calculated to position a couch to be movable in six dimensions. Results: Registration accuracies and average errors of 2.12 mm ± 0.50 mm for transformations and 1.23° ± 0.40° for rotations were acquired by 2D/3D registration using an anthropomorphic Alderson-Rando phantom. In addition, registration accuracies and average errors of 0.90 mm ± 0.30 mm for transformations and 1.00° ± 0.2° for rotations were acquired using CT image sets. Conclusion: We demonstrated that this validation tool could compensate for patient positioning error. In addition, this research could be the fundamental step for compensating patient positioning error at the first Korea heavy-ion medical accelerator treatment center.« less

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.

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.

Electrocardiogram ST-Segment Morphology Delineation Method Using Orthogonal Transformations

PubMed Central

2016-01-01

Differentiation between ischaemic and non-ischaemic transient ST segment events of long term ambulatory electrocardiograms is a persisting weakness in present ischaemia detection systems. Traditional ST segment level measuring is not a sufficiently precise technique due to the single point of measurement and severe noise which is often present. We developed a robust noise resistant orthogonal-transformation based delineation method, which allows tracing the shape of transient ST segment morphology changes from the entire ST segment in terms of diagnostic and morphologic feature-vector time series, and also allows further analysis. For these purposes, we developed a new Legendre Polynomials based Transformation (LPT) of ST segment. Its basis functions have similar shapes to typical transient changes of ST segment morphology categories during myocardial ischaemia (level, slope and scooping), thus providing direct insight into the types of time domain morphology changes through the LPT feature-vector space. We also generated new Karhunen and Lo ève Transformation (KLT) ST segment basis functions using a robust covariance matrix constructed from the ST segment pattern vectors derived from the Long Term ST Database (LTST DB). As for the delineation of significant transient ischaemic and non-ischaemic ST segment episodes, we present a study on the representation of transient ST segment morphology categories, and an evaluation study on the classification power of the KLT- and LPT-based feature vectors to classify between ischaemic and non-ischaemic ST segment episodes of the LTST DB. Classification accuracy using the KLT and LPT feature vectors was 90% and 82%, respectively, when using the k-Nearest Neighbors (k = 3) classifier and 10-fold cross-validation. New sets of feature-vector time series for both transformations were derived for the records of the LTST DB which is freely available on the PhysioNet website and were contributed to the LTST DB. The KLT and LPT present new possibilities for human-expert diagnostics, and for automated ischaemia detection. PMID:26863140

40-fs hydrogen Raman laser

NASA Astrophysics Data System (ADS)

Didenko, N. V.; Konyashchenko, A. V.; Kostryukov, P. V.; Losev, L. L.; Pazyuk, V. S.; Tenyakov, S. Yu; Molchanov, V. Ya; Chizhikov, S. I.; Yushkov, K. B.

2015-12-01

40-fs first Stokes pulses at a wavelength of 1.2 μm were generated in a hydrogen SRS-converter pumped by orthogonally polarised double chirped pulses of a Ti : sapphire laser. To obtain a Stokes pulse close to a transform-limited one, a programmed acousto-optic dispersive delay line was placed between the master oscillator and regenerative amplifier. The energy efficiency of Stokes radiation conversion reached 22%.

Fidelity under isospectral perturbations: a random matrix study

NASA Astrophysics Data System (ADS)

Leyvraz, F.; García, A.; Kohler, H.; Seligman, T. H.

2013-07-01

The set of Hamiltonians generated by all unitary transformations from a single Hamiltonian is the largest set of isospectral Hamiltonians we can form. Taking advantage of the fact that the unitary group can be generated from Hermitian matrices we can take the ones generated by the Gaussian unitary ensemble with a small parameter as small perturbations. Similarly, the transformations generated by Hermitian antisymmetric matrices from orthogonal matrices form isospectral transformations among symmetric matrices. Based on this concept we can obtain the fidelity decay of a system that decays under a random isospectral perturbation with well-defined properties regarding time-reversal invariance. If we choose the Hamiltonian itself also from a classical random matrix ensemble, then we obtain solutions in terms of form factors in the limit of large matrices.

Measurement of in-plane displacements using the phase singularities generated by directional wavelet transforms of speckle pattern images.

PubMed

Vadnjal, Ana Laura; Etchepareborda, Pablo; Federico, Alejandro; Kaufmann, Guillermo H

2013-03-20

We present a method to determine micro and nano in-plane displacements based on the phase singularities generated by application of directional wavelet transforms to speckle pattern images. The spatial distribution of the obtained phase singularities by the wavelet transform configures a network, which is characterized by two quasi-orthogonal directions. The displacement value is determined by identifying the intersection points of the network before and after the displacement produced by the tested object. The performance of this method is evaluated using simulated speckle patterns and experimental data. The proposed approach is compared with the optical vortex metrology and digital image correlation methods in terms of performance and noise robustness, and the advantages and limitations associated to each method are also discussed.

Use of the wavelet transform to investigate differences in brain PET images between patient groups

NASA Astrophysics Data System (ADS)

Ruttimann, Urs E.; Unser, Michael A.; Rio, Daniel E.; Rawlings, Robert R.

1993-06-01

Suitability of the wavelet transform was studied for the analysis of glucose utilization differences between subject groups as displayed in PET images. To strengthen statistical inference, it was of particular interest investigating the tradeoff between signal localization and image decomposition into uncorrelated components. This tradeoff is shown to be controlled by wavelet regularity, with the optimal compromise attained by third-order orthogonal spline wavelets. Testing of the ensuing wavelet coefficients identified only about 1.5% as statistically different (p < .05) from noise, which then served to resynthesize the difference images by the inverse wavelet transform. The resulting images displayed relatively uniform, noise-free regions of significant differences with, due to the good localization maintained by the wavelets, very little reconstruction artifacts.

Zernike Basis to Cartesian Transformations

NASA Astrophysics Data System (ADS)

Mathar, R. J.

2009-12-01

The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle) defines the Zernike functions, for which we derive transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Warsi, Z. U. A.; Mastin, C. W.

1982-01-01

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Principal shapes and squeezed limits in the effective field theory of large scale structure

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

Bertolini, Daniele; Solon, Mikhail P., E-mail: dbertolini@lbl.gov, E-mail: mpsolon@lbl.gov

2016-11-01

We apply an orthogonalization procedure on the effective field theory of large scale structure (EFT of LSS) shapes, relevant for the angle-averaged bispectrum and non-Gaussian covariance of the matter power spectrum at one loop. Assuming natural-sized EFT parameters, this identifies a linear combination of EFT shapes—referred to as the principal shape—that gives the dominant contribution for the whole kinematic plane, with subdominant combinations suppressed by a few orders of magnitude. For the covariance, our orthogonal transformation is in excellent agreement with a principal component analysis applied to available data. Additionally we find that, for both observables, the coefficients of themore » principal shapes are well approximated by the EFT coefficients appearing in the squeezed limit, and are thus measurable from power spectrum response functions. Employing data from N-body simulations for the growth-only response, we measure the single EFT coefficient describing the angle-averaged bispectrum with Ο (10%) precision. These methods of shape orthogonalization and measurement of coefficients from response functions are valuable tools for developing the EFT of LSS framework, and can be applied to more general observables.« less

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

Strout, Michelle

Programming parallel machines is fraught with difficulties: the obfuscation of algorithms due to implementation details such as communication and synchronization, the need for transparency between language constructs and performance, the difficulty of performing program analysis to enable automatic parallelization techniques, and the existence of important "dusty deck" codes. The SAIMI project developed abstractions that enable the orthogonal specification of algorithms and implementation details within the context of existing DOE applications. The main idea is to enable the injection of small programming models such as expressions involving transcendental functions, polyhedral iteration spaces with sparse constraints, and task graphs into full programsmore » through the use of pragmas. These smaller, more restricted programming models enable orthogonal specification of many implementation details such as how to map the computation on to parallel processors, how to schedule the computation, and how to allocation storage for the computation. At the same time, these small programming models enable the expression of the most computationally intense and communication heavy portions in many scientific simulations. The ability to orthogonally manipulate the implementation for such computations will significantly ease performance programming efforts and expose transformation possibilities and parameter to automated approaches such as autotuning. At Colorado State University, the SAIMI project was supported through DOE grant DE-SC3956 from April 2010 through August 2015. The SAIMI project has contributed a number of important results to programming abstractions that enable the orthogonal specification of implementation details in scientific codes. This final report summarizes the research that was funded by the SAIMI project.« less

Modular and Orthogonal Synthesis of Hybrid Polymers and Networks

PubMed Central

Liu, Shuang; Dicker, Kevin T.; Jia, Xinqiao

2015-01-01

Biomaterials scientists strive to develop polymeric materials with distinct chemical make-up, complex molecular architectures, robust mechanical properties and defined biological functions by drawing inspirations from biological systems. Salient features of biological designs include (1) repetitive presentation of basic motifs; and (2) efficient integration of diverse building blocks. Thus, an appealing approach to biomaterials synthesis is to combine synthetic and natural building blocks in a modular fashion employing novel chemical methods. Over the past decade, orthogonal chemistries have become powerful enabling tools for the modular synthesis of advanced biomaterials. These reactions require building blocks with complementary functionalities, occur under mild conditions in the presence of biological molecules and living cells and proceed with high yield and exceptional selectivity. These chemistries have facilitated the construction of complex polymers and networks in a step-growth fashion, allowing facile modulation of materials properties by simple variations of the building blocks. In this review, we first summarize features of several types of orthogonal chemistries. We then discuss recent progress in the synthesis of step growth linear polymers, dendrimers and networks that find application in drug delivery, 3D cell culture and tissue engineering. Overall, orthogonal reactions and modulular synthesis have not only minimized the steps needed for the desired chemical transformations but also maximized the diversity and functionality of the final products. The modular nature of the design, combined with the potential synergistic effect of the hybrid system, will likely result in novel hydrogel matrices with robust structures and defined functions. PMID:25572255

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.

Fast orthogonal transforms and generation of Brownian paths

PubMed Central

Leobacher, Gunther

2012-01-01

We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length n can be generated in O(nlog(n)) floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples. PMID:23471545

Scattering Matrix Elements for the Nonadiabatic Collision

DTIC Science & Technology

2010-12-01

orthogonality relationship expressed in (77). This technique, known as the Channel Packet Method (CPM), is laid out by Weeks and Tannor [2...time and energy are Fourier transform pairs, and share the same relationship as the coordinate/momentum pairs: max min 2E t t π ∆ = − (99) As...elements, will exibit ringing. Selection of an inappropriatly large time step introduces an erroneous phase shift in the correlation funtion . This

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.

A New Look at Rainfall Fluctuations and Scaling Properties of Spatial Rainfall Using Orthogonal Wavelets.

NASA Astrophysics Data System (ADS)

Kumar, Praveen; Foufoula-Georgiou, Efi

1993-02-01

It has been observed that the finite-dimensional distribution functions of rainfall cannot obey simple scaling laws due to rainfall intermittency (mixed distribution with an atom at zero) and the probability of rainfall being an increasing function of area. Although rainfall fluctuations do not suffer these limitations, it is interesting to note that very few attempts have been made to study them in terms of their self-similarity characteristics. This is due to the lack of unambiguous definition of fluctuations in multidimensions. This paper shows that wavelet transforms offer a convenient and consistent method for the decomposition of inhomogeneous and anisotropic rainfall fields in two dimensions and that the components of this decomposition can be looked at as fluctuations of the rainfall field. It is also shown that under some mild assumptions, the component fields can be treated as homogeneous and thus are amenable to second-order analysis, which can provide useful insight into the nature of the process. The fact that wavelet transforms are a space-scale method also provides a convenient tool to study scaling characteristics of the process. Orthogonal wavelets are used, and these properties are investigated for a squall-line storm to study the presence of self-similarity.

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.

A new look at rainfall fluctuations and scaling properties of spatial rainfall using orthogonal wavelets

NASA Technical Reports Server (NTRS)

Kumar, Praveen; Foufoula-Georgiou, Efi

1993-01-01

It has been observed that the finite-dimensional distribution functions of rainfall cannot obey simple scaling laws due to rainfall intermittency (mixed distribution with an atom at zero) and the probability of rainfall being an increasing function of area. Although rainfall fluctuations do not suffer these limitations, it is interesting to note that very few attempts have been made to study them in terms of their self-similarity characteristics. This is due to the lack of unambiguous definition of fluctuations in multidimensions. This paper shows that wavelet transforms offer a convenient and consistent method for the decomposition of inhomogeneous and anisotropic rainfall fields in two dimensions and that the components of this decomposition can be looked at as fluctuations of the rainfall field. It is also shown that under some mild assumptions, the component fields can be treated as homogeneous and thus are amenable to second-order analysis, which can provide useful insight into the nature of the process. The fact that wavelet transforms are a space-scale method also provides a convenient tool to study scaling characteristics of the process. Orthogonal wavelets are used, and these properties are investigated for a squall-line storm to study the presence of self-similarity.

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.

Quadrature rules with multiple nodes for evaluating integrals with strong singularities

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2006-05-01

We present a method based on the Chakalov-Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turan quadrature rules, Numer. Algorithms 10 (1995), 27-39; Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhauser, Basel, 1999, pp. 109-119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.

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.

Exploring item and higher order factor structure with the Schmid-Leiman solution: syntax codes for SPSS and SAS.

PubMed

Wolff, Hans-Georg; Preising, Katja

2005-02-01

To ease the interpretation of higher order factor analysis, the direct relationships between variables and higher order factors may be calculated by the Schmid-Leiman solution (SLS; Schmid & Leiman, 1957). This simple transformation of higher order factor analysis orthogonalizes first-order and higher order factors and thereby allows the interpretation of the relative impact of factor levels on variables. The Schmid-Leiman solution may also be used to facilitate theorizing and scale development. The rationale for the procedure is presented, supplemented by syntax codes for SPSS and SAS, since the transformation is not part of most statistical programs. Syntax codes may also be downloaded from www.psychonomic.org/archive/.

Ruthenium-Catalyzed Cascade C—H Functionalization of Phenylacetophenones**

PubMed Central

Mehta, Vaibhav P; García-López, José-Antonio; Greaney, Michael F

2014-01-01

Three orthogonal cascade C—H functionalization processes are described, based on ruthenium-catalyzed C—H alkenylation. 1-Indanones, indeno indenes, and indeno furanones were accessed through cascade pathways by using arylacetophenones as substrates under conditions of catalytic [{Ru(p-cymene)Cl2}2] and stoichiometric Cu(OAc)2. Each transformation uses C—H functionalization methods to form C—C bonds sequentially, with the indeno furanone synthesis featuring a C—O bond formation as the terminating step. This work demonstrates the power of ruthenium-catalyzed alkenylation as a platform reaction to develop more complex transformations, with multiple C—H functionalization steps taking place in a single operation to access novel carbocyclic structures. PMID:24453063

Dynamic biometric identification from multiple views using the GLBP-TOP method.

PubMed

Wang, Yu; Shen, Xuanjing; Chen, Haipeng; Zhai, Yujie

2014-01-01

To realize effective and rapid dynamic biometric identification with low computational complexity, a video-based facial texture program that extracts local binary patterns from three orthogonal planes in the frequency domain of the Gabor transform (GLBP-TOP) was proposed. Firstly, each normalized face was transformed by Gabor wavelet to get the enhanced Gabor magnitude map, and then the LBP-TOP operator was applied to the maps to extract video texture. Finally, weighted Chi square statistics based on the Fisher Criterion were used to realize the identification. The proposed algorithm was proved effective through the biometric experiments using the Honda/UCSD database, and was robust against changes of illumination and expressions.

Performance Analysis of OFDM in Frequency Selective, Slowly Fading Nakagami Channels

DTIC Science & Technology

2001-12-01

starting with some background, then moving into how to generate an OFDM signal, and finally discussing the implementation of OFDM using one specific...application, the IEEE 802.11a standard. The application of some more general communications concepts such as the discrete Fourier transform (DFT...provide orthogonal cover to the sub-carriers, some may argue that the FFT’s complexity makes up for the loss of equalization complexity, however, as Ch

Radar Measurements of Ocean Surface Waves using Proper Orthogonal Decomposition

DTIC Science & Technology

2017-03-30

rely on use of Fourier transforms (FFT) and filtering spectra on the linear dispersion relationship for ocean surface waves. This report discusses...the measured signal (e.g., Young et al., 1985). In addition, the methods often rely on filtering the FFT of radar backscatter or Doppler velocities...to those obtained with conventional FFT and dispersion curve filtering techniques (iv) Compare both results of(iii) to ground truth sensors (i .e

Human Motion Capture Data Tailored Transform Coding.

PubMed

Junhui Hou; Lap-Pui Chau; Magnenat-Thalmann, Nadia; Ying He

2015-07-01

Human motion capture (mocap) is a widely used technique for digitalizing human movements. With growing usage, compressing mocap data has received increasing attention, since compact data size enables efficient storage and transmission. Our analysis shows that mocap data have some unique characteristics that distinguish themselves from images and videos. Therefore, directly borrowing image or video compression techniques, such as discrete cosine transform, does not work well. In this paper, we propose a novel mocap-tailored transform coding algorithm that takes advantage of these features. Our algorithm segments the input mocap sequences into clips, which are represented in 2D matrices. Then it computes a set of data-dependent orthogonal bases to transform the matrices to frequency domain, in which the transform coefficients have significantly less dependency. Finally, the compression is obtained by entropy coding of the quantized coefficients and the bases. Our method has low computational cost and can be easily extended to compress mocap databases. It also requires neither training nor complicated parameter setting. Experimental results demonstrate that the proposed scheme significantly outperforms state-of-the-art algorithms in terms of compression performance and speed.

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.

Bianchi's Bäcklund transformation for higher dimensional quadrics

NASA Astrophysics Data System (ADS)

Dincă, Ion I.

2016-12-01

We provide a generalization of Bianchi's Bäcklund transformation from 2-dimensional quadrics to higher dimensional quadrics (which is also a generalization of Tenenblat-Terng's Bäcklund transformation of isometric deformations of Hn(R) in R 2 n - 1 to general quadrics). Our investigation is the higher dimensional version of Bianchi's main three theorems on the theory of isometric deformations of quadrics and Bianchi's treatment of the Bäcklund transformation for diagonal paraboloids via conjugate systems. It became the driving force which led to the flourishing of the classical differential geometry in the second half of the XIX th century and its profound study by illustrious geometers led to interesting results. Today it is still an open problem in its full generality, but basic familiar results like the Gauß-Bonnet fundamental theorem of surfaces and the Codazzi-Mainardi equations (independently discovered also by Peterson) were first communicated to the French Academy of Sciences. A list (most likely incomplete) of the winners of the prize includes Bianchi, Bonnet, Guichard, Weingarten.Up to 1899 isometric deformations of the (pseudo-)sphere and isotropic quadrics without center (from a metric point of view they can be considered as metrically degenerate quadrics without center) together with their Bäcklund transformation and the complementary transformation of isometric deformations of surfaces of revolution were investigated by geometers such as Bäcklund, Bianchi, Bonnet, Darboux, Goursat, Hazzidakis, Lie, Weingarten, etc.In 1899 Guichard discovered that when quadrics with(out) center and of revolution around the focal axis roll on their isometric deformations their foci describe constant mean curvature (minimal) surfaces (and Bianchi proved the converse: all constant mean curvature (minimal) surfaces can be realized in this way).With Guichard's result the race to find the isometric deformations of general quadrics was on; it ended with Bianchi's discovery [1] from 1906 of the Bäcklund transformation for quadrics and the isometric correspondence provided by the Ivory affine transformation.In what concerns isometric deformations of higher dimensional non-degenerate quadrics the first result is that of Cartan's: in 1919-1920 Cartan has shown in [2], using mostly projective arguments and his exterior differential systems in involution and exteriorly orthogonal forms tools, that space forms of dimension n admit rich families of isometric deformations in surrounding space forms of dimension 2 n - 1, depending on n(n - 1) functions of one variable, that such isometric deformations admit lines of curvature given by a canonical form of exteriorly orthogonal forms and that the codimension n - 1 cannot be lowered without obtaining rigidity as the isometric deformation being the defining quadric. Because these isometric deformations admit lines of curvature they have flat normal bundle. Since the lines of curvature on n-dimensional space forms, when they are considered by definition as quadrics in surrounding (n + 1) -dimensional space forms, are undetermined, the lines of curvature on the isometric deformation and their corresponding curves on the quadric provide the common conjugate system (that is the second fundamental form is diagonal).From Cartan's papers until 1979 no further progress had been made in the isometric deformation problem for higher dimensional quadrics.In 1979, upon a suggestion from S.S. Chern and using Chebyshev coordinates on Hn(R) , which by the Cartan-Moore Theorem are lines of curvature and thus in bijective correspondence with isometric deformations of Hn(R) in R 2 n - 1, Tenenblat-Terng have developed in [3] the Bäcklund transformation of Hn(R) in R 2 n - 1 and Terng in [4] has developed the Bianchi Permutability Theorem for this Bäcklund transformation.In 1983 Berger, Bryant and Griffiths [5] proved, including by use of tools from algebraic geometry, in particular that Cartan's essentially projective arguments, including the exterior part of his exteriorly orthogonal forms tool, can be used to generalize his results on the n-dimensional pseudosphere to n-dimensional non-degenerate quadrics with positive definite metric, which thus can appear as quadrics in R n + 1 or as space-like quadrics in Rn ×(iR) . Thus they proved that n-dimensional quadrics with positive definite metric admit rich families of isometric deformations in surrounding Euclidean space R 2 n - 1, depending on n(n - 1) functions of one variable, that the codimension n - 1 cannot be lowered without obtaining rigidity as the isometric deformation being the defining quadric and that quadrics are the only Riemannian n-dimensional manifolds that admit a family of isometric deformations in R 2 n - 1 as rich as possible for which the exteriorly orthogonal forms tool (naturally appearing from the Gauß equations) can be applied.With the result of Berger, Bryant and Griffiths [5] the natural question appears of generalizing Bianchi's Bäcklund transformation of 2-dimensional non-degenerate quadrics to higher dimensions, which is also a generalization of the Bäcklund transformation of Tenenblat-Terng [3] from the higher dimensional pseudosphere to higher dimensional general quadrics.

Generalized transformations and coordinates for static spherically symmetric general relativity

NASA Astrophysics Data System (ADS)

Hill, James M.; O'Leary, Joseph

2018-04-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

Development and evaluation of a Hadamard transform imaging spectrometer and a Hadamard transform thermal imager

NASA Technical Reports Server (NTRS)

Harwit, M.; Swift, R.; Wattson, R.; Decker, J.; Paganetti, R.

1976-01-01

A spectrometric imager and a thermal imager, which achieve multiplexing by the use of binary optical encoding masks, were developed. The masks are based on orthogonal, pseudorandom digital codes derived from Hadamard matrices. Spatial and/or spectral data is obtained in the form of a Hadamard transform of the spatial and/or spectral scene; computer algorithms are then used to decode the data and reconstruct images of the original scene. The hardware, algorithms and processing/display facility are described. A number of spatial and spatial/spectral images are presented. The achievement of a signal-to-noise improvement due to the signal multiplexing was also demonstrated. An analysis of the results indicates both the situations for which the multiplex advantage may be gained, and the limitations of the technique. A number of potential applications of the spectrometric imager are discussed.

Generalized transformations and coordinates for static spherically symmetric general relativity.

PubMed

Hill, James M; O'Leary, Joseph

2018-04-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

Generalized transformations and coordinates for static spherically symmetric general relativity

PubMed Central

2018-01-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington–Finkelstein transformation and the Kruskal–Szekeres coordinates. PMID:29765624

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.

Development of a patient positioning error compensation tool for Korea Heavy-Ion Medical Accelerator Treatment Center

NASA Astrophysics Data System (ADS)

Kim, Min-Joo; Suh, Tae-Suk; Cho, Woong; Jung, Won-Gyun

2015-07-01

In this study, a potential validation tool for compensating for the patient positioning error was developed by using 2D/3D and 3D/3D image registration. For 2D/3D registration, digitallyreconstructed radiography (DRR) and three-dimensional computed tomography (3D-CT) images were applied. The ray-casting algorithm is the most straightforward method for generating DRR, so we adopted the traditional ray-casting method, which finds the intersections of a ray with all objects, voxels of the 3D-CT volume in the scene. The similarity between the extracted DRR and the orthogonal image was measured by using a normalized mutual information method. Two orthogonal images were acquired from a Cyber-knife system from the anterior-posterior (AP) and right lateral (RL) views. The 3D-CT and the two orthogonal images of an anthropomorphic phantom and of the head and neck of a cancer patient were used in this study. For 3D/3D registration, planning CT and in-room CT images were applied. After registration, the translation and the rotation factors were calculated to position a couch to be movable in six dimensions. Registration accuracies and average errors of 2.12 mm ± 0.50 mm for transformations and 1.23 ° ± 0.40 ° for rotations were acquired by using 2D/3D registration with the anthropomorphic Alderson-Rando phantom. In addition, registration accuracies and average errors of 0.90 mm ± 0.30 mm for transformations and 1.00 ° ± 0.2 ° for rotations were acquired by using CT image sets. We demonstrated that this validation tool could compensate for patient positioning errors. In addition, this research could be a fundamental step in compensating for patient positioning errors at the Korea Heavy-ion Medical Accelerator Treatment Center.

Design and fabrication of nano-imprint templates using unique pattern transforms and primitives

NASA Astrophysics Data System (ADS)

MacDonald, Susan; Mellenthin, David; Rentzsch, Kevin; Kramer, Kenneth; Ellenson, James; Hostetler, Tim; Enck, Ron

2005-11-01

Increasing numbers of MEMS, photonic, and integrated circuit manufacturers are investigating the use of Nano-imprint Lithography or Step and Flash Imprint Lithography (SFIL) as a lithography choice for making various devices and products. Their main interests in using these technologies are the lack of aberrations inherent in traditional optical reduction lithography, and the relative low cost of imprint tools. Since imprint templates are at 1X scale, the small sizes of these structures have necessitated the use of high-resolution 50KeV, and 100KeV e-beam lithography tools to build these templates. For MEMS and photonic applications, the structures desired are often circles, arches, and other non-orthogonal shapes. It has long been known that both 50keV, and especially 100keV e-beam lithography tools are extremely accurate, and can produce very high resolution structures, but the trade off is long write times. The main drivers in write time are shot count and stage travel. This work will show how circles and other non-orthogonal shapes can be produced with a 50KeV Variable Shaped Beam (VSB) e-beam lithography system using unique pattern transforms and primitive shapes, while keeping the shot count and write times under control. The quality of shapes replicated into the resist on wafer using an SFIL tool will also be presented.

On the use of a Euclidean norm function for the estimation of local dynamic stability from 3D kinematics using time-delayed Lyapunov analyses.

PubMed

Beaudette, Shawn M; Howarth, Samuel J; Graham, Ryan B; Brown, Stephen H M

2016-10-01

Several different state-space reconstruction methods have been employed to assess the local dynamic stability (LDS) of a 3D kinematic system. One common method is to use a Euclidean norm (N) transformation of three orthogonal x, y, and z time-series' followed by the calculation of the maximum finite-time Lyapunov exponent (λmax) from the resultant N waveform (using a time-delayed state space reconstruction technique). By essentially acting as a weighted average, N has been suggested to account for simultaneous expansion and contraction along separate degrees of freedom within a 3D system (e.g. the coupling of dynamic movements between orthogonal planes). However, when estimating LDS using N, non-linear transformations inherent within the calculation of N should be accounted for. Results demonstrate that the use of N on 3D time-series data with arbitrary magnitudes of relative bias and zero-crossings cause the introduction of error in estimates of λmax obtained through N. To develop a standard for the analysis of 3D dynamic kinematic waveforms, we suggest that all dimensions of a 3D signal be independently shifted to avoid the incidence of zero-crossings prior to the calculation of N and subsequent estimation of LDS through the use of λmax. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

Application of Fourier transform infrared spectroscopy and orthogonal projections to latent structures/partial least squares regression for estimation of procyanidins average degree of polymerisation.

PubMed

Passos, Cláudia P; Cardoso, Susana M; Barros, António S; Silva, Carlos M; Coimbra, Manuel A

2010-02-28

Fourier transform infrared (FTIR) spectroscopy has being emphasised as a widespread technique in the quick assess of food components. In this work, procyanidins were extracted with methanol and acetone/water from the seeds of white and red grape varieties. A fractionation by graded methanol/chloroform precipitations allowed to obtain 26 samples that were characterised using thiolysis as pre-treatment followed by HPLC-UV and MS detection. The average degree of polymerisation (DPn) of the procyanidins in the samples ranged from 2 to 11 flavan-3-ol residues. FTIR spectroscopy within the wavenumbers region of 1800-700 cm(-1) allowed to build a partial least squares (PLS1) regression model with 8 latent variables (LVs) for the estimation of the DPn, giving a RMSECV of 11.7%, with a R(2) of 0.91 and a RMSEP of 2.58. The application of orthogonal projection to latent structures (O-PLS1) clarifies the interpretation of the regression model vectors. Moreover, the O-PLS procedure has removed 88% of non-correlated variations with the DPn, allowing to relate the increase of the absorbance peaks at 1203 and 1099 cm(-1) with the increase of the DPn due to the higher proportion of substitutions in the aromatic ring of the polymerised procyanidin molecules. Copyright 2009 Elsevier B.V. All rights reserved.

Theoretical model of a polarization diffractive elements for the light beams conversion holographic formation in PDLCs

NASA Astrophysics Data System (ADS)

Sharangovich, Sergey N.; Semkin, Artem O.

2017-12-01

In this work a theoretical model of the holographic formation of the polarization diffractive optical elements for the transformation of Gaussian light beams into Bessel-like ones in polymer-dispersed liquid crystals (PDLC) is developed. The model is based on solving the equations of photo-induced Fredericks transition processes for polarization diffractive elements formation by orthogonally polarized light beams with inhomogeneous amplitude and phase profiles. The results of numerical simulation of the material's dielectric tensor changing due to the structure's formation process are presented for various recording beams' polarization states. Based on the results of numerical simulation, the ability to form the diffractive optical elements for light beams transformation by the polarization holography methods is shown.

From sequences to polynomials and back, via operator orderings

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

Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu

2013-12-15

Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

Multispectral histogram normalization contrast enhancement

NASA Technical Reports Server (NTRS)

Soha, J. M.; Schwartz, A. A.

1979-01-01

A multispectral histogram normalization or decorrelation enhancement which achieves effective color composites by removing interband correlation is described. The enhancement procedure employs either linear or nonlinear transformations to equalize principal component variances. An additional rotation to any set of orthogonal coordinates is thus possible, while full histogram utilization is maintained by avoiding the reintroduction of correlation. For the three-dimensional case, the enhancement procedure may be implemented with a lookup table. An application of the enhancement to Landsat multispectral scanning imagery is presented.

On complex matrices with simple spectrum that are unitarily similar to real matrices

NASA Astrophysics Data System (ADS)

Ikramov, Khakim D.

2011-04-01

Suppose that one should verify whether a given complex n × n matrix can be converted into a real matrix by a unitary similarity transformation. Sufficient conditions for this property to hold were found in an earlier publication of this author. These conditions are relaxed in the following way: as before, the spectrum is required to be simple, but pairs of complex conjugate eigenvalues λ ,bar λ are now allowed. However, the eigenvectors corresponding to such eigenvalues must not be orthogonal.

Time-Domain Computation Of Electromagnetic Fields In MMICs

NASA Technical Reports Server (NTRS)

Lansing, Faiza S.; Rascoe, Daniel L.

1995-01-01

Maxwell's equations solved on three-dimensional, conformed orthogonal grids by finite-difference techniques. Method of computing frequency-dependent electrical parameters of monolithic microwave integrated circuit (MMIC) involves time-domain computation of propagation of electromagnetic field in response to excitation by single pulse at input terminal, followed by computation of Fourier transforms to obtain frequency-domain response from time-domain response. Parameters computed include electric and magnetic fields, voltages, currents, impedances, scattering parameters, and effective dielectric constants. Powerful and efficient means for analyzing performance of even complicated MMIC.

Low-peak-to-average power ratio and low-complexity asymmetrically clipped optical orthogonal frequency-division multiplexing uplink transmission scheme for long-reach passive optical network.

PubMed

Zhou, Ji; Qiao, Yaojun

2015-09-01

In this Letter, we propose a discrete Hartley transform (DHT)-spread asymmetrically clipped optical orthogonal frequency-division multiplexing (DHT-S-ACO-OFDM) uplink transmission scheme in which the multiplexing/demultiplexing process also uses the DHT algorithm. By designing a simple encoding structure, the computational complexity of the transmitter can be reduced from O(Nlog(2)(N)) to O(N). At the probability of 10(-3), the peak-to-average power ratio (PAPR) of 2-ary pulse amplitude modulation (2-PAM)-modulated DHT-S-ACO-OFDM is approximately 9.7 dB lower than that of 2-PAM-modulated conventional ACO-OFDM. To verify the feasibility of the proposed scheme, a 4-Gbit/s DHT-S-ACO-OFDM uplink transmission scheme with a 1∶64 way split has been experimentally implemented using 100-km standard single-mode fiber (SSMF) for a long-reach passive optical network (LR-PON).

Applying wavelet transforms to analyse aircraft-measured turbulence and turbulent fluxes in the atmospheric boundary layer over eastern Siberia

NASA Astrophysics Data System (ADS)

Strunin, M. A.; Hiyama, T.

2004-11-01

The wavelet spectral method was applied to aircraft-based measurements of atmospheric turbulence obtained during joint Russian-Japanese research on the atmospheric boundary layer near Yakutsk (eastern Siberia) in April-June 2000. Practical ways to apply Fourier and wavelet methods for aircraft-based turbulence data are described. Comparisons between Fourier and wavelet transform results are shown and they demonstrate, in conjunction with theoretical and experimental restrictions, that the Fourier transform method is not useful for studying non-homogeneous turbulence. The wavelet method is free from many disadvantages of Fourier analysis and can yield more informative results. Comparison of Fourier and Morlet wavelet spectra showed good agreement at high frequencies (small scales). The quality of the wavelet transform and corresponding software was estimated by comparing the original data with restored data constructed with an inverse wavelet transform. A Haar wavelet basis was inappropriate for the turbulence data; the mother wavelet function recommended in this study is the Morlet wavelet. Good agreement was also shown between variances and covariances estimated with different mathematical techniques, i.e. through non-orthogonal wavelet spectra and through eddy correlation methods.

Proposal for automated transformations on single-photon multipath qudits

NASA Astrophysics Data System (ADS)

Baldijão, R. D.; Borges, G. F.; Marques, B.; Solís-Prosser, M. A.; Neves, L.; Pádua, S.

2017-09-01

We propose a method for implementing automated state transformations on single-photon multipath qudits encoded in a one-dimensional transverse spatial domain. It relies on transferring the encoding from this domain to the orthogonal one by applying a spatial phase modulation with diffraction gratings, merging all the initial propagation paths by using a stable interferometric network, and filtering out the unwanted diffraction orders. The automation feature is attained by utilizing a programmable phase-only spatial light modulator (SLM) where properly designed diffraction gratings displayed on its screen will implement the desired transformations, including, among others, projections, permutations, and random operations. We discuss the losses in the process which is, in general, inherently nonunitary. Some examples of transformations are presented and, considering a realistic scenario, we analyze how they will be affected by the pixelated structure of the SLM screen. The method proposed here enables one to implement much more general transformations on multipath qudits than is possible with a SLM alone operating in the diagonal basis of which-path states. Therefore, it will extend the range of applicability for this encoding in high-dimensional quantum information and computing protocols as well as fundamental studies in quantum theory.

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.

Two-level image authentication by two-step phase-shifting interferometry and compressive sensing

NASA Astrophysics Data System (ADS)

Zhang, Xue; Meng, Xiangfeng; Yin, Yongkai; Yang, Xiulun; Wang, Yurong; Li, Xianye; Peng, Xiang; He, Wenqi; Dong, Guoyan; Chen, Hongyi

2018-01-01

A two-level image authentication method is proposed; the method is based on two-step phase-shifting interferometry, double random phase encoding, and compressive sensing (CS) theory, by which the certification image can be encoded into two interferograms. Through discrete wavelet transform (DWT), sparseness processing, Arnold transform, and data compression, two compressed signals can be generated and delivered to two different participants of the authentication system. Only the participant who possesses the first compressed signal attempts to pass the low-level authentication. The application of Orthogonal Match Pursuit CS algorithm reconstruction, inverse Arnold transform, inverse DWT, two-step phase-shifting wavefront reconstruction, and inverse Fresnel transform can result in the output of a remarkable peak in the central location of the nonlinear correlation coefficient distributions of the recovered image and the standard certification image. Then, the other participant, who possesses the second compressed signal, is authorized to carry out the high-level authentication. Therefore, both compressed signals are collected to reconstruct the original meaningful certification image with a high correlation coefficient. Theoretical analysis and numerical simulations verify the feasibility of the proposed method.

Comparison Of The Performance Of Hybrid Coders Under Different Configurations

NASA Astrophysics Data System (ADS)

Gunasekaran, S.; Raina J., P.

1983-10-01

Picture bandwidth reduction employing DPCM and Orthogonal Transform (OT) coding for TV transmission have been widely discussed in literature; both the techniques have their own advantages and limitations in terms of compression ratio, implementation, sensitivity to picture statistics and their sensitivity to the channel noise. Hybrid coding introduced by Habibi, - a cascade of the two techniques, offers excellent performance and proves to be attractive retaining the special advantages of both the techniques. In the recent times, the interest has shifted over to Hybrid coding, and in the absence of a report on the relative performance specifications of hybrid coders at different configurations, an attempt has been made to colate the information. Fourier, Hadamard, Slant, Sine, Cosine and Harr transforms have been considered for the present work.

Multiset canonical correlations analysis and multispectral, truly multitemporal remote sensing data.

PubMed

Nielsen, Allan Aasbjerg

2002-01-01

This paper describes two- and multiset canonical correlations analysis (CCA) for data fusion, multisource, multiset, or multitemporal exploratory data analysis. These techniques transform multivariate multiset data into new orthogonal variables called canonical variates (CVs) which, when applied in remote sensing, exhibit ever-decreasing similarity (as expressed by correlation measures) over sets consisting of 1) spectral variables at fixed points in time (R-mode analysis), or 2) temporal variables with fixed wavelengths (T-mode analysis). The CVs are invariant to linear and affine transformations of the original variables within sets which means, for example, that the R-mode CVs are insensitive to changes over time in offset and gain in a measuring device. In a case study, CVs are calculated from Landsat Thematic Mapper (TM) data with six spectral bands over six consecutive years. Both Rand T-mode CVs clearly exhibit the desired characteristic: they show maximum similarity for the low-order canonical variates and minimum similarity for the high-order canonical variates. These characteristics are seen both visually and in objective measures. The results from the multiset CCA R- and T-mode analyses are very different. This difference is ascribed to the noise structure in the data. The CCA methods are related to partial least squares (PLS) methods. This paper very briefly describes multiset CCA-based multiset PLS. Also, the CCA methods can be applied as multivariate extensions to empirical orthogonal functions (EOF) techniques. Multiset CCA is well-suited for inclusion in geographical information systems (GIS).

Analysis and Synthesis of Pseudo-Periodic[InlineEquation not available: see fulltext.]-Like Noise by Means of Wavelets with Applications to Digital Audio

NASA Astrophysics Data System (ADS)

Polotti, Pietro; Evangelista, Gianpaolo

2001-12-01

Voiced musical sounds have nonzero energy in sidebands of the frequency partials. Our work is based on the assumption, often experimentally verified, that the energy distribution of the sidebands is shaped as powers of the inverse of the distance from the closest partial. The power spectrum of these pseudo-periodic processes is modeled by means of a superposition of modulated[InlineEquation not available: see fulltext.] components, that is, by a pseudo-periodic[InlineEquation not available: see fulltext.]-like process. Due to the fundamental selfsimilar character of the wavelet transform,[InlineEquation not available: see fulltext.] processes can be fruitfully analyzed and synthesized by means of wavelets. We obtain a set of very loosely correlated coefficients at each scale level that can be well approximated by white noise in the synthesis process. Our computational scheme is based on an orthogonal[InlineEquation not available: see fulltext.]-band filter bank and a dyadic wavelet transform per channel. The[InlineEquation not available: see fulltext.] channels are tuned to the left and right sidebands of the harmonics so that sidebands are mutually independent. The structure computes the expansion coefficients of a new orthogonal and complete set of harmonic-band wavelets. The main point of our scheme is that we need only two parameters per harmonic in order to model the stochastic fluctuations of sounds from a pure periodic behavior.

QRS analysis using wavelet transformation for the prediction of response to cardiac resynchronization therapy: a prospective pilot study.

PubMed

Vassilikos, Vassilios P; Mantziari, Lilian; Dakos, Georgios; Kamperidis, Vasileios; Chouvarda, Ioanna; Chatzizisis, Yiannis S; Kalpidis, Panagiotis; Theofilogiannakos, Efstratios; Paraskevaidis, Stelios; Karvounis, Haralambos; Mochlas, Sotirios; Maglaveras, Nikolaos; Styliadis, Ioannis H

2014-01-01

Wider QRS and left bundle branch block morphology are related to response to cardiac resynchronization therapy (CRT). A novel time-frequency analysis of the QRS complex may provide additional information in predicting response to CRT. Signal-averaged electrocardiograms were prospectively recorded, before CRT, in orthogonal leads and QRS decomposition in three frequency bands was performed using the Morlet wavelet transformation. Thirty eight patients (age 65±10years, 31 males) were studied. CRT responders (n=28) had wider baseline QRS compared to non-responders and lower QRS energies in all frequency bands. The combination of QRS duration and mean energy in the high frequency band had the best predicting ability (AUC 0.833, 95%CI 0.705-0.962, p=0.002) followed by the maximum energy in the high frequency band (AUC 0.811, 95%CI 0.663-0.960, p=0.004). Wavelet transformation of the QRS complex is useful in predicting response to CRT. © 2013.

Parametric symmetries in exactly solvable real and PT symmetric complex potentials

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

Yadav, Rajesh Kumar, E-mail: rajeshastrophysics@gmail.com; Khare, Avinash, E-mail: khare@physics.unipune.ac.in; Bagchi, Bijan, E-mail: bbagchi123@gmail.com

In this paper, we discuss the parametric symmetries in different exactly solvable systems characterized by real or complex PT symmetric potentials. We focus our attention on the conventional potentials such as the generalized Pöschl Teller (GPT), Scarf-I, and PT symmetric Scarf-II which are invariant under certain parametric transformations. The resulting set of potentials is shown to yield a completely different behavior of the bound state solutions. Further, the supersymmetric partner potentials acquire different forms under such parametric transformations leading to new sets of exactly solvable real and PT symmetric complex potentials. These potentials are also observed to be shape invariantmore » (SI) in nature. We subsequently take up a study of the newly discovered rationally extended SI potentials, corresponding to the above mentioned conventional potentials, whose bound state solutions are associated with the exceptional orthogonal polynomials (EOPs). We discuss the transformations of the corresponding Casimir operator employing the properties of the so(2, 1) algebra.« less

Accurate reconstruction in digital holographic microscopy using Fresnel dual-tree complex wavelet transform

NASA Astrophysics Data System (ADS)

Zhang, Xiaolei; Zhang, Xiangchao; Yuan, He; Zhang, Hao; Xu, Min

2018-02-01

Digital holography is a promising measurement method in the fields of bio-medicine and micro-electronics. But the captured images of digital holography are severely polluted by the speckle noise because of optical scattering and diffraction. Via analyzing the properties of Fresnel diffraction and the topographies of micro-structures, a novel reconstruction method based on the dual-tree complex wavelet transform (DT-CWT) is proposed. This algorithm is shiftinvariant and capable of obtaining sparse representations for the diffracted signals of salient features, thus it is well suited for multiresolution processing of the interferometric holograms of directional morphologies. An explicit representation of orthogonal Fresnel DT-CWT bases and a specific filtering method are developed. This method can effectively remove the speckle noise without destroying the salient features. Finally, the proposed reconstruction method is compared with the conventional Fresnel diffraction integration and Fresnel wavelet transform with compressive sensing methods to validate its remarkable superiority on the aspects of topography reconstruction and speckle removal.

A Fast Hermite Transform★

PubMed Central

Leibon, Gregory; Rockmore, Daniel N.; Park, Wooram; Taintor, Robert; Chirikjian, Gregory S.

2008-01-01

We present algorithms for fast and stable approximation of the Hermite transform of a compactly supported function on the real line, attainable via an application of a fast algebraic algorithm for computing sums associated with a three-term relation. Trade-offs between approximation in bandlimit (in the Hermite sense) and size of the support region are addressed. Numerical experiments are presented that show the feasibility and utility of our approach. Generalizations to any family of orthogonal polynomials are outlined. Applications to various problems in tomographic reconstruction, including the determination of protein structure, are discussed. PMID:20027202

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

Redox Reactions between Mn(II) and Hexagonal Birnessite Change Its Layer Symmetry.

PubMed

Zhao, Huaiyan; Zhu, Mengqiang; Li, Wei; Elzinga, Evert J; Villalobos, Mario; Liu, Fan; Zhang, Jing; Feng, Xionghan; Sparks, Donald L

2016-02-16

Birnessite, a phyllomanganate and the most common type of Mn oxide, affects the fate and transport of numerous contaminants and nutrients in nature. Birnessite exhibits hexagonal (HexLayBir) or orthogonal (OrthLayBir) layer symmetry. The two types of birnessite contain contrasting content of layer vacancies and Mn(III), and accordingly have different sorption and oxidation abilities. OrthLayBir can transform to HexLayBir, but it is still vaguely understood if and how the reverse transformation occurs. Here, we show that HexLayBir (e.g., δ-MnO2 and acid birnessite) transforms to OrthLayBir after reaction with aqueous Mn(II) at low Mn(II)/Mn (in HexLayBir) molar ratios (5-24%) and pH ≥ 8. The transformation is promoted by higher pH values, as well as smaller particle size, and/or greater stacking disorder of HexLayBir. The transformation is ascribed to Mn(III) formation via the comproportionation reaction between Mn(II) adsorbed on vacant sites and the surrounding layer Mn(IV), and the subsequent migration of the Mn(III) into the vacancies with an ordered distribution in the birnessite layers. This study indicates that aqueous Mn(II) and pH are critical environmental factors controlling birnessite layer structure and reactivity in the environment.

3D Model Generation From the Engineering Drawing

NASA Astrophysics Data System (ADS)

Vaský, Jozef; Eliáš, Michal; Bezák, Pavol; Červeňanská, Zuzana; Izakovič, Ladislav

2010-01-01

The contribution deals with the transformation of engineering drawings in a paper form into a 3D computer representation. A 3D computer model can be further processed in CAD/CAM system, it can be modified, archived, and a technical drawing can be then generated from it as well. The transformation process from paper form to the data one is a complex and difficult one, particularly owing to the different types of drawings, forms of displayed objects and encountered errors and deviations from technical standards. The algorithm for 3D model generating from an orthogonal vector input representing a simplified technical drawing of the rotational part is described in this contribution. The algorithm was experimentally implemented as ObjectARX application in the AutoCAD system and the test sample as the representation of the rotational part was used for verificaton.

Anomaly transform methods based on total energy and ocean heat content norms for generating ocean dynamic disturbances for ensemble climate forecasts

NASA Astrophysics Data System (ADS)

Romanova, Vanya; Hense, Andreas

2017-08-01

In our study we use the anomaly transform, a special case of ensemble transform method, in which a selected set of initial oceanic anomalies in space, time and variables are defined and orthogonalized. The resulting orthogonal perturbation patterns are designed such that they pick up typical balanced anomaly structures in space and time and between variables. The metric used to set up the eigen problem is taken either as the weighted total energy with its zonal, meridional kinetic and available potential energy terms having equal contributions, or the weighted ocean heat content in which a disturbance is applied only to the initial temperature fields. The choices of a reference state for defining the initial anomalies are such that either perturbations on seasonal timescales and or on interannual timescales are constructed. These project a-priori only the slow modes of the ocean physical processes, such that the disturbances grow mainly in the Western Boundary Currents, in the Antarctic Circumpolar Current and the El Nino Southern Oscillation regions. An additional set of initial conditions is designed to fit in a least square sense data from global ocean reanalysis. Applying the AT produced sets of disturbances to oceanic initial conditions initialized by observations of the MPIOM-ESM coupled model on T63L47/GR15 resolution, four ensemble and one hind-cast experiments were performed. The weighted total energy norm is used to monitor the amplitudes and rates of the fastest growing error modes. The results showed minor dependence of the instabilities or error growth on the selected metric but considerable change due to the magnitude of the scaling amplitudes of the perturbation patterns. In contrast to similar atmospheric applications, we find an energy conversion from kinetic to available potential energy, which suggests a different source of uncertainty generation in the ocean than in the atmosphere mainly associated with changes in the density field.

Combined peak-to-average power ratio reduction and physical layer security enhancement in optical orthogonal frequency division multiplexing visible-light communication systems

NASA Astrophysics Data System (ADS)

Wang, Zhongpeng; Chen, Shoufa

2016-07-01

A physical encryption scheme for discrete Hartley transform (DHT) precoded orthogonal frequency division multiplexing (OFDM) visible-light communication (VLC) systems using frequency domain chaos scrambling is proposed. In the scheme, the chaos scrambling, which is generated by a modified logistic mapping, is utilized to enhance the physical layer of security, and the DHT precoding is employed to reduce of OFDM signal for OFDM-based VLC. The influence of chaos scrambling on peak-to-average power ratio (PAPR) and bit error rate (BER) of systems is studied. The experimental simulation results prove the efficiency of the proposed encryption method for DHT-precoded, OFDM-based VLC systems. Furthermore, the influence of the proposed encryption to the PAPR and BER of systems is evaluated. The experimental results show that the proposed security scheme can protect the DHT-precoded, OFDM-based VLC from eavesdroppers, while keeping the good BER performance of DHT-precoded systems. The BER performance of the encrypted and DHT-precoded system is almost the same as that of the conventional DHT-precoded system without encryption.

Orthonormal vector polynomials in a unit circle, Part I: Basis set derived from gradients of Zernike polynomials.

PubMed

Zhao, Chunyu; Burge, James H

2007-12-24

Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. These functions are generated from gradients of Zernike polynomials, made orthonormal using the Gram- Schmidt technique. This set provides a complete basis for representing vector fields that can be defined as a gradient of some scalar function. It is then efficient to transform from the coefficients of the vector functions to the scalar Zernike polynomials that represent the function whose gradient was fit. These new vector functions have immediate application for fitting data from a Shack-Hartmann wavefront sensor or for fitting mapping distortion for optical testing. A subsequent paper gives an additional set of vector functions consisting only of rotational terms with zero divergence. The two sets together provide a complete basis that can represent all vector distributions in a circular domain.

Analytic derivative couplings and first-principles exciton/phonon coupling constants for an ab initio Frenkel-Davydov exciton model: Theory, implementation, and application to compute triplet exciton mobility parameters for crystalline tetracene.

PubMed

Morrison, Adrian F; Herbert, John M

2017-06-14

Recently, we introduced an ab initio version of the Frenkel-Davydov exciton model for computing excited-state properties of molecular crystals and aggregates. Within this model, supersystem excited states are approximated as linear combinations of excitations localized on molecular sites, and the electronic Hamiltonian is constructed and diagonalized in a direct-product basis of non-orthogonal configuration state functions computed for isolated fragments. Here, we derive and implement analytic derivative couplings for this model, including nuclear derivatives of the natural transition orbital and symmetric orthogonalization transformations that are part of the approximation. Nuclear derivatives of the exciton Hamiltonian's matrix elements, required in order to compute the nonadiabatic couplings, are equivalent to the "Holstein" and "Peierls" exciton/phonon couplings that are widely discussed in the context of model Hamiltonians for energy and charge transport in organic photovoltaics. As an example, we compute the couplings that modulate triplet exciton transport in crystalline tetracene, which is relevant in the context of carrier diffusion following singlet exciton fission.

A Numerical Scheme for the Solution of the Space Charge Problem on a Multiply Connected Region

NASA Astrophysics Data System (ADS)

Budd, C. J.; Wheeler, A. A.

1991-11-01

In this paper we extend the work of Budd and Wheeler ( Proc. R. Soc. London A, 417, 389, 1988) , who described a new numerical scheme for the solution of the space charge equation on a simple connected domain, to multiply connected regions. The space charge equation, ▿ · ( Δ overlineϕ ▽ overlineϕ) = 0 , is a third-order nonlinear partial differential equation for the electric potential overlineϕ which models the electric field in the vicinity of a coronating conductor. Budd and Wheeler described a new way of analysing this equation by constructing an orthogonal coordinate system ( overlineϕ, overlineψ) and recasting the equation in terms of x, y, and ▽ overlineϕ as functions of ( overlineϕ, overlineψ). This transformation is singular on multiply connected regions and in this paper we show how this may be overcome to provide an efficient numerical scheme for the solution of the space charge equation. This scheme also provides a new method for the solution of Laplaces equation and the calculation of orthogonal meshes on multiply connected regions.

An analysis dictionary learning algorithm under a noisy data model with orthogonality constraint.

PubMed

Zhang, Ye; Yu, Tenglong; Wang, Wenwu

2014-01-01

Two common problems are often encountered in analysis dictionary learning (ADL) algorithms. The first one is that the original clean signals for learning the dictionary are assumed to be known, which otherwise need to be estimated from noisy measurements. This, however, renders a computationally slow optimization process and potentially unreliable estimation (if the noise level is high), as represented by the Analysis K-SVD (AK-SVD) algorithm. The other problem is the trivial solution to the dictionary, for example, the null dictionary matrix that may be given by a dictionary learning algorithm, as discussed in the learning overcomplete sparsifying transform (LOST) algorithm. Here we propose a novel optimization model and an iterative algorithm to learn the analysis dictionary, where we directly employ the observed data to compute the approximate analysis sparse representation of the original signals (leading to a fast optimization procedure) and enforce an orthogonality constraint on the optimization criterion to avoid the trivial solutions. Experiments demonstrate the competitive performance of the proposed algorithm as compared with three baselines, namely, the AK-SVD, LOST, and NAAOLA algorithms.

Spectral-domain low-coherence interferometry for phase-sensitive measurement of Faraday rotation at multiple depths.

PubMed

Yeh, Yi-Jou; Black, Adam J; Akkin, Taner

2013-10-10

We describe a method for differential phase measurement of Faraday rotation from multiple depth locations simultaneously. A polarization-maintaining fiber-based spectral-domain interferometer that utilizes a low-coherent light source and a single camera is developed. Light decorrelated by the orthogonal channels of the fiber is launched on a sample as two oppositely polarized circular states. These states reflect from sample surfaces and interfere with the corresponding states of the reference arm. A custom spectrometer, which is designed to simplify camera alignment, separates the orthogonal channels and records the interference-related oscillations on both spectra. Inverse Fourier transform of the spectral oscillations in k-space yields complex depth profiles, whose amplitudes and phase difference are related to reflectivity and Faraday rotation within the sample, respectively. Information along a full depth profile is produced at the camera speed without performing an axial scan for a multisurface sample. System sensitivity for the Faraday rotation measurement is 0.86 min of arc. Verdet constants of clear liquids and turbid media are measured at 687 nm.

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

Necessary and sufficient condition for the realization of the complex wavelet

NASA Astrophysics Data System (ADS)

Keita, Alpha; Qing, Qianqin; Wang, Nengchao

1997-04-01

Wavelet theory is a whole new signal analysis theory in recent years, and the appearance of which is attracting lots of experts in many different fields giving it a deepen study. Wavelet transformation is a new kind of time. Frequency domain analysis method of localization in can-be- realized time domain or frequency domain. It has many perfect characteristics that many other kinds of time frequency domain analysis, such as Gabor transformation or Viginier. For example, it has orthogonality, direction selectivity, variable time-frequency domain resolution ratio, adjustable local support, parsing data in little amount, and so on. All those above make wavelet transformation a very important new tool and method in signal analysis field. Because the calculation of complex wavelet is very difficult, in application, real wavelet function is used. In this paper, we present a necessary and sufficient condition that the real wavelet function can be obtained by the complex wavelet function. This theorem has some significant values in theory. The paper prepares its technique from Hartley transformation, then, it gives the complex wavelet was a signal engineering expert. His Hartley transformation, which also mentioned by Hartley, had been overlooked for about 40 years, for the social production conditions at that time cannot help to show its superiority. Only when it came to the end of 70s and the early 80s, after the development of the fast algorithm of Fourier transformation and the hardware implement to some degree, the completely some positive-negative transforming method was coming to take seriously. W transformation, which mentioned by Zhongde Wang, pushed the studying work of Hartley transformation and its fast algorithm forward. The kernel function of Hartley transformation.

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.

Understanding software faults and their role in software reliability modeling

NASA Technical Reports Server (NTRS)

Munson, John C.

1994-01-01

This study is a direct result of an on-going project to model the reliability of a large real-time control avionics system. In previous modeling efforts with this system, hardware reliability models were applied in modeling the reliability behavior of this system. In an attempt to enhance the performance of the adapted reliability models, certain software attributes were introduced in these models to control for differences between programs and also sequential executions of the same program. As the basic nature of the software attributes that affect software reliability become better understood in the modeling process, this information begins to have important implications on the software development process. A significant problem arises when raw attribute measures are to be used in statistical models as predictors, for example, of measures of software quality. This is because many of the metrics are highly correlated. Consider the two attributes: lines of code, LOC, and number of program statements, Stmts. In this case, it is quite obvious that a program with a high value of LOC probably will also have a relatively high value of Stmts. In the case of low level languages, such as assembly language programs, there might be a one-to-one relationship between the statement count and the lines of code. When there is a complete absence of linear relationship among the metrics, they are said to be orthogonal or uncorrelated. Usually the lack of orthogonality is not serious enough to affect a statistical analysis. However, for the purposes of some statistical analysis such as multiple regression, the software metrics are so strongly interrelated that the regression results may be ambiguous and possibly even misleading. Typically, it is difficult to estimate the unique effects of individual software metrics in the regression equation. The estimated values of the coefficients are very sensitive to slight changes in the data and to the addition or deletion of variables in the regression equation. Since most of the existing metrics have common elements and are linear combinations of these common elements, it seems reasonable to investigate the structure of the underlying common factors or components that make up the raw metrics. The technique we have chosen to use to explore this structure is a procedure called principal components analysis. Principal components analysis is a decomposition technique that may be used to detect and analyze collinearity in software metrics. When confronted with a large number of metrics measuring a single construct, it may be desirable to represent the set by some smaller number of variables that convey all, or most, of the information in the original set. Principal components are linear transformations of a set of random variables that summarize the information contained in the variables. The transformations are chosen so that the first component accounts for the maximal amount of variation of the measures of any possible linear transform; the second component accounts for the maximal amount of residual variation; and so on. The principal components are constructed so that they represent transformed scores on dimensions that are orthogonal. Through the use of principal components analysis, it is possible to have a set of highly related software attributes mapped into a small number of uncorrelated attribute domains. This definitively solves the problem of multi-collinearity in subsequent regression analysis. There are many software metrics in the literature, but principal component analysis reveals that there are few distinct sources of variation, i.e. dimensions, in this set of metrics. It would appear perfectly reasonable to characterize the measurable attributes of a program with a simple function of a small number of orthogonal metrics each of which represents a distinct software attribute domain.

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.

Face verification with balanced thresholds.

PubMed

Yan, Shuicheng; Xu, Dong; Tang, Xiaoou

2007-01-01

The process of face verification is guided by a pre-learned global threshold, which, however, is often inconsistent with class-specific optimal thresholds. It is, hence, beneficial to pursue a balance of the class-specific thresholds in the model-learning stage. In this paper, we present a new dimensionality reduction algorithm tailored to the verification task that ensures threshold balance. This is achieved by the following aspects. First, feasibility is guaranteed by employing an affine transformation matrix, instead of the conventional projection matrix, for dimensionality reduction, and, hence, we call the proposed algorithm threshold balanced transformation (TBT). Then, the affine transformation matrix, constrained as the product of an orthogonal matrix and a diagonal matrix, is optimized to improve the threshold balance and classification capability in an iterative manner. Unlike most algorithms for face verification which are directly transplanted from face identification literature, TBT is specifically designed for face verification and clarifies the intrinsic distinction between these two tasks. Experiments on three benchmark face databases demonstrate that TBT significantly outperforms the state-of-the-art subspace techniques for face verification.

Relation between the chord length distribution of an infinitely long cylinder and that of its base

NASA Astrophysics Data System (ADS)

Sukiasian, H. S.; Gille, Wilfried

2007-05-01

Chord length distributions are defined for planar and spatial geometric figures. There exist connections between the planar and the spatial cases: The chord length distribution densities (CLDs) of a cylinder B and its base S (the cylinder's orthogonal cross section) are interrelated by a simple, surveyable integral transformation. From this transformation, it was concluded that the odd moments of the CLD f(x ) of S define the leading asymptotic terms of the CLD Aμ(r) of B. The power series of Aμ(r) at r =0 can be traced back to the derivatives of f(x ) in the origin. As a general conclusion, there exist different geometric bodies B in R3 with the same CLD Aμ(r). An exact recognition of B via its CLD is not possible. CLDs do not characterize spatial sets. This result is of importance in materials science in order to avoid wrong interpretations in structure research. The new CLD integral transformation has been illustrated in connection with the transitions triangle→triangular rod and rectangle→rectangular rod.

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Group theoretical methods and wavelet theory: coorbit theory and applications

NASA Astrophysics Data System (ADS)

Feichtinger, Hans G.

2013-05-01

Before the invention of orthogonal wavelet systems by Yves Meyer1 in 1986 Gabor expansions (viewed as discretized inversion of the Short-Time Fourier Transform2 using the overlap and add OLA) and (what is now perceived as) wavelet expansions have been treated more or less at an equal footing. The famous paper on painless expansions by Daubechies, Grossman and Meyer3 is a good example for this situation. The description of atomic decompositions for functions in modulation spaces4 (including the classical Sobolev spaces) given by the author5 was directly modeled according to the corresponding atomic characterizations by Frazier and Jawerth,6, 7 more or less with the idea of replacing the dyadic partitions of unity of the Fourier transform side by uniform partitions of unity (so-called BUPU's, first named as such in the early work on Wiener-type spaces by the author in 19808). Watching the literature in the subsequent two decades one can observe that the interest in wavelets "took over", because it became possible to construct orthonormal wavelet systems with compact support and of any given degree of smoothness,9 while in contrast the Balian-Low theorem is prohibiting the existence of corresponding Gabor orthonormal bases, even in the multi-dimensional case and for general symplectic lattices.10 It is an interesting historical fact that* his construction of band-limited orthonormal wavelets (the Meyer wavelet, see11) grew out of an attempt to prove the impossibility of the existence of such systems, and the final insight was that it was not impossible to have such systems, and in fact quite a variety of orthonormal wavelet system can be constructed as we know by now. Meanwhile it is established wisdom that wavelet theory and time-frequency analysis are two different ways of decomposing signals in orthogonal resp. non-orthogonal ways. The unifying theory, covering both cases, distilling from these two situations the common group theoretical background lead to the theory of coorbit spaces,12, 13 established by the author jointly with K. Gröchenig. Starting from an integrable and irreducible representation of some locally compact group (such as the "ax+b"-group or the Heisenberg group) one can derive families of Banach spaces having natural atomic characterizations, or alternatively a continuous transform associated to it. So at the end function spaces of locally compact groups come into play, and their generic properties help to explain why and how it is possible to obtain (nonorthogonal) decompositions. While unification of these two groups was one important aspect of the approach given in the late 80th, it was also clear that this approach allows to formulate and exploit the analogy to Banach spaces of analytic functions invariant under the Moebius group have been at the heart in this context. Recent years have seen further new instances and generalizations. Among them shearlets or the Blaschke product should be mentioned here, and the increased interest in the connections between wavelet theory and complex analysis. The talk will try to summarize a few of the general principles which can be derived from the general theory, but also highlight the difference between the different groups and signal expansions arising from corresponding group representations. There is still a lot more to be done, also from the point of view of applications and the numerical realization of such non-orthogonal expansions.

Representation and design of wavelets using unitary circuits

NASA Astrophysics Data System (ADS)

Evenbly, Glen; White, Steven R.

2018-05-01

The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multiscale representation of quantum many-body wave functions using unitary circuits, further cementing the relation established in the literature between classical and quantum multiscale methods. An algorithm for constructing the circuit representation of known orthogonal, dyadic, discrete WTs is presented, and the explicit representation for Daubechies wavelets, coiflets, and symlets is provided. Furthermore, we demonstrate the usefulness of the circuit formalism in designing WTs, including various classes of symmetric wavelets and multiwavelets, boundary wavelets, and biorthogonal wavelets.

Complete regioselective addition of grignard reagents to pyrazine N-oxides, toward an efficient enantioselective synthesis of substituted piperazines.

PubMed

Andersson, Hans; Banchelin, Thomas Sainte-Luce; Das, Sajal; Gustafsson, Magnus; Olsson, Roger; Almqvist, Fredrik

2010-01-15

A conceptually new one-pot strategy for the synthesis of protected substituted piperazines via the addition of Grignard reagents to pyrazine N-oxides is presented. This strategy is high yielding (33-91% over three steps), step-efficient, and fast. The synthesized N,N-diprotected piperazines are convenient to handle and allow for orthogonal deprotection at either nitrogen for selective transformations. In addition, this is a synthetic route to enantiomerically enriched piperazines by using a combination of phenyl magnesium chloride and (-)-sparteine, which resulted in enantiomeric excesses up to 83%.

Optical ranging and communication method based on all-phase FFT

NASA Astrophysics Data System (ADS)

Li, Zening; Chen, Gang

2014-10-01

This paper describes an optical ranging and communication method based on all-phase fast fourier transform (FFT). This kind of system is mainly designed for vehicle safety application. Particularly, the phase shift of the reflecting orthogonal frequency division multiplexing (OFDM) symbol is measured to determine the signal time of flight. Then the distance is calculated according to the time of flight. Several key factors affecting the phase measurement accuracy are studied. The all-phase FFT, which can reduce the effects of frequency offset, phase noise and the inter-carrier interference (ICI), is applied to measure the OFDM symbol phase shift.

Spinors in Hilbert Space

NASA Astrophysics Data System (ADS)

Plymen, Roger; Robinson, Paul

1995-01-01

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

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.

Expression patterns of Eph genes in the "dual visual development" of the lamprey and their significance in the evolution of vision in vertebrates.

PubMed

Suzuki, Daichi G; Murakami, Yasunori; Yamazaki, Yuji; Wada, Hiroshi

2015-01-01

Image-forming vision is crucial to animals for recognizing objects in their environment. In vertebrates, this type of vision is achieved with paired camera eyes and topographic projection of the optic nerve. Topographic projection is established by an orthogonal gradient of axon guidance molecules, such as Ephs. To explore the evolution of image-forming vision in vertebrates, lampreys, which belong to the basal lineage of vertebrates, are key animals because they show unique "dual visual development." In the embryonic and pre-ammocoete larval stage (the "primary" phase), photoreceptive "ocellus-like" eyes develop, but there is no retinotectal optic nerve projection. In the late ammocoete larval stage (the "secondary" phase), the eyes grow and form into camera eyes, and retinotectal projection is newly formed. After metamorphosis, this retinotectal projection in adult lampreys is topographic, similar to that of gnathostomes. In this study, we explored the involvement of Ephs in lamprey "dual visual development" and establishment of the image-form vision. We found that gnathostome-like orthogonal gradient expression was present in the retina during the "secondary" phase; i.e., EphB showed a gradient of expression along the dorsoventral axis, while EphC was expressed along the anteroposterior axis. However, no orthogonal gradient expression was observed during the "primary" phase. These observations suggest that Ephs are likely recruited de novo for the guidance of topographical "second" optic nerve projection. Transformations during lamprey "dual visual development" may represent "recapitulation" from a protochordate-like ancestor to a gnathostome-like vertebrate ancestor. © 2015 Wiley Periodicals, Inc.

Rainbow Fourier Transform

NASA Technical Reports Server (NTRS)

Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.

2012-01-01

We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).

A Comparative Analysis for Selection of Appropriate Mother Wavelet for Detection of Stationary Disturbances

NASA Astrophysics Data System (ADS)

Kamble, Saurabh Prakash; Thawkar, Shashank; Gaikwad, Vinayak G.; Kothari, D. P.

2017-12-01

Detection of disturbances is the first step of mitigation. Power electronics plays a crucial role in modern power system which makes system operation efficient but it also bring stationary disturbances in the power system and added impurities to the supply. It happens because of the non-linear loads used in modern day power system which inject disturbances like harmonic disturbances, flickers, sag etc. in power grid. These impurities can damage equipments so it is necessary to mitigate these impurities present in the supply very quickly. So, digital signal processing techniques are incorporated for detection purpose. Signal processing techniques like fast Fourier transform, short-time Fourier transform, Wavelet transform etc. are widely used for the detection of disturbances. Among all, wavelet transform is widely used because of its better detection capabilities. But, which mother wavelet has to use for detection is still a mystery. Depending upon the periodicity, the disturbances are classified as stationary and non-stationary disturbances. This paper presents the importance of selection of mother wavelet for analyzing stationary disturbances using discrete wavelet transform. Signals with stationary disturbances of various frequencies are generated using MATLAB. The analysis of these signals is done using various mother wavelets like Daubechies and bi-orthogonal wavelets and the measured root mean square value of stationary disturbance is obtained. The measured value obtained by discrete wavelet transform is compared with the exact RMS value of the frequency component and the percentage differences are presented which helps to select optimum mother wavelet.

Linear Transformation of the Polarization Modes in Coiled Optical Spun-Fibers with Strong Unperturbed Linear Birefringence. I. Nonresonant Transformation

NASA Astrophysics Data System (ADS)

Malykin, G. B.; Pozdnyakova, V. I.

2018-03-01

A linear transformation of orthogonal polarization modes in coiled optical spun-fibers with strong unperturbed linear birefringence, which causes the emergence of the dependences of the integrated elliptical birefringence and the ellipticity and azimuth of the major axis of the ellipse, as well as the polarization state of radiation (PSR), on the length of optical fiber has been considered. Optical spun-fibers are subjected to a strong mechanical twisting, which is frozen into the structure of the optical fiber upon cooling, in the process of being drawn out from the workpiece. Since the values of the local polarization parameters of coiled spunwaveguides vary according to a rather complex law, the calculations were carried out by numerical modeling of the parameters of the Jones matrices. Since the rotation speed of the axes of the birefringence is constant on a relatively short segment of a coiled optical spun-fiber in the accompanying torsion (helical) coordinate system, the so-called "Ginzburg helical polarization modes" (GHPMs)—two mutually orthogonal ellipses with the opposite directions of traversal, the axis of which rotate relative to the fixed coordinate system uniformly and unidirectionally—are approximately the local normal polarization modes of such optical fiber. It has been shown that, despite the fact that the unperturbed linear birefringence of the spun-fibers significantly exceeds the linear birefringence, which is caused by the winding on a coil, the integral birefringence of an extended segment of such a fiber coincides in order of magnitude with the linear birefringence, which is caused by the winding on the coil, and the integral polarization modes tend asymptotically to circular ones. It has been also shown that the values of the circular birefringence of twisted single-mode fibers, which were calculated in a nonrotating and torsion helical coordinate systems, differ significantly. It has been shown that the polarization phenomena occur in the process of linear transformation of local polarization modes, which lead to small quasi-harmonic oscillations of the birefringence integral parameters of the optical spun-fibers, which depend on their length, and the period of these oscillations is approximately equal to half of the effective period of polarization beating.

Compositions of orthogonal lysyl-tRNA and aminoacyl-tRNA synthetase pairs and uses thereof

DOEpatents

Anderson, J Christopher [San Francisco, CA; Wu, Ning [Brookline, MA; Santoro, Stephen [Cambridge, MA; Schultz, Peter G [La Jolla, CA

2009-12-29

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal lysyl-tRNAs, orthogonal lysyl-aminoacyl-tRNA synthetases, and orthogonal pairs of lysyl-tRNAs/synthetases, which incorporate homoglutamines into proteins are provided in response to a four base codon. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with homoglutamines using these orthogonal pairs.

Compositions of orthogonal lysyl-tRNA and aminoacyl-tRNA synthetase pairs and uses thereof

DOEpatents

Anderson, J Christopher [San Francisco, CA; Wu, Ning [Brookline, MA; Santoro, Stephen [Cambridge, MA; Schultz, Peter G [La Jolla, CA

2011-10-04

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal lysyl-tRNAs, orthogonal lysyl-aminoacyl-tRNA synthetases, and orthogonal pairs of lysyl-tRNAs/synthetases, which incorporate homoglutamines into proteins are provided in response to a four base codon. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with homoglutamines using these orthogonal pairs.

Compositions of orthogonal lysyl-tRNA and aminoacyl-tRNA synthetase pairs and uses thereof

DOEpatents

Anderson, J Christopher [San Francisco, CA; Wu, Ning [Brookline, MA; Santoro, Stephen [Cambridge, MA; Schultz, Peter G [La Jolla, CA

2009-08-18

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal lysyl-tRNAs, orthogonal lysyl-aminoacyl-tRNA synthetases, and orthogonal pairs of lysyl-tRNAs/synthetases, which incorporate homoglutamines into proteins are provided in response to a four base codon. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with homoglutamines using these orthogonal pairs.

[A quality controllable algorithm for ECG compression based on wavelet transform and ROI coding].

PubMed

Zhao, An; Wu, Baoming

2006-12-01

This paper presents an ECG compression algorithm based on wavelet transform and region of interest (ROI) coding. The algorithm has realized near-lossless coding in ROI and quality controllable lossy coding outside of ROI. After mean removal of the original signal, multi-layer orthogonal discrete wavelet transform is performed. Simultaneously,feature extraction is performed on the original signal to find the position of ROI. The coefficients related to the ROI are important coefficients and kept. Otherwise, the energy loss of the transform domain is calculated according to the goal PRDBE (Percentage Root-mean-square Difference with Baseline Eliminated), and then the threshold of the coefficients outside of ROI is determined according to the loss of energy. The important coefficients, which include the coefficients of ROI and the coefficients that are larger than the threshold outside of ROI, are put into a linear quantifier. The map, which records the positions of the important coefficients in the original wavelet coefficients vector, is compressed with a run-length encoder. Huffman coding has been applied to improve the compression ratio. ECG signals taken from the MIT/BIH arrhythmia database are tested, and satisfactory results in terms of clinical information preserving, quality and compress ratio are obtained.

Mechanistic consideration of the photochemical transformation of domoic acid (algal toxin) in DOM-Rich brackish water.

PubMed

Jin, Hangxing; Lian, Lushi; Zhou, Huaxi; Yan, Shuwen; Song, Weihua

2018-06-14

Domoic acid (DA) is a neurotoxin generated by several diatom species in harmful algae blooms (HABs). We report the photo-induced transformation products (TPs) and degradation mechanisms of DA in dissolved organic matter (DOM)-rich freshwater and brackish water. High-resolution quadrupole time-of-flight mass spectrometry (QTOF-MS) and the multivariate statistical strategy orthogonal partial least-squares discriminant analysis (OPLS-DA) identified 36 and 23 potential TPs in DOM-rich freshwater and brackish water, respectively. The main reactive sites of DA are the conjugated double bond and proline ring. Isomerization is the predominant transformation pathway induced by excited-state triplet DOM ( 3 DOM ∗ ). The second-order rate constant of the isomerization reaction was measured as (3.8 ± 0.2) × 10 8  M -1  s -1 . The inverse correlation between the dissolved oxygen (DO) concentration and the rate of photo-induced DA isomerization was revealed. Furthermore, under halide-present conditions, halide radicals are mainly responsible for the differentiation of products by quenching hydroxyl radicals and generating unique organic peroxide products. Our results indicated that halide radicals could be important in the photochemical transformation of organic contaminants in high saline environments. Copyright © 2018 Elsevier Ltd. All rights reserved.

The Riesz transform and simultaneous representations of phase, energy and orientation in spatial vision.

PubMed

Langley, Keith; Anderson, Stephen J

2010-08-06

To represent the local orientation and energy of a 1-D image signal, many models of early visual processing employ bandpass quadrature filters, formed by combining the original signal with its Hilbert transform. However, representations capable of estimating an image signal's 2-D phase have been largely ignored. Here, we consider 2-D phase representations using a method based upon the Riesz transform. For spatial images there exist two Riesz transformed signals and one original signal from which orientation, phase and energy may be represented as a vector in 3-D signal space. We show that these image properties may be represented by a Singular Value Decomposition (SVD) of the higher-order derivatives of the original and the Riesz transformed signals. We further show that the expected responses of even and odd symmetric filters from the Riesz transform may be represented by a single signal autocorrelation function, which is beneficial in simplifying Bayesian computations for spatial orientation. Importantly, the Riesz transform allows one to weight linearly across orientation using both symmetric and asymmetric filters to account for some perceptual phase distortions observed in image signals - notably one's perception of edge structure within plaid patterns whose component gratings are either equal or unequal in contrast. Finally, exploiting the benefits that arise from the Riesz definition of local energy as a scalar quantity, we demonstrate the utility of Riesz signal representations in estimating the spatial orientation of second-order image signals. We conclude that the Riesz transform may be employed as a general tool for 2-D visual pattern recognition by its virtue of representing phase, orientation and energy as orthogonal signal quantities.

Genetic Transformation System for Woody Plant Tripterygium wilfordii and Its Application to Product Natural Celastrol.

PubMed

Zhao, Yujun; Zhang, Yifeng; Su, Ping; Yang, Jian; Huang, Luqi; Gao, Wei

2017-01-01

Tripterygium wilfordii is a perennial woody liana medicinal plant with several crucial biological activities. Although studies on tissue culture have previously been conducted, research on genetic transformation is much more challenging and therefore results in slower progress. In the present study, a highly efficient transformation system involving the particle bombardment of T. wilfordii with the reporter egfp gene using the PDS-1000/He system was established. A total of seven parameters affecting the genetic transformation were investigated using an L 18 (6 × 3 6 )-type orthogonal array. The result indicated that DNA delivery conditions of 3-cm target distance, 1100 psi helium pressure, 28 mmHg chamber vacuum pressure, three times number of bombardment, CaCl 2 as precipitation agent, 2 μg plasmid DNA concentration and 48 h post-bombardment incubation time were optimal for T. wilfordii cell suspensions transformation. The average transformation efficiency was 19.17%. Based on this transformation system, the overexpression of two T. wilfordii farnesyl pyrophosphate synthase genes ( TwFPSs ) was performed in cell suspensions. Integration of the TwFPSs in the genome was verified by PCR analysis and also by Southern blotting using hygromycin gene as a probe. Real-time quantitative PCR analysis showed that the expression of TwFPS1&2 was highly up regulated in transgenic cell suspensions compared with control cells. The detection of metabolites showed that TwFPS1 & 2 could highly increase the celastrol content (973.60 μg/g) in transgenic cells. These results indicated that this transformation system is an effective protocol for characterizing the function of genes in the terpenoid biosynthetic pathway.

Multivariate quantum memory as controllable delayed multi-port beamsplitter

NASA Astrophysics Data System (ADS)

Vetlugin, A. N.; Sokolov, I. V.

2016-03-01

The addressability of parallel spatially multimode quantum memory for light allows one to control independent collective spin waves within the same cold atomic ensemble. Generally speaking, there are transverse and longitudinal degrees of freedom of the memory that one can address by a proper choice of the pump (control) field spatial pattern. Here we concentrate on the mutual evolution and transformation of quantum states of the longitudinal modes of collective spin coherence in the cavity-based memory scheme. We assume that these modes are coherently controlled by the pump waves of the on-demand transverse profile, that is, by the superpositions of waves propagating in the directions close to orthogonal to the cavity axis. By the write-in, this allows one to couple a time sequence of the incoming quantized signals to a given set of superpositions of orthogonal spin waves. By the readout, one can retrieve quantum states of the collective spin waves that are controllable superpositions of the initial ones and are coupled on demand to the output signal sequence. In a general case, the memory is able to operate as a controllable delayed multi-port beamsplitter, capable of transformation of the delays, the durations and time shapes of signals in the sequence. We elaborate the theory of such light-matter interface for the spatially multivariate cavity-based off-resonant Raman-type quantum memory. Since, in order to speed up the manipulation of complex signals in multivariate memories, it might be of interest to store relatively short light pulses of a given time shape, we also address some issues of the cavity-based memory operation beyond the bad cavity limit.

Orthogonal projection approach and continuous wavelet transform-feed forward neural networks for simultaneous spectrophotometric determination of some heavy metals in diet samples.

PubMed

Abbasi Tarighat, Maryam

2016-02-01

Simultaneous spectrophotometric determination of a mixture of overlapped complexes of Fe(3+), Mn(2+), Cu(2+), and Zn(2+) ions with 2-(3-hydroxy-1-phenyl-but-2-enylideneamino) pyridine-3-ol(HPEP) by orthogonal projection approach-feed forward neural network (OPA-FFNN) and continuous wavelet transform-feed forward neural network (CWT-FFNN) is discussed. Ionic complexes HPEP were formulated with varying reagent concentration, pH and time of color formation for completion of complexation reactions. It was found that, at 5.0 × 10(-4) mol L(-1) of HPEP, pH 9.5 and 10 min after mixing the complexation reactions were completed. The spectral data were analyzed using partial response plots, and identified non-linearity modeled using FFNN. Reducing the number of OPA-FFNN and CWT-FFNN inputs were simplified using dissimilarity pure spectra of OPA and selected wavelet coefficients. Once the pure dissimilarity plots ad optimal wavelet coefficients are selected, different ANN models were employed for the calculation of the final calibration models. The performance of these two approaches were tested with regard to root mean square errors of prediction (RMSE %) values, using synthetic solutions. Under the working conditions, the proposed methods were successfully applied to the simultaneous determination of metal ions in different vegetable and foodstuff samples. The results show that, OPA-FFNN and CWT-FFNN were effective in simultaneously determining Fe(3+), Mn(2+), Cu(2+), and Zn(2+) concentration. Also, concentrations of metal ions in the samples were determined by flame atomic absorption spectrometry (FAAS). The amounts of metal ions obtained by the proposed methods were in good agreement with those obtained by FAAS. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

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.

Methods and compositions for the production of orthogonal tRNA-aminoacyl tRNA synthetase pairs

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

Schultz, Peter G.; Wang, Lei; Anderson, John Christopher

2015-10-20

This invention provides compositions and methods for generating components of protein biosynthetic machinery including orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases. Methods for identifying orthogonal pairs are also provided. These components can be used to incorporate unnatural amino acids into proteins in vivo.

Methods and composition for the production of orthogonal tRNA-aminoacyltRNA synthetase pairs

DOEpatents

Schultz, Peter G.; Wang, Lei; Anderson, John Christopher; Chin, Jason; Liu, David R.; Magliery, Thomas J.; Meggers, Eric L.; Mehl, Ryan Aaron; Pastrnak, Miro; Santoro, Stephen William; Zhang, Zhiwen

2010-05-11

This invention provides compositions and methods for generating components of protein biosynthetic machinery including orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases. Methods for identifying orthogonal pairs are also provided. These components can be used to incorporate unnatural amino acids into proteins in vivo.

Methods and composition for the production of orthogonal tRNA-aminoacyltRNA synthetase pairs

DOEpatents

Schultz, Peter G [La Jolla, CA; Wang, Lei [San Diego, CA; Anderson, John Christopher [San Diego, CA; Chin, Jason [Cambridge, GB; Liu, David R [Lexington, MA; Magliery, Thomas J [North Haven, CT; Meggers, Eric L [Philadelphia, PA; Mehl, Ryan Aaron [Lancaster, PA; Pastrnak, Miro [San Diego, CA; Santoro, Steven William [Cambridge, MA; Zhang, Zhiwen [San Diego, CA

2012-05-22

This invention provides compositions and methods for generating components of protein biosynthetic machinery including orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases. Methods for identifying orthogonal pairs are also provided. These components can be used to incorporate unnatural amino acids into proteins in vivo.

Methods and compositions for the production of orthogonal tRNA-aminoacyl tRNA synthetase pairs

DOEpatents

Schultz, Peter; Wang, Lei; Anderson, John Christopher; Chin, Jason; Liu, David R.; Magliery, Thomas J.; Meggers, Eric L.; Mehl, Ryan Aaron; Pastrnak, Miro; Santoro, Stephen William; Zhang, Zhiwen

2006-08-01

This invention provides compositions and methods for generating components of protein biosynthetic machinery including orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases. Methods for identifying orthogonal pairs are also provided. These components can be used to incorporate unnatural amino acids into proteins in vivo.

Methods and composition for the production of orthogonal tRNA-aminoacyl tRNA synthetase pairs

DOEpatents

Schultz, Peter G [La Jolla, CA; Wang, Lei [San Diego, CA; Anderson, John Christopher [San Diego, CA; Chin, Jason W [San Diego, CA; Liu, David R [Lexington, MA; Magliery, Thomas J [North Haven, CT; Meggers, Eric L [Philadelphia, PA; Mehl, Ryan Aaron [San Diego, CA; Pastrnak, Miro [San Diego, CA; Santoro, Stephen William [San Diego, CA; Zhang, Zhiwen [San Diego, CA

2012-05-08

This invention provides compositions and methods for generating components of protein biosynthetic machinery including orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases. Methods for identifying orthogonal pairs are also provided. These components can be used to incorporate unnatural amino acids into proteins in vivo.

Methods and compositions for the production of orthogonal tRNA-aminoacyl-tRNA synthetase pairs

DOEpatents

Schultz, Peter G [La Jolla, CA; Wang, Lei [San Diego, CA; Anderson, John Christopher [San Diego, CA; Chin, Jason W [San Diego, CA; Liu, David R [Lexington, MA; Magliery, Thomas J [North Haven, CT; Meggers, Eric L [Philadelphia, PA; Mehl, Ryan Aaron [San Diego, CA; Pastrnak, Miro [San Diego, CA; Santoro, Stephen William [San Diego, CA; Zhang, Zhiwen [San Diego, CA

2011-09-06

This invention provides compositions and methods for generating components of protein biosynthetic machinery including orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases. Methods for identifying orthogonal pairs are also provided. These components can be used to incorporate unnatural amino acids into proteins in vivo.

Methods and composition for the production of orthogonal tRNA-aminoacyltRNA synthetase pairs

DOEpatents

Schultz, Peter G [La Jolla, CA; Wang, Lei [San Diego, CA; Anderson, John Christopher [San Diego, CA; Chin, Jason [Cambridge, GB; Liu, David R [Lexington, MA; Magliery, Thomas J [North Haven, CT; Meggers, Eric L [Philadelphia, PA; Mehl, Ryan Aaron [Lancaster, PA; Pastrnak, Miro [San Diego, CA; Santoro, Steven William [Cambridge, MA; Zhang, Zhiwen [San Diego, CA

2008-04-08

This invention provides compositions and methods for generating components of protein biosynthetic machinery including orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases. Methods for identifying orthogonal pairs are also provided. These components can be used to incorporate unnatural amino acids into proteins in vivo.

Bi-orthogonal Symbol Mapping and Detection in Optical CDMA Communication System

NASA Astrophysics Data System (ADS)

Liu, Maw-Yang

2017-12-01

In this paper, the bi-orthogonal symbol mapping and detection scheme is investigated in time-spreading wavelength-hopping optical CDMA communication system. The carrier-hopping prime code is exploited as signature sequence, whose put-of-phase autocorrelation is zero. Based on the orthogonality of carrier-hopping prime code, the equal weight orthogonal signaling scheme can be constructed, and the proposed scheme using bi-orthogonal symbol mapping and detection can be developed. The transmitted binary data bits are mapped into corresponding bi-orthogonal symbols, where the orthogonal matrix code and its complement are utilized. In the receiver, the received bi-orthogonal data symbol is fed into the maximum likelihood decoder for detection. Under such symbol mapping and detection, the proposed scheme can greatly enlarge the Euclidean distance; hence, the system performance can be drastically improved.

Site-specific incorporation of redox active amino acids into proteins

DOEpatents

Alfonta, Lital [San Diego, CA; Schultz, Peter G [La Jolla, CA; Zhang, Zhiwen [Austin, TX

2011-08-30

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases, which incorporate redox active amino acids into proteins are provided. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with redox active amino acids using these orthogonal pairs.

Site-specific incorporation of redox active amino acids into proteins

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

Alfonta, Lital; Schultz, Peter G.; Zhang, Zhiwen

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases, which incorporate redox active amino acids into proteins are provided. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with redox active amino acids using these orthogonal pairs.

Site specific incorporation of keto amino acids into proteins

DOEpatents

Schultz, Peter G [La Jolla, CA; Wang, Lei [San Diego, CA

2011-03-22

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases, which incorporate keto amino acids into proteins are provided. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with keto amino acids using these orthogonal pairs.

Site-specific incorporation of redox active amino acids into proteins

DOEpatents

Alfonta, Lital [San Diego, CA; Schultz, Peter G [La Jolla, CA; Zhang, Zhiwen [San Diego, CA

2012-02-14

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases, which incorporate redox active amino acids into proteins are provided. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with redox active amino acids using these orthogonal pairs.

Site specific incorporation of keto amino acids into proteins

DOEpatents

Schultz, Peter G [La Jolla, CA; Wang, Lei [San Diego, CA

2008-10-07

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases, which incorporate keto amino acids into proteins are provided. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with keto amino acids using these orthogonal pairs.

Site-specific incorporation of redox active amino acids into proteins

DOEpatents

Alfonta; Lital , Schultz; Peter G. , Zhang; Zhiwen

2010-10-12

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases, which incorporate redox active amino acids into proteins are provided. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with redox active amino acids using these orthogonal pairs.

Site specific incorporation of keto amino acids into proteins

DOEpatents

Schultz, Peter G [La Jolla, CA; Wang, Lei [San Diego, CA

2011-12-06

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases, which incorporate keto amino acids into proteins are provided. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with keto amino acids using these orthogonal pairs.

Site-specific incorporation of redox active amino acids into proteins

DOEpatents

Alfonta, Lital [San Diego, CA; Schultz, Peter G [La Jolla, CA; Zhang, Zhiwen [San Diego, CA

2009-02-24

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases, which incorporate redox active amino acids into proteins are provided. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with redox active amino acids using these orthogonal pairs.

Site specific incorporation of keto amino acids into proteins

DOEpatents

Schultz, Peter G [La Jolla, CA; Wang, Lei [San Diego, CA

2012-02-14

Compositions and methods of producing components of protein biosynthetic machinery that include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, and orthogonal pairs of tRNAs/synthetases, which incorporate keto amino acids into proteins are provided. Methods for identifying these orthogonal pairs are also provided along with methods of producing proteins with keto amino acids using these orthogonal pairs.

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.

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.

Multicarrier orthogonal spread-spectrum (MOSS) data communications

DOEpatents

Smith, Stephen F [London, TN; Dress, William B [Camas, WA

2008-01-01

Systems and methods are described for multicarrier orthogonal spread-spectrum (MOSS) data communication. A method includes individually spread-spectrum modulating at least two of a set of orthogonal frequency division multiplexed carriers, wherein the resulting individually spread-spectrum modulated at least two of a set of orthogonal frequency division multiplexed carriers are substantially mutually orthogonal with respect to both frequency division multiplexing and spread-spectrum modulation.

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.

An orthogonal wavelet division multiple-access processor architecture for LTE-advanced wireless/radio-over-fiber systems over heterogeneous networks

NASA Astrophysics Data System (ADS)

Mahapatra, Chinmaya; Leung, Victor CM; Stouraitis, Thanos

2014-12-01

The increase in internet traffic, number of users, and availability of mobile devices poses a challenge to wireless technologies. In long-term evolution (LTE) advanced system, heterogeneous networks (HetNet) using centralized coordinated multipoint (CoMP) transmitting radio over optical fibers (LTE A-ROF) have provided a feasible way of satisfying user demands. In this paper, an orthogonal wavelet division multiple-access (OWDMA) processor architecture is proposed, which is shown to be better suited to LTE advanced systems as compared to orthogonal frequency division multiple access (OFDMA) as in LTE systems 3GPP rel.8 (3GPP, http://www.3gpp.org/DynaReport/36300.htm). ROF systems are a viable alternative to satisfy large data demands; hence, the performance in ROF systems is also evaluated. To validate the architecture, the circuit is designed and synthesized on a Xilinx vertex-6 field-programmable gate array (FPGA). The synthesis results show that the circuit performs with a clock period as short as 7.036 ns (i.e., a maximum clock frequency of 142.13 MHz) for transform size of 512. A pipelined version of the architecture reduces the power consumption by approximately 89%. We compare our architecture with similar available architectures for resource utilization and timing and provide performance comparison with OFDMA systems for various quality metrics of communication systems. The OWDMA architecture is found to perform better than OFDMA for bit error rate (BER) performance versus signal-to-noise ratio (SNR) in wireless channel as well as ROF media. It also gives higher throughput and mitigates the bad effect of peak-to-average-power ratio (PAPR).

Synthesis of orthogonally protected bacterial, rare-sugar and D-glycosamine building blocks.

PubMed

Emmadi, Madhu; Kulkarni, Suvarn S

2013-10-01

Bacterial glycoconjugates comprise atypical deoxy amino sugars that are not present on the human cell surface, making them good targets for drug discovery and carbohydrate-based vaccine development. Unfortunately, they cannot be isolated with sufficient purity in acceptable amounts, and therefore chemical synthesis is a crucial step toward the development of these products. Here we describe a detailed protocol for the synthesis of orthogonally protected bacterial deoxy amino hexopyranoside (2,4-diacetamido-2,4,6-trideoxyhexose (DATDH), D-bacillosamine, D-fucosamine, and 2-acetamido-4-amino-2,4,6-trideoxy-D-galactose (AAT)), D-glucosamine and D-galactosamine building blocks starting from β-D-thiophenylmannoside. Readily available β-D-thiophenylmannoside was first converted into the corresponding 2,4-diols via deoxygenation or silylation at C6, followed by O3 acylation. The 2,4-diols were converted into 2,4-bis-trifluoromethanesulfonates, which underwent highly regioselective, one-pot, double-serial and double-parallel displacements by azide, phthalimide, acetate and nitrite ions as nucleophiles. Thus, D-rhamnosyl- and D-mannosyl 2,4-diols can be efficiently transformed into various rare sugars and D-galactosamine, respectively, as orthogonally protected thioglycoside building blocks on a gram scale in 1-2 d, in 54-85% overall yields, after a single chromatographic purification. This would otherwise take 1-2 weeks. D-Glucosamine building blocks can be prepared from β-D-thiophenylmannoside in four steps via C2 displacement of triflates by azide in 2 d and in 66-70% overall yields. These procedures have been applied to the synthesis of L-serine-linked trisaccharide of Neisseria meningitidis and a rare disaccharide fragment of the zwitterionic polysaccharide (ZPS) A1 (ZPS A1) of Bacteroides fragilis.

Vortex Airy beams directly generated via liquid crystal q-Airy-plates

NASA Astrophysics Data System (ADS)

Wei, Bing-Yan; Liu, Sheng; Chen, Peng; Qi, Shu-Xia; Zhang, Yi; Hu, Wei; Lu, Yan-Qing; Zhao, Jian-Lin

2018-03-01

Liquid crystal q-Airy-plates with director distributions integrated by q-plates and polarization Airy masks are proposed and demonstrated via the photoalignment technique. Single/dual vortex Airy beams of opposite topological charges and orthogonal circular polarizations are directly generated with polarization-controllable characteristic. The singular phase of the vortex part is verified by both astigmatic transformation and digital holography. The trajectory of vortex Airy beams is investigated, manifesting separate propagation dynamics of optical vortices and Airy beams. Meanwhile, Airy beams still keep their intrinsic transverse acceleration, self-healing, and nondiffraction features. This work provides a versatile candidate for generating high-quality vortex Airy beams.

Broadband spectral shaping in regenerative amplifier based on modified polarization-encoded chirped pulse amplification

NASA Astrophysics Data System (ADS)

Wang, Xinliang; Lu, Xiaoming; Liu, Yanqi; Xu, Yi; Wang, Cheng; Li, Shuai; Yu, Linpeng; Liu, Xingyan; Liu, Keyang; Xu, Rongjie; Leng, Yuxin

2018-06-01

We present an intra-cavity spectral shaping method to suppress the spectral narrowing in a Ti:sapphire (Ti:Sa) regenerative amplifier. The spectral shaping is realized by manipulating the stored energies of two Ti:Sa crystals with orthogonal c-axes, changing the length of a quartz plate, and rotating a broadband achromatic half-wave plate. Using this method, in our proof-of-concept experiment, an 84-nm-(FWHM)-broadband amplified pulse with an energy gain larger than 106 is obtained, which supports a 17.8 fs Fourier-transform-limited pulse duration. The pulse is compressed to 18.9 fs.

Double-pulse digital speckle pattern interferometry for vibration analysis

NASA Astrophysics Data System (ADS)

Zhang, Dazhi; Xue, Jingfeng; Chen, Lu; Wen, Juying; Wang, Jingjing

2014-12-01

The double-pulse Digital Speckle Pattern Interferometry (DSPI) in the laboratory is established. Two good performances have been achieved at the same time, which is uniform distribution of laser beam energy by space filter and recording two successive pictures by a CCD camera successfully. Then two-dimensional discrete orthogonal wavelet transform method is used for the process of filtering method. By using the DSPI, speckle pattern of a vibrated object is obtained with interval of (2~800)μs, and 3D plot of the transient vibration is achieved. Moreover, good agreements of the mode shapes and displacement are obtained by comparing with Laser Doppler Vibrometer (LDV) .

Real-Time Frequency Response Estimation Using Joined-Wing SensorCraft Aeroelastic Wind-Tunnel Data

NASA Technical Reports Server (NTRS)

Grauer, Jared A; Heeg, Jennifer; Morelli, Eugene A

2012-01-01

A new method is presented for estimating frequency responses and their uncertainties from wind-tunnel data in real time. The method uses orthogonal phase-optimized multi- sine excitation inputs and a recursive Fourier transform with a least-squares estimator. The method was first demonstrated with an F-16 nonlinear flight simulation and results showed that accurate short period frequency responses were obtained within 10 seconds. The method was then applied to wind-tunnel data from a previous aeroelastic test of the Joined- Wing SensorCraft. Frequency responses describing bending strains from simultaneous control surface excitations were estimated in a time-efficient manner.

Design of two blackbody sources for millimeter and sub-millimeter wave Fourier transform spectrometry

NASA Astrophysics Data System (ADS)

Colin, Angel

2014-03-01

This paper describes an experimental setup for the spectral calibration of bolometric detectors used in radioastronomy. The system is composed of a Martin-Puplett interferometer with two identical artificial blackbody sources operating in the vacuum mode at 77 K and 300 K simultaneously. One source is integrated into a liquid nitrogen cryostat, and the other one into a vacuum chamber at room temperature. The sources were designed with a combination of conical with cylindrical geometries thus forming an orthogonal configuration to match the internal optics of the interfermometer. With a simple mathematical model we estimated emissivities of ε 0.995 for each source.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

Discrete wavelet transform: a tool in smoothing kinematic data.

PubMed

Ismail, A R; Asfour, S S

1999-03-01

Motion analysis systems typically introduce noise to the displacement data recorded. Butterworth digital filters have been used to smooth the displacement data in order to obtain smoothed velocities and accelerations. However, this technique does not yield satisfactory results, especially when dealing with complex kinematic motions that occupy the low- and high-frequency bands. The use of the discrete wavelet transform, as an alternative to digital filters, is presented in this paper. The transform passes the original signal through two complementary low- and high-pass FIR filters and decomposes the signal into an approximation function and a detail function. Further decomposition of the signal results in transforming the signal into a hierarchy set of orthogonal approximation and detail functions. A reverse process is employed to perfectly reconstruct the signal (inverse transform) back from its approximation and detail functions. The discrete wavelet transform was applied to the displacement data recorded by Pezzack et al., 1977. The smoothed displacement data were twice differentiated and compared to Pezzack et al.'s acceleration data in order to choose the most appropriate filter coefficients and decomposition level on the basis of maximizing the percentage of retained energy (PRE) and minimizing the root mean square error (RMSE). Daubechies wavelet of the fourth order (Db4) at the second decomposition level showed better results than both the biorthogonal and Coiflet wavelets (PRE = 97.5%, RMSE = 4.7 rad s-2). The Db4 wavelet was then used to compress complex displacement data obtained from a noisy mathematically generated function. Results clearly indicate superiority of this new smoothing approach over traditional filters.

Segmentation-based wavelet transform for still-image compression

NASA Astrophysics Data System (ADS)

Mozelle, Gerard; Seghier, Abdellatif; Preteux, Francoise J.

1996-10-01

In order to address simultaneously the two functionalities, content-based scalability required by MPEG-4, we introduce a segmentation-based wavelet transform (SBWT). SBWT takes into account both the mathematical properties of multiresolution analysis and the flexibility of region-based approaches for image compression. The associated methodology has two stages: 1) image segmentation into convex and polygonal regions; 2) 2D-wavelet transform of the signal corresponding to each region. In this paper, we have mathematically studied a method for constructing a multiresolution analysis (VjOmega)j (epsilon) N adapted to a polygonal region which provides an adaptive region-based filtering. The explicit construction of scaling functions, pre-wavelets and orthonormal wavelets bases defined on a polygon is carried out by using scaling functions is established by using the theory of Toeplitz operators. The corresponding expression can be interpreted as a location property which allow defining interior and boundary scaling functions. Concerning orthonormal wavelets and pre-wavelets, a similar expansion is obtained by taking advantage of the properties of the orthogonal projector P(V(j(Omega )) perpendicular from the space Vj(Omega ) + 1 onto the space (Vj(Omega )) perpendicular. Finally the mathematical results provide a simple and fast algorithm adapted to polygonal regions.

Elliptic surface grid generation on minimal and parmetrized surfaces

NASA Technical Reports Server (NTRS)

Spekreijse, S. P.; Nijhuis, G. H.; Boerstoel, J. W.

1995-01-01

An elliptic grid generation method is presented which generates excellent boundary conforming grids in domains in 2D physical space. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the familiar Poisson grid generation system with control functions specified by the algebraic transformation. New expressions are given for the control functions. Grid orthogonality at the boundary is achieved by modification of the algebraic transformation. It is shown that grid generation on a minimal surface in 3D physical space is in fact equivalent to grid generation in a domain in 2D physical space. A second elliptic grid generation method is presented which generates excellent boundary conforming grids on smooth surfaces. It is assumed that the surfaces are parametrized and that the grid only depends on the shape of the surface and is independent of the parametrization. Concerning surface modeling, it is shown that bicubic Hermite interpolation is an excellent method to generate a smooth surface which is passing through a given discrete set of control points. In contrast to bicubic spline interpolation, there is extra freedom to model the tangent and twist vectors such that spurious oscillations are prevented.

Pyramid image codes

NASA Technical Reports Server (NTRS)

Watson, Andrew B.

1990-01-01

All vision systems, both human and machine, transform the spatial image into a coded representation. Particular codes may be optimized for efficiency or to extract useful image features. Researchers explored image codes based on primary visual cortex in man and other primates. Understanding these codes will advance the art in image coding, autonomous vision, and computational human factors. In cortex, imagery is coded by features that vary in size, orientation, and position. Researchers have devised a mathematical model of this transformation, called the Hexagonal oriented Orthogonal quadrature Pyramid (HOP). In a pyramid code, features are segregated by size into layers, with fewer features in the layers devoted to large features. Pyramid schemes provide scale invariance, and are useful for coarse-to-fine searching and for progressive transmission of images. The HOP Pyramid is novel in three respects: (1) it uses a hexagonal pixel lattice, (2) it uses oriented features, and (3) it accurately models most of the prominent aspects of primary visual cortex. The transform uses seven basic features (kernels), which may be regarded as three oriented edges, three oriented bars, and one non-oriented blob. Application of these kernels to non-overlapping seven-pixel neighborhoods yields six oriented, high-pass pyramid layers, and one low-pass (blob) layer.

[Glossary of terms used by radiologists in image processing].

PubMed

Rolland, Y; Collorec, R; Bruno, A; Ramée, A; Morcet, N; Haigron, P

1995-01-01

We give the definition of 166 words used in image processing. Adaptivity, aliazing, analog-digital converter, analysis, approximation, arc, artifact, artificial intelligence, attribute, autocorrelation, bandwidth, boundary, brightness, calibration, class, classification, classify, centre, cluster, coding, color, compression, contrast, connectivity, convolution, correlation, data base, decision, decomposition, deconvolution, deduction, descriptor, detection, digitization, dilation, discontinuity, discretization, discrimination, disparity, display, distance, distorsion, distribution dynamic, edge, energy, enhancement, entropy, erosion, estimation, event, extrapolation, feature, file, filter, filter floaters, fitting, Fourier transform, frequency, fusion, fuzzy, Gaussian, gradient, graph, gray level, group, growing, histogram, Hough transform, Houndsfield, image, impulse response, inertia, intensity, interpolation, interpretation, invariance, isotropy, iterative, JPEG, knowledge base, label, laplacian, learning, least squares, likelihood, matching, Markov field, mask, matching, mathematical morphology, merge (to), MIP, median, minimization, model, moiré, moment, MPEG, neural network, neuron, node, noise, norm, normal, operator, optical system, optimization, orthogonal, parametric, pattern recognition, periodicity, photometry, pixel, polygon, polynomial, prediction, pulsation, pyramidal, quantization, raster, reconstruction, recursive, region, rendering, representation space, resolution, restoration, robustness, ROC, thinning, transform, sampling, saturation, scene analysis, segmentation, separable function, sequential, smoothing, spline, split (to), shape, threshold, tree, signal, speckle, spectrum, spline, stationarity, statistical, stochastic, structuring element, support, syntaxic, synthesis, texture, truncation, variance, vision, voxel, windowing.

Equivalences of the multi-indexed orthogonal polynomials

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

Odake, Satoru

2014-01-15

Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.

Wideband Spectroscopy: The Design and Implementation of a 3 GHz Bandwidth, 8192 Channel, Polyphase Digital Spectrometer

NASA Technical Reports Server (NTRS)

Monroe, Ryan M.

2011-01-01

A family of state-of-the-art digital Fourier transform spectrometers has been developed, with a combination of high bandwidth and fine resolution unavailable elsewhere. Analog signals consisting of radiation emitted by constituents in planetary atmospheres or galactic sources are downconverted and subsequently digitized by a pair of interleaved Analog-to-Digital Converters, (ADC). This 6 Gsps (giga-sample per second) digital representation of the analog signal is then processed through an FPGA-based streaming Fast Fourier Transform (FFT), the key development described below. Digital spectrometers have many advantages over previously used analog spectrometers, especially in terms of accuracy and resolution, both of which are particularly important for the type of scientific questions to be addressed with next-generation radiometers. the implementation, results and underlying math for this spectrometer, as well as, potential for future extension to even higher bandwidth, resolution and channel orthogonality, needed to support proposed future advanced atmospheric science and radioastronomy, are discussed.

Wideband Spectroscopy: The Design and Implementation of a 3 GHz, 2048 Channel Digital Spectrometer

NASA Technical Reports Server (NTRS)

Monroe, Ryan M.

2011-01-01

A state-of-the-art digital Fourier Transform spectrometer has been developed, with a combination of high bandwidth and fine resolution unavailable elsewhere. Analog signals consisting of radiation emitted by constituents in planetary atmospheres or galactic sources are downconverted and subsequently digitized by a pair of interleaved Analog-to-Digital Converters (ADC). This 6 Gsps (giga sample per second) digital representation of the analog signal is then processed through an FPGA-based streaming Fast Fourier Transform (FFT), the key development described below. Digital spectrometers have many advantages over previously used analog spectrometers, especially in terms of accuracy and resolution, both of which are particularly important for the type of scientific questions to be addressed with next-generation radiometers. The implementation, results and underlying math for this spectrometer, as well as potential for future extension to even higher bandwidth, resolution and channel orthogonality, needed to support proposed future advanced atmospheric science and radioastronomy, are discussed.

A novel joint timing/frequency synchronization scheme based on Radon-Wigner transform of LFM signals in CO-OFDM systems

NASA Astrophysics Data System (ADS)

Liu, Jianfei; Wei, Ying; Zeng, Xiangye; Lu, Jia; Zhang, Shuangxi; Wang, Mengjun

2018-03-01

A joint timing and frequency synchronization method has been proposed for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system in this paper. The timing offset (TO), integer frequency offset (FO) and the fractional FO can be realized by only one training symbol, which consists of two linear frequency modulation (LFM) signals with opposite chirp rates. By detecting the peak of LFM signals after Radon-Wigner transform (RWT), the TO and the integer FO can be estimated at the same time, moreover, the fractional FO can be acquired correspondingly through the self-correlation characteristic of the same training symbol. Simulation results show that the proposed method can give a more accurate TO estimation than the existing methods, especially at poor OSNR conditions; for the FO estimation, both the fractional and the integer FO can be estimated through the proposed training symbol with no extra overhead, a more accurate estimation and a large FO estimation range of [ - 5 GHz, 5GHz] can be acquired.

A group filter algorithm for sea mine detection

NASA Astrophysics Data System (ADS)

Cobb, J. Tory; An, Myoung; Tolimieri, Richard

2005-06-01

Automatic detection of sea mines in coastal regions is a difficult task due to the highly variable sea bottom conditions present in the underwater environment. Detection systems must be able to discriminate objects which vary in size, shape, and orientation from naturally occurring and man-made clutter. Additionally, these automated systems must be computationally efficient to be incorporated into unmanned underwater vehicle (UUV) sensor systems characterized by high sensor data rates and limited processing abilities. Using noncommutative group harmonic analysis, a fast, robust sea mine detection system is created. A family of unitary image transforms associated to noncommutative groups is generated and applied to side scan sonar image files supplied by Naval Surface Warfare Center Panama City (NSWC PC). These transforms project key image features, geometrically defined structures with orientations, and localized spectral information into distinct orthogonal components or feature subspaces of the image. The performance of the detection system is compared against the performance of an independent detection system in terms of probability of detection (Pd) and probability of false alarm (Pfa).

Motion in the north Iceland volcanic rift zone accommodated by bookshelf faulting

NASA Astrophysics Data System (ADS)

Green, Robert G.; White, Robert S.; Greenfield, Tim

2014-01-01

Along mid-ocean ridges the extending crust is segmented on length scales of 10-1,000km. Where rift segments are offset from one another, motion between segments is accommodated by transform faults that are oriented orthogonally to the main rift axis. Where segments overlap, non-transform offsets with a variety of geometries accommodate shear motions. Here we use micro-seismic data to analyse the geometries of faults at two overlapping rift segments exposed on land in north Iceland. Between the rift segments, we identify a series of faults that are aligned sub-parallel to the orientation of the main rift. These faults slip through left-lateral strike-slip motion. Yet, movement between the overlapping rift segments is through right-lateral motion. Together, these motions induce a clockwise rotation of the faults and intervening crustal blocks in a motion that is consistent with a bookshelf-faulting mechanism, named after its resemblance to a tilting row of books on a shelf. The faults probably reactivated existing crustal weaknesses, such as dyke intrusions, that were originally oriented parallel to the main rift and have since rotated about 15° clockwise. Reactivation of pre-existing, rift-parallel weaknesses contrasts with typical mid-ocean ridge transform faults and is an important illustration of a non-transform offset accommodating shear motion between overlapping rift segments.

Orthogonal Multi-Carrier DS-CDMA with Frequency-Domain Equalization

NASA Astrophysics Data System (ADS)

Tanaka, Ken; Tomeba, Hiromichi; Adachi, Fumiyuki

Orthogonal multi-carrier direct sequence code division multiple access (orthogonal MC DS-CDMA) is a combination of orthogonal frequency division multiplexing (OFDM) and time-domain spreading, while multi-carrier code division multiple access (MC-CDMA) is a combination of OFDM and frequency-domain spreading. In MC-CDMA, a good bit error rate (BER) performance can be achieved by using frequency-domain equalization (FDE), since the frequency diversity gain is obtained. On the other hand, the conventional orthogonal MC DS-CDMA fails to achieve any frequency diversity gain. In this paper, we propose a new orthogonal MC DS-CDMA that can obtain the frequency diversity gain by applying FDE. The conditional BER analysis is presented. The theoretical average BER performance in a frequency-selective Rayleigh fading channel is evaluated by the Monte-Carlo numerical computation method using the derived conditional BER and is confirmed by computer simulation of the orthogonal MC DS-CDMA signal transmission.

[A plane-based hand-eye calibration method for surgical robots].

PubMed

Zeng, Bowei; Meng, Fanle; Ding, Hui; Liu, Wenbo; Wu, Di; Wang, Guangzhi

2017-04-01

In order to calibrate the hand-eye transformation of the surgical robot and laser range finder (LRF), a calibration algorithm based on a planar template was designed. A mathematical model of the planar template had been given and the approach to address the equations had been derived. Aiming at the problems of the measurement error in a practical system, we proposed a new algorithm for selecting coplanar data. This algorithm can effectively eliminate considerable measurement error data to improve the calibration accuracy. Furthermore, three orthogonal planes were used to improve the calibration accuracy, in which a nonlinear optimization for hand-eye calibration was used. With the purpose of verifying the calibration precision, we used the LRF to measure some fixed points in different directions and a cuboid's surfaces. Experimental results indicated that the precision of a single planar template method was (1.37±0.24) mm, and that of the three orthogonal planes method was (0.37±0.05) mm. Moreover, the mean FRE of three-dimensional (3D) points was 0.24 mm and mean TRE was 0.26 mm. The maximum angle measurement error was 0.4 degree. Experimental results show that the method presented in this paper is effective with high accuracy and can meet the requirements of surgical robot precise location.

Adaptive pixel-to-pixel projection intensity adjustment for measuring a shiny surface using orthogonal color fringe pattern projection

NASA Astrophysics Data System (ADS)

Chen, Chao; Gao, Nan; Wang, Xiangjun; Zhang, Zonghua

2018-05-01

Three-dimensional (3D) shape measurement based on fringe pattern projection techniques has been commonly used in various fields. One of the remaining challenges in fringe pattern projection is that camera sensor saturation may occur if there is a large range of reflectivity variation across the surface that causes measurement errors. To overcome this problem, a novel fringe pattern projection method is proposed to avoid image saturation and maintain high-intensity modulation for measuring shiny surfaces by adaptively adjusting the pixel-to-pixel projection intensity according to the surface reflectivity. First, three sets of orthogonal color fringe patterns and a sequence of uniform gray-level patterns with different gray levels are projected onto a measured surface by a projector. The patterns are deformed with respect to the object surface and captured by a camera from a different viewpoint. Subsequently, the optimal projection intensity at each pixel is determined by fusing different gray levels and transforming the camera pixel coordinate system into the projector pixel coordinate system. Finally, the adapted fringe patterns are created and used for 3D shape measurement. Experimental results on a flat checkerboard and shiny objects demonstrate that the proposed method can measure shiny surfaces with high accuracy.

Stochastic spectral projection of electrochemical thermal model for lithium-ion cell state estimation

NASA Astrophysics Data System (ADS)

Tagade, Piyush; Hariharan, Krishnan S.; Kolake, Subramanya Mayya; Song, Taewon; Oh, Dukjin

2017-03-01

A novel approach for integrating a pseudo-two dimensional electrochemical thermal (P2D-ECT) model and data assimilation algorithm is presented for lithium-ion cell state estimation. This approach refrains from making any simplifications in the P2D-ECT model while making it amenable for online state estimation. Though deterministic, uncertainty in the initial states induces stochasticity in the P2D-ECT model. This stochasticity is resolved by spectrally projecting the stochastic P2D-ECT model on a set of orthogonal multivariate Hermite polynomials. Volume averaging in the stochastic dimensions is proposed for efficient numerical solution of the resultant model. A state estimation framework is developed using a transformation of the orthogonal basis to assimilate the measurables with this system of equations. Effectiveness of the proposed method is first demonstrated by assimilating the cell voltage and temperature data generated using a synthetic test bed. This validated method is used with the experimentally observed cell voltage and temperature data for state estimation at different operating conditions and drive cycle protocols. The results show increased prediction accuracy when the data is assimilated every 30s. High accuracy of the estimated states is exploited to infer temperature dependent behavior of the lithium-ion cell.

Two-dimensional correlation spectroscopy — Biannual survey 2007-2009

NASA Astrophysics Data System (ADS)

Noda, Isao

2010-06-01

The publication activities in the field of 2D correlation spectroscopy are surveyed with the emphasis on papers published during the last two years. Pertinent review articles and conference proceedings are discussed first, followed by the examination of noteworthy developments in the theory and applications of 2D correlation spectroscopy. Specific topics of interest include Pareto scaling, analysis of randomly sampled spectra, 2D analysis of data obtained under multiple perturbations, evolution of 2D spectra along additional variables, comparison and quantitative analysis of multiple 2D spectra, orthogonal sample design to eliminate interfering cross peaks, quadrature orthogonal signal correction and other data transformation techniques, data pretreatment methods, moving window analysis, extension of kernel and global phase angle analysis, covariance and correlation coefficient mapping, variant forms of sample-sample correlation, and different display methods. Various static and dynamic perturbation methods used in 2D correlation spectroscopy, e.g., temperature, composition, chemical reactions, H/D exchange, physical phenomena like sorption, diffusion and phase transitions, optical and biological processes, are reviewed. Analytical probes used in 2D correlation spectroscopy include IR, Raman, NIR, NMR, X-ray, mass spectrometry, chromatography, and others. Application areas of 2D correlation spectroscopy are diverse, encompassing synthetic and natural polymers, liquid crystals, proteins and peptides, biomaterials, pharmaceuticals, food and agricultural products, solutions, colloids, surfaces, and the like.

Interference tables: a useful model for interference analysis in asynchronous multicarrier transmission

NASA Astrophysics Data System (ADS)

Medjahdi, Yahia; Terré, Michel; Ruyet, Didier Le; Roviras, Daniel

2014-12-01

In this paper, we investigate the impact of timing asynchronism on the performance of multicarrier techniques in a spectrum coexistence context. Two multicarrier schemes are considered: cyclic prefix-based orthogonal frequency division multiplexing (CP-OFDM) with a rectangular pulse shape and filter bank-based multicarrier (FBMC) with physical layer for dynamic spectrum access and cognitive radio (PHYDYAS) and isotropic orthogonal transform algorithm (IOTA) waveforms. First, we present the general concept of the so-called power spectral density (PSD)-based interference tables which are commonly used for multicarrier interference characterization in spectrum sharing context. After highlighting the limits of this approach, we propose a new family of interference tables called `instantaneous interference tables'. The proposed tables give the interference power caused by a given interfering subcarrier on a victim one, not only as a function of the spectral distance separating both subcarriers but also with respect to the timing misalignment between the subcarrier holders. In contrast to the PSD-based interference tables, the accuracy of the proposed tables has been validated through different simulation results. Furthermore, due to the better frequency localization of both PHYDYAS and IOTA waveforms, FBMC technique is demonstrated to be more robust to timing asynchronism compared to OFDM one. Such a result makes FBMC a potential candidate for the physical layer of future cognitive radio systems.

Orthogonal Procrustes Analysis for Dictionary Learning in Sparse Linear Representation.

PubMed

Grossi, Giuliano; Lanzarotti, Raffaella; Lin, Jianyi

2017-01-01

In the sparse representation model, the design of overcomplete dictionaries plays a key role for the effectiveness and applicability in different domains. Recent research has produced several dictionary learning approaches, being proven that dictionaries learnt by data examples significantly outperform structured ones, e.g. wavelet transforms. In this context, learning consists in adapting the dictionary atoms to a set of training signals in order to promote a sparse representation that minimizes the reconstruction error. Finding the best fitting dictionary remains a very difficult task, leaving the question still open. A well-established heuristic method for tackling this problem is an iterative alternating scheme, adopted for instance in the well-known K-SVD algorithm. Essentially, it consists in repeating two stages; the former promotes sparse coding of the training set and the latter adapts the dictionary to reduce the error. In this paper we present R-SVD, a new method that, while maintaining the alternating scheme, adopts the Orthogonal Procrustes analysis to update the dictionary atoms suitably arranged into groups. Comparative experiments on synthetic data prove the effectiveness of R-SVD with respect to well known dictionary learning algorithms such as K-SVD, ILS-DLA and the online method OSDL. Moreover, experiments on natural data such as ECG compression, EEG sparse representation, and image modeling confirm R-SVD's robustness and wide applicability.

Transformation pathways and acute toxicity variation of 4-hydroxyl benzophenone in chlorination disinfection process.

PubMed

Liu, Wei; Wei, Dongbin; Liu, Qi; Du, Yuguo

2016-07-01

Benzophenones compounds (BPs) are widely used as UV filters, and have been frequently found in multiple environmental matrices. The residual of BPs in water would cause potential threats on ecological safety and human health. Chlorination disinfection is necessary in water treatment process, in which many chemicals remained in water would react with disinfectant chlorine and form toxic by-products. By using ultra performance liquid phase chromatography quadrupole time of flight mass spectrometer (UPLC-QTOF-MS), nuclear magnetic resonance (NMR), the transformation of 4-hydroxyl benezophenone (4HB) with free available chlorine (FAC) was characterized. Eight major products were detected and seven of them were identified. Transformation pathways of 4HB under acid, neutral, and alkaline conditions were proposed respectively. The transformation mechanisms involved electrophilic chlorine substitution of 4HB, Baeyer-Villiger oxidation of ketones, hydrolysis of esters and oxidative breakage of benzene ring. The orthogonal experiments of pH and dosages of disinfectant chlorine were conducted. The results suggested that pH conditions determined the occurrence of reaction types, and the dosages of disinfectant chlorine affected the extent of reactions. Photobacterium assay demonstrated that acute toxicity had significant increase after chlorination disinfection of 4HB. It was proved that 3,5-dichloro-4HB, one of the major transformation products, was responsible for the increasing acute toxicity after chlorination. It is notable that, 4HB at low level in real ambient water matrices could be transformed during simulated chlorination disinfection practice. Especially, two major products 3-chloro-4HB and 3,5-dichloro-4HB were detected out, implying the potential ecological risk after chlorination disinfection of 4HB. Copyright © 2016 Elsevier Ltd. All rights reserved.

Orthogonality preserving infinite dimensional quadratic stochastic operators

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

Akın, Hasan; Mukhamedov, Farrukh

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

Legendre modified moments for Euler's constant

NASA Astrophysics Data System (ADS)

Prévost, Marc

2008-10-01

Polynomial moments are often used for the computation of Gauss quadrature to stabilize the numerical calculation of the orthogonal polynomials, see [W. Gautschi, Computational aspects of orthogonal polynomials, in: P. Nevai (Ed.), Orthogonal Polynomials-Theory and Practice, NATO ASI Series, Series C: Mathematical and Physical Sciences, vol. 294. Kluwer, Dordrecht, 1990, pp. 181-216 [6]; W. Gautschi, On the sensitivity of orthogonal polynomials to perturbations in the moments, Numer. Math. 48(4) (1986) 369-382 [5]; W. Gautschi, On generating orthogonal polynomials, SIAM J. Sci. Statist. Comput. 3(3) (1982) 289-317 [4

Sequential Least-Squares Using Orthogonal Transformations. [spacecraft communication/spacecraft tracking-data smoothing

NASA Technical Reports Server (NTRS)

Bierman, G. J.

1975-01-01

Square root information estimation, starting from its beginnings in least-squares parameter estimation, is considered. Special attention is devoted to discussions of sensitivity and perturbation matrices, computed solutions and their formal statistics, consider-parameters and consider-covariances, and the effects of a priori statistics. The constant-parameter model is extended to include time-varying parameters and process noise, and the error analysis capabilities are generalized. Efficient and elegant smoothing results are obtained as easy consequences of the filter formulation. The value of the techniques is demonstrated by the navigation results that were obtained for the Mariner Venus-Mercury (Mariner 10) multiple-planetary space probe and for the Viking Mars space mission.

The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation

NASA Astrophysics Data System (ADS)

Filipuk, Galina; Van Assche, Walter; Zhang, Lun

2012-05-01

We show that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semi-classical extension of the Laguerre weight satisfy the fourth Painlevé equation when viewed as functions of one of the parameters in the weight. We compare different approaches to derive this result, namely, the ladder operators approach, the isomonodromy deformations approach and combining the Toda system for the recurrence coefficients with a discrete equation. We also discuss a relation between the recurrence coefficients for the Freud weight and the semi-classical Laguerre weight and show how it arises from the Bäcklund transformation of the fourth Painlevé equation.

An Algebraic Formulation of Level One Wess-Zumino Models

NASA Astrophysics Data System (ADS)

Böckenhauer, Jens

The highest weight modules of the chiral algebra of orthogonal WZW models at level one possess a realization in fermionic representation spaces; the Kac-Moody and Virasoro generators are represented as unbounded limits of even CAR algebras. It is shown that the representation theory of the underlying even CAR algebras reproduces precisely the sectors of the chiral algebra. This fact allows to develop a theory of local von Neumann algebras on the punctured circle, fitting nicely in the Doplicher-Haag-Roberts framework. The relevant localized endomorphisms which generate the charged sectors are explicitly constructed by means of Bogoliubov transformations. Using CAR theory, the fusion rules in terms of sector equivalence classes are proven.

Hierarchical image-based rendering using texture mapping hardware

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

Max, N

1999-01-15

Multi-layered depth images containing color and normal information for subobjects in a hierarchical scene model are precomputed with standard z-buffer hardware for six orthogonal views. These are adaptively selected according to the proximity of the viewpoint, and combined using hardware texture mapping to create ''reprojected'' output images for new viewpoints. (If a subobject is too close to the viewpoint, the polygons in the original model are rendered.) Specific z-ranges are selected from the textures with the hardware alpha test to give accurate 3D reprojection. The OpenGL color matrix is used to transform the precomputed normals into their orientations in themore » final view, for hardware shading.« less

Reflection and transmission coefficients for guided waves reflected by defects in viscoelastic material plates.

PubMed

Hosten, Bernard; Moreau, Ludovic; Castaings, Michel

2007-06-01

The paper presents a Fourier transform-based signal processing procedure for quantifying the reflection and transmission coefficients and mode conversion of guided waves diffracted by defects in plates made of viscoelastic materials. The case of the S(0) Lamb wave mode incident on a notch in a Perspex plate is considered. The procedure is applied to numerical data produced by a finite element code that simulates the propagation of attenuated guided modes and their diffraction by the notch, including mode conversion. Its validity and precision are checked by the way of the energy balance computation and by comparison with results obtained using an orthogonality relation-based processing method.

Polarization-dependent photon switch in a one-dimensional coupled-resonator waveguide.

PubMed

Zhang, Zhe-Yong; Dong, Yu-Li; Zhang, Sheng-Li; Zhu, Shi-Qun

2013-09-09

Polarization-dependent photon switch is one of the most important ingredients in building future large-scale all-optical quantum network. We present a scheme for a single-photon switch in a one-dimensional coupled-resonator waveguide, where N(a) Λ-type three-level atoms are individually embedded in each of the resonator. By tuning the interaction between atom and field, we show that an initial incident photon with a certain polarization can be transformed into its orthogonal polarization state. Finally, we use the fidelity as a figure of merit and numerically evaluate the performance of our photon switch scheme in varieties of system parameters, such as number of atoms, energy detuning and dipole couplings.

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.

Entropy-stabilized oxides

PubMed Central

Rost, Christina M.; Sachet, Edward; Borman, Trent; Moballegh, Ali; Dickey, Elizabeth C.; Hou, Dong; Jones, Jacob L.; Curtarolo, Stefano; Maria, Jon-Paul

2015-01-01

Configurational disorder can be compositionally engineered into mixed oxide by populating a single sublattice with many distinct cations. The formulations promote novel and entropy-stabilized forms of crystalline matter where metal cations are incorporated in new ways. Here, through rigorous experiments, a simple thermodynamic model, and a five-component oxide formulation, we demonstrate beyond reasonable doubt that entropy predominates the thermodynamic landscape, and drives a reversible solid-state transformation between a multiphase and single-phase state. In the latter, cation distributions are proven to be random and homogeneous. The findings validate the hypothesis that deliberate configurational disorder provides an orthogonal strategy to imagine and discover new phases of crystalline matter and untapped opportunities for property engineering. PMID:26415623

Toward self-consistent tectono-magmatic numerical model of rift-to-ridge transition

NASA Astrophysics Data System (ADS)

Gerya, Taras; Bercovici, David; Liao, Jie

2017-04-01

Natural data from modern and ancient lithospheric extension systems suggest three-dimensional (3D) character of deformation and complex relationship between magmatism and tectonics during the entire rift-to-ridge transition. Therefore, self-consistent high-resolution 3D magmatic-thermomechanical numerical approaches stand as a minimum complexity requirement for modeling and understanding of this transition. Here we present results from our new high-resolution 3D finite-difference marker-in-cell rift-to-ridge models, which account for magmatic accretion of the crust and use non-linear strain-weakened visco-plastic rheology of rocks that couples brittle/plastic failure and ductile damage caused by grain size reduction. Numerical experiments suggest that nucleation of rifting and ridge-transform patterns are decoupled in both space and time. At intermediate stages, two patterns can coexist and interact, which triggers development of detachment faults, failed rift arms, hyper-extended margins and oblique proto-transforms. En echelon rift patterns typically develop in the brittle upper-middle crust whereas proto-ridge and proto-transform structures nucleate in the lithospheric mantle. These deep proto-structures propagate upward, inter-connect and rotate toward a mature orthogonal ridge-transform patterns on the timescale of millions years during incipient thermal-magmatic accretion of the new oceanic-like lithosphere. Ductile damage of the extending lithospheric mantle caused by grain size reduction assisted by Zenner pinning plays critical role in rift-to-ridge transition by stabilizing detachment faults and transform structures. Numerical results compare well with observations from incipient spreading regions and passive continental margins.

A Transform-Based Feature Extraction Approach for Motor Imagery Tasks Classification

PubMed Central

Khorshidtalab, Aida; Mesbah, Mostefa; Salami, Momoh J. E.

2015-01-01

In this paper, we present a new motor imagery classification method in the context of electroencephalography (EEG)-based brain–computer interface (BCI). This method uses a signal-dependent orthogonal transform, referred to as linear prediction singular value decomposition (LP-SVD), for feature extraction. The transform defines the mapping as the left singular vectors of the LP coefficient filter impulse response matrix. Using a logistic tree-based model classifier; the extracted features are classified into one of four motor imagery movements. The proposed approach was first benchmarked against two related state-of-the-art feature extraction approaches, namely, discrete cosine transform (DCT) and adaptive autoregressive (AAR)-based methods. By achieving an accuracy of 67.35%, the LP-SVD approach outperformed the other approaches by large margins (25% compared with DCT and 6 % compared with AAR-based methods). To further improve the discriminatory capability of the extracted features and reduce the computational complexity, we enlarged the extracted feature subset by incorporating two extra features, namely, Q- and the Hotelling’s \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} }{}$T^{2}$ \\end{document} statistics of the transformed EEG and introduced a new EEG channel selection method. The performance of the EEG classification based on the expanded feature set and channel selection method was compared with that of a number of the state-of-the-art classification methods previously reported with the BCI IIIa competition data set. Our method came second with an average accuracy of 81.38%. PMID:27170898

Transformation mechanism of benzophenone-4 in free chlorine promoted chlorination disinfection.

PubMed

Xiao, Ming; Wei, Dongbin; Yin, Junxia; Wei, Guohua; Du, Yuguo

2013-10-15

The UV-filter BP-4 (2-hydroxy-4-methoxybenzophenone-5-sulfonic acid) has been frequently observed in the environment, showing high potentials to invade drinking water, swimming water, or wastewater reclamation treatment systems. With the help of high performance liquid chromatography-high resolution mass spectrometry and nuclear magnetic resonance spectroscopy, 10 new products from free chlorine-promoted BP-4 disinfection have been disclosed and their possible transformation routes have been investigated. The first route is chlorine substitution of BP-4 and its transformation products, forming mono-, di-, and tri-chlorinated BP-4 analogs. The second is Baeyer-Villiger-Type oxidation, converting diphenyl ketone to phenyl ester derivatives. The third is ester hydrolysis, generating corresponding phenolic and benzoic products. The fourth is decarboxylation, replacing the carboxyl group by chloride in the benzoic-type intermediate. The fifth is desulfonation, degrading the sulfonic group through an alternative chlorine substitution on the benzene ring. Orthogonal experiments have been established to investigate the species transformed from BP-4 at different pH values and free available chlorine (FAC) dosages. The reaction pathways are strongly dependent on pH conditions, while an excessive amount of FAC eliminates BP-4 to the smaller molecules. The initial transformation of BP-4 in chlorination system follows pseudo-first-order kinetics, and its half-lives ranged from 7.48 s to 1.26 × 10(2) s. More importantly, we have observed that the FAC-treated BP-4 aqueous solution might increase the genotoxic potentials due to the generation of chlorinated disinfection by-products. Copyright © 2013 Elsevier Ltd. All rights reserved.

[Orthogonal Vector Projection Algorithm for Spectral Unmixing].

PubMed

Song, Mei-ping; Xu, Xing-wei; Chang, Chein-I; An, Ju-bai; Yao, Li

2015-12-01

Spectrum unmixing is an important part of hyperspectral technologies, which is essential for material quantity analysis in hyperspectral imagery. Most linear unmixing algorithms require computations of matrix multiplication and matrix inversion or matrix determination. These are difficult for programming, especially hard for realization on hardware. At the same time, the computation costs of the algorithms increase significantly as the number of endmembers grows. Here, based on the traditional algorithm Orthogonal Subspace Projection, a new method called. Orthogonal Vector Projection is prompted using orthogonal principle. It simplifies this process by avoiding matrix multiplication and inversion. It firstly computes the final orthogonal vector via Gram-Schmidt process for each endmember spectrum. And then, these orthogonal vectors are used as projection vector for the pixel signature. The unconstrained abundance can be obtained directly by projecting the signature to the projection vectors, and computing the ratio of projected vector length and orthogonal vector length. Compared to the Orthogonal Subspace Projection and Least Squares Error algorithms, this method does not need matrix inversion, which is much computation costing and hard to implement on hardware. It just completes the orthogonalization process by repeated vector operations, easy for application on both parallel computation and hardware. The reasonability of the algorithm is proved by its relationship with Orthogonal Sub-space Projection and Least Squares Error algorithms. And its computational complexity is also compared with the other two algorithms', which is the lowest one. At last, the experimental results on synthetic image and real image are also provided, giving another evidence for effectiveness of the method.

Underestimates of sensible heat flux due to vertical velocity measurement errors in non-orthogonal sonic anemometers

Treesearch

John M. Frank; William J. Massman; Brent E. Ewers

2013-01-01

Sonic thermometry and anemometry are fundamental to all eddy-covariance studies of surface energy balance. Recent studies have suggested that sonic anemometers with non-orthogonal transducers can underestimate vertical wind velocity (w) and sensible heat flux (H) when compared to orthogonal designs. In this study we tested whether a non-orthogonal sonic anemometer (...

Application of neural networks with orthogonal activation functions in control of dynamical systems

NASA Astrophysics Data System (ADS)

Nikolić, Saša S.; Antić, Dragan S.; Milojković, Marko T.; Milovanović, Miroslav B.; Perić, Staniša Lj.; Mitić, Darko B.

2016-04-01

In this article, we present a new method for the synthesis of almost and quasi-orthogonal polynomials of arbitrary order. Filters designed on the bases of these functions are generators of generalised quasi-orthogonal signals for which we derived and presented necessary mathematical background. Based on theoretical results, we designed and practically implemented generalised first-order (k = 1) quasi-orthogonal filter and proved its quasi-orthogonality via performed experiments. Designed filters can be applied in many scientific areas. In this article, generated functions were successfully implemented in Nonlinear Auto Regressive eXogenous (NARX) neural network as activation functions. One practical application of the designed orthogonal neural network is demonstrated through the example of control of the complex technical non-linear system - laboratory magnetic levitation system. Obtained results were compared with neural networks with standard activation functions and orthogonal functions of trigonometric shape. The proposed network demonstrated superiority over existing solutions in the sense of system performances.

Superpixel Based Factor Analysis and Target Transformation Method for Martian Minerals Detection

NASA Astrophysics Data System (ADS)

Wu, X.; Zhang, X.; Lin, H.

2018-04-01

The Factor analysis and target transformation (FATT) is an effective method to test for the presence of particular mineral on Martian surface. It has been used both in thermal infrared (Thermal Emission Spectrometer, TES) and near-infrared (Compact Reconnaissance Imaging Spectrometer for Mars, CRISM) hyperspectral data. FATT derived a set of orthogonal eigenvectors from a mixed system and typically selected first 10 eigenvectors to least square fit the library mineral spectra. However, minerals present only in a limited pixels will be ignored because its weak spectral features compared with full image signatures. Here, we proposed a superpixel based FATT method to detect the mineral distributions on Mars. The simple linear iterative clustering (SLIC) algorithm was used to partition the CRISM image into multiple connected image regions with spectral homogeneous to enhance the weak signatures by increasing their proportion in a mixed system. A least square fitting was used in target transformation and performed to each region iteratively. Finally, the distribution of the specific minerals in image was obtained, where fitting residual less than a threshold represent presence and otherwise absence. We validate our method by identifying carbonates in a well analysed CRISM image in Nili Fossae on Mars. Our experimental results indicate that the proposed method work well both in simulated and real data sets.

2D DOST based local phase pattern for face recognition

NASA Astrophysics Data System (ADS)

Moniruzzaman, Md.; Alam, Mohammad S.

2017-05-01

A new two dimensional (2-D) Discrete Orthogonal Stcokwell Transform (DOST) based Local Phase Pattern (LPP) technique has been proposed for efficient face recognition. The proposed technique uses 2-D DOST as preliminary preprocessing and local phase pattern to form robust feature signature which can effectively accommodate various 3D facial distortions and illumination variations. The S-transform, is an extension of the ideas of the continuous wavelet transform (CWT), is also known for its local spectral phase properties in time-frequency representation (TFR). It provides a frequency dependent resolution of the time-frequency space and absolutely referenced local phase information while maintaining a direct relationship with the Fourier spectrum which is unique in TFR. After utilizing 2-D Stransform as the preprocessing and build local phase pattern from extracted phase information yield fast and efficient technique for face recognition. The proposed technique shows better correlation discrimination compared to alternate pattern recognition techniques such as wavelet or Gabor based face recognition. The performance of the proposed method has been tested using the Yale and extended Yale facial database under different environments such as illumination variation and 3D changes in facial expressions. Test results show that the proposed technique yields better performance compared to alternate time-frequency representation (TFR) based face recognition techniques.

Single-pixel imaging by Hadamard transform and its application for hyperspectral imaging

NASA Astrophysics Data System (ADS)

Mizutani, Yasuhiro; Shibuya, Kyuki; Taguchi, Hiroki; Iwata, Tetsuo; Takaya, Yasuhiro; Yasui, Takeshi

2016-10-01

In this paper, we report on comparisons of single-pixel imagings using Hadamard Transform (HT) and the ghost imaging (GI) in the view point of the visibility under weak light conditions. For comparing the two methods, we have discussed about qualities of images based on experimental results and numerical analysis. To detect images by the TH method, we have illuminated the Hadamard-pattern mask and calculated by orthogonal transform. On the other hand, the GH method can detect images by illuminating random patterns and a correlation measurement. For comparing two methods under weak light intensity, we have controlled illuminated intensities of a DMD projector about 0.1 in signal-to-noise ratio. Though a process speed of the HT image was faster then an image via the GI, the GI method has an advantage of detection under weak light condition. An essential difference between the HT and the GI method is discussed about reconstruction process. Finally, we also show a typical application of the single-pixel imaging such as hyperspectral images by using dual-optical frequency combs. An optical setup consists of two fiber lasers, spatial light modulated for generating patten illumination, and a single pixel detector. We are successful to detect hyperspectrul images in a range from 1545 to 1555 nm at 0.01nm resolution.

Pilot-Assisted Channel Estimation for Orthogonal Multi-Carrier DS-CDMA with Frequency-Domain Equalization

NASA Astrophysics Data System (ADS)

Shima, Tomoyuki; Tomeba, Hiromichi; Adachi, Fumiyuki

Orthogonal multi-carrier direct sequence code division multiple access (orthogonal MC DS-CDMA) is a combination of time-domain spreading and orthogonal frequency division multiplexing (OFDM). In orthogonal MC DS-CDMA, the frequency diversity gain can be obtained by applying frequency-domain equalization (FDE) based on minimum mean square error (MMSE) criterion to a block of OFDM symbols and can improve the bit error rate (BER) performance in a severe frequency-selective fading channel. FDE requires an accurate estimate of the channel gain. The channel gain can be estimated by removing the pilot modulation in the frequency domain. In this paper, we propose a pilot-assisted channel estimation suitable for orthogonal MC DS-CDMA with FDE and evaluate, by computer simulation, the BER performance in a frequency-selective Rayleigh fading channel.

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.

Complete set of invariants of a 4th order tensor: the 12 tasks of HARDI from ternary quartics.

PubMed

Papadopoulo, Théo; Ghosh, Aurobrata; Deriche, Rachid

2014-01-01

Invariants play a crucial role in Diffusion MRI. In DTI (2nd order tensors), invariant scalars (FA, MD) have been successfully used in clinical applications. But DTI has limitations and HARDI models (e.g. 4th order tensors) have been proposed instead. These, however, lack invariant features and computing them systematically is challenging. We present a simple and systematic method to compute a functionally complete set of invariants of a non-negative 3D 4th order tensor with respect to SO3. Intuitively, this transforms the tensor's non-unique ternary quartic (TQ) decomposition (from Hilbert's theorem) to a unique canonical representation independent of orientation - the invariants. The method consists of two steps. In the first, we reduce the 18 degrees-of-freedom (DOF) of a TQ representation by 3-DOFs via an orthogonal transformation. This transformation is designed to enhance a rotation-invariant property of choice of the 3D 4th order tensor. In the second, we further reduce 3-DOFs via a 3D rotation transformation of coordinates to arrive at a canonical set of invariants to SO3 of the tensor. The resulting invariants are, by construction, (i) functionally complete, (ii) functionally irreducible (if desired), (iii) computationally efficient and (iv) reversible (mappable to the TQ coefficients or shape); which is the novelty of our contribution in comparison to prior work. Results from synthetic and real data experiments validate the method and indicate its importance.

Design of almost symmetric orthogonal wavelet filter bank via direct optimization.

PubMed

Murugesan, Selvaraaju; Tay, David B H

2012-05-01

It is a well-known fact that (compact-support) dyadic wavelets [based on the two channel filter banks (FBs)] cannot be simultaneously orthogonal and symmetric. Although orthogonal wavelets have the energy preservation property, biorthogonal wavelets are preferred in image processing applications because of their symmetric property. In this paper, a novel method is presented for the design of almost symmetric orthogonal wavelet FB. Orthogonality is structurally imposed by using the unnormalized lattice structure, and this leads to an objective function, which is relatively simple to optimize. The designed filters have good frequency response, flat group delay, almost symmetric filter coefficients, and symmetric wavelet function.

Evaluating the morphological completeness of a training image.

PubMed

Gao, Mingliang; Teng, Qizhi; He, Xiaohai; Feng, Junxi; Han, Xue

2017-05-01

Understanding the three-dimensional (3D) stochastic structure of a porous medium is helpful for studying its physical properties. A 3D stochastic structure can be reconstructed from a two-dimensional (2D) training image (TI) using mathematical modeling. In order to predict what specific morphology belonging to a TI can be reconstructed at the 3D orthogonal slices by the method of 3D reconstruction, this paper begins by introducing the concept of orthogonal chords. After analyzing the relationship among TI morphology, orthogonal chords, and the 3D morphology of orthogonal slices, a theory for evaluating the morphological completeness of a TI is proposed for the cases of three orthogonal slices and of two orthogonal slices. The proposed theory is evaluated using four TIs of porous media that represent typical but distinct morphological types. The significance of this theoretical evaluation lies in two aspects: It allows special morphologies, for which the attributes of a TI can be reconstructed at a special orthogonal slice of a 3D structure, to be located and quantified, and it can guide the selection of an appropriate reconstruction method for a special TI.

Effectiveness of Modal Decomposition for Tapping Atomic Force Microscopy Microcantilevers in Liquid Environment.

PubMed

Kim, Il Kwang; Lee, Soo Il

2016-05-01

The modal decomposition of tapping mode atomic force microscopy microcantilevers in liquid environments was studied experimentally. Microcantilevers with different lengths and stiffnesses and two sample surfaces with different elastic moduli were used in the experiment. The response modes of the microcantilevers were extracted as proper orthogonal modes through proper orthogonal decomposition. Smooth orthogonal decomposition was used to estimate the resonance frequency directly. The effects of the tapping setpoint and the elastic modulus of the sample under test were examined in terms of their multi-mode responses with proper orthogonal modes, proper orthogonal values, smooth orthogonal modes and smooth orthogonal values. Regardless of the stiffness of the microcantilever under test, the first mode was dominant in tapping mode atomic force microscopy under normal operating conditions. However, at lower tapping setpoints, the flexible microcantilever showed modal distortion and noise near the tip when tapping on a hard sample. The stiff microcantilever had a higher mode effect on a soft sample at lower tapping setpoints. Modal decomposition for tapping mode atomic force microscopy can thus be used to estimate the characteristics of samples in liquid environments.

Orthogonal stimulus-response compatibility effects emerge even when the stimulus position is task irrelevant.

PubMed

Nishimura, Akio; Yokosawa, Kazuhiko

2006-06-01

The above-right/below-left mapping advantage with vertical stimuli and horizontal responses is known as the orthogonal stimulus-response compatibility (SRC) effect. We investigated whether the orthogonal SRC effect emerges with irrelevant stimulus dimensions. In Experiment 1, participants responded with a right or left key press to the colour of the stimulus presented above or below the fixation. We observed an above-right/below-left advantage (orthogonal Simon effect). In Experiment 2, we manipulated the polarity in the response dimension by varying the horizontal location of the response set. The orthogonal Simon effect decreased and even reversed as the left response code became more positive. This result provides evidence for the automatic activation of the positive and negative response codes by the corresponding positive and negative stimulus codes. These findings extended the orthogonal SRC effect based on coding asymmetry to an irrelevant stimulus dimension.

Non-Orthogonal Corneal Astigmatism among Normal and Keratoconic Brazilian and Chinese populations.

PubMed

Abass, Ahmed; Clamp, John; Bao, FangJun; Ambrósio, Renato; Elsheikh, Ahmed

2018-06-01

To investigate the prevalence of non-orthogonal astigmatism among normal and keratoconic Brazilian and Chinese populations. Topography data were obtained using the Pentacam High Resolution (HR) system ® from 458 Brazilian (aged 35.6 ± 15.8 years) and 505 Chinese (aged 31.6 ± 10.8 years) eyes with no history of keratoconus or refractive surgery, and 314 Brazilian (aged 24.2 ± 5.7 years) and 74 Chinese (aged 22.0 ± 5.5 years) keratoconic eyes. Orthogonal values of optical flat and steep powers were determined by finding the angular positions of two perpendicular meridians that gave the maximum difference in power. Additionally, the angular positions of the meridians with the minimum and maximum optical powers were located while being unrestricted by the usual orthogonality assumption. Eyes were determined to have non-orthogonal astigmatism if the angle between the two meridians with maximum and minimum optical power deviated by more than 5° from 90°. Evidence of non-orthogonal astigmatism was found in 39% of the Brazilian keratoconic eyes, 26% of the Chinese keratoconic eyes, 29% of the Brazilian normal eyes and 20% of the Chinese normal eyes. The large percentage of participants with non-orthogonal astigmatism in both normal and keratoconic eyes illustrates the need for the common orthogonality assumption to be reviewed when correcting for astigmatism. The prevalence of non-orthogonality should be considered by expanding the prescription system to consider the two power meridians and their independent positions.

A CU-Level Rate and Distortion Estimation Scheme for RDO of Hardware-Friendly HEVC Encoders Using Low-Complexity Integer DCTs.

PubMed

Lee, Bumshik; Kim, Munchurl

2016-08-01

In this paper, a low complexity coding unit (CU)-level rate and distortion estimation scheme is proposed for High Efficiency Video Coding (HEVC) hardware-friendly implementation where a Walsh-Hadamard transform (WHT)-based low-complexity integer discrete cosine transform (DCT) is employed for distortion estimation. Since HEVC adopts quadtree structures of coding blocks with hierarchical coding depths, it becomes more difficult to estimate accurate rate and distortion values without actually performing transform, quantization, inverse transform, de-quantization, and entropy coding. Furthermore, DCT for rate-distortion optimization (RDO) is computationally high, because it requires a number of multiplication and addition operations for various transform block sizes of 4-, 8-, 16-, and 32-orders and requires recursive computations to decide the optimal depths of CU or transform unit. Therefore, full RDO-based encoding is highly complex, especially for low-power implementation of HEVC encoders. In this paper, a rate and distortion estimation scheme is proposed in CU levels based on a low-complexity integer DCT that can be computed in terms of WHT whose coefficients are produced in prediction stages. For rate and distortion estimation in CU levels, two orthogonal matrices of 4×4 and 8×8 , which are applied to WHT that are newly designed in a butterfly structure only with addition and shift operations. By applying the integer DCT based on the WHT and newly designed transforms in each CU block, the texture rate can precisely be estimated after quantization using the number of non-zero quantized coefficients and the distortion can also be precisely estimated in transform domain without de-quantization and inverse transform required. In addition, a non-texture rate estimation is proposed by using a pseudoentropy code to obtain accurate total rate estimates. The proposed rate and the distortion estimation scheme can effectively be used for HW-friendly implementation of HEVC encoders with 9.8% loss over HEVC full RDO, which much less than 20.3% and 30.2% loss of a conventional approach and Hadamard-only scheme, respectively.

Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique

NASA Astrophysics Data System (ADS)

Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi

2013-09-01

According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.

New Approaches to Coding Information using Inverse Scattering Transform

NASA Astrophysics Data System (ADS)

Frumin, L. L.; Gelash, A. A.; Turitsyn, S. K.

2017-06-01

Remarkable mathematical properties of the integrable nonlinear Schrödinger equation (NLSE) can offer advanced solutions for the mitigation of nonlinear signal distortions in optical fiber links. Fundamental optical soliton, continuous, and discrete eigenvalues of the nonlinear spectrum have already been considered for the transmission of information in fiber-optic channels. Here, we propose to apply signal modulation to the kernel of the Gelfand-Levitan-Marchenko equations that offers the advantage of a relatively simple decoder design. First, we describe an approach based on exploiting the general N -soliton solution of the NLSE for simultaneous coding of N symbols involving 4 ×N coding parameters. As a specific elegant subclass of the general schemes, we introduce a soliton orthogonal frequency division multiplexing (SOFDM) method. This method is based on the choice of identical imaginary parts of the N -soliton solution eigenvalues, corresponding to equidistant soliton frequencies, making it similar to the conventional OFDM scheme, thus, allowing for the use of the efficient fast Fourier transform algorithm to recover the data. Then, we demonstrate how to use this new approach to control signal parameters in the case of the continuous spectrum.

Vestibulo-Ocular Reflex Responses to a Multichannel Vestibular Prosthesis Incorporating a 3D Coordinate Transformation for Correction of Misalignment

PubMed Central

Fridman, Gene Y.; Davidovics, Natan S.; Dai, Chenkai; Migliaccio, Americo A.

2010-01-01

There is no effective treatment available for individuals unable to compensate for bilateral profound loss of vestibular sensation, which causes chronic disequilibrium and blurs vision by disrupting vestibulo-ocular reflexes that normally stabilize the eyes during head movement. Previous work suggests that a multichannel vestibular prosthesis can emulate normal semicircular canals by electrically stimulating vestibular nerve branches to encode head movements detected by mutually orthogonal gyroscopes affixed to the skull. Until now, that approach has been limited by current spread resulting in distortion of the vestibular nerve activation pattern and consequent inability to accurately encode head movements throughout the full 3-dimensional (3D) range normally transduced by the labyrinths. We report that the electrically evoked 3D angular vestibulo-ocular reflex exhibits vector superposition and linearity to a sufficient degree that a multichannel vestibular prosthesis incorporating a precompensatory 3D coordinate transformation to correct misalignment can accurately emulate semicircular canals for head rotations throughout the range of 3D axes normally transduced by a healthy labyrinth. PMID:20177732

Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing.

PubMed

Benlachtar, Yannis; Watts, Philip M; Bouziane, Rachid; Milder, Peter; Rangaraj, Deepak; Cartolano, Anthony; Koutsoyannis, Robert; Hoe, James C; Püschel, Markus; Glick, Madeleine; Killey, Robert I

2009-09-28

We demonstrate a field programmable gate array (FPGA) based optical orthogonal frequency division multiplexing (OFDM) transmitter implementing real time digital signal processing at a sample rate of 21.4 GS/s. The QPSK-OFDM signal is generated using an 8 bit, 128 point inverse fast Fourier transform (IFFT) core, performing one transform per clock cycle at a clock speed of 167.2 MHz and can be deployed with either a direct-detection or a coherent receiver. The hardware design and the main digital signal processing functions are described, and we show that the main performance limitation is due to the low (4-bit) resolution of the digital-to-analog converter (DAC) and the 8-bit resolution of the IFFT core used. We analyze the back-to-back performance of the transmitter generating an 8.36 Gb/s optical single sideband (SSB) OFDM signal using digital up-conversion, suitable for direct-detection. Additionally, we use the device to transmit 8.36 Gb/s SSB OFDM signals over 200 km of uncompensated standard single mode fiber achieving an overall BER<10(-3).

A hybrid spatial-spectral denoising method for infrared hyperspectral images using 2DPCA

NASA Astrophysics Data System (ADS)

Huang, Jun; Ma, Yong; Mei, Xiaoguang; Fan, Fan

2016-11-01

The traditional noise reduction methods for 3-D infrared hyperspectral images typically operate independently in either the spatial or spectral domain, and such methods overlook the relationship between the two domains. To address this issue, we propose a hybrid spatial-spectral method in this paper to link both domains. First, principal component analysis and bivariate wavelet shrinkage are performed in the 2-D spatial domain. Second, 2-D principal component analysis transformation is conducted in the 1-D spectral domain to separate the basic components from detail ones. The energy distribution of noise is unaffected by orthogonal transformation; therefore, the signal-to-noise ratio of each component is used as a criterion to determine whether a component should be protected from over-denoising or denoised with certain 1-D denoising methods. This study implements the 1-D wavelet shrinking threshold method based on Stein's unbiased risk estimator, and the quantitative results on publicly available datasets demonstrate that our method can improve denoising performance more effectively than other state-of-the-art methods can.

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.

Wavelet versus DCT-based spread spectrum watermarking of image databases

NASA Astrophysics Data System (ADS)

Mitrea, Mihai P.; Zaharia, Titus B.; Preteux, Francoise J.; Vlad, Adriana

2004-05-01

This paper addresses the issue of oblivious robust watermarking, within the framework of colour still image database protection. We present an original method which complies with all the requirements nowadays imposed to watermarking applications: robustness (e.g. low-pass filtering, print & scan, StirMark), transparency (both quality and fidelity), low probability of false alarm, obliviousness and multiple bit recovering. The mark is generated from a 64 bit message (be it a logo, a serial number, etc.) by means of a Spread Spectrum technique and is embedded into DWT (Discrete Wavelet Transform) domain, into certain low frequency coefficients, selected according to the hierarchy of their absolute values. The best results were provided by the (9,7) bi-orthogonal transform. The experiments were carried out on 1200 image sequences, each of them of 32 images. Note that these sequences represented several types of images: natural, synthetic, medical, etc. and each time we obtained the same good results. These results are compared with those we already obtained for the DCT domain, the differences being pointed out and discussed.

Optimization of an Advanced Multi-Junction Solar-Cell Design for Space Environments (AM0) Using Nearly Orthogonal Latin Hypercubes

DTIC Science & Technology

2017-06-01

AN ADVANCED MULTI-JUNCTION SOLAR -CELL DESIGN FOR SPACE ENVIRONMENTS (AM0) USING NEARLY ORTHOGONAL LATIN HYPERCUBES by Silvio Pueschel June...ADVANCED MULTI-JUNCTION SOLAR -CELL DESIGN FOR SPACE ENVIRONMENTS (AM0) USING NEARLY ORTHOGONAL LATIN HYPERCUBES 5. FUNDING NUMBERS 6. AUTHOR(S) Silvio...multi-junction solar cells with Silvaco Atlas simulation software. It introduces the nearly orthogonal Latin hypercube (NOLH) design of experiments (DoE

Clinical Study of Orthogonal-View Phase-Matched Digital Tomosynthesis for Lung Tumor Localization.

PubMed

Zhang, You; Ren, Lei; Vergalasova, Irina; Yin, Fang-Fang

2017-01-01

Compared to cone-beam computed tomography, digital tomosynthesis imaging has the benefits of shorter scanning time, less imaging dose, and better mechanical clearance for tumor localization in radiation therapy. However, for lung tumors, the localization accuracy of the conventional digital tomosynthesis technique is affected by the lack of depth information and the existence of lung tumor motion. This study investigates the clinical feasibility of using an orthogonal-view phase-matched digital tomosynthesis technique to improve the accuracy of lung tumor localization. The proposed orthogonal-view phase-matched digital tomosynthesis technique benefits from 2 major features: (1) it acquires orthogonal-view projections to improve the depth information in reconstructed digital tomosynthesis images and (2) it applies respiratory phase-matching to incorporate patient motion information into the synthesized reference digital tomosynthesis sets, which helps to improve the localization accuracy of moving lung tumors. A retrospective study enrolling 14 patients was performed to evaluate the accuracy of the orthogonal-view phase-matched digital tomosynthesis technique. Phantom studies were also performed using an anthropomorphic phantom to investigate the feasibility of using intratreatment aggregated kV and beams' eye view cine MV projections for orthogonal-view phase-matched digital tomosynthesis imaging. The localization accuracy of the orthogonal-view phase-matched digital tomosynthesis technique was compared to that of the single-view digital tomosynthesis techniques and the digital tomosynthesis techniques without phase-matching. The orthogonal-view phase-matched digital tomosynthesis technique outperforms the other digital tomosynthesis techniques in tumor localization accuracy for both the patient study and the phantom study. For the patient study, the orthogonal-view phase-matched digital tomosynthesis technique localizes the tumor to an average (± standard deviation) error of 1.8 (0.7) mm for a 30° total scan angle. For the phantom study using aggregated kV-MV projections, the orthogonal-view phase-matched digital tomosynthesis localizes the tumor to an average error within 1 mm for varying magnitudes of scan angles. The pilot clinical study shows that the orthogonal-view phase-matched digital tomosynthesis technique enables fast and accurate localization of moving lung tumors.

Probing the degenerate states of V-point singularities.

PubMed

Ram, B S Bhargava; Sharma, Anurag; Senthilkumaran, Paramasivam

2017-09-15

V-points are polarization singularities in spatially varying linearly polarized optical fields and are characterized by the Poincare-Hopf index η. Each V-point singularity is a superposition of two oppositely signed orbital angular momentum states in two orthogonal spin angular momentum states. Hence, a V-point singularity has zero net angular momentum. V-points with given |η| have the same (amplitude) intensity distribution but have four degenerate polarization distributions. Each of these four degenerate states also produce identical diffraction patterns. Hence to distinguish these degenerate states experimentally, we present in this Letter a method involving a combination of polarization transformation and diffraction. This method also shows the possibility of using polarization singularities in place of phase singularities in optical communication and quantum information processing.

A method of transition conflict resolving in hierarchical control

NASA Astrophysics Data System (ADS)

Łabiak, Grzegorz

2016-09-01

The paper concerns the problem of automatic solving of transition conflicts in hierarchical concurrent state machines (also known as UML state machine). Preparing by the designer a formal specification of a behaviour free from conflicts can be very complex. In this paper, it is proposed a method for solving conflicts through transition predicates modification. Partially specified predicates in the nondeterministic diagram are transformed into a symbolic Boolean space, whose points of the space code all possible valuations of transition predicates. Next, all valuations under partial specifications are logically multiplied by a function which represents all possible orthogonal predicate valuations. The result of this operation contains all possible collections of predicates, which under given partial specification make that the original diagram is conflict free and deterministic.

A nonclassical Radau collocation method for solving the Lane-Emden equations of the polytropic index 4.75 ≤ α < 5

NASA Astrophysics Data System (ADS)

Tirani, M. D.; Maleki, M.; Kajani, M. T.

2014-11-01

A numerical method for solving the Lane-Emden equations of the polytropic index α when 4.75 ≤ α ≤ 5 is introduced. The method is based upon nonclassical Gauss-Radau collocation points and Freud type weights. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced and are utilized in the interval [0,1]. A smooth, strictly monotonic transformation is used to map the infinite domain x ∈ [0,∞) onto a half-open interval t ∈ [0,1). The resulting problem on the finite interval is then transcribed to a system of nonlinear algebraic equations using collocation. The method is easy to implement and yields very accurate results.

Principal components analysis in clinical studies.

PubMed

Zhang, Zhongheng; Castelló, Adela

2017-09-01

In multivariate analysis, independent variables are usually correlated to each other which can introduce multicollinearity in the regression models. One approach to solve this problem is to apply principal components analysis (PCA) over these variables. This method uses orthogonal transformation to represent sets of potentially correlated variables with principal components (PC) that are linearly uncorrelated. PCs are ordered so that the first PC has the largest possible variance and only some components are selected to represent the correlated variables. As a result, the dimension of the variable space is reduced. This tutorial illustrates how to perform PCA in R environment, the example is a simulated dataset in which two PCs are responsible for the majority of the variance in the data. Furthermore, the visualization of PCA is highlighted.

Hyperbolic geometry of cosmological attractors

NASA Astrophysics Data System (ADS)

Carrasco, John Joseph M.; Kallosh, Renata; Linde, Andrei; Roest, Diederik

2015-08-01

Cosmological α attractors give a natural explanation for the spectral index ns of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r , consistent with all observations, to be measured more precisely in future B-mode experiments. We highlight the crucial role of the hyperbolic geometry of the Poincaré disk or half plane in the supergravity construction. These geometries are isometric under Möbius transformations, which include the shift symmetry of the inflaton field. We introduce a new Kähler potential frame that explicitly preserves this symmetry, enabling the inflaton to be light. Moreover, we include higher-order curvature deformations, which can stabilize a direction orthogonal to the inflationary trajectory. We illustrate this new framework by stabilizing the single superfield α attractors.

Chain mapping approach of Hamiltonian for FMO complex using associated, generalized and exceptional Jacobi polynomials

NASA Astrophysics Data System (ADS)

Mahdian, M.; Arjmandi, M. B.; Marahem, F.

2016-06-01

The excitation energy transfer (EET) in photosynthesis complex has been widely investigated in recent years. However, one of the main problems is simulation of this complex under realistic condition. In this paper by using the associated, generalized and exceptional Jacobi polynomials, firstly, we introduce the spectral density of Fenna-Matthews-Olson (FMO) complex. Afterward, we obtain a map that transforms the Hamiltonian of FMO complex as an open quantum system to a one-dimensional chain of oscillatory modes with only nearest neighbor interaction in which the system is coupled only to first mode of chain. The frequency and coupling strength of each mode can be analytically obtained from recurrence coefficient of mentioned orthogonal polynomials.

On Certain Wronskians of Multiple Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Zhang, Lun; Filipuk, Galina

2014-11-01

We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep a constant sign in some cases, while in some other cases oscillatory behavior appears, which generalizes classical results for orthogonal polynomials due to Karlin and Szegő. There are two applications of our results. The first application arises from the observation that the m-th moment of the average characteristic polynomials for multiple orthogonal polynomial ensembles can be expressed as a Wronskian of the type II multiple orthogonal polynomials. Hence, it is straightforward to obtain the distinct behavior of the moments for odd and even m in a special multiple orthogonal ensemble - the AT ensemble. As the second application, we derive some Turán type inequalities for m! ultiple Hermite and multiple Laguerre polynomials (of two kinds). Finally, we study numerically the geometric configuration of zeros for the Wronskians of these multiple orthogonal polynomials. We observe that the zeros have regular configurations in the complex plane, which might be of independent interest.

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.

Optimization of solid-state fermentation conditions for Trichoderma harzianum using an orthogonal test.

PubMed

Zhang, J D; Yang, Q

2015-03-13

The aim of this study was to develop a protocol for the production of fungal bio-pesticides with high efficiency, low cost, and non-polluting fermentation, while also increasing their survival rate under field conditions. This is the first study to develop biocontrol Trichoderma harzianum transformants TS1 that are resistant to benzimidazole fungicides. Agricultural corn stover and wheat bran waste were used as a medium and inducing carbon source for solid fermentation. Spore production was observed, and the method was optimized using single-factor tests with 4 factors at 3 levels in an orthogonal experimental design to determine the optimal culture conditions for T. harzianum TS1. In this step, we determined the best conditions for fermenting the biocontrol fungi. The optimal culture conditions for T. harzianum TS1 were cultivated for 8 days, a ratio of straw to wheat bran of 1:3, ammonium persulfate as the nitrogen source, and a water content of 30 mL. Under optimal culture conditions, the sporulation of T. harzianum TS1 reached 1.49 x 10(10) CFU/g, which was 1.46-fold higher than that achieved before optimization. Increased sporulation of T. harzianum TS1 results in better utilization of space and nutrients to achieve control of plant pathogens. This method allows for the recycling of agricultural waste straw.

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

Worst-Case Energy Efficiency Maximization in a 5G Massive MIMO-NOMA System.

PubMed

Chinnadurai, Sunil; Selvaprabhu, Poongundran; Jeong, Yongchae; Jiang, Xueqin; Lee, Moon Ho

2017-09-18

In this paper, we examine the robust beamforming design to tackle the energy efficiency (EE) maximization problem in a 5G massive multiple-input multiple-output (MIMO)-non-orthogonal multiple access (NOMA) downlink system with imperfect channel state information (CSI) at the base station. A novel joint user pairing and dynamic power allocation (JUPDPA) algorithm is proposed to minimize the inter user interference and also to enhance the fairness between the users. This work assumes imperfect CSI by adding uncertainties to channel matrices with worst-case model, i.e., ellipsoidal uncertainty model (EUM). A fractional non-convex optimization problem is formulated to maximize the EE subject to the transmit power constraints and the minimum rate requirement for the cell edge user. The designed problem is difficult to solve due to its nonlinear fractional objective function. We firstly employ the properties of fractional programming to transform the non-convex problem into its equivalent parametric form. Then, an efficient iterative algorithm is proposed established on the constrained concave-convex procedure (CCCP) that solves and achieves convergence to a stationary point of the above problem. Finally, Dinkelbach's algorithm is employed to determine the maximum energy efficiency. Comprehensive numerical results illustrate that the proposed scheme attains higher worst-case energy efficiency as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme.

Worst-Case Energy Efficiency Maximization in a 5G Massive MIMO-NOMA System

PubMed Central

Jeong, Yongchae; Jiang, Xueqin; Lee, Moon Ho

2017-01-01

In this paper, we examine the robust beamforming design to tackle the energy efficiency (EE) maximization problem in a 5G massive multiple-input multiple-output (MIMO)-non-orthogonal multiple access (NOMA) downlink system with imperfect channel state information (CSI) at the base station. A novel joint user pairing and dynamic power allocation (JUPDPA) algorithm is proposed to minimize the inter user interference and also to enhance the fairness between the users. This work assumes imperfect CSI by adding uncertainties to channel matrices with worst-case model, i.e., ellipsoidal uncertainty model (EUM). A fractional non-convex optimization problem is formulated to maximize the EE subject to the transmit power constraints and the minimum rate requirement for the cell edge user. The designed problem is difficult to solve due to its nonlinear fractional objective function. We firstly employ the properties of fractional programming to transform the non-convex problem into its equivalent parametric form. Then, an efficient iterative algorithm is proposed established on the constrained concave-convex procedure (CCCP) that solves and achieves convergence to a stationary point of the above problem. Finally, Dinkelbach’s algorithm is employed to determine the maximum energy efficiency. Comprehensive numerical results illustrate that the proposed scheme attains higher worst-case energy efficiency as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme. PMID:28927019

Orthogonal Procrustes Analysis for Dictionary Learning in Sparse Linear Representation

PubMed Central

Grossi, Giuliano; Lin, Jianyi

2017-01-01

In the sparse representation model, the design of overcomplete dictionaries plays a key role for the effectiveness and applicability in different domains. Recent research has produced several dictionary learning approaches, being proven that dictionaries learnt by data examples significantly outperform structured ones, e.g. wavelet transforms. In this context, learning consists in adapting the dictionary atoms to a set of training signals in order to promote a sparse representation that minimizes the reconstruction error. Finding the best fitting dictionary remains a very difficult task, leaving the question still open. A well-established heuristic method for tackling this problem is an iterative alternating scheme, adopted for instance in the well-known K-SVD algorithm. Essentially, it consists in repeating two stages; the former promotes sparse coding of the training set and the latter adapts the dictionary to reduce the error. In this paper we present R-SVD, a new method that, while maintaining the alternating scheme, adopts the Orthogonal Procrustes analysis to update the dictionary atoms suitably arranged into groups. Comparative experiments on synthetic data prove the effectiveness of R-SVD with respect to well known dictionary learning algorithms such as K-SVD, ILS-DLA and the online method OSDL. Moreover, experiments on natural data such as ECG compression, EEG sparse representation, and image modeling confirm R-SVD’s robustness and wide applicability. PMID:28103283

Quadratures with multiple nodes, power orthogonality, and moment-preserving spline approximation

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.

2001-01-01

Quadrature formulas with multiple nodes, power orthogonality, and some applications of such quadratures to moment-preserving approximation by defective splines are considered. An account on power orthogonality (s- and [sigma]-orthogonal polynomials) and generalized Gaussian quadratures with multiple nodes, including stable algorithms for numerical construction of the corresponding polynomials and Cotes numbers, are given. In particular, the important case of Chebyshev weight is analyzed. Finally, some applications in moment-preserving approximation of functions by defective splines are discussed.

Compact orthogonal NMR field sensor

DOEpatents

Gerald, II, Rex E.; Rathke, Jerome W [Homer Glen, IL

2009-02-03

A Compact Orthogonal Field Sensor for emitting two orthogonal electro-magnetic fields in a common space. More particularly, a replacement inductor for existing NMR (Nuclear Magnetic Resonance) sensors to allow for NMR imaging. The Compact Orthogonal Field Sensor has a conductive coil and a central conductor electrically connected in series. The central conductor is at least partially surrounded by the coil. The coil and central conductor are electrically or electro-magnetically connected to a device having a means for producing or inducing a current through the coil and central conductor. The Compact Orthogonal Field Sensor can be used in NMR imaging applications to determine the position and the associated NMR spectrum of a sample within the electro-magnetic field of the central conductor.

Gaussian quadrature for multiple orthogonal polynomials

NASA Astrophysics Data System (ADS)

Coussement, Jonathan; van Assche, Walter

2005-06-01

We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix Ln, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of Ln.

Distance-constrained orthogonal Latin squares for brain-computer interface.

PubMed

Luo, Gang; Min, Wanli

2012-02-01

The P300 brain-computer interface (BCI) using electroencephalogram (EEG) signals can allow amyotrophic lateral sclerosis (ALS) patients to instruct computers to perform tasks. To strengthen the P300 response and increase classification accuracy, we proposed an experimental design where characters are intensified according to orthogonal Latin square pairs. These orthogonal Latin square pairs satisfy certain distance constraint so that neighboring characters are not intensified simultaneously. However, it is unknown whether such distance-constrained, orthogonal Latin square pairs actually exist. In this paper, we show that for every matrix size commonly used in P300 BCI, thousands to millions of such distance-constrained, orthogonal Latin square pairs can be systematically and efficiently constructed and are sufficient for the purpose of being used in P300 BCI.

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

PubMed

Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

2014-10-01

Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

Orthogonal optimization of a water hydraulic pilot-operated pressure-reducing valve

NASA Astrophysics Data System (ADS)

Mao, Xuyao; Wu, Chao; Li, Bin; Wu, Di

2017-12-01

In order to optimize the comprehensive characteristics of a water hydraulic pilot-operated pressure-reducing valve, numerical orthogonal experimental design was adopted. Six parameters of the valve, containing diameters of damping plugs, volume of spring chamber, half cone angle of main spool, half cone angle of pilot spool, mass of main spool and diameter of main spool, were selected as the orthogonal factors, and each factor has five different levels. An index of flowrate stability, pressure stability and pressure overstrike stability (iFPOS) was used to judge the merit of each orthogonal attempt. Embedded orthogonal process turned up and a final optimal combination of these parameters was obtained after totally 50 numerical orthogonal experiments. iFPOS could be low to a fairly low value which meant that the valve could have much better stabilities. During the optimization, it was also found the diameters of damping plugs and main spool played important roles in stability characteristics of the valve.

The Gibbs Phenomenon for Series of Orthogonal Polynomials

ERIC Educational Resources Information Center

Fay, T. H.; Kloppers, P. Hendrik

2006-01-01

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

Determinants with orthogonal polynomial entries

NASA Astrophysics Data System (ADS)

Ismail, Mourad E. H.

2005-06-01

We use moment representations of orthogonal polynomials to evaluate the corresponding Hankel determinants formed by the orthogonal polynomials. We also study the Hankel determinants which start with pn on the top left-hand corner. As examples we evaluate the Hankel determinants whose entries are q-ultraspherical or Al-Salam-Chihara polynomials.

Prostate Specific Membrane Antigen (PSMA) Targeted Bio-orthogonal Therapy for Metastatic Prostate Cancer

DTIC Science & Technology

2017-10-01

AWARD NUMBER: W81XWH-16-1-0595 TITLE: Prostate-Specific Membrane Antigen (PSMA) Targeted Bio -orthogonal Therapy for Metastatic Prostate Cancer...Sep 2016 - 14 Sep 2017 4. TITLE AND SUBTITLE Prostate-Specific Membrane Antigen (PSMA) Targeted Bio -orthogonal Therapy for Metastatic Prostate

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.

The Coordinate Orthogonality Check (corthog)

NASA Astrophysics Data System (ADS)

Avitabile, P.; Pechinsky, F.

1998-05-01

A new technique referred to as the coordinate orthogonality check (CORTHOG) helps to identify how each physical degree of freedom contributes to the overall orthogonality relationship between analytical and experimental modal vectors on a mass-weighted basis. Using the CORTHOG technique together with the pseudo-orthogonality check (POC) clarifies where potential discrepancies exist between the analytical and experimental modal vectors. CORTHOG improves the understanding of the correlation (or lack of correlation) that exists between modal vectors. The CORTHOG theory is presented along with the evaluation of several cases to show the use of the technique.

Conversion from non-orthogonally to orthogonally polarized optical single-sideband modulation using optically injected semiconductor lasers.

PubMed

Hung, Yu-Han; Tseng, Chin-Hao; Hwang, Sheng-Kwang

2018-06-01

This Letter investigates an optically injected semiconductor laser for conversion from non-orthogonally to orthogonally polarized optical single-sideband modulation. The underlying mechanism relies solely on nonlinear laser characteristics and, thus, only a typical semiconductor laser is required as the key conversion unit. This conversion can be achieved for a broadly tunable frequency range up to at least 65 GHz. After conversion, the microwave phase quality, including linewidth and phase noise, is mostly preserved, and simultaneous microwave amplification up to 23 dB is feasible.

On orthogonality preserving quadratic stochastic operators

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

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

2015-05-15

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

Majorana fermions and orthogonal complex structures

NASA Astrophysics Data System (ADS)

Calderón-García, J. S.; Reyes-Lega, A. F.

2018-05-01

Ground states of quadratic Hamiltonians for fermionic systems can be characterized in terms of orthogonal complex structures. The standard way in which such Hamiltonians are diagonalized makes use of a certain “doubling” of the Hilbert space. In this work, we show that this redundancy in the Hilbert space can be completely lifted if the relevant orthogonal structure is taken into account. Such an approach allows for a treatment of Majorana fermions which is both physically and mathematically transparent. Furthermore, an explicit connection between orthogonal complex structures and the topological ℤ2-invariant is given.

An all-digital receiver for satellite audio broadcasting signals using trellis coded quasi-orthogonal code-division multiplexing

NASA Astrophysics Data System (ADS)

Braun, Walter; Eglin, Peter; Abello, Ricard

1993-02-01

Spread Spectrum Code Division Multiplex is an attractive scheme for the transmission of multiple signals over a satellite transponder. By using orthogonal or quasi-orthogonal spreading codes the interference between the users can be virtually eliminated. However, the acquisition and tracking of the spreading code phase can not take advantage of the code orthogonality since sequential acquisition and Delay-Locked loop tracking depend on correlation with code phases other than the optimal despreading phase. Hence, synchronization is a critical issue in such a system. A demonstration hardware for the verification of the orthogonal CDM synchronization and data transmission concept is being designed and implemented. The system concept, the synchronization scheme, and the implementation are described. The performance of the system is discussed based on computer simulations.

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.

Interference-Assisted Techniques for Transmission and Multiple Access in Optical Communications

NASA Astrophysics Data System (ADS)

Guan, Xun

Optical communications can be in wired or wireless form. Fiber optics communication (FOC) connects transmitters and receivers with optical fiber. Benefiting from its high bandwidth, low cost per volume and stability, it gains a significant market share in long-haul networks, access networks and data centers. Meanwhile, optical wireless communication (OWC) is also emerging as a crucial player in the communication market. In OWC, free-space optical communication (FSO) and visible light communication (VLC) are being studied and commercially deployed extensively. Interference is a common phenomenon in multi-user communication systems. In both FOC and OWC, interference has long been treated as a detrimental effect. However, it could also be beneficial to system applications. The effort of harnessing interference has spurred numerous innovations. Interesting examples are physical-layer network coding (PNC) and non-orthogonal multiple access (NOMA). The first part of this thesis in on the topic of PNC. PNC was firstly proposed in wireless communication to improve the throughput of a two-way relay network (TWRN). As a variation of network coding (NC), PNC turns the common channel interference (CCI) as a natural network coding operation. In this thesis, PNC is introduced into optical communication. Three schemes are proposed in different scenarios. Firstly, PNC is applied to a coherent optical orthogonal frequency division multiplexing (CO-OFDM) system so as to improve the throughput of the multicast network. The optical signal to noise ratio (OSNR) penalty is quite low. Secondly, we investigate the application of PNC in an OFDM passive optical network (OFDM-PON) supporting heterogeneous services. It is found that only minor receiver power penalties are observed to realize PNC-based virtual private networks (VPN), both in the wired service part and the wireless service part in an OFDM-PON with heterogeneous services. Thirdly, we innovate relay-based visible light communication (VLC) by adopting PNC, with a newly proposed phase-aligning method. PNC could improve the throughput at the bottlenecking relay node in a VLC system, and the proposed phase aligning method can improve the BER performance. The second part of this thesis discusses another interference-assisted technology in communication, that is, non-orthogonal multiple access (NOMA). NOMA multiplexes signals from multiple users in another dimension: power domain, with a non-orthogonal multiplexing in other dimensions such as time, frequency and code. Three schemes are proposed in this part. The first and the second schemes both realize NOMA in VLC, with different multiuser detection (MUD) techniques and a proposed phase pre-distortion method. Although both can decrease the system BER compared to conventional NOMA, the scheme using joint detection (JD) outperforms the one using successive interference cancellation (SIC). The third scheme investigated in this part is a combination of NOMA and a multicarrier precoding (MP) technology based on an orthogonal circulant transform matrix (OCT). This combination can avoid the complicated adaptive bit loading or electronic equalization, making NOMA more attractive in a practical system.

Styles of Deformation on Either Side of a Ridge-Transform Intersection, Troodos Ophiolite, Cyprus

NASA Astrophysics Data System (ADS)

Titus, S.; Wagner, C.; Alexander, S. O.; Scott, C. P.; Davis, J. R.

2015-12-01

The Troodos ophiolite in Cyprus includes two orthogonal structures - the NS-striking Solea graben and the EW-striking Arakapas fault - that form a ridge-transform intersection. Sheeted dikes and gabbros are preserved on both the inside and outside corners providing a view of mid-crustal deformation in the system. We examine and model these patterns of deformation using existing map and paleomagnetic data combined with new rock magnetic data. The inside corner of the system has been well studied. The most notable feature is the changing orientation of sheeted dikes, which shift from NW- to NE- to E-striking with increasing proximity to the Arakapas fault. Paleomagnetic data from many studies, including our own, show declination anomalies that vary with distance from the ridge and the transform. The three principal axes from anisotropy of magnetic susceptibility (AMS) ellipsoids in the gabbros seem to be correlated with local sheeted dike orientations. The outside corner of the system has been less well studied. Sheeted dike orientations change more subtly; many are NS-striking and dip towards the Solea Graben, but near the inferred ridge-transform intersection, they are NNE-striking. Our new paleomagnetic data from 26 sites record declination and inclination anomalies that vary spatially within the outside corner. AMS data from the gabbros and sheeted dikes again seem loosely linked to sheeted dike orientations. To summarize, the structural and rock magnetic results on either side of the Solea Graben are distinct, confirming the idea that these rocks formed on different sides of a ridge-transform system. The paleomagnetic data yield insights about the styles of deformation following crystallization. The AMS data may yield insights about magmatic plumbing systems when combined systematically with paleomagnetic results. Our results from the outside corner show that patterns of deformation can be complex even on the non-plate boundary side of a ridge-transform system.

A note on the zeros of Freud-Sobolev orthogonal polynomials

NASA Astrophysics Data System (ADS)

Moreno-Balcazar, Juan J.

2007-10-01

We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e-x4 on are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e-x4. Some numerical examples are shown.

Encrypted holographic data storage based on orthogonal-phase-code multiplexing.

PubMed

Heanue, J F; Bashaw, M C; Hesselink, L

1995-09-10

We describe an encrypted holographic data-storage system that combines orthogonal-phase-code multiplexing with a random-phase key. The system offers the security advantages of random-phase coding but retains the low cross-talk performance and the minimum code storage requirements typical in an orthogonal-phase-code-multiplexing system.

Orthogonal Regression: A Teaching Perspective

ERIC Educational Resources Information Center

Carr, James R.

2012-01-01

A well-known approach to linear least squares regression is that which involves minimizing the sum of squared orthogonal projections of data points onto the best fit line. This form of regression is known as orthogonal regression, and the linear model that it yields is known as the major axis. A similar method, reduced major axis regression, is…

Redesigning metabolism based on orthogonality principles

PubMed Central

Pandit, Aditya Vikram; Srinivasan, Shyam; Mahadevan, Radhakrishnan

2017-01-01

Modifications made during metabolic engineering for overproduction of chemicals have network-wide effects on cellular function due to ubiquitous metabolic interactions. These interactions, that make metabolic network structures robust and optimized for cell growth, act to constrain the capability of the cell factory. To overcome these challenges, we explore the idea of an orthogonal network structure that is designed to operate with minimal interaction between chemical production pathways and the components of the network that produce biomass. We show that this orthogonal pathway design approach has significant advantages over contemporary growth-coupled approaches using a case study on succinate production. We find that natural pathways, fundamentally linked to biomass synthesis, are less orthogonal in comparison to synthetic pathways. We suggest that the use of such orthogonal pathways can be highly amenable for dynamic control of metabolism and have other implications for metabolic engineering. PMID:28555623

Orthogonal Chirp-Based Ultrasonic Positioning

PubMed Central

Khyam, Mohammad Omar; Ge, Shuzhi Sam; Li, Xinde; Pickering, Mark

2017-01-01

This paper presents a chirp based ultrasonic positioning system (UPS) using orthogonal chirp waveforms. In the proposed method, multiple transmitters can simultaneously transmit chirp signals, as a result, it can efficiently utilize the entire available frequency spectrum. The fundamental idea behind the proposed multiple access scheme is to utilize the oversampling methodology of orthogonal frequency-division multiplexing (OFDM) modulation and orthogonality of the discrete frequency components of a chirp waveform. In addition, the proposed orthogonal chirp waveforms also have all the advantages of a classical chirp waveform. Firstly, the performance of the waveforms is investigated through correlation analysis and then, in an indoor environment, evaluated through simulations and experiments for ultrasonic (US) positioning. For an operational range of approximately 1000 mm, the positioning root-mean-square-errors (RMSEs) &90% error were 4.54 mm and 6.68 mm respectively. PMID:28448454

Orthogonal Chirp-Based Ultrasonic Positioning.

PubMed

Khyam, Mohammad Omar; Ge, Shuzhi Sam; Li, Xinde; Pickering, Mark

2017-04-27

This paper presents a chirp based ultrasonic positioning system (UPS) using orthogonal chirp waveforms. In the proposed method, multiple transmitters can simultaneously transmit chirp signals, as a result, it can efficiently utilize the entire available frequency spectrum. The fundamental idea behind the proposed multiple access scheme is to utilize the oversampling methodology of orthogonal frequency-division multiplexing (OFDM) modulation and orthogonality of the discrete frequency components of a chirp waveform. In addition, the proposed orthogonal chirp waveforms also have all the advantages of a classical chirp waveform. Firstly, the performance of the waveforms is investigated through correlation analysis and then, in an indoor environment, evaluated through simulations and experiments for ultrasonic (US) positioning. For an operational range of approximately 1000 mm, the positioning root-mean-square-errors (RMSEs) &90% error were 4.54 mm and 6.68 mm respectively.

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.

Evaluation of a six-DOF electrodynamic shaker system.

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

Gregory, Danny Lynn; Smallwood, David Ora

2009-03-01

The paper describes the preliminary evaluation of a 6 degree of freedom electrodynamic shaker system. The 8 by 8 inch (20.3 cm) table is driven by 12 electrodynamic shakers producing motion in all 6 rigid body modes. A small electrodynamic shaker system suitable for small component testing is described. The principal purpose of the system is to demonstrate the technology. The shaker is driven by 12 electrodynamic shakers each with a force capability of about 50 lbs (220 N). The system was developed through an informal cooperative agreement between Sandia National Laboratories, Team Corp. and Spectral Dynamics Corporation. Sandia providedmore » the laboratory space and some development funds. Team provided the mechanical system, and Spectral Dynamics provided the control system. Spectral Dynamics was chosen to provide the control system partly because of their experience in MIMO control and partly because Sandia already had part of the system in house. The shaker system was conceived and manufactured by TEAM Corp. Figure 1 shows the overall system. The vibration table, electrodynamic shakers, hydraulic pumps, and amplifiers are all housed in a single cabinet. Figure 2 is a drawing showing how the electrodynamic shakers are coupled to the table. The shakers are coupled to the table through a hydraulic spherical pad bearing providing 5 degrees of freedom and one stiff degree of freedom. The pad bearing must be preloaded with a static force as they are unable to provide any tension forces. The horizontal bearings are preloaded with steel springs. The drawing shows a spring providing the vertical preload. This was changed in the final design. The vertical preload is provided by multiple strands of an O-ring material as shown in Figure 4. Four shakers provide excitation in each of the three orthogonal axes. The specifications of the shaker are outlined in Table 1. Four shakers provide inputs in each of the three orthogonal directions. By choosing the phase relationships between the shakers all six rigid body modes (three translation, and three rotations) can be excited. The system is over determined. There are more shakers than degrees of freedom. This provided an interesting control problem. The problem was approached using the input-output transformation matrices provided in the Spectral control system. Twelve accelerometers were selected for the control accelerometers (a tri-axial accelerometer at each corner of the table (see Figure 5). Figure 6 shows the nomenclature used to identify the shakers and control accelerometers. A fifth tri-axial accelerometer was placed at the center of the table, but it was not used for control. Thus we had 12 control accelerometers and 12 shakers to control a 6-dof shaker. The 12 control channels were reduced to a 6-dof control using a simple input transformation matrix. The control was defined by a 6x6 spectral density matrix. The six outputs in the control variable coordinates were transformed to twelve physical drive signals using another simple output transformation matrix. It was assumed that the accelerometers and shakers were well matched such that the transformation matrices were independent of frequency and could be deduced from rigid body considerations. The input/output transformations are shown in Equations 1 and 2.« less

Simple techniques for improving deep neural network outcomes on commodity hardware

NASA Astrophysics Data System (ADS)

Colina, Nicholas Christopher A.; Perez, Carlos E.; Paraan, Francis N. C.

2017-08-01

We benchmark improvements in the performance of deep neural networks (DNN) on the MNIST data test upon imple-menting two simple modifications to the algorithm that have little overhead computational cost. First is GPU parallelization on a commodity graphics card, and second is initializing the DNN with random orthogonal weight matrices prior to optimization. Eigenspectra analysis of the weight matrices reveal that the initially orthogonal matrices remain nearly orthogonal after training. The probability distributions from which these orthogonal matrices are drawn are also shown to significantly affect the performance of these deep neural networks.

Polarization-phase diagnostics of latent course of cholelithiasis in patients with chronic cholecystitis combined with diabetes mellitus type 2

NASA Astrophysics Data System (ADS)

Fediv, O. I.; Ivashchuk, O. I.; Marchuk, Yu. F.; Andriychuk, D. R.

2011-09-01

The principles of optical model of human bile polycrystalline structure are described. The three optical levels - isotropic, liquid-crystal and solid-crystal have been proposed. It has been introduced and proposed the scenarios of phase distribution formation in the boundary field of laser radiation, transformed by bile layers. The experimental scheme of direct measurement of coordinate phase distributions has been presented. The results of investigating the interrelation between the values of correlation and fractal parameters are presented. They characterize the coordinate distributions of phase shifts between the orthogonal components of the amplitude in the points of laser images of bile smears of cholelithiasis patients in combination with other pathologies. The diagnostic criteria of the cholelithiasis nascency and its severity degree differentiation are determined.

Self spectrum window method in wigner-ville distribution.

PubMed

Liu, Zhongguo; Liu, Changchun; Liu, Boqiang; Lv, Yangsheng; Lei, Yinsheng; Yu, Mengsun

2005-01-01

Wigner-Ville distribution (WVD) is an important type of time-frequency analysis in biomedical signal processing. The cross-term interference in WVD has a disadvantageous influence on its application. In this research, the Self Spectrum Window (SSW) method was put forward to suppress the cross-term interference, based on the fact that the cross-term and auto-WVD- terms in integral kernel function are orthogonal. With the Self Spectrum Window (SSW) algorithm, a real auto-WVD function was used as a template to cross-correlate with the integral kernel function, and the Short Time Fourier Transform (STFT) spectrum of the signal was used as window function to process the WVD in time-frequency plane. The SSW method was confirmed by computer simulation with good analysis results. Satisfactory time- frequency distribution was obtained.

A non-orthogonal decomposition of flows into discrete events

NASA Astrophysics Data System (ADS)

Boxx, Isaac; Lewalle, Jacques

1998-11-01

This work is based on the formula for the inverse Hermitian wavelet transform. A signal can be interpreted as a (non-unique) superposition of near-singular, partially overlapping events arising from Dirac functions and/or its derivatives combined with diffusion.( No dynamics implied: dimensionless diffusion is related to the definition of the analyzing wavelets.) These events correspond to local maxima of spectral energy density. We successfully fitted model events of various orders on a succession of fields, ranging from elementary signals to one-dimensional hot-wire traces. We document edge effects, event overlap and its implications on the algorithm. The interpretation of the discrete singularities as flow events (such as coherent structures) and the fundamental non-uniqueness of the decomposition are discussed. The dynamics of these events will be examined in the companion paper.

A chaotic modified-DFT encryption scheme for physical layer security and PAPR reduction in OFDM-PON

NASA Astrophysics Data System (ADS)

Fu, Xiaosong; Bi, Meihua; Zhou, Xuefang; Yang, Guowei; Li, Qiliang; Zhou, Zhao; Yang, Xuelin

2018-05-01

This letter proposes a modified discrete Fourier transform (DFT) encryption scheme with multi-dimensional chaos for the physical layer security and peak-to-average power ratio (PAPR) reduction in orthogonal frequency division multiplexing passive optical network (OFDM-PON) system. This multiple-fold encryption algorithm is mainly composed by using the column vectors permutation and the random phase encryption in the standard DFT matrix, which can create ∼10551 key space. The transmission of ∼10 Gb/s encrypted OFDM signal is verified over 20-km standard single mode fiber (SMF). Moreover, experimental results show that, the proposed scheme can achieve ∼2.6-dB PAPR reduction and ∼1-dB improvement of receiver sensitivity if compared with the common OFDM-PON.

Simultaneous orthogonal plane imaging.

PubMed

Mickevicius, Nikolai J; Paulson, Eric S

2017-11-01

Intrafraction motion can result in a smearing of planned external beam radiation therapy dose distributions, resulting in an uncertainty in dose actually deposited in tissue. The purpose of this paper is to present a pulse sequence that is capable of imaging a moving target at a high frame rate in two orthogonal planes simultaneously for MR-guided radiotherapy. By balancing the zero gradient moment on all axes, slices in two orthogonal planes may be spatially encoded simultaneously. The orthogonal slice groups may be acquired with equal or nonequal echo times. A Cartesian spoiled gradient echo simultaneous orthogonal plane imaging (SOPI) sequence was tested in phantom and in vivo. Multiplexed SOPI acquisitions were performed in which two parallel slices were imaged along two orthogonal axes simultaneously. An autocalibrating phase-constrained 2D-SENSE-GRAPPA (generalized autocalibrating partially parallel acquisition) algorithm was implemented to reconstruct the multiplexed data. SOPI images without intraslice motion artifacts were reconstructed at a maximum frame rate of 8.16 Hz. The 2D-SENSE-GRAPPA reconstruction separated the parallel slices aliased along each orthogonal axis. The high spatiotemporal resolution provided by SOPI has the potential to be beneficial for intrafraction motion management during MR-guided radiation therapy or other MRI-guided interventions. Magn Reson Med 78:1700-1710, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

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

Functional Implications of Ubiquitous Semicircular Canal Non-Orthogonality in Mammals

PubMed Central

Berlin, Jeri C.; Kirk, E. Christopher; Rowe, Timothy B.

2013-01-01

The ‘canonical model’ of semicircular canal orientation in mammals assumes that 1) the three ipsilateral canals of an inner ear exist in orthogonal planes (i.e., orthogonality), 2) corresponding left and right canal pairs have equivalent angles (i.e., angle symmetry), and 3) contralateral synergistic canals occupy parallel planes (i.e., coplanarity). However, descriptions of vestibular anatomy that quantify semicircular canal orientation in single species often diverge substantially from this model. Data for primates further suggest that semicircular canal orthogonality varies predictably with the angular head velocities encountered in locomotion. These observations raise the possibility that orthogonality, symmetry, and coplanarity are misleading descriptors of semicircular canal orientation in mammals, and that deviations from these norms could have significant functional consequences. Here we critically assess the canonical model of semicircular canal orientation using high-resolution X-ray computed tomography scans of 39 mammal species. We find that substantial deviations from orthogonality, angle symmetry, and coplanarity are the rule for the mammals in our comparative sample. Furthermore, the degree to which the semicircular canals of a given species deviate from orthogonality is negatively correlated with estimated vestibular sensitivity. We conclude that the available comparative morphometric data do not support the canonical model and that its overemphasis as a heuristic generalization obscures a large amount of functionally relevant variation in semicircular canal orientation between species. PMID:24260256

Proton triggered circularly polarized luminescence in orthogonal- and co-assemblies of chiral gelators with achiral perylene bisimide.

PubMed

Han, Dongxue; Han, Jianlei; Huo, Shengwei; Qu, Zuoming; Jiao, Tifeng; Liu, Minghua; Duan, Pengfei

2018-05-29

The orthogonal- or co-assembly of achiral perylene bisimide (PBI) with chiral gelators can be regulated by solvents. While the coassembly leads to the formation of chiroptical nanofibers through chirality transfer, the orthogonal assemblies could not. Moreover, protonation on the coassembled nanofibers could light up the circularly polarized luminescence (CPL).

Unnatural reactive amino acid genetic code additions

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

Deiters, Alexander; Cropp, T. Ashton; Chin, Jason W.

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

Expanding the eukaryotic genetic code

DOEpatents

Chin, Jason W.; Cropp, T. Ashton; Anderson, J. Christopher; Schultz, Peter G.

2013-01-22

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

The Computation of Orthogonal Independent Cluster Solutions and Their Oblique Analogs in Factor Analysis.

ERIC Educational Resources Information Center

Hofmann, Richard J.

A very general model for the computation of independent cluster solutions in factor analysis is presented. The model is discussed as being either orthogonal or oblique. Furthermore, it is demonstrated that for every orthogonal independent cluster solution there is an oblique analog. Using three illustrative examples, certain generalities are made…

Expanding the eukaryotic genetic code

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

Chin, Jason W.; Cropp, T. Ashton; Anderson, J. Christopher

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

Expanding the eukaryotic genetic code

DOEpatents

Chin, Jason W [Cambridge, GB; Cropp, T Ashton [Bethesda, MD; Anderson, J Christopher [San Francisco, CA; Schultz, Peter G [La Jolla, CA

2009-10-27

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

Expanding the eukaryotic genetic code

DOEpatents

Chin, Jason W; Cropp, T. Ashton; Anderson, J. Christopher; Schultz, Peter G

2015-02-03

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

Expanding the eukaryotic genetic code

DOEpatents

Chin, Jason W [Cambridge, GB; Cropp, T Ashton [Bethesda, MD; Anderson, J Christopher [San Francisco, CA; Schultz, Peter G [La Jolla, CA

2009-12-01

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

Expanding the eukaryotic genetic code

DOEpatents

Chin, Jason W [Cambridge, GB; Cropp, T Ashton [Bethesda, MD; Anderson, J Christopher [San Francisco, CA; Schultz, Peter G [La Jolla, CA

2012-02-14

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

Expanding the eukaryotic genetic code

DOEpatents

Chin, Jason W [Cambridge, GB; Cropp, T Ashton [Bethesda, MD; Anderson, J Christopher [San Francisco, CA; Schultz, Peter G [La Jolla, CA

2009-11-17

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

Expanding the eukaryotic genetic code

DOEpatents

Chin, Jason W.; Cropp, T. Ashton; Anderson, J. Christopher; Schultz, Peter G.

2010-09-14

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

Expanding the eukaryotic genetic code

DOEpatents

Chin, Jason W [Cambridge, GB; Cropp, T Ashton [Bethesda, MD; Anderson, J Christopher [San Francisco, CA; Schultz, Peter G [La Jolla, CA

2012-05-08

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

Unnatural reactive amino acid genetic code additions

DOEpatents

Deiters, Alexander [La Jolla, CA; Cropp, T Ashton [San Diego, CA; Chin, Jason W [Cambridge, GB; Anderson, J Christopher [San Francisco, CA; Schultz, Peter G [La Jolla, CA

2011-02-15

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

Unnatural reactive amino acid genetic code additions

DOEpatents

Deiters, Alexander; Cropp, T. Ashton; Chin, Jason W.; Anderson, J. Christopher; Schultz, Peter G.

2014-08-26

This invention provides compositions and methods for producing translational components that expand the number of genetically encoded amino acids in eukaryotic cells. The components include orthogonal tRNAs, orthogonal aminoacyl-tRNA synthetases, orthogonal pairs of tRNAs/synthetases and unnatural amino acids. Proteins and methods of producing proteins with unnatural amino acids in eukaryotic cells are also provided.

Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos

DTIC Science & Technology

2001-09-11

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc...scheme, which is represented as a tree structure in figure 1 (following [24]), classifies the hypergeometric orthogonal polynomials and indicates the...2F0(1) 2F0(0) Figure 1: The Askey scheme of orthogonal polynomials The orthogonal polynomials associated with the generalized polynomial chaos,

Mathematical construction and perturbation analysis of Zernike discrete orthogonal points.

PubMed

Shi, Zhenguang; Sui, Yongxin; Liu, Zhenyu; Peng, Ji; Yang, Huaijiang

2012-06-20

Zernike functions are orthogonal within the unit circle, but they are not over the discrete points such as CCD arrays or finite element grids. This will result in reconstruction errors for loss of orthogonality. By using roots of Legendre polynomials, a set of points within the unit circle can be constructed so that Zernike functions over the set are discretely orthogonal. Besides that, the location tolerances of the points are studied by perturbation analysis, and the requirements of the positioning precision are not very strict. Computer simulations show that this approach provides a very accurate wavefront reconstruction with the proposed sampling set.

Prescription Proportion of Pomegranate Extract Gallic Acid Gel by Orthogonal Design

NASA Astrophysics Data System (ADS)

Fan, Gaofu; Liu, Xiushu; Tang, Jie; Gong, Jumei; Fu, Entao; Cai, Yuhua; Xu, Zhenguo

2018-05-01

The aim of the present work was to optimize the formulation of pomegranate extract gallic acid gel by orthogonal design. Using orthogonal design, propylene glycol, carbomer-940 and gel pH level as influencing factors, the evaluation key index was external apearance malleability, uniformity, and eccentric for gel, and the optimum formula was selected. The present findings suggest that 10% propylene glycol, 1.5% Carbopol-940, and gel pH in the range of 4.5∼5.5, and the indexes of the optimal. The inclusion complexes showed that after the orthogonal design, the preparation process was simple, stable and controllable quality, with production feasibility.

Subjective ranking of concert halls substantiated through orthogonal objective parameters.

PubMed

Cerdá, Salvador; Giménez, Alicia; Cibrián, Rosa; Girón, Sara; Zamarreño, Teófilo

2015-02-01

This paper studies the global subjective assessment, obtained from mean values of the results of surveys addressed to members of the audience of live concerts in Spanish auditoriums, through the mean values of the three orthogonal objective parameters (Tmid, IACCE3, and LEV), expressed in just noticeable differences (JNDs), regarding the best-valued hall. Results show that a linear combination of the relative variations of orthogonal parameters can largely explain the overall perceived quality of the sample. However, the mean values of certain orthogonal parameters are not representative, which shows that an alternative approach to the problem is necessary. Various possibilities are proposed.

Orthogonality of embedded wave functions for different states in frozen-density embedding theory

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

Zech, Alexander; Wesolowski, Tomasz A.; Aquilante, Francesco

2015-10-28

Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles — embedded wave functions are only auxiliary objects used to obtain stationary densities — working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematicalmore » structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities.« less

A sigma factor toolbox for orthogonal gene expression in Escherichia coli

PubMed Central

Van Brempt, Maarten; Van Nerom, Katleen; Van Hove, Bob; Maertens, Jo; De Mey, Marjan; Charlier, Daniel

2018-01-01

Abstract Synthetic genetic sensors and circuits enable programmable control over timing and conditions of gene expression and, as a result, are increasingly incorporated into the control of complex and multi-gene pathways. Size and complexity of genetic circuits are growing, but stay limited by a shortage of regulatory parts that can be used without interference. Therefore, orthogonal expression and regulation systems are needed to minimize undesired crosstalk and allow for dynamic control of separate modules. This work presents a set of orthogonal expression systems for use in Escherichia coli based on heterologous sigma factors from Bacillus subtilis that recognize specific promoter sequences. Up to four of the analyzed sigma factors can be combined to function orthogonally between each other and toward the host. Additionally, the toolbox is expanded by creating promoter libraries for three sigma factors without loss of their orthogonal nature. As this set covers a wide range of transcription initiation frequencies, it enables tuning of multiple outputs of the circuit in response to different sensory signals in an orthogonal manner. This sigma factor toolbox constitutes an interesting expansion of the synthetic biology toolbox and may contribute to the assembly of more complex synthetic genetic systems in the future. PMID:29361130

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.

Reduced field-of-view imaging for single-shot MRI with an amplitude-modulated chirp pulse excitation and Fourier transform reconstruction.

PubMed

Li, Jing; Zhang, Miao; Chen, Lin; Cai, Congbo; Sun, Huijun; Cai, Shuhui

2015-06-01

We employ an amplitude-modulated chirp pulse to selectively excite spins in one or more regions of interest (ROIs) to realize reduced field-of-view (rFOV) imaging based on single-shot spatiotemporally encoded (SPEN) sequence and Fourier transform reconstruction. The proposed rFOV imaging method was theoretically analyzed and illustrated with numerical simulation and tested with phantom experiments and in vivo rat experiments. In addition, point spread function was applied to demonstrate the feasibility of the proposed method. To evaluate the proposed method, the rFOV results were compared with those obtained using the EPI method with orthogonal RF excitation. The simulation and experimental results show that the proposed method can image one or two separated ROIs along the SPEN dimension in a single shot with higher spatial resolution, less sensitive to field inhomogeneity, and practically no aliasing artifacts. In addition, the proposed method may produce rFOV images with comparable signal-to-noise ratio to the rFOV EPI images. The proposed method is promising for the applications under severe susceptibility heterogeneities and for imaging separate ROIs simultaneously. Copyright © 2015 Elsevier Inc. All rights reserved.

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution. Appendix 7. [Transform Domain Skiprope Observer for tethered satellites

NASA Technical Reports Server (NTRS)

Ioup, George E.; Ioup, Juliette W.

1993-01-01

Because of the interesting science which can be performed using a satellite attached by a very long tether to a mother vehicle in orbit, such as the Space Shuttle, NASA will deploy TSS-1 (Tethered Satellite System) in 1992. A very long tether (20 km in this case) has the possibility of undergoing oscillations of several different types, or modes, and higher harmonics of these modes. The purpose of this document is to describe a method for detecting the amplitude, frequency, and phase (and predicting future motion in the steady state) of these modes, in particular, the skiprope mode, using tethered satellite dynamics measurements. Specifically the rotation rate data about two orthogonal axes, calculated from output from satellite gyroscopes, are used. The data of interest are the satellite pitch and roll rate measurements. NASA has determined to use two methods to diagnose skiprope properties and predict future values. One of these, a Fourier transform domain approach, is the subject of this notebook. The main program and all subroutines are described along with the test plan for evaluating the Frequency Domain Skiprope Observer.

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.

A Software Architecture for Intelligent Synthesis Environments

NASA Technical Reports Server (NTRS)

Filman, Robert E.; Norvig, Peter (Technical Monitor)

2001-01-01

The NASA's Intelligent Synthesis Environment (ISE) program is a grand attempt to develop a system to transform the way complex artifacts are engineered. This paper discusses a "middleware" architecture for enabling the development of ISE. Desirable elements of such an Intelligent Synthesis Architecture (ISA) include remote invocation; plug-and-play applications; scripting of applications; management of design artifacts, tools, and artifact and tool attributes; common system services; system management; and systematic enforcement of policies. This paper argues that the ISA extend conventional distributed object technology (DOT) such as CORBA and Product Data Managers with flexible repositories of product and tool annotations and "plug-and-play" mechanisms for inserting "ility" or orthogonal concerns into the system. I describe the Object Infrastructure Framework, an Aspect Oriented Programming (AOP) environment for developing distributed systems that provides utility insertion and enables consistent annotation maintenance. This technology can be used to enforce policies such as maintaining the annotations of artifacts, particularly the provenance and access control rules of artifacts-, performing automatic datatype transformations between representations; supplying alternative servers of the same service; reporting on the status of jobs and the system; conveying privileges throughout an application; supporting long-lived transactions; maintaining version consistency; and providing software redundancy and mobility.

Harmonic analysis of traction power supply system based on wavelet decomposition

NASA Astrophysics Data System (ADS)

Dun, Xiaohong

2018-05-01

With the rapid development of high-speed railway and heavy-haul transport, AC drive electric locomotive and EMU large-scale operation in the country on the ground, the electrified railway has become the main harmonic source of China's power grid. In response to this phenomenon, the need for timely monitoring of power quality problems of electrified railway, assessment and governance. Wavelet transform is developed on the basis of Fourier analysis, the basic idea comes from the harmonic analysis, with a rigorous theoretical model, which has inherited and developed the local thought of Garbor transformation, and has overcome the disadvantages such as window fixation and lack of discrete orthogonally, so as to become a more recently studied spectral analysis tool. The wavelet analysis takes the gradual and precise time domain step in the high frequency part so as to focus on any details of the signal being analyzed, thereby comprehensively analyzing the harmonics of the traction power supply system meanwhile use the pyramid algorithm to increase the speed of wavelet decomposition. The matlab simulation shows that the use of wavelet decomposition of the traction power supply system for harmonic spectrum analysis is effective.

622-Mbps Orthogonal Frequency Division Multiplexing (OFDM) Digital Modem Implemented

NASA Technical Reports Server (NTRS)

Kifle, Muli; Bizon, Thomas P.; Nguyen, Nam T.; Tran, Quang K.; Mortensen, Dale J.

2002-01-01

Future generation space communications systems feature significantly higher data rates and relatively smaller frequency spectrum allocations than systems currently deployed. This requires the application of bandwidth- and power-efficient signal transmission techniques. There are a number of approaches to implementing such techniques, including analog, digital, mixed-signal, single-channel, or multichannel systems. In general, the digital implementations offer more advantages; however, a fully digital implementation is very difficult because of the very high clock speeds required. Multichannel techniques are used to reduce the sampling rate. One such technique, multicarrier modulation, divides the data into a number of low-rate channels that are stacked in frequency. Orthogonal frequency division multiplexing (OFDM), a form of multicarrier modulation, is being proposed for numerous systems, including mobile wireless and digital subscriber link communication systems. In response to this challenge, NASA Glenn Research Center's Communication Technology Division has developed an OFDM digital modem (modulator and demodulator) with an aggregate information throughput of 622 Mbps. The basic OFDM waveform is constructed by dividing an incoming data stream into four channels, each using either 16- ary quadrature amplitude modulation (16-QAM) or 8-phase shift keying (8-PSK). An efficient implementation for an OFDM architecture is being achieved using the combination of a discrete Fourier transform (DFT) at the transmitter to digitally stack the individual carriers, inverse DFT at the receiver to perform the frequency translations, and a polyphase filter to facilitate the pulse shaping.

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.

Stochastic uncertainty analysis for unconfined flow systems

USGS Publications Warehouse

Liu, Gaisheng; Zhang, Dongxiao; Lu, Zhiming

2006-01-01

A new stochastic approach proposed by Zhang and Lu (2004), called the Karhunen‐Loeve decomposition‐based moment equation (KLME), has been extended to solving nonlinear, unconfined flow problems in randomly heterogeneous aquifers. This approach is on the basis of an innovative combination of Karhunen‐Loeve decomposition, polynomial expansion, and perturbation methods. The random log‐transformed hydraulic conductivity field (lnKS) is first expanded into a series in terms of orthogonal Gaussian standard random variables with their coefficients obtained as the eigenvalues and eigenfunctions of the covariance function of lnKS. Next, head h is decomposed as a perturbation expansion series Σh(m), where h(m) represents the mth‐order head term with respect to the standard deviation of lnKS. Then h(m) is further expanded into a polynomial series of m products of orthogonal Gaussian standard random variables whose coefficients hi1,i2,...,im(m) are deterministic and solved sequentially from low to high expansion orders using MODFLOW‐2000. Finally, the statistics of head and flux are computed using simple algebraic operations on hi1,i2,...,im(m). A series of numerical test results in 2‐D and 3‐D unconfined flow systems indicated that the KLME approach is effective in estimating the mean and (co)variance of both heads and fluxes and requires much less computational effort as compared to the traditional Monte Carlo simulation technique.

Orthogonal higher order structure and confirmatory factor analysis of the French Wechsler Adult Intelligence Scale (WAIS-III).

PubMed

Golay, Philippe; Lecerf, Thierry

2011-03-01

According to the most widely accepted Cattell-Horn-Carroll (CHC) model of intelligence measurement, each subtest score of the Wechsler Intelligence Scale for Adults (3rd ed.; WAIS-III) should reflect both 1st- and 2nd-order factors (i.e., 4 or 5 broad abilities and 1 general factor). To disentangle the contribution of each factor, we applied a Schmid-Leiman orthogonalization transformation (SLT) to the standardization data published in the French technical manual for the WAIS-III. Results showed that the general factor accounted for 63% of the common variance and that the specific contributions of the 1st-order factors were weak (4.7%-15.9%). We also addressed this issue by using confirmatory factor analysis. Results indicated that the bifactor model (with 1st-order group and general factors) better fit the data than did the traditional higher order structure. Models based on the CHC framework were also tested. Results indicated that a higher order CHC model showed a better fit than did the classical 4-factor model; however, the WAIS bifactor structure was the most adequate. We recommend that users do not discount the Full Scale IQ when interpreting the index scores of the WAIS-III because the general factor accounts for the bulk of the common variance in the French WAIS-III. The 4 index scores cannot be considered to reflect only broad ability because they include a strong contribution of the general factor.

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.

Deformable registration for image-guided spine surgery: preserving rigid body vertebral morphology in free-form transformations

NASA Astrophysics Data System (ADS)

Reaungamornrat, S.; Wang, A. S.; Uneri, A.; Otake, Y.; Zhao, Z.; Khanna, A. J.; Siewerdsen, J. H.

2014-03-01

Purpose: Deformable registration of preoperative and intraoperative images facilitates accurate localization of target and critical anatomy in image-guided spine surgery. However, conventional deformable registration fails to preserve the morphology of rigid bone anatomy and can impart distortions that confound high-precision intervention. We propose a constrained registration method that preserves rigid morphology while allowing deformation of surrounding soft tissues. Method: The registration method aligns preoperative 3D CT to intraoperative cone-beam CT (CBCT) using free-form deformation (FFD) with penalties on rigid body motion imposed according to a simple intensity threshold. The penalties enforced 3 properties of a rigid transformation - namely, constraints on affinity (AC), orthogonality (OC), and properness (PC). The method also incorporated an injectivity constraint (IC) to preserve topology. Physical experiments (involving phantoms, an ovine spine, and a human cadaver) as well as digital simulations were performed to evaluate the sensitivity to registration parameters, preservation of rigid body morphology, and overall registration accuracy of constrained FFD in comparison to conventional unconstrained FFD (denoted uFFD) and Demons registration. Result: FFD with orthogonality and injectivity constraints (denoted FFD+OC+IC) demonstrated improved performance compared to uFFD and Demons. Affinity and properness constraints offered little or no additional improvement. The FFD+OC+IC method preserved rigid body morphology at near-ideal values of zero dilatation (D = 0.05, compared to 0.39 and 0.56 for uFFD and Demons, respectively) and shear (S = 0.08, compared to 0.36 and 0.44 for uFFD and Demons, respectively). Target registration error (TRE) was similarly improved for FFD+OC+IC (0.7 mm), compared to 1.4 and 1.8 mm for uFFD and Demons. Results were validated in human cadaver studies using CT and CBCT images, with FFD+OC+IC providing excellent preservation of rigid morphology and equivalent or improved TRE. Conclusions: A promising method for deformable registration in CBCT-guided spine surgery has been identified incorporating a constrained FFD to preserve bone morphology. The approach overcomes distortions intrinsic to unconstrained FFD and could better facilitate high-precision image-guided spine surgery.

On multiple orthogonal polynomials for discrete Meixner measures

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

Sorokin, Vladimir N

2010-12-07

The paper examines two examples of multiple orthogonal polynomials generalizing orthogonal polynomials of a discrete variable, meaning thereby the Meixner polynomials. One example is bound up with a discrete Nikishin system, and the other leads to essentially new effects. The limit distribution of the zeros of polynomials is obtained in terms of logarithmic equilibrium potentials and in terms of algebraic curves. Bibliography: 9 titles.

OFDM Coupled Compressive Sensing Algorithm for Stepped-Frequency Ground Penetrating Radar

DTIC Science & Technology

2014-10-01

These frequencies are combined in such a way to achieve orthogonality between the carrier frequencies, while mitigating any interference between...in such a way to achieve orthogonality between the carrier frequencies, while mitigating any interference between said frequencies. In CS, a signal...frequency tones is mitigated . Orthogonality requires that the sub-bands are spaced at = is the OFDM symbol period, and k is any

SU-E-J-17: Intra-Fractional Prostate Movement Correction During Treatment Delivery Period for Prostate Cancer Using the Intra-Fractional Orthogonal KV-MV Image Pairs

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

Zhang, J; Azawi, S; Cho-Lim, J

Purpose: To evaluate the intra-fractional prostate movement range during the beam delivery and implement new IGRT method to correct the prostate movement during the hypofractionated prostate treatment delivery. Methods: To evaluate the prostate internal motion range during the beam delivery, 11 conventional treatments were utilized. Two-arc RapidArc plans were used for the treatment delivery. Orthogonal KV imaging is performed in the middle of the treatment to correct intra-fractional prostate movement. However, it takes gantry-mounted on-board imaging system relative long time to finish the orthogonal KV imaging because of gantry rotation. To avoid gantry movement and accelerate the IGRT processing time,more » orthogonal KV-MV image pair is tested using the OBI daily QA Cube phantom. Results: The average prostate movement between two orthogonal KV image pairs was 0.38cm (0.20cm ∼ 0.85cm). And the interval time between them was 6.71 min (4.64min ∼ 9.22 min). 2-arc beam delivery time is within 3 minutes for conventional RapidArc treatment delivery. Hypofractionated treatment or SBRT need 4 partial arc and possible non-coplanar technology, which need much longer beam delivery time. Therefore prostate movement might be larger. New orthogonal KV-MV image pair is a new method to correct the prostate movement in the middle of the beam delivery if real time tracking method is not available. Orthogonal KV-MV image pair doesn’t need gantry rotation. Images were acquired quickly which minimized possible new prostate movement. Therefore orthogonal KV-MV image pair is feasible for IGRT. Conclusion: Hypofractionated prostate treatment with less PTV margin always needs longer beam delivery time. Therefore prostate movement correction during the treatment delivery is critical. Orthogonal KV-MV imaging pair is efficient and accurate to correct the prostate movement during treatment beam delivery. Due to limited fraction number and high dose per fraction, the MV imaging dose is negligible.« less

Uncertainty Quantification given Discontinuous Climate Model Response and a Limited Number of Model Runs

NASA Astrophysics Data System (ADS)

Sargsyan, K.; Safta, C.; Debusschere, B.; Najm, H.

2010-12-01

Uncertainty quantification in complex climate models is challenged by the sparsity of available climate model predictions due to the high computational cost of model runs. Another feature that prevents classical uncertainty analysis from being readily applicable is bifurcative behavior in climate model response with respect to certain input parameters. A typical example is the Atlantic Meridional Overturning Circulation. The predicted maximum overturning stream function exhibits discontinuity across a curve in the space of two uncertain parameters, namely climate sensitivity and CO2 forcing. We outline a methodology for uncertainty quantification given discontinuous model response and a limited number of model runs. Our approach is two-fold. First we detect the discontinuity with Bayesian inference, thus obtaining a probabilistic representation of the discontinuity curve shape and location for arbitrarily distributed input parameter values. Then, we construct spectral representations of uncertainty, using Polynomial Chaos (PC) expansions on either side of the discontinuity curve, leading to an averaged-PC representation of the forward model that allows efficient uncertainty quantification. The approach is enabled by a Rosenblatt transformation that maps each side of the discontinuity to regular domains where desirable orthogonality properties for the spectral bases hold. We obtain PC modes by either orthogonal projection or Bayesian inference, and argue for a hybrid approach that targets a balance between the accuracy provided by the orthogonal projection and the flexibility provided by the Bayesian inference - where the latter allows obtaining reasonable expansions without extra forward model runs. The model output, and its associated uncertainty at specific design points, are then computed by taking an ensemble average over PC expansions corresponding to possible realizations of the discontinuity curve. The methodology is tested on synthetic examples of discontinuous model data with adjustable sharpness and structure. This work was supported by the Sandia National Laboratories Seniors’ Council LDRD (Laboratory Directed Research and Development) program. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Company, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

A genomically modified Escherichia coli strain carrying an orthogonal E. coli histidyl-tRNA synthetase•tRNAHis pair.

PubMed

Englert, Markus; Vargas-Rodriguez, Oscar; Reynolds, Noah M; Wang, Yane-Shih; Söll, Dieter; Umehara, Takuya

2017-11-01

Development of new aminoacyl-tRNA synthetase (aaRS)•tRNA pairs is central for incorporation of novel non-canonical amino acids (ncAAs) into proteins via genetic code expansion (GCE). The Escherichia coli and Caulobacter crescentus histidyl-tRNA synthetases (HisRS) evolved divergent mechanisms of tRNA His recognition that prevent their cross-reactivity. Although the E. coli HisRS•tRNA His pair is a good candidate for GCE, its use in C. crescentus is limited by the lack of established genetic selection methods and by the low transformation efficiency of C. crescentus. E. coli was genetically engineered to use a C. crescentus HisRS•tRNA His pair. Super-folder green fluorescent protein (sfGFP) and chloramphenicol acetyltransferase (CAT) were used as reporters for read-through assays. A library of 313 ncAAs coupled with the sfGFP reporter system was employed to investigate the specificity of E. coli HisRS in vivo. A genomically modified E. coli strain (named MEOV1) was created. MEVO1 requires an active C. crescentus HisRS•tRNA His pair for growth, and displays a similar doubling time as the parental E. coli strain. sfGFP- and CAT-based assays showed that the E. coli HisRS•tRNA His pair is orthogonal in MEOV1 cells. A mutation in the anticodon loop of E. coli tRNA His CUA elevated its suppression efficiency by 2-fold. The C. crescentus HisRS•tRNA His pair functionally complements an E. coli ΔhisS strain. The E. coli HisRS•tRNA His is orthogonal in MEOV1 cells. E. coli tRNA His CUA is an efficient amber suppressor in MEOV1. We developed a platform that allows protein engineering of E. coli HisRS that should facilitate GCE in E. coli. This article is part of a Special Issue entitled "Biochemistry of Synthetic Biology - Recent Developments" Guest Editor: Dr. Ilka Heinemann and Dr. Patrick O'Donoghue. Copyright © 2017 Elsevier B.V. All rights reserved.

Stable orthogonal local discriminant embedding for linear dimensionality reduction.

PubMed

Gao, Quanxue; Ma, Jingjie; Zhang, Hailin; Gao, Xinbo; Liu, Yamin

2013-07-01

Manifold learning is widely used in machine learning and pattern recognition. However, manifold learning only considers the similarity of samples belonging to the same class and ignores the within-class variation of data, which will impair the generalization and stableness of the algorithms. For this purpose, we construct an adjacency graph to model the intraclass variation that characterizes the most important properties, such as diversity of patterns, and then incorporate the diversity into the discriminant objective function for linear dimensionality reduction. Finally, we introduce the orthogonal constraint for the basis vectors and propose an orthogonal algorithm called stable orthogonal local discriminate embedding. Experimental results on several standard image databases demonstrate the effectiveness of the proposed dimensionality reduction approach.

Orthogonality of spherical harmonic coefficients

NASA Astrophysics Data System (ADS)

McLeod, M. G.

1980-08-01

Orthogonality relations are obtained for the spherical harmonic coefficients of functions defined on the surface of a sphere. Following a brief discussion of the orthogonality of Fourier series coefficients, consideration is given to the values averaged over all orientations of the coordinate system of the spherical harmonic coefficients of a function defined on the surface of a sphere that can be expressed in terms of Legendre polynomials for the special case where the function is the sum of two delta functions located at two different points on the sphere, and for the case of an essentially arbitrary function. It is noted that the orthogonality relations derived have found applications in statistical studies of the geomagnetic field.

Orthogonal system of fractural and integrated diagnostic features in vibration analysis

NASA Astrophysics Data System (ADS)

Kostyukov, V. N.; Boychenko, S. N.

2017-08-01

The paper presents the results obtained in the studies of the orthogonality of the vibration diagnostic features system comprising the integrated features, particularly - root mean square values of vibration acceleration, vibration velocity, vibration displacement and fractal feature (Hurst exponent). To diagnose the condition of the equipment by the vibration signal, the orthogonality of the vibration diagnostic features is important. The fact of orthogonality shows that the system of features is not superfluous and allows the maximum coverage of the state space of the object being diagnosed. This, in turn, increases reliability of the machinery condition monitoring results. The studies were carried out on the models of vibration signals using the programming language R.

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.

A novel all-optical label processing based on multiple optical orthogonal codes sequences for optical packet switching networks

NASA Astrophysics Data System (ADS)

Zhang, Chongfu; Qiu, Kun; Xu, Bo; Ling, Yun

2008-05-01

This paper proposes an all-optical label processing scheme that uses the multiple optical orthogonal codes sequences (MOOCS)-based optical label for optical packet switching (OPS) (MOOCS-OPS) networks. In this scheme, each MOOCS is a permutation or combination of the multiple optical orthogonal codes (MOOC) selected from the multiple-groups optical orthogonal codes (MGOOC). Following a comparison of different optical label processing (OLP) schemes, the principles of MOOCS-OPS network are given and analyzed. Firstly, theoretical analyses are used to prove that MOOCS is able to greatly enlarge the number of available optical labels when compared to the previous single optical orthogonal code (SOOC) for OPS (SOOC-OPS) network. Then, the key units of the MOOCS-based optical label packets, including optical packet generation, optical label erasing, optical label extraction and optical label rewriting etc., are given and studied. These results are used to verify that the proposed MOOCS-OPS scheme is feasible.

Sample-independent approach to normalize two-dimensional data for orthogonality evaluation using whole separation space scaling.

PubMed

Jáčová, Jaroslava; Gardlo, Alžběta; Friedecký, David; Adam, Tomáš; Dimandja, Jean-Marie D

2017-08-18

Orthogonality is a key parameter that is used to evaluate the separation power of chromatography-based two-dimensional systems. It is necessary to scale the separation data before the assessment of the orthogonality. Current scaling approaches are sample-dependent, and the extent of the retention space that is converted into a normalized retention space is set according to the retention times of the first and last analytes contained in a unique sample to elute. The presence or absence of a highly retained analyte in a sample can thus significantly influence the amount of information (in terms of the total amount of separation space) contained in the normalized retention space considered for the calculation of the orthogonality. We propose a Whole Separation Space Scaling (WOSEL) approach that accounts for the whole separation space delineated by the analytical method, and not the sample. This approach enables an orthogonality-based evaluation of the efficiency of the analytical system that is independent of the sample selected. The WOSEL method was compared to two currently used orthogonality approaches through the evaluation of in silico-generated chromatograms and real separations of human biofluids and petroleum samples. WOSEL exhibits sample-to-sample stability values of 3.8% on real samples, compared to 7.0% and 10.1% for the two other methods, respectively. Using real analyses, we also demonstrate that some previously developed approaches can provide misleading conclusions on the overall orthogonality of a two-dimensional chromatographic system. Copyright © 2017 Elsevier B.V. All rights reserved.

Reproducibility of Abdominal Aortic Aneurysm Diameter Measurement and Growth Evaluation on Axial and Multiplanar Computed Tomography Reformations

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

Dugas, Alexandre; Therasse, Eric; Kauffmann, Claude

2012-08-15

Purpose: To compare different methods measuring abdominal aortic aneurysm (AAA) maximal diameter (Dmax) and its progression on multidetector computed tomography (MDCT) scan. Materials and Methods: Forty AAA patients with two MDCT scans acquired at different times (baseline and follow-up) were included. Three observers measured AAA diameters by seven different methods: on axial images (anteroposterior, transverse, maximal, and short-axis views) and on multiplanar reformation (MPR) images (coronal, sagittal, and orthogonal views). Diameter measurement and progression were compared over time for the seven methods. Reproducibility of measurement methods was assessed by intraclass correlation coefficient (ICC) and Bland-Altman analysis. Results: Dmax, as measuredmore » on axial slices at baseline and follow-up (FU) MDCTs, was greater than that measured using the orthogonal method (p = 0.046 for baseline and 0.028 for FU), whereas Dmax measured with the orthogonal method was greater those using all other measurement methods (p-value range: <0.0001-0.03) but anteroposterior diameter (p = 0.18 baseline and 0.10 FU). The greatest interobserver ICCs were obtained for the orthogonal and transverse methods (0.972) at baseline and for the orthogonal and sagittal MPR images at FU (0.973 and 0.977). Interobserver ICC of the orthogonal method to document AAA progression was greater (ICC = 0.833) than measurements taken on axial images (ICC = 0.662-0.780) and single-plane MPR images (0.772-0.817). Conclusion: AAA Dmax measured on MDCT axial slices overestimates aneurysm size. Diameter as measured by the orthogonal method is more reproducible, especially to document AAA progression.« less

Reference hypernetted chain theory for ferrofluid bilayer: Distribution functions compared with Monte Carlo

NASA Astrophysics Data System (ADS)

Polyakov, Evgeny A.; Vorontsov-Velyaminov, Pavel N.

2014-08-01

Properties of ferrofluid bilayer (modeled as a system of two planar layers separated by a distance h and each layer carrying a soft sphere dipolar liquid) are calculated in the framework of inhomogeneous Ornstein-Zernike equations with reference hypernetted chain closure (RHNC). The bridge functions are taken from a soft sphere (1/r12) reference system in the pressure-consistent closure approximation. In order to make the RHNC problem tractable, the angular dependence of the correlation functions is expanded into special orthogonal polynomials according to Lado. The resulting equations are solved using the Newton-GRMES algorithm as implemented in the public-domain solver NITSOL. Orientational densities and pair distribution functions of dipoles are compared with Monte Carlo simulation results. A numerical algorithm for the Fourier-Hankel transform of any positive integer order on a uniform grid is presented.

Gesture recognition for smart home applications using portable radar sensors.

PubMed

Wan, Qian; Li, Yiran; Li, Changzhi; Pal, Ranadip

2014-01-01

In this article, we consider the design of a human gesture recognition system based on pattern recognition of signatures from a portable smart radar sensor. Powered by AAA batteries, the smart radar sensor operates in the 2.4 GHz industrial, scientific and medical (ISM) band. We analyzed the feature space using principle components and application-specific time and frequency domain features extracted from radar signals for two different sets of gestures. We illustrate that a nearest neighbor based classifier can achieve greater than 95% accuracy for multi class classification using 10 fold cross validation when features are extracted based on magnitude differences and Doppler shifts as compared to features extracted through orthogonal transformations. The reported results illustrate the potential of intelligent radars integrated with a pattern recognition system for high accuracy smart home and health monitoring purposes.

Alkynyl Moiety for Triggering 1,2‐Metallate Shifts: Enantiospecific sp2–sp3 Coupling of Boronic Esters with p‐Arylacetylenes

PubMed Central

Ganesh, Venkataraman; Odachowski, Marcin

2017-01-01

Abstract The enantiospecific coupling of secondary and tertiary boronic esters to aromatics has been investigated. Using p‐lithiated phenylacetylenes and a range of boronic esters coupling has been achieved by the addition of N‐bromosuccinimide (NBS). The alkyne functionality of the intermediate boronate complex reacts with NBS triggering the 1,2‐migration of the group on boron to carbon giving a dearomatized bromoallene intermediate. At this point elimination and rearomatization occurs with neopentyl boronic esters, giving the coupled products. However, using pinacol boronic esters, the boron moiety migrates to the adjacent carbon resulting in formation of ortho boron‐incorporated coupled products. The synthetic utility of the boron incorporated product has been demonstrated by orthogonal transformation of both the alkyne and boronic ester functionalities. PMID:28618129

Continuum modeling of the mechanical and thermal behavior of discrete large structures

NASA Technical Reports Server (NTRS)

Nayfeh, A. H.; Hefzy, M. S.

1980-01-01

In the present paper we introduce a rather straightforward construction procedure in order to derive continuum equivalence of discrete truss-like repetitive structures. Once the actual structure is specified, the construction procedure can be outlined by the following three steps: (a) all sets of parallel members are identified, (b) unidirectional 'effective continuum' properties are derived for each of these sets and (c) orthogonal transformations are finally used to determine the contribution of each set to the 'overall effective continuum' properties of the structure. Here the properties includes mechanical (stiffnesses), thermal (coefficients of thermal expansions) and material densities. Once expanded descriptions of the steps (b) and (c) are done, the construction procedure will be applied to a wide variety of discrete structures and the results will be compared with those of other existing methods.

On the theory of group generation of stars

NASA Technical Reports Server (NTRS)

Zhilyayev, B. Y.; Porfiryev, V. V.; Shulman, L. M.

1973-01-01

The hypothesis proposed is that topology of a rotating gaseous cloud can be variable in the contraction process. Due to rotation an originally spherical cloud is transformed into a toroidal body. The contraction of a thin torus is considered with different suppositions on cooling the gas. In the determined time the torus will become gravitationally unstable. The excitation of Jeans' waves is shown to result in the disintegration of the torus into fragments. The number of the fragments and their mass distributions are calculated. The proposed hypothesis on toroidal stages in stellar evolution can remove some difficulties in the theory of structure and evolution of stars, such as absence of limitary stars, distribution of rotation velocities of early-type stars, origin of poloidal magnetic fields and decline rotators with the magnetic axis orthogonal to the axis of rotation.

On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

NASA Astrophysics Data System (ADS)

Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

2017-01-01

In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.

Definition of a parametric form of nonsingular Mueller matrices.

PubMed

Devlaminck, Vincent; Terrier, Patrick

2008-11-01

The goal of this paper is to propose a mathematical framework to define and analyze a general parametric form of an arbitrary nonsingular Mueller matrix. Starting from previous results about nondepolarizing matrices, we generalize the method to any nonsingular Mueller matrix. We address this problem in a six-dimensional space in order to introduce a transformation group with the same number of degrees of freedom and explain why subsets of O(5,1), the orthogonal group associated with six-dimensional Minkowski space, is a physically admissible solution to this question. Generators of this group are used to define possible expressions of an arbitrary nonsingular Mueller matrix. Ultimately, the problem of decomposition of these matrices is addressed, and we point out that the "reverse" and "forward" decomposition concepts recently introduced may be inferred from the formalism we propose.

Motions, efforts and actuations in constrained dynamic systems: a multi-link open-chain example

NASA Astrophysics Data System (ADS)

Duke Perreira, N.

1999-08-01

The effort-motion method, which describes the dynamics of open- and closed-chain topologies of rigid bodies interconnected with revolute and prismatic pairs, is interpreted geometrically. Systems are identified for which the simultaneous control of forces and velocities is desirable, and a representative open-chain system is selected for use in the ensuing analysis. Gauge invariant transformations are used to recast the commonly used kinetic and kinematic equations into a dimensional gauge invariant form. Constraint elimination techniques based on singular value decompositions then recast the invariant equations into orthogonal and reciprocal sets of motion and effort equations written in state variable form. The ideal actuation is found that simultaneously achieves the obtainable portions of the desired constraining efforts and motions. The performance is then evaluated of using the actuation closest to the ideal actuation.

A complete active space valence bond method with nonorthogonal orbitals

NASA Astrophysics Data System (ADS)

Hirao, Kimihiko; Nakano, Haruyuki; Nakayama, Kenichi

1997-12-01

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

Global finite-time attitude stabilization for rigid spacecraft in the exponential coordinates

NASA Astrophysics Data System (ADS)

Shi, Xiao-Ning; Zhou, Zhi-Gang; Zhou, Di

2018-06-01

This paper addresses the global finite-time attitude stabilisation problem on the special orthogonal group (SO(3)) for a rigid spacecraft via homogeneous feedback approach. Considering the topological and geometric properties of SO(3), the logarithm map is utilised to transform the stabilisation problem on SO(3) into the one on its associated Lie algebra (?). A model-independent discontinuous state feedback plus dynamics compensation scheme is constructed to achieve the global finite-time attitude stabilisation in a coordinate-invariant way. In addition, to address the absence of angular velocity measurements, a sliding mode observer is proposed to reconstruct the unknown angular velocity information within finite time. Then, an observer-based finite-time output feedback control strategy is obtained. Numerical simulations are finally performed to demonstrate the effectiveness of the proposed finite-time controllers.

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

A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or 6 - j Symbols.

DTIC Science & Technology

1978-03-01

Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. [11] D. Stanton, Some basic hypergeometric polynomials arising from... Some bas ic hypergeometr ic an a logues of the classical orthogonal polynomials and applications , to appear. [3] C. de Boor and G. H. Golub , The...Report #1833 A SET OF ORTHOGONAL POLYNOMIALS THAT GENERALIZE THE RACAR COEFFICIENTS OR 6 — j SYMBOLS Richard Askey and James Wilson •

A Code Division Multiple Access Communication System for the Low Frequency Band.

DTIC Science & Technology

1983-04-01

frequency channels spread-spectrum communication / complex sequences, orthogonal codes impulsive noise 20. ABSTRACT (Continue an reverse side It...their transmissions with signature sequences. Our LF/CDMA scheme is different in that each user’s signature sequence set consists of M orthogonal ...signature sequences. Our LF/CDMA scheme is different in that each user’s signature sequence set consists of M orthogonal sequences and thus log 2 M

Polarization-balanced beamsplitter

DOEpatents

Decker, D.E.

1998-02-17

A beamsplitter assembly is disclosed that includes several beamsplitter cubes arranged to define a plurality of polarization-balanced light paths. Each polarization-balanced light path contains one or more balanced pairs of light paths, where each balanced pair of light paths includes either two transmission light paths with orthogonal polarization effects or two reflection light paths with orthogonal polarization effects. The orthogonal pairing of said transmission and reflection light paths cancels polarization effects otherwise caused by beamsplitting. 10 figs.

University of California San Francisco (UCSF-1): Construction of Directional Regulatory Networks Using Orthogonal CRISPR/Cas Screens | Office of Cancer Genomics

Cancer.gov

UCSF investigators developed an orthogonal CRISPR/Cas system which can be used to quantify gene regulation and construct directional regulatory networks. They combined two orthogonal Cas9 proteins from Streptococcus pyogenes and Staphylococcus aureus to carry out a dual screen in which one gene is activated while a second gene is deleted in the same cell. Read the abstract.

Generations of orthogonal surface coordinates

NASA Technical Reports Server (NTRS)

Blottner, F. G.; Moreno, J. B.

1980-01-01

Two generation methods were developed for three dimensional flows where the computational domain normal to the surface is small. With this restriction the coordinate system requires orthogonality only at the body surface. The first method uses the orthogonal condition in finite-difference form to determine the surface coordinates with the metric coefficients and curvature of the coordinate lines calculated numerically. The second method obtains analytical expressions for the metric coefficients and for the curvature of the coordinate lines.

Recurrence relations for orthogonal polynomials for PDEs in polar and cylindrical geometries.

PubMed

Richardson, Megan; Lambers, James V

2016-01-01

This paper introduces two families of orthogonal polynomials on the interval (-1,1), with weight function [Formula: see text]. The first family satisfies the boundary condition [Formula: see text], and the second one satisfies the boundary conditions [Formula: see text]. These boundary conditions arise naturally from PDEs defined on a disk with Dirichlet boundary conditions and the requirement of regularity in Cartesian coordinates. The families of orthogonal polynomials are obtained by orthogonalizing short linear combinations of Legendre polynomials that satisfy the same boundary conditions. Then, the three-term recurrence relations are derived. Finally, it is shown that from these recurrence relations, one can efficiently compute the corresponding recurrences for generalized Jacobi polynomials that satisfy the same boundary conditions.

Study on multiple-hops performance of MOOC sequences-based optical labels for OPS networks

NASA Astrophysics Data System (ADS)

Zhang, Chongfu; Qiu, Kun; Ma, Chunli

2009-11-01

In this paper, we utilize a new study method that is under independent case of multiple optical orthogonal codes to derive the probability function of MOOCS-OPS networks, discuss the performance characteristics for a variety of parameters, and compare some characteristics of the system employed by single optical orthogonal code or multiple optical orthogonal codes sequences-based optical labels. The performance of the system is also calculated, and our results verify that the method is effective. Additionally it is found that performance of MOOCS-OPS networks would, negatively, be worsened, compared with single optical orthogonal code-based optical label for optical packet switching (SOOC-OPS); however, MOOCS-OPS networks can greatly enlarge the scalability of optical packet switching networks.

Experimental quantum-cryptography scheme based on orthogonal states

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

Avella, Alessio; Brida, Giorgio; Degiovanni, Ivo Pietro

2010-12-15

Since, in general, nonorthogonal states cannot be cloned, any eavesdropping attempt in a quantum-communication scheme using nonorthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in quantum-cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman [Phys. Rev. Lett. 75, 1239 (1995)] proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal statesmore » are superpositions of two localized wave packets traveling along separate channels. Here we present an experiment realizing this scheme.« less

Generation of orthogonally polarized self-mode-locked Nd:YAG lasers with tunable beat frequencies from the thermally induced birefringence.

PubMed

Sung, C L; Cheng, H P; Lee, C Y; Cho, C Y; Liang, H C; Chen, Y F

2016-04-15

The simultaneous self-mode-locking of two orthogonally polarized states in a Nd:YAG laser is demonstrated by using a short linear cavity. A total output power of 3.8 W can be obtained at an incident pump power of 8.2 W. The beat frequency Δfc between two orthogonally polarized mode-locked components is observed and measured precisely. It is found that the beat frequency increases linearly with an increase in the absorbed pump power. The origin of the beat frequency can be utterly manifested by considering the thermally induced birefringence in the Nd:YAG crystal. The present result offers a promising approach to generate orthogonally polarized mode-locked lasers with tunable beat frequency.

Umbral orthogonal polynomials

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

Lopez-Sendino, J. E.; del Olmo, M. A.

2010-12-23

We present an umbral operator version of the classical orthogonal polynomials. We obtain three families which are the umbral counterpart of the Jacobi, Laguerre and Hermite polynomials in the classical case.

A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

NASA Astrophysics Data System (ADS)

Deift, P.; Kriecherbauer, T.; McLaughlin, K. T.-R.; Venakides, S.; Zhou, X.

2001-08-01

A few years ago the authors introduced a new approach to study asymptotic questions for orthogonal polynomials. In this paper we give an overview of our method and review the results which have been obtained in Deift et al. (Internat. Math. Res. Notices (1997) 759, Comm. Pure Appl. Math. 52 (1999) 1491, 1335), Deift (Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes, Vol. 3, New York University, 1999), Kriecherbauer and McLaughlin (Internat. Math. Res. Notices (1999) 299) and Baik et al. (J. Amer. Math. Soc. 12 (1999) 1119). We mainly consider orthogonal polynomials with respect to weights on the real line which are either (1) Freud-type weights d[alpha](x)=e-Q(x) dx (Q polynomial or Q(x)=x[beta], [beta]>0), or (2) varying weights d[alpha]n(x)=e-nV(x) dx (V analytic, limx-->[infinity] V(x)/logx=[infinity]). We obtain Plancherel-Rotach-type asymptotics in the entire complex plane as well as asymptotic formulae with error estimates for the leading coefficients, for the recurrence coefficients, and for the zeros of the orthogonal polynomials. Our proof starts from an observation of Fokas et al. (Comm. Math. Phys. 142 (1991) 313) that the orthogonal polynomials can be determined as solutions of certain matrix valued Riemann-Hilbert problems. We analyze the Riemann-Hilbert problems by a steepest descent type method introduced by Deift and Zhou (Ann. Math. 137 (1993) 295) and further developed in Deift and Zhou (Comm. Pure Appl. Math. 48 (1995) 277) and Deift et al. (Proc. Nat. Acad. Sci. USA 95 (1998) 450). A crucial step in our analysis is the use of the well-known equilibrium measure which describes the asymptotic distribution of the zeros of the orthogonal polynomials.

A comparison between orthogonal and parallel plating methods for distal humerus fractures: a prospective randomized trial.

PubMed

Lee, Sang Ki; Kim, Kap Jung; Park, Kyung Hoon; Choy, Won Sik

2014-10-01

With the continuing improvements in implants for distal humerus fractures, it is expected that newer types of plates, which are anatomically precontoured, thinner and less irritating to soft tissue, would have comparable outcomes when used in a clinical study. The purpose of this study was to compare the clinical and radiographic outcomes in patients with distal humerus fractures who were treated with orthogonal and parallel plating methods using precontoured distal humerus plates. Sixty-seven patients with a mean age of 55.4 years (range 22-90 years) were included in this prospective study. The subjects were randomly assigned to receive 1 of 2 treatments: orthogonal or parallel plating. The following results were assessed: operating time, time to fracture union, presence of a step or gap at the articular margin, varus-valgus angulation, functional recovery, and complications. No intergroup differences were observed based on radiological and clinical results between the groups. In our practice, no significant differences were found between the orthogonal and parallel plating methods in terms of clinical outcomes, mean operation time, union time, or complication rates. There were no cases of fracture nonunion in either group; heterotrophic ossification was found 3 patients in orthogonal plating group and 2 patients in parallel plating group. In our practice, no significant differences were found between the orthogonal and parallel plating methods in terms of clinical outcomes or complication rates. However, orthogonal plating method may be preferred in cases of coronal shear fractures, where posterior to anterior fixation may provide additional stability to the intraarticular fractures. Additionally, parallel plating method may be the preferred technique used for fractures that occur at the most distal end of the humerus.

Radar Polarimetry: Theory, Analysis, and Applications

NASA Astrophysics Data System (ADS)

Hubbert, John Clark

The fields of radar polarimetry and optical polarimetry are compared. The mathematics of optic polarimetry are formulated such that a local right handed coordinate system is always used to describe the polarization states. This is not done in radar polarimetry. Radar optimum polarization theory is redeveloped within the framework of optical polarimetry. The radar optimum polarizations and optic eigenvalues of common scatterers are compared. In addition a novel definition of an eigenpolarization state is given and the accompanying mathematics is developed. The polarization response calculated using optic, radar and novel definitions is presented for a variety of scatterers. Polarimetric transformation provides a means to characterize scatters in more than one polarization basis. Polarimetric transformation for an ensemble of scatters is obtained via two methods: (1) the covariance method and (2) the instantaneous scattering matrix (ISM) method. The covariance method is used to relate the mean radar parameters of a +/-45^circ linear polarization basis to those of a horizontal and vertical polarization basis. In contrast the ISM method transforms the individual time samples. Algorithms are developed for transforming the time series from fully polarimetric radars that switch between orthogonal states. The transformed time series are then used to calculate the mean radar parameters of interest. It is also shown that propagation effects do not need to be removed from the ISM's before transformation. The techniques are demonstrated using data collected by POLDIRAD, the German Aerospace Research Establishment's fully polarimetric C-band radar. The differential phase observed between two copolar states, Psi_{CO}, is composed of two phases: (1) differential propagation phase, phi_{DP}, and (2) differential backscatter phase, delta. The slope of phi_{DP } with range is an estimate of the specific differential phase, K_{DP}. The process of estimating K_{DP} is complicated when delta is present. Algorithms are presented for estimating delta and K_{DP} from range profiles of Psi_ {CO}. Also discussed are procedures for the estimation and interpretation of other radar measurables such as reflectivity, Z_{HH}, differential reflectivity, Z_{DR }, the magnitude of the copolar correlation coefficient, rho_{HV}(0), and Doppler spectrum width, sigma _{v}. The techniques are again illustrated with data collected by POLDIRAD.

Wavelet transform analysis of transient signals: the seismogram and the electrocardiogram

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

Anant, K.S.

1997-06-01

In this dissertation I quantitatively demonstrate how the wavelet transform can be an effective mathematical tool for the analysis of transient signals. The two key signal processing applications of the wavelet transform, namely feature identification and representation (i.e., compression), are shown by solving important problems involving the seismogram and the electrocardiogram. The seismic feature identification problem involved locating in time the P and S phase arrivals. Locating these arrivals accurately (particularly the S phase) has been a constant issue in seismic signal processing. In Chapter 3, I show that the wavelet transform can be used to locate both the Pmore » as well as the S phase using only information from single station three-component seismograms. This is accomplished by using the basis function (wave-let) of the wavelet transform as a matching filter and by processing information across scales of the wavelet domain decomposition. The `pick` time results are quite promising as compared to analyst picks. The representation application involved the compression of the electrocardiogram which is a recording of the electrical activity of the heart. Compression of the electrocardiogram is an important problem in biomedical signal processing due to transmission and storage limitations. In Chapter 4, I develop an electrocardiogram compression method that applies vector quantization to the wavelet transform coefficients. The best compression results were obtained by using orthogonal wavelets, due to their ability to represent a signal efficiently. Throughout this thesis the importance of choosing wavelets based on the problem at hand is stressed. In Chapter 5, I introduce a wavelet design method that uses linear prediction in order to design wavelets that are geared to the signal or feature being analyzed. The use of these designed wavelets in a test feature identification application led to positive results. The methods developed in this thesis; the feature identification methods of Chapter 3, the compression methods of Chapter 4, as well as the wavelet design methods of Chapter 5, are general enough to be easily applied to other transient signals.« less

Research and application of multi-agent genetic algorithm in tower defense game

NASA Astrophysics Data System (ADS)

Jin, Shaohua

2018-04-01

In this paper, a new multi-agent genetic algorithm based on orthogonal experiment is proposed, which is based on multi-agent system, genetic algorithm and orthogonal experimental design. The design of neighborhood competition operator, orthogonal crossover operator, Son and self-learning operator. The new algorithm is applied to mobile tower defense game, according to the characteristics of the game, the establishment of mathematical models, and finally increases the value of the game's monster.

On the orthogonal dissipative lax-phillips scattering theory

NASA Astrophysics Data System (ADS)

Neidhardt, Hagen

1988-08-01

The paper is devoted to the so-called orthogonal dissipative Lax-Phillips scattering theory. A parametrization of all possible orthogonal dissipative Lax-Phillips scattering theories is obtained in terms of ordered 6-tuples consisting of unilateral shifts and contractions which can be, roughly speaking, freely chosen. In this parametrization the wave and scattering operators as well as the scattering matrix are explicitly calculated. Moreover, a description of all analytical contraction-valued functions admitting a Darlington synthesis is found.

Riemann-Liouville Fractional Calculus of Certain Finite Class of Classical Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Malik, Pradeep; Swaminathan, A.

2010-11-01

In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann-Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.

Orthogonal translation components for the in vivo incorporation of unnatural amino acids

DOEpatents

Schultz, Peter G.; Alfonta, Lital; Chittuluru, Johnathan R.; Deiters, Alexander; Groff, Dan; Summerer, Daniel; Tsao, Meng -Lin; Wang, Jiangyun; Wu, Ning; Xie, Jianming; Zeng, Huaqiang; Seyedsayamdost, Mohammad; Turner, James

2015-08-11

The invention relates to orthogonal pairs of tRNAs and aminoacyl-tRNA synthetase that can incorporate unnatural amino acid into proteins produced in eubacterial host cells such as E. coli, or in a eukaryotic host such as a yeast cell. The invention provides, for example but not limited to, novel orthogonal synthetases, methods for identifying and making the novel synthetases, methods for producing proteins containing unnatural amino acids, and translation systems.

Orthogonal translation components for the in vivo incorporation of unnatural amino acids

DOEpatents

Schultz, Peter G.; Xie, Jianming; Zeng, Huaqiang

2012-07-10

The invention relates to orthogonal pairs of tRNAs and aminoacyl-tRNA synthetases that can incorporate unnatural amino acids into proteins produced in eubacterial host cells such as E. coli, or in a eukaryotic host such as a yeast cell. The invention provides, for example but not limited to, novel orthogonal synthetases, methods for identifying and making the novel synthetases, methods for producing proteins containing unnatural amino acids, and translation systems.

Three-dimensional MRI-linac intra-fraction guidance using multiple orthogonal cine-MRI planes

NASA Astrophysics Data System (ADS)

Bjerre, Troels; Crijns, Sjoerd; Rosenschöld, Per Munck af; Aznar, Marianne; Specht, Lena; Larsen, Rasmus; Keall, Paul

2013-07-01

The introduction of integrated MRI-radiation therapy systems will offer live intra-fraction imaging. We propose a feasible low-latency multi-plane MRI-linac guidance strategy. In this work we demonstrate how interleaved acquired, orthogonal cine-MRI planes can be used for low-latency tracking of the 3D trajectory of a soft-tissue target structure. The proposed strategy relies on acquiring a pre-treatment 3D breath-hold scan, extracting a 3D target template and performing template matching between this 3D template and pairs of orthogonal 2D cine-MRI planes intersecting the target motion path. For a 60 s free-breathing series of orthogonal cine-MRI planes, we demonstrate that the method was capable of accurately tracking the respiration related 3D motion of the left kidney. Quantitative evaluation of the method using a dataset designed for this purpose revealed a translational error of 1.15 mm for a translation of 39.9 mm. We have demonstrated how interleaved acquired, orthogonal cine-MRI planes can be used for online tracking of soft-tissue target volumes.

Three-dimensional MRI-linac intra-fraction guidance using multiple orthogonal cine-MRI planes.

PubMed

Bjerre, Troels; Crijns, Sjoerd; af Rosenschöld, Per Munck; Aznar, Marianne; Specht, Lena; Larsen, Rasmus; Keall, Paul

2013-07-21

The introduction of integrated MRI-radiation therapy systems will offer live intra-fraction imaging. We propose a feasible low-latency multi-plane MRI-linac guidance strategy. In this work we demonstrate how interleaved acquired, orthogonal cine-MRI planes can be used for low-latency tracking of the 3D trajectory of a soft-tissue target structure. The proposed strategy relies on acquiring a pre-treatment 3D breath-hold scan, extracting a 3D target template and performing template matching between this 3D template and pairs of orthogonal 2D cine-MRI planes intersecting the target motion path. For a 60 s free-breathing series of orthogonal cine-MRI planes, we demonstrate that the method was capable of accurately tracking the respiration related 3D motion of the left kidney. Quantitative evaluation of the method using a dataset designed for this purpose revealed a translational error of 1.15 mm for a translation of 39.9 mm. We have demonstrated how interleaved acquired, orthogonal cine-MRI planes can be used for online tracking of soft-tissue target volumes.

Orthogonal chemical functionalization of patterned gold on silica surfaces

PubMed Central

Léonard, Didier; Le Mogne, Thierry; Zuttion, Francesca; Chevalier, Céline; Phaner-Goutorbe, Magali; Souteyrand, Éliane

2015-01-01

Summary Single-step orthogonal chemical functionalization procedures have been developed with patterned gold on silica surfaces. Different combinations of a silane and a thiol were simultaneously deposited on a gold/silica heterogeneous substrate. The orthogonality of the functionalization (i.e., selective grafting of the thiol on the gold areas and the silane on the silica) was demonstrated by X-ray photoelectron spectroscopy (XPS) as well as time-of-flight secondary ion mass spectrometry (ToF–SIMS) mapping. The orthogonal functionalization was used to immobilize proteins onto gold nanostructures on a silica substrate, as demonstrated by atomic force microscopy (AFM). These results are especially promising in the development of future biosensors where the selective anchoring of target molecules onto nanostructured transducers (e.g., nanoplasmonic biosensors) is a major challenge. PMID:26734519

Designing Uniquely Addressable Bio-orthogonal Synthetic Scaffolds for DNA and RNA Origami.

PubMed

Kozyra, Jerzy; Ceccarelli, Alessandro; Torelli, Emanuela; Lopiccolo, Annunziata; Gu, Jing-Ying; Fellermann, Harold; Stimming, Ulrich; Krasnogor, Natalio

2017-07-21

Nanotechnology and synthetic biology are rapidly converging, with DNA origami being one of the leading bridging technologies. DNA origami was shown to work well in a wide array of biotic environments. However, the large majority of extant DNA origami scaffolds utilize bacteriophages or plasmid sequences thus severely limiting its future applicability as a bio-orthogonal nanotechnology platform. In this paper we present the design of biologically inert (i.e., "bio-orthogonal") origami scaffolds. The synthetic scaffolds have the additional advantage of being uniquely addressable (unlike biologically derived ones) and hence are better optimized for high-yield folding. We demonstrate our fully synthetic scaffold design with both DNA and RNA origamis and describe a protocol to produce these bio-orthogonal and uniquely addressable origami scaffolds.

Experimental quantum-cryptography scheme based on orthogonal states

NASA Astrophysics Data System (ADS)

Avella, Alessio; Brida, Giorgio; Degiovanni, Ivo Pietro; Genovese, Marco; Gramegna, Marco; Traina, Paolo

2010-12-01

Since, in general, nonorthogonal states cannot be cloned, any eavesdropping attempt in a quantum-communication scheme using nonorthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in quantum-cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.75.1239 75, 1239 (1995)] proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal states are superpositions of two localized wave packets traveling along separate channels. Here we present an experiment realizing this scheme.

Geometrical approach to neural net control of movements and posture

NASA Technical Reports Server (NTRS)

Pellionisz, A. J.; Ramos, C. F.

1993-01-01

In one approach to modeling brain function, sensorimotor integration is described as geometrical mapping among coordinates of non-orthogonal frames that are intrinsic to the system; in such a case sensors represent (covariant) afferents and motor effectors represent (contravariant) motor efferents. The neuronal networks that perform such a function are viewed as general tensor transformations among different expressions and metric tensors determining the geometry of neural functional spaces. Although the non-orthogonality of a coordinate system does not impose a specific geometry on the space, this "Tensor Network Theory of brain function" allows for the possibility that the geometry is non-Euclidean. It is suggested that investigation of the non-Euclidean nature of the geometry is the key to understanding brain function and to interpreting neuronal network function. This paper outlines three contemporary applications of such a theoretical modeling approach. The first is the analysis and interpretation of multi-electrode recordings. The internal geometries of neural networks controlling external behavior of the skeletomuscle system is experimentally determinable using such multi-unit recordings. The second application of this geometrical approach to brain theory is modeling the control of posture and movement. A preliminary simulation study has been conducted with the aim of understanding the control of balance in a standing human. The model appears to unify postural control strategies that have previously been considered to be independent of each other. Third, this paper emphasizes the importance of the geometrical approach for the design and fabrication of neurocomputers that could be used in functional neuromuscular stimulation (FNS) for replacing lost motor control.

Modeling of a pitching and plunging airfoil using experimental flow field and load measurements

NASA Astrophysics Data System (ADS)

Troshin, Victor; Seifert, Avraham

2018-01-01

The main goal of the current paper is to outline a low-order modeling procedure of a heaving airfoil in a still fluid using experimental measurements. Due to its relative simplicity, the proposed procedure is applicable for the analysis of flow fields within complex and unsteady geometries and it is suitable for analyzing the data obtained by experimentation. Currently, this procedure is used to model and predict the flow field evolution using a small number of low profile load sensors and flow field measurements. A time delay neural network is used to estimate the flow field. The neural network estimates the amplitudes of the most energetic modes using four sensory inputs. The modes are calculated using proper orthogonal decomposition of the flow field data obtained experimentally by time-resolved, phase-locked particle imaging velocimetry. To permit the use of proper orthogonal decomposition, the measured flow field is mapped onto a stationary domain using volume preserving transformation. The analysis performed by the model showed good estimation quality within the parameter range used in the training procedure. However, the performance deteriorates for cases out of this range. This situation indicates that, to improve the robustness of the model, both the decomposition and the training data sets must be diverse in terms of input parameter space. In addition, the results suggest that the property of volume preservation of the mapping does not affect the model quality as long as the model is not based on the Galerkin approximation. Thus, it may be relaxed for cases with more complex geometry and kinematics.

Wavefront reconstruction for multi-lateral shearing interferometry using difference Zernike polynomials fitting

NASA Astrophysics Data System (ADS)

Liu, Ke; Wang, Jiannian; Wang, Hai; Li, Yanqiu

2018-07-01

For the multi-lateral shearing interferometers (multi-LSIs), the measurement accuracy can be enhanced by estimating the wavefront under test with the multidirectional phase information encoded in the shearing interferogram. Usually the multi-LSIs reconstruct the test wavefront from the phase derivatives in multiple directions using the discrete Fourier transforms (DFT) method, which is only suitable to small shear ratios and relatively sensitive to noise. To improve the accuracy of multi-LSIs, wavefront reconstruction from the multidirectional phase differences using the difference Zernike polynomials fitting (DZPF) method is proposed in this paper. For the DZPF method applied in the quadriwave LSI, difference Zernike polynomials in only two orthogonal shear directions are required to represent the phase differences in multiple shear directions. In this way, the test wavefront can be reconstructed from the phase differences in multiple shear directions using a noise-variance weighted least-squares method with almost no extra computational burden, compared with the usual recovery from the phase differences in two orthogonal directions. Numerical simulation results show that the DZPF method can maintain high reconstruction accuracy in a wider range of shear ratios and has much better anti-noise performance than the DFT method. A null test experiment of the quadriwave LSI has been conducted and the experimental results show that the measurement accuracy of the quadriwave LSI can be improved from 0.0054 λ rms to 0.0029 λ rms (λ = 632.8 nm) by substituting the DFT method with the proposed DZPF method in the wavefront reconstruction process.

Orthogonal array deciphering MRS medium requirements for isolated Lactobacillus rhamnosus ZY with cell properties characterization.

PubMed

Zhang, Yu; Ng, I-Son; Yao, Chuanyi; Lu, Yinghua

2014-09-01

Lactobacillus rhamnosus is a well-known lactic acid bacterium (LAB), but a new ZY strain was isolated for the first time from commercial probiotic powder recently. Although many studies have focused on developing cost-effective media for the production of LAB, the de Man, Rogosa and Sharpe (MRS) medium is still the most common medium for bioprocesses. The aim of the current study is to decipher the composition of MRS based on a statistical approach, which will allow a higher biomass of Lactobacillus to be obtained. In Taguchi's approach, an L27 orthogonal array was adopted to evaluate the significance of 10 ingredients in MRS, in which the effects of the components were ranked according to their effect on biomass at OD600 as dextrose > MnSO4·H2O > beef extract > CH3COONa > MgSO4 > yeast extract > proteose peptone > K2HPO4 > ammonium citrate > Tween 80. Although the individual trace elements of ammonium citrate, K2HPO4, CH3COONa and MgSO4 in MRS had an insignificant influence on the biomass after statistical analysis, the total elimination of trace elements would predominantly affect the cell growth of Lactobacillus. Further characterization of the cell properties through attenuated total reflectance of Fourier transform infrared (ATR-FTIR) spectroscopy and protein identification via SDS-PAGE coupled with tandem mass spectrometry implied that dextrose as major carbon source in MRS played the most crucial role for L. rhamnosus production. Copyright © 2014 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.

Orthogonal-state-based cryptography in quantum mechanics and local post-quantum theories

NASA Astrophysics Data System (ADS)

Aravinda, S.; Banerjee, Anindita; Pathak, Anirban; Srikanth, R.

2014-02-01

We introduce the concept of cryptographic reduction, in analogy with a similar concept in computational complexity theory. In this framework, class A of crypto-protocols reduces to protocol class B in a scenario X, if for every instance a of A, there is an instance b of B and a secure transformation X that reproduces a given b, such that the security of b guarantees the security of a. Here we employ this reductive framework to study the relationship between security in quantum key distribution (QKD) and quantum secure direct communication (QSDC). We show that replacing the streaming of independent qubits in a QKD scheme by block encoding and transmission (permuting the order of particles block by block) of qubits, we can construct a QSDC scheme. This forms the basis for the block reduction from a QSDC class of protocols to a QKD class of protocols, whereby if the latter is secure, then so is the former. Conversely, given a secure QSDC protocol, we can of course construct a secure QKD scheme by transmitting a random key as the direct message. Then the QKD class of protocols is secure, assuming the security of the QSDC class which it is built from. We refer to this method of deduction of security for this class of QKD protocols, as key reduction. Finally, we propose an orthogonal-state-based deterministic key distribution (KD) protocol which is secure in some local post-quantum theories. Its security arises neither from geographic splitting of a code state nor from Heisenberg uncertainty, but from post-measurement disturbance.

Nanoparticle Analysis by Online Comprehensive Two-Dimensional Liquid Chromatography combining Hydrodynamic Chromatography and Size-Exclusion Chromatography with Intermediate Sample Transformation

PubMed Central

2017-01-01

Polymeric nanoparticles have become indispensable in modern society with a wide array of applications ranging from waterborne coatings to drug-carrier-delivery systems. While a large range of techniques exist to determine a multitude of properties of these particles, relating physicochemical properties of the particle to the chemical structure of the intrinsic polymers is still challenging. A novel, highly orthogonal separation system based on comprehensive two-dimensional liquid chromatography (LC × LC) has been developed. The system combines hydrodynamic chromatography (HDC) in the first-dimension to separate the particles based on their size, with ultrahigh-performance size-exclusion chromatography (SEC) in the second dimension to separate the constituting polymer molecules according to their hydrodynamic radius for each of 80 to 100 separated fractions. A chip-based mixer is incorporated to transform the sample by dissolving the separated nanoparticles from the first-dimension online in tetrahydrofuran. The polymer bands are then focused using stationary-phase-assisted modulation to enhance sensitivity, and the water from the first-dimension eluent is largely eliminated to allow interaction-free SEC. Using the developed system, the combined two-dimensional distribution of the particle-size and the molecular-size of a mixture of various polystyrene (PS) and polyacrylate (PACR) nanoparticles has been obtained within 60 min. PMID:28745485

Custom instruction set NIOS-based OFDM processor for FPGAs

NASA Astrophysics Data System (ADS)

Meyer-Bäse, Uwe; Sunkara, Divya; Castillo, Encarnacion; Garcia, Antonio

2006-05-01

Orthogonal Frequency division multiplexing (OFDM) spread spectrum technique, sometimes also called multi-carrier or discrete multi-tone modulation, are used in bandwidth-efficient communication systems in the presence of channel distortion. The benefits of OFDM are high spectral efficiency, resiliency to RF interference, and lower multi-path distortion. OFDM is the basis for the European digital audio broadcasting (DAB) standard, the global asymmetric digital subscriber line (ADSL) standard, in the IEEE 802.11 5.8 GHz band standard, and ongoing development in wireless local area networks. The modulator and demodulator in an OFDM system can be implemented by use of a parallel bank of filters based on the discrete Fourier transform (DFT), in case the number of subchannels is large (e.g. K > 25), the OFDM system are efficiently implemented by use of the fast Fourier transform (FFT) to compute the DFT. We have developed a custom FPGA-based Altera NIOS system to increase the performance, programmability, and low power in mobil wireless systems. The overall gain observed for a 1024-point FFT ranges depending on the multiplier used by the NIOS processor between a factor of 3 and 16. A careful optimization described in the appendix yield a performance gain of up to 77% when compared with our preliminary results.

On a new method for calculating the potential flow past a body of revolution

NASA Technical Reports Server (NTRS)

Kaplan, Carl

1943-01-01

A new method is presented for obtaining the velocity potential of the flow about a body of revolution moving uniformly in the direction of its axis of symmetry in a fluid otherwise at rest. This method is based essentially on the fact that the form of the differential equation for the velocity potential is invariant with regard to conformal transformation of the meridian plane. By means of the conformal transformation of the meridian profile into a circle a system of orthogonal curvilinear coordinates is obtained, the main feature of which is that one of the coordinate lines is the meridian profile itself. The use of this type of coordinate system yields a simple expression of the boundary condition at the surface of the solid and leads to a rational process of iteration for the solution of the differential equation for the velocity potential. It is shown that the velocity potential for an arbitrary body of revolution may be expressed in terms of universal functions which, although not normal, are obtainable by means of simple quadratures. The general results are applied to a body of revolution obtained by revolving a symmetrical Joukowski profile about its axis of symmetry. A numerical example further serves to illustrate the theory.

Graph Databases for Large-Scale Healthcare Systems: A Framework for Efficient Data Management and Data Services

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

Park, Yubin; Shankar, Mallikarjun; Park, Byung H.

Designing a database system for both efficient data management and data services has been one of the enduring challenges in the healthcare domain. In many healthcare systems, data services and data management are often viewed as two orthogonal tasks; data services refer to retrieval and analytic queries such as search, joins, statistical data extraction, and simple data mining algorithms, while data management refers to building error-tolerant and non-redundant database systems. The gap between service and management has resulted in rigid database systems and schemas that do not support effective analytics. We compose a rich graph structure from an abstracted healthcaremore » RDBMS to illustrate how we can fill this gap in practice. We show how a healthcare graph can be automatically constructed from a normalized relational database using the proposed 3NF Equivalent Graph (3EG) transformation.We discuss a set of real world graph queries such as finding self-referrals, shared providers, and collaborative filtering, and evaluate their performance over a relational database and its 3EG-transformed graph. Experimental results show that the graph representation serves as multiple de-normalized tables, thus reducing complexity in a database and enhancing data accessibility of users. Based on this finding, we propose an ensemble framework of databases for healthcare applications.« less

"Orthogonality" in Learning and Assessment

ERIC Educational Resources Information Center

Leslie, David

2014-01-01

This chapter proposes a simple framework, "orthogonality," to help clarify what stakeholders think about learning in college, how we assess outcomes, and how clear assessment methods might help increase confidence in returns on investment.

3D endoscopic pulsed digital holography

NASA Astrophysics Data System (ADS)

Saucedo Anaya, T.; Mendoza Santoyo, F.; Pedrini, G.; Osten, W.

2006-06-01

A rigid endoscope is used in pulsed digital holography to simultaneously evaluate the three orthogonal displacement components from hidden areas of a harmonically vibrating metallic cylinder. The cylinder is illuminated from three different illuminating directions. The optical path for each illumination direction is matched to its corresponding reference beam, but also in such a way that each object-reference beam pair optical path is mismatched such that they are incoherent and can be stored in a single CCD frame. As is typical in these types of interferometric arrangements, two digital holograms are needed in order to compare two different states of the cylinder. Each hologram is Fourier transformed and due to the incoherence introduced three separate spectra are readily identified, each belonging to a object-reference beam pair. On comparing by subtraction the phase obtained from the two pulsed digital holograms it is possible to gather quantitative 3D results from harmonic displacements.

Thermoacoustic magnetohydrodynamic electrical generator

DOEpatents

Wheatley, J.C.; Swift, G.W.; Migliori, A.

1984-11-16

A thermoacoustic magnetohydrodynamic electrical generator includes an intrinsically irreversible thermoacoustic heat engine coupled to a magnetohydrodynamic electrical generator. The heat engine includes an electrically conductive liquid metal as the working fluid and includes two heat exchange and thermoacoustic structure assemblies which drive the liquid in a push-pull arrangement to cause the liquid metal to oscillate at a resonant acoustic frequency on the order of 1000 Hz. The engine is positioned in the field of a magnet and is oriented such that the liquid metal oscillates in a direction orthogonal to the field of the magnet, whereby an alternating electrical potential is generated in the liquid metal. Low-loss, low-inductance electrical conductors electrically connected to opposite sides of the liquid metal conduct an output signal to a transformer adapted to convert the low-voltage, high-current output signal to a more usable higher voltage, lower current signal.

Omniview motionless camera orientation system

NASA Technical Reports Server (NTRS)

Martin, H. Lee (Inventor); Kuban, Daniel P. (Inventor); Zimmermann, Steven D. (Inventor); Busko, Nicholas (Inventor)

2010-01-01

An apparatus and method is provided for converting digital images for use in an imaging system. The apparatus includes a data memory which stores digital data representing an image having a circular or spherical field of view such as an image captured by a fish-eye lens, a control input for receiving a signal for selecting a portion of the image, and a converter responsive to the control input for converting digital data corresponding to the selected portion into digital data representing a planar image for subsequent display. Various methods include the steps of storing digital data representing an image having a circular or spherical field of view, selecting a portion of the image, and converting the stored digital data corresponding to the selected portion into digital data representing a planar image for subsequent display. In various embodiments, the data converter and data conversion step may use an orthogonal set of transformation algorithms.

Digital EPR with an arbitrary waveform generator and direct detection at the carrier frequency

PubMed Central

Tseitlin, Mark; Quine, Richard W.; Rinard, George A.; Eaton, Sandra S.; Eaton, Gareth R.

2011-01-01

A digital EPR spectrometer was constructed by replacing the traditional bridge with an arbitrary waveform generator (AWG) to produce excitation patterns and a high-speed digitizer for direct detection of the spin system response at the carrier frequency. Digital down-conversion produced baseband signals in quadrature with very precise orthogonality. Real-time resonator tuning was performed by monitoring the Fourier transforms of signals reflected from the resonator during frequency sweeps generated by the AWG. The capabilities of the system were demonstrated by rapid magnetic field scans at 256 MHz carrier frequency, and FID and spin echo experiments at 1 and 10 GHz carrier frequencies. For the rapid scan experiments the leakage through a cross-loop resonator was compensated by adjusting the amplitude and phase of a sinusoid at the carrier frequency that was generated with another AWG channel. PMID:21968420

Sub-natural width resonances in Cs vapor confined in micrometric thickness optical cell

NASA Astrophysics Data System (ADS)

Cartaleva, S.; Krasteva, A.; Sargsyan, A.; Sarkisyan, D.; Slavov, D.; Vartanyan, T.

2013-03-01

We present here the behavior of Electromagnetically Induced Transparency (EIT), Velocity Selective Optical Pumping (VSOP) resonances and Velocity Selective Excitation (VSE) resonances observed in Cs vapor confined in а micrometric optical cell (MC) with thickness L = 6λ, λ = 852nm. For comparison of behavior of VSE resonance another conventional optical cell with thickness L=2.5 cm is used. Cells are irradiated in orthogonal to their windows directions by probe beam scanned on the Fg = 4 → Fe= 3, 4, 5 set of transitions and pump beam fixed at the Fg = 3 → Fe = 4 transition, on the D2 line of Cs. The enhanced absorption (fluorescence) narrow VSOP resonance at the closed transition transforms into reduced absorption (fluorescence) one with small increase of atomic concentration or light intensity. A striking difference appears between the VSE resonance broadening in L = 6λ and conventional L = 2.5cm cells.

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.

Probabilistic finite elements for transient analysis in nonlinear continua

NASA Technical Reports Server (NTRS)

Liu, W. K.; Belytschko, T.; Mani, A.

1985-01-01

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Chaotic reconfigurable ZCMT precoder for OFDM data encryption and PAPR reduction

NASA Astrophysics Data System (ADS)

Chen, Han; Yang, Xuelin; Hu, Weisheng

2017-12-01

A secure orthogonal frequency division multiplexing (OFDM) transmission scheme precoded by chaotic Zadoff-Chu matrix transform (ZCMT) is proposed and demonstrated. It is proved that the reconfigurable ZCMT matrices after row/column permutations can be applied as an alternative precoder for peak-to-average power ratio (PAPR) reduction. The permutations and the reconfigurable parameters in ZCMT matrix are generated by a hyper digital chaos, in which a huge key space of ∼ 10800 is created for physical-layer OFDM data encryption. An encrypted data transmission of 8.9 Gb/s optical OFDM signals is successfully demonstrated over 20 km standard single-mode fiber (SSMF) for 16-QAM. The BER performance of the encrypted signals is improved by ∼ 2 dB (BER@ 10-3), which is mainly attributed to the effective reduction of PAPR via chaotic ZCMT precoding. Moreover, the chaotic ZCMT precoding scheme requires no sideband information, thus the spectrum efficiency is enhanced during transmission.

Characterization of the Atacama B-mode Search

NASA Astrophysics Data System (ADS)

Simon, S. M.; Raghunathan, S.; Appel, J. W.; Becker, D. T.; Campusano, L. E.; Cho, H. M.; Essinger-Hileman, T.; Ho, S. P.; Irwin, K. D.; Jarosik, N.; Kusaka, A.; Niemack, M. D.; Nixon, G. W.; Nolta, M. R.; Page, L. A.; Palma, G. A.; Parker, L. P.; Sievers, J. L.; Staggs, S. T.; Visnjic, K.

2014-07-01

The Atacama B-mode Search (ABS), which began observations in February of 2012, is a crossed-Dragone telescope located at an elevation of 5190 m in the Atacama Desert in Chile. ABS is searching for the B-mode polarization spectrum of the cosmic microwave background (CMB) at large angular scales from multipole moments of ` ~ 50 ~ 500, a range that includes the primor- dial B-mode peak from inflationary gravity waves at ~ 100. The ABS focal plane consists of 240 pixels sensitive to 145 GHz, each containing two transition-edge sensor bolometers coupled to orthogonal polarizations with a planar ortho-mode transducer. An ambient-temperature con- tinuously rotating half-wave plate and 4 K optics make the ABS instrument unique. We discuss the characterization of the detector spectral responses with a Fourier transform spectrometer and demonstrate that the pointing model is adequate. We also present measurements of the beam from point sources and compare them with simulations.

Disconjugacy, regularity of multi-indexed rationally extended potentials, and Laguerre exceptional polynomials

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

Grandati, Y.; Quesne, C.

2013-07-15

The power of the disconjugacy properties of second-order differential equations of Schrödinger type to check the regularity of rationally extended quantum potentials connected with exceptional orthogonal polynomials is illustrated by re-examining the extensions of the isotonic oscillator (or radial oscillator) potential derived in kth-order supersymmetric quantum mechanics or multistep Darboux-Bäcklund transformation method. The function arising in the potential denominator is proved to be a polynomial with a nonvanishing constant term, whose value is calculated by induction over k. The sign of this term being the same as that of the already known highest degree term, the potential denominator has themore » same sign at both extremities of the definition interval, a property that is shared by the seed eigenfunction used in the potential construction. By virtue of disconjugacy, such a property implies the nodeless character of both the eigenfunction and the resulting potential.« less

Lifting q-difference operators for Askey-Wilson polynomials and their weight function

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

Atakishiyeva, M. K.; Atakishiyev, N. M., E-mail: natig_atakishiyev@hotmail.com

2011-06-15

We determine an explicit form of a q-difference operator that transforms the continuous q-Hermite polynomials H{sub n}(x | q) of Rogers into the Askey-Wilson polynomials p{sub n}(x; a, b, c, d | q) on the top level in the Askey q-scheme. This operator represents a special convolution-type product of four one-parameter q-difference operators of the form {epsilon}{sub q}(c{sub q}D{sub q}) (where c{sub q} are some constants), defined as Exton's q-exponential function {epsilon}{sub q}(z) in terms of the Askey-Wilson divided q-difference operator D{sub q}. We also determine another q-difference operator that lifts the orthogonality weight function for the continuous q-Hermite polynomialsH{submore » n}(x | q) up to the weight function, associated with the Askey-Wilson polynomials p{sub n}(x; a, b, c, d | q).« less

A Synthetic Biology Framework for Programming Eukaryotic Transcription Functions

PubMed Central

Khalil, Ahmad S.; Lu, Timothy K.; Bashor, Caleb J.; Ramirez, Cherie L.; Pyenson, Nora C.; Joung, J. Keith; Collins, James J.

2013-01-01

SUMMARY Eukaryotic transcription factors (TFs) perform complex and combinatorial functions within transcriptional networks. Here, we present a synthetic framework for systematically constructing eukaryotic transcription functions using artificial zinc fingers, modular DNA-binding domains found within many eukaryotic TFs. Utilizing this platform, we construct a library of orthogonal synthetic transcription factors (sTFs) and use these to wire synthetic transcriptional circuits in yeast. We engineer complex functions, such as tunable output strength and transcriptional cooperativity, by rationally adjusting a decomposed set of key component properties, e.g., DNA specificity, affinity, promoter design, protein-protein interactions. We show that subtle perturbations to these properties can transform an individual sTF between distinct roles (activator, cooperative factor, inhibitory factor) within a transcriptional complex, thus drastically altering the signal processing behavior of multi-input systems. This platform provides new genetic components for synthetic biology and enables bottom-up approaches to understanding the design principles of eukaryotic transcriptional complexes and networks. PMID:22863014

Attitude stability of spinning flexible spacecraft

NASA Technical Reports Server (NTRS)

Likins, P. W.; Barbera, F. J.

1971-01-01

The stability of spinning flexible satellites in a force-free environment was analyzed. The satellite was modeled as a rigid core having attached to it a flexible appendage idealized as a collection of particles (point masses) interconnected by springs. Both Liapunov and Routh-Hurwitz stability procedures are used. In the former, the Hamiltonian of the system, constrained through the angular momentum integral so as to admit complete damping, is used as a testing function. Equations of motion are written using the hybrid coordinate formulation, which readily accepts a modal coordinate transformation ultimately allowing truncation to a level amenable to literal stability analysis. Closed form stability criteria are generated for the first mode of a restricted appendage model lying in a plane containing the system center of mass and orthogonal to the spin axis. The effects of spin on flexible bodies are discussed by considering a very elementary particle model. Control of passively unstable spacecraft is briefly considered.

Thermoacoustic magnetohydrodynamic electrical generator

DOEpatents

Wheatley, John C.; Swift, Gregory W.; Migliori, Albert

1986-01-01

A thermoacoustic magnetohydrodynamic electrical generator includes an intrinsically irreversible thermoacoustic heat engine coupled to a magnetohydrodynamic electrical generator. The heat engine includes an electrically conductive liquid metal as the working fluid and includes two heat exchange and thermoacoustic structure assemblies which drive the liquid in a push-pull arrangement to cause the liquid metal to oscillate at a resonant acoustic frequency on the order of 1,000 Hz. The engine is positioned in the field of a magnet and is oriented such that the liquid metal oscillates in a direction orthogonal to the field of the magnet, whereby an alternating electrical potential is generated in the liquid metal. Low-loss, low-inductance electrical conductors electrically connected to opposite sides of the liquid metal conduct an output signal to a transformer adapted to convert the low-voltage, high-current output signal to a more usable higher voltage, lower current signal.

Static terrestrial laser scanning of juvenile understory trees for field phenotyping

NASA Astrophysics Data System (ADS)

Wang, Huanhuan; Lin, Yi

2014-11-01

This study was to attempt the cutting-edge 3D remote sensing technique of static terrestrial laser scanning (TLS) for parametric 3D reconstruction of juvenile understory trees. The data for test was collected with a Leica HDS6100 TLS system in a single-scan way. The geometrical structures of juvenile understory trees are extracted by model fitting. Cones are used to model trunks and branches. Principal component analysis (PCA) is adopted to calculate their major axes. Coordinate transformation and orthogonal projection are used to estimate the parameters of the cones. Then, AutoCAD is utilized to simulate the morphological characteristics of the understory trees, and to add secondary branches and leaves in a random way. Comparison of the reference values and the estimated values gives the regression equation and shows that the proposed algorithm of extracting parameters is credible. The results have basically verified the applicability of TLS for field phenotyping of juvenile understory trees.

PAPR reduction based on tone reservation scheme for DCO-OFDM indoor visible light communications.

PubMed

Bai, Jurong; Li, Yong; Yi, Yang; Cheng, Wei; Du, Huimin

2017-10-02

High peak-to-average power ratio (PAPR) leads to out-of-band power and in-band distortion in the direct current-biased optical orthogonal frequency division multiplexing (DCO-OFDM) systems. In order to effectively reduce the PAPR with faster convergence and lower complexity, this paper proposes a tone reservation based scheme, which is the combination of the signal-to-clipping noise ratio (SCR) procedure and the least squares approximation (LSA) procedure. In the proposed scheme, the transmitter of the DCO-OFDM indoor visible light communication (VLC) system is designed to transform the PAPR reduced signal into real-valued positive OFDM signal without doubling the transmission bandwidth. Moreover, the communication distance and the light emitting diode (LED) irradiance angle are taking into consideration in the evaluation of the system bit error rate (BER). The PAPR reduction efficiency of the proposed scheme is remarkable for DCO-OFDM indoor VLC systems.

A Shifted Block Lanczos Algorithm 1: The Block Recurrence

NASA Technical Reports Server (NTRS)

Grimes, Roger G.; Lewis, John G.; Simon, Horst D.

1990-01-01

In this paper we describe a block Lanczos algorithm that is used as the key building block of a software package for the extraction of eigenvalues and eigenvectors of large sparse symmetric generalized eigenproblems. The software package comprises: a version of the block Lanczos algorithm specialized for spectrally transformed eigenproblems; an adaptive strategy for choosing shifts, and efficient codes for factoring large sparse symmetric indefinite matrices. This paper describes the algorithmic details of our block Lanczos recurrence. This uses a novel combination of block generalizations of several features that have only been investigated independently in the past. In particular new forms of partial reorthogonalization, selective reorthogonalization and local reorthogonalization are used, as is a new algorithm for obtaining the M-orthogonal factorization of a matrix. The heuristic shifting strategy, the integration with sparse linear equation solvers and numerical experience with the code are described in a companion paper.

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.

An astronomer's guide to period searching

NASA Astrophysics Data System (ADS)

Schwarzenberg-Czerny, A.

2003-03-01

We concentrate on analysis of unevenly sampled time series, interrupted by periodic gaps, as often encountered in astronomy. While some of our conclusions may appear surprising, all are based on classical statistical principles of Fisher & successors. Except for discussion of the resolution issues, it is best for the reader to forget temporarily about Fourier transforms and to concentrate on problems of fitting of a time series with a model curve. According to their statistical content we divide the issues into several sections, consisting of: (ii) statistical numerical aspects of model fitting, (iii) evaluation of fitted models as hypotheses testing, (iv) the role of the orthogonal models in signal detection (v) conditions for equivalence of periodograms (vi) rating sensitivity by test power. An experienced observer working with individual objects would benefit little from formalized statistical approach. However, we demonstrate the usefulness of this approach in evaluation of performance of periodograms and in quantitative design of large variability surveys.

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.

An approach enabling adaptive FEC for OFDM in fiber-VLLC system

NASA Astrophysics Data System (ADS)

Wei, Yiran; He, Jing; Deng, Rui; Shi, Jin; Chen, Shenghai; Chen, Lin

2017-12-01

In this paper, we propose an orthogonal circulant matrix transform (OCT)-based adaptive frame-level-forward error correction (FEC) scheme for fiber-visible laser light communication (VLLC) system and experimentally demonstrate by Reed-Solomon (RS) Code. In this method, no extra bits are spent for adaptive message, except training sequence (TS), which is simultaneously used for synchronization and channel estimation. Therefore, RS-coding can be adaptively performed frames by frames via the last received codeword-error-rate (CER) feedback estimated by the TSs of the previous few OFDM frames. In addition, the experimental results exhibit that over 20 km standard single-mode fiber (SSMF) and 8 m visible light transmission, the costs of RS codewords are at most 14.12% lower than those of conventional adaptive subcarrier-RS-code based 16-QAM OFDM at bit error rate (BER) of 10-5.

Preparation of the oligosaccharides derived from Flammulina velutipes and their antioxidant activities.

PubMed

Xia, Zhenqiang

2015-03-15

The oligosaccharides were prepared from Flammulina velutipes by hydrolysis of F. velutipes polysaccharides with hydrogen peroxide (H2O2). The yields of F. velutipes derived oligosaccharides (FVOs) were monitored during the hydrolysis process. FVOs yields were affected by three factors, i.e. reaction temperature, H2O2 concentration, and time, which were optimized by using an orthogonal design experiments as follows: reaction temperature 70°C, H2O2 concentration 3%, and reaction time 6h. Under these optimum conditions, the maximal yield of the oligosaccharides reached 17.10%, which was higher than that of hot water extraction method. The oligosaccharides were partially characterized by Fourier transform infrared spectrum, monosaccharide composition, and antioxidant activity. The results indicate that the oligosaccharides derived from F. velutipes showed strong hydroxyl radical activity and reducing capacity at the concentration of 100 μg/mL. Copyright © 2014 Elsevier Ltd. All rights reserved.

Medical image diagnoses by artificial neural networks with image correlation, wavelet transform, simulated annealing

NASA Astrophysics Data System (ADS)

Szu, Harold H.

1993-09-01

Classical artificial neural networks (ANN) and neurocomputing are reviewed for implementing a real time medical image diagnosis. An algorithm known as the self-reference matched filter that emulates the spatio-temporal integration ability of the human visual system might be utilized for multi-frame processing of medical imaging data. A Cauchy machine, implementing a fast simulated annealing schedule, can determine the degree of abnormality by the degree of orthogonality between the patient imagery and the class of features of healthy persons. An automatic inspection process based on multiple modality image sequences is simulated by incorporating the following new developments: (1) 1-D space-filling Peano curves to preserve the 2-D neighborhood pixels' relationship; (2) fast simulated Cauchy annealing for the global optimization of self-feature extraction; and (3) a mini-max energy function for the intra-inter cluster-segregation respectively useful for top-down ANN designs.

Speckle noise removal applied to ultrasound image of carotid artery based on total least squares model.

PubMed

Yang, Lei; Lu, Jun; Dai, Ming; Ren, Li-Jie; Liu, Wei-Zong; Li, Zhen-Zhou; Gong, Xue-Hao

2016-10-06

An ultrasonic image speckle noise removal method by using total least squares model is proposed and applied onto images of cardiovascular structures such as the carotid artery. On the basis of the least squares principle, the related principle of minimum square method is applied to cardiac ultrasound image speckle noise removal process to establish the model of total least squares, orthogonal projection transformation processing is utilized for the output of the model, and the denoising processing for the cardiac ultrasound image speckle noise is realized. Experimental results show that the improved algorithm can greatly improve the resolution of the image, and meet the needs of clinical medical diagnosis and treatment of the cardiovascular system for the head and neck. Furthermore, the success in imaging of carotid arteries has strong implications in neurological complications such as stroke.

Actuation for simultaneous motions and constraining efforts: an open chain example

NASA Astrophysics Data System (ADS)

Perreira, N. Duke

1997-06-01

A brief discussion on systems where simultaneous control of forces and velocities are desirable is given and an example linkage with revolute and prismatic joint is selected for further analysis. The Newton-Euler approach for dynamic system analysis is applied to the example to provide a basis of comparison. Gauge invariant transformations are used to convert the dynamic equations into invariant form suitable for use in a new dynamic system analysis method known as the motion-effort approach. This approach uses constraint elimination techniques based on singular value decompositions to recast the invariant form of dynamic system equations into orthogonal sets of motion and effort equations. Desired motions and constraining efforts are partitioned into ideally obtainable and unobtainable portions which are then used to determine the required actuation. The method is applied to the example system and an analytic estimate to its success is made.

Simultaneous multi-beam planar array IR (pair) spectroscopy

DOEpatents

Elmore, Douglas L.; Rabolt, John F.; Tsao, Mei-Wei

2005-09-13

An apparatus and method capable of providing spatially multiplexed IR spectral information simultaneously in real-time for multiple samples or multiple spatial areas of one sample using IR absorption phenomena requires no moving parts or Fourier Transform during operation, and self-compensates for background spectra and degradation of component performance over time. IR spectral information and chemical analysis of the samples is determined by using one or more IR sources, sampling accessories for positioning the samples, optically dispersive elements, a focal plane array (FPA) arranged to detect the dispersed light beams, and a processor and display to control the FPA, and display an IR spectrograph. Fiber-optic coupling can be used to allow remote sensing. Portability, reliability, and ruggedness is enhanced due to the no-moving part construction. Applications include determining time-resolved orientation and characteristics of materials, including polymer monolayers. Orthogonal polarizers may be used to determine certain material characteristics.

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.

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.

Toolpath strategy for cutter life improvement in plunge milling of AISI H13 tool steel

NASA Astrophysics Data System (ADS)

Adesta, E. Y. T.; Avicenna; hilmy, I.; Daud, M. R. H. C.

2018-01-01

Machinability of AISI H13 tool steel is a prominent issue since the material has the characteristics of high hardenability, excellent wear resistance, and hot toughness. A method of improving cutter life of AISI H13 tool steel plunge milling by alternating the toolpath and cutting conditions is proposed. Taguchi orthogonal array with L9 (3^4) resolution will be employed with one categorical factor of toolpath strategy (TS) and three numeric factors of cutting speed (Vc), radial depth of cut (ae ), and chip load (fz ). It is expected that there are significant differences for each application of toolpath strategy and each cutting condition factor toward the cutting force and tool wear mechanism of the machining process, and medial axis transform toolpath could provide a better tool life improvement by a reduction of cutting force during machining.

Position and orientation tracking system

DOEpatents

Burks, Barry L.; DePiero, Fred W.; Armstrong, Gary A.; Jansen, John F.; Muller, Richard C.; Gee, Timothy F.

1998-01-01

A position and orientation tracking system presents a laser scanning appaus having two measurement pods, a control station, and a detector array. The measurement pods can be mounted in the dome of a radioactive waste storage silo. Each measurement pod includes dual orthogonal laser scanner subsystems. The first laser scanner subsystem is oriented to emit a first line laser in the pan direction. The second laser scanner is oriented to emit a second line laser in the tilt direction. Both emitted line lasers scan planes across the radioactive waste surface to encounter the detector array mounted on a target robotic vehicle. The angles of incidence of the planes with the detector array are recorded by the control station. Combining measurements describing each of the four planes provides data for a closed form solution of the algebraic transform describing the position and orientation of the target robotic vehicle.

Position and orientation tracking system

DOEpatents

Burks, B.L.; DePiero, F.W.; Armstrong, G.A.; Jansen, J.F.; Muller, R.C.; Gee, T.F.

1998-05-05

A position and orientation tracking system presents a laser scanning apparatus having two measurement pods, a control station, and a detector array. The measurement pods can be mounted in the dome of a radioactive waste storage silo. Each measurement pod includes dual orthogonal laser scanner subsystems. The first laser scanner subsystem is oriented to emit a first line laser in the pan direction. The second laser scanner is oriented to emit a second line laser in the tilt direction. Both emitted line lasers scan planes across the radioactive waste surface to encounter the detector array mounted on a target robotic vehicle. The angles of incidence of the planes with the detector array are recorded by the control station. Combining measurements describing each of the four planes provides data for a closed form solution of the algebraic transform describing the position and orientation of the target robotic vehicle. 14 figs.

Golay sequences coded coherent optical OFDM for long-haul transmission

NASA Astrophysics Data System (ADS)

Qin, Cui; Ma, Xiangrong; Hua, Tao; Zhao, Jing; Yu, Huilong; Zhang, Jian

2017-09-01

We propose to use binary Golay sequences in coherent optical orthogonal frequency division multiplexing (CO-OFDM) to improve the long-haul transmission performance. The Golay sequences are generated by binary Reed-Muller codes, which have low peak-to-average power ratio and certain error correction capability. A low-complexity decoding algorithm for the Golay sequences is then proposed to recover the signal. Under same spectral efficiency, the QPSK modulated OFDM with binary Golay sequences coding with and without discrete Fourier transform (DFT) spreading (DFTS-QPSK-GOFDM and QPSK-GOFDM) are compared with the normal BPSK modulated OFDM with and without DFT spreading (DFTS-BPSK-OFDM and BPSK-OFDM) after long-haul transmission. At a 7% forward error correction code threshold (Q2 factor of 8.5 dB), it is shown that DFTS-QPSK-GOFDM outperforms DFTS-BPSK-OFDM by extending the transmission distance by 29% and 18%, in non-dispersion managed and dispersion managed links, respectively.

Measuring Joule heating and strain induced by electrical current with Moire interferometry

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

Chen Bicheng; Basaran, Cemal

2011-04-01

This study proposes a new method to locate and measure the temperature of the hot spots caused by Joule Heating by measuring the free thermal expansion in-plane strain. It is demonstrated that the hotspot caused by the Joule heating in a thin metal film/plate structure can be measured by Phase shifting Moire interferometry with continuous wavelet transform (PSMI/CWT) at the microscopic scale. A demonstration on a copper film is conducted to verify the theory under different current densities. A correlation between the current density and strain in two orthogonal directions (one in the direction of the current flow) is proposed.more » The method can also be used for the measurement of the Joule heating in the microscopic solid structures in the electronic packaging devices. It is shown that a linear relationship exists between current density squared and normal strains.« less

Numerical implementation of complex orthogonalization, parallel transport on Stiefel bundles, and analyticity

NASA Astrophysics Data System (ADS)

Avitabile, Daniele; Bridges, Thomas J.

2010-06-01

Numerical integration of complex linear systems of ODEs depending analytically on an eigenvalue parameter are considered. Complex orthogonalization, which is required to stabilize the numerical integration, results in non-analytic systems. It is shown that properties of eigenvalues are still efficiently recoverable by extracting information from a non-analytic characteristic function. The orthonormal systems are constructed using the geometry of Stiefel bundles. Different forms of continuous orthogonalization in the literature are shown to correspond to different choices of connection one-form on the Stiefel bundle. For the numerical integration, Gauss-Legendre Runge-Kutta algorithms are the principal choice for preserving orthogonality, and performance results are shown for a range of GLRK methods. The theory and methods are tested by application to example boundary value problems including the Orr-Sommerfeld equation in hydrodynamic stability.

More nonlocality with less purity.

PubMed

Bandyopadhyay, Somshubhro

2011-05-27

Quantum information is nonlocal in the sense that local measurements on a composite quantum system, prepared in one of many mutually orthogonal states, may not reveal in which state the system was prepared. It is shown that in the many copy limit this kind of nonlocality is fundamentally different for pure and mixed quantum states. In particular, orthogonal mixed states may not be distinguishable by local operations and classical communication, no matter how many copies are supplied, whereas any set of N orthogonal pure states can be perfectly discriminated with m copies, where m

Axial Cone-Beam Reconstruction by Weighted BPF/DBPF and Orthogonal Butterfly Filtering.

PubMed

Tang, Shaojie; Tang, Xiangyang

2016-09-01

The backprojection-filtration (BPF) and the derivative backprojection filtered (DBPF) algorithms, in which Hilbert filtering is the common algorithmic feature, are originally derived for exact helical reconstruction from cone-beam (CB) scan data and axial reconstruction from fan beam data, respectively. These two algorithms can be heuristically extended for image reconstruction from axial CB scan data, but induce severe artifacts in images located away from the central plane, determined by the circular source trajectory. We propose an algorithmic solution herein to eliminate the artifacts. The solution is an integration of three-dimensional (3-D) weighted axial CB-BPF/DBPF algorithm with orthogonal butterfly filtering, namely axial CB-BPF/DBPF cascaded with orthogonal butterfly filtering. Using the computer simulated Forbild head and thoracic phantoms that are rigorous in inspecting the reconstruction accuracy, and an anthropomorphic thoracic phantom with projection data acquired by a CT scanner, we evaluate the performance of the proposed algorithm. Preliminary results show that the orthogonal butterfly filtering can eliminate the severe streak artifacts existing in the images reconstructed by the 3-D weighted axial CB-BPF/DBPF algorithm located at off-central planes. Integrated with orthogonal butterfly filtering, the 3-D weighted CB-BPF/DBPF algorithm can perform at least as well as the 3-D weighted CB-FBP algorithm in image reconstruction from axial CB scan data. The proposed 3-D weighted axial CB-BPF/DBPF cascaded with orthogonal butterfly filtering can be an algorithmic solution for CT imaging in extensive clinical and preclinical applications.

Frictionless Contact of Multilayered Composite Half Planes Containing Layers With Complex Eigenvalues

NASA Technical Reports Server (NTRS)

Zhang, Wang; Binienda, Wieslaw K.; Pindera, Marek-Jerzy

1997-01-01

A previously developed local-global stiffness matrix methodology for the response of a composite half plane, arbitrarily layered with isotropic, orthotropic or monoclinic plies, to indentation by a rigid parabolic punch is further extended to accommodate the presence of layers with complex eigenvalues (e.g., honeycomb or piezoelectric layers). First, a generalized plane deformation solution for the displacement field in an orthotropic layer or half plane characterized by complex eigenvalues is obtained using Fourier transforms. A local stiffness matrix in the transform domain is subsequently constructed for this class of layers and half planes, which is then assembled into a global stiffness matrix for the entire multilayered half plane by enforcing continuity conditions along the interfaces. Application of the mixed boundary condition on the top surface of the half plane indented by a rigid punch results in an integral equation for the unknown pressure in the contact region. The integral possesses a divergent kernel which is decomposed into Cauchy-type and regular parts using the asymptotic properties of the local stiffness matrix and a relationship between Fourier and finite Hilbert transform of the contact pressure. The solution of the resulting singular integral equation is obtained using a collocation technique based on the properties of orthogonal polynomials developed by Erdogan and Gupta. Examples are presented that illustrate the important influence of low transverse properties of layers with complex eigenvalues, such as those exhibited by honeycomb, on the load versus contact length response and contact pressure distributions for half planes containing typical composite materials.

Necessary condition for local distinguishability of maximally entangled states: Beyond orthogonality preservation

NASA Astrophysics Data System (ADS)

Singal, Tanmay; Rahaman, Ramij; Ghosh, Sibasish; Kar, Guruprasad

2017-10-01

The (im)possibility of local distinguishability of orthogonal multipartite quantum states still remains an intriguing question. Beyond C3⊗C3 , the problem remains unsolved even for maximally entangled states (MESs). So far, the only known condition for the local distinguishability of states is the well-known orthogonality preservation (OP). Using an upper bound on the locally accessible information for bipartite states, we derive a very simple necessary condition for any set of pairwise orthogonal MESs in Cd⊗Cd to be perfectly locally distinguishable. It is seen that particularly when the number of pairwise orthogonal MES states in Cd⊗Cd is equal to d , then this necessary condition, along with the OP condition, imposes more constraints (for said states to be perfectly locally distinguishable) than the OP condition does. When testing this condition for the local distinguishability of all sets of four generalized Bell states in C4⊗C4 , we find that it is not only necessary but also sufficient to determine their local distinguishability. This demonstrates that the aforementioned upper bound may play a significant role in the general scenario of local distinguishability of bipartite states.

Research and design on orthogonal diffraction grating-based 3D nanometer displacement sensor

NASA Astrophysics Data System (ADS)

Liu, Baoshuai; Yuan, Yibao; Yin, Zhehao

2017-10-01

This study concerns an orthogonal diffraction grating-based nanometer displacement sensor. In this study, we performed calculation of displacements in the XYZ directions. In the optical measured path part, we used a two-dimensional orthogonal motion grating and a two-dimensional orthogonal reference grating with the pitch of 0.5um to measure the displacement of XYZ in three directions by detecting ±1st diffraction fringes. The self-collimated structure of the grating greatly extended the Z-axis range. We also simulated the optical path of the sensor with ZEMAX software and verified the feasibility of the scheme. For signal subdivision and processing, we combined large number counting (completed grating line) with small number counting (digital subdivision), realizing high multiples of subdivision of grating interference signals. We used PC to process the interference fringes and greatly improved the processing speed. In the scheme, the theoretical multiples of subdivision could reach 1024 with 10-bit AD conversion, but the actual multiples of subdivision was limited by the quality of the grating interference signals. So we introduced an orthogonal compensation circuit and a filter circuit to improve the signal quality.

Wind Tunnel Database Development using Modern Experiment Design and Multivariate Orthogonal Functions

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.; DeLoach, Richard

2003-01-01

A wind tunnel experiment for characterizing the aerodynamic and propulsion forces and moments acting on a research model airplane is described. The model airplane called the Free-flying Airplane for Sub-scale Experimental Research (FASER), is a modified off-the-shelf radio-controlled model airplane, with 7 ft wingspan, a tractor propeller driven by an electric motor, and aerobatic capability. FASER was tested in the NASA Langley 12-foot Low-Speed Wind Tunnel, using a combination of traditional sweeps and modern experiment design. Power level was included as an independent variable in the wind tunnel test, to allow characterization of power effects on aerodynamic forces and moments. A modeling technique that employs multivariate orthogonal functions was used to develop accurate analytic models for the aerodynamic and propulsion force and moment coefficient dependencies from the wind tunnel data. Efficient methods for generating orthogonal modeling functions, expanding the orthogonal modeling functions in terms of ordinary polynomial functions, and analytical orthogonal blocking were developed and discussed. The resulting models comprise a set of smooth, differentiable functions for the non-dimensional aerodynamic force and moment coefficients in terms of ordinary polynomials in the independent variables, suitable for nonlinear aircraft simulation.

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.

Killing-Yano tensors in spaces admitting a hypersurface orthogonal Killing vector

NASA Astrophysics Data System (ADS)

Garfinkle, David; Glass, E. N.

2013-03-01

Methods are presented for finding Killing-Yano tensors, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector. These methods are similar to a method developed by the authors for finding Killing tensors. In all cases one decomposes both the tensor and the equation it satisfies into pieces along the Killing vector and pieces orthogonal to the Killing vector. Solving the separate equations that result from this decomposition requires less computing than integrating the original equation. In each case, examples are given to illustrate the method.

Quantitative Boltzmann-Gibbs Principles via Orthogonal Polynomial Duality

NASA Astrophysics Data System (ADS)

Ayala, Mario; Carinci, Gioia; Redig, Frank

2018-06-01

We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can be quantified. This implies a quantitative generalization of the Boltzmann-Gibbs principle. In the context of independent random walkers, we complete this program, including also fluctuation fields in non-stationary context (local equilibrium). For other interacting particle systems with duality such as the symmetric exclusion process, similar results can be obtained, under precise conditions on the n particle dynamics.

Weak measurements beyond the Aharonov-Albert-Vaidman formalism

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

Wu Shengjun; Li Yang

2011-05-15

We extend the idea of weak measurements to the general case, provide a complete treatment, and obtain results for both the regime when the preselected and postselected states (PPS) are almost orthogonal and the regime when they are exactly orthogonal. We surprisingly find that for a fixed interaction strength, there may exist a maximum signal amplification and a corresponding optimum overlap of PPS to achieve it. For weak measurements in the orthogonal regime, we find interesting quantities that play the same role that weak values play in the nonorthogonal regime.

13. Credit JTL: Detail, orthogonal view of Egyptian Revivial decorative ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

13. Credit JTL: Detail, orthogonal view of Egyptian Revivial decorative motifs used typically at midpoints of diagonals - Reading-Halls Station Bridge, U.S. Route 220, spanning railroad near Halls Station, Muncy, Lycoming County, PA

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.

All-Elastomer 3-Axis Contact Resistive Tactile Sensor Arrays and Micromilled Manufacturing Methods Thereof

NASA Technical Reports Server (NTRS)

Penskiy, Ivan (Inventor); Charalambides, Alexandros (Inventor); Bergbreiter, Sarah (Inventor)

2018-01-01

At least one tactile sensor includes an insulating layer and a conductive layer formed on the surface of the insulating layer. The conductive layer defines at least one group of flexible projections extending orthogonally from the surface of the insulating layer. The flexible projections include a major projection extending a distance orthogonally from the surface and at least one minor projection that is adjacent to and separate from the major projection wherein the major projection extends a distance orthogonally that is greater than the distance that the minor projection extends orthogonally. Upon a compressive force normal to, or a shear force parallel to, the surface, the major projection and the minor projection flex such that an electrical contact resistance is formed between the major projection and the minor projection. A capacitive tactile sensor is also disclosed that responds to the normal and shear forces.

Stockholder projector analysis: A Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

NASA Astrophysics Data System (ADS)

Vanfleteren, Diederik; Van Neck, Dimitri; Bultinck, Patrick; Ayers, Paul W.; Waroquier, Michel

2012-01-01

A previously introduced partitioning of the molecular one-electron density matrix over atoms and bonds [D. Vanfleteren et al., J. Chem. Phys. 133, 231103 (2010)] is investigated in detail. Orthogonal projection operators are used to define atomic subspaces, as in Natural Population Analysis. The orthogonal projection operators are constructed with a recursive scheme. These operators are chemically relevant and obey a stockholder principle, familiar from the Hirshfeld-I partitioning of the electron density. The stockholder principle is extended to density matrices, where the orthogonal projectors are considered to be atomic fractions of the summed contributions. All calculations are performed as matrix manipulations in one-electron Hilbert space. Mathematical proofs and numerical evidence concerning this recursive scheme are provided in the present paper. The advantages associated with the use of these stockholder projection operators are examined with respect to covalent bond orders, bond polarization, and transferability.

Orthogonality catastrophe and fractional exclusion statistics

NASA Astrophysics Data System (ADS)

Ares, Filiberto; Gupta, Kumar S.; de Queiroz, Amilcar R.

2018-02-01

We show that the N -particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the N -body ground state wave functions with two different values of the inverse-square interaction term goes to zero in the thermodynamic limit. When the two values of the inverse-square coupling differ by an infinitesimal amount, the wave function overlap shows an exponential suppression. This is qualitatively different from the usual power law suppression observed in the Anderson's orthogonality catastrophe. We also obtain an analytic expression for the wave function overlaps for an arbitrary set of couplings, whose properties are analyzed numerically. The quasiparticles constituting the ground state wave functions of the Sutherland model are known to obey fractional exclusion statistics. Our analysis indicates that the orthogonality catastrophe may be valid in systems with more general kinds of statistics than just the fermionic type.

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.

Effector identity and orthogonal stimulus-response compatibility in blindness to response-compatible stimuli.

PubMed

Nishimura, Akio; Yokosawa, Kazuhiko

2010-03-01

Perceiving a visual stimulus is hampered when the stimulus is compatible with simultaneously prepared or executed action (blindness effect). We explored the roles of the effector identity of the responding hand and of orthogonal compatibility (above-right/below-left correspondence) in the blindness effect. In Experiment 1, participants conducted bimanual key presses with vertically arranged responses while perceiving a brief presentation of rightward or leftward arrowheads. A blindness effect based on the effector identity did emerge, but only with the above-right/below-left key-hand arrangement. An orthogonal blindness effect was not found in Experiment 2 with a horizontal key-press action task and a vertical arrowhead perception task. We concluded that the anatomical identity of the responding hand was not integrated into the action plan with an orthogonally incompatible key-hand arrangement. The findings are discussed in terms of the generality and limits of the blindness effect, and hierarchical response coding.

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

Bio-orthogonal Fluorescent Labelling of Biopolymers through Inverse-Electron-Demand Diels-Alder Reactions.

PubMed

Kozma, Eszter; Demeter, Orsolya; Kele, Péter

2017-03-16

Bio-orthogonal labelling schemes based on inverse-electron-demand Diels-Alder (IEDDA) cycloaddition have attracted much attention in chemical biology recently. The appealing features of this reaction, such as the fast reaction kinetics, fully bio-orthogonal nature and high selectivity, have helped chemical biologists gain deeper understanding of biochemical processes at the molecular level. Listing the components and discussing the possibilities and limitations of these reagents, we provide a recent snapshot of the field of IEDDA-based biomolecular manipulation with special focus on fluorescent modulation approaches through the use of bio-orthogonalized building blocks. At the end, we discuss challenges that need to be addressed for further developments in order to overcome recent limitations and to enable researchers to answer biomolecular questions in more detail. © 2017 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.

Orthogonality catastrophe and fractional exclusion statistics.

PubMed

Ares, Filiberto; Gupta, Kumar S; de Queiroz, Amilcar R

2018-02-01

We show that the N-particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the N-body ground state wave functions with two different values of the inverse-square interaction term goes to zero in the thermodynamic limit. When the two values of the inverse-square coupling differ by an infinitesimal amount, the wave function overlap shows an exponential suppression. This is qualitatively different from the usual power law suppression observed in the Anderson's orthogonality catastrophe. We also obtain an analytic expression for the wave function overlaps for an arbitrary set of couplings, whose properties are analyzed numerically. The quasiparticles constituting the ground state wave functions of the Sutherland model are known to obey fractional exclusion statistics. Our analysis indicates that the orthogonality catastrophe may be valid in systems with more general kinds of statistics than just the fermionic type.

A square-plate ultrasonic linear motor operating in two orthogonal first bending modes.

PubMed

Chen, Zhijiang; Li, Xiaotian; Chen, Jianguo; Dong, Shuxiang

2013-01-01

A novel square-plate piezoelectric ultrasonic linear motor operated in two orthogonal first bending vibration modes (B₁) is proposed. The piezoelectric vibrator of the linear motor is simply made of a single PZT ceramic plate (sizes: 15 x 15 x 2 mm) and poled in its thickness direction. The top surface electrode of the square ceramic plate was divided into four active areas along its two diagonal lines for exciting two orthogonal B₁ modes. The achieved driving force and speed from the linear motor are 1.8 N and 230 mm/s, respectively, under one pair orthogonal voltage drive of 150 V(p-p) at the resonance frequency of 92 kHz. The proposed linear motor has advantages over conventional ultrasonic linear motors, such as relatively larger driving force, very simple working mode and structure, and low fabrication cost.

Experimental verification of beam quality in high-contrast imaging with orthogonal bremsstrahlung photon beams.

PubMed

Sarfehnia, Arman; Jabbari, Keyvan; Seuntjens, Jan; Podgorsak, Ervin B

2007-07-01

Since taken with megavoltage, forward-directed bremsstrahlung beams, the image quality of current portal images is inferior to that of diagnostic quality images produced by kilovoltage beams. In this paper, the beam quality of orthogonal bremsstrahlung beams defined as the 90 degrees component of the bremsstrahlung distribution produced from megavoltage electron pencil beams striking various targets is presented, and the suitability of their use for improved radiotherapy imaging is evaluated. A 10 MeV electron beam emerging through the research port of a Varian Clinac-18 linac was made to strike targets of carbon, aluminum, and copper. PDD and attenuation measurements of both the forward and orthogonal beams were carried out, and the results were also used to estimate the effective and mean energy of the beams. The mean energy of a spectrum produced by a carbon target dropped by 83% from 1296 keV in the forward direction to 217 keV in the orthogonal direction, while for an aluminum target it dropped by 77% to 412 keV, and for a copper target by 65% to 793 keV. An in-depth Monte Carlo study of photon yield and electron contamination was also performed. Photon yield and effective energy are lower for orthogonal beams than for forward beams, and the differences are more pronounced for targets of lower atomic number. Using their relatively low effective energy, orthogonal bremsstrahlung beams produced by megavoltage electrons striking low atomic number targets yield images with a higher contrast in comparison with forward bremsstrahlung beams.

Axial Cone Beam Reconstruction by Weighted BPF/DBPF and Orthogonal Butterfly Filtering

PubMed Central

Tang, Shaojie; Tang, Xiangyang

2016-01-01

Goal The backprojection-filtration (BPF) and the derivative backprojection filtered (DBPF) algorithms, in which Hilbert filtering is the common algorithmic feature, are originally derived for exact helical reconstruction from cone beam (CB) scan data and axial reconstruction from fan beam data, respectively. These two algorithms can be heuristically extended for image reconstruction from axial CB scan data, but induce severe artifacts in images located away from the central plane determined by the circular source trajectory. We propose an algorithmic solution herein to eliminate the artifacts. Methods The solution is an integration of three-dimensional (3D) weighted axial CB-BPF/ DBPF algorithm with orthogonal butterfly filtering, namely axial CB-BPF/DBPF cascaded with orthogonal butterfly filtering. Using the computer simulated Forbild head and thoracic phantoms that are rigorous in inspecting reconstruction accuracy and an anthropomorphic thoracic phantom with projection data acquired by a CT scanner, we evaluate performance of the proposed algorithm. Results Preliminary results show that the orthogonal butterfly filtering can eliminate the severe streak artifacts existing in the images reconstructed by the 3D weighted axial CB-BPF/DBPF algorithm located at off-central planes. Conclusion Integrated with orthogonal butterfly filtering, the 3D weighted CB-BPF/DBPF algorithm can perform at least as well as the 3D weighted CB-FBP algorithm in image reconstruction from axial CB scan data. Significance The proposed 3D weighted axial CB-BPF/DBPF cascaded with orthogonal butterfly filtering can be an algorithmic solution for CT imaging in extensive clinical and preclinical applications. PMID:26660512

Orthogonal Cas9 proteins for RNA-guided gene regulation and editing

DOEpatents

Church, George M.; Esvelt, Kevin; Mali, Prashant

2017-03-07

Methods of modulating expression of a target nucleic acid in a cell are provided including use of multiple orthogonal Cas9 proteins to simultaneously and independently regulate corresponding genes or simultaneously and independently edit corresponding genes.

Accurate solution of the Helmholtz equation by Lanczos orthogonalization for media with loss or gain.

PubMed

Ratowsky, R P; Fleck, J A; Feit, M D

1992-01-01

The numerical scheme for solving the Helmholtz equation, based on the Lanczos orthogonalization scheme, is generalized so that it can be applied to media with space-dependent absorption or gain profiles.

Visually induced adaptation in three-dimensional organization of primate vestibuloocular reflex

NASA Technical Reports Server (NTRS)

Angelaki, D. E.; Hess, B. J.

1998-01-01

The adaptive plasticity of the spatial organization of the vestibuloocular reflex (VOR) has been investigated in intact and canal-plugged primates using 2-h exposure to conflicting visual (optokinetic, OKN) and vestibular rotational stimuli about mutually orthogonal axes (generating torsional VOR + vertical OKN, torsional VOR + horizontal OKN, vertical VOR + horizontal OKN, and horizontal VOR + vertical OKN). Adaptation protocols with 0.5-Hz (+/-18 degrees ) head movements about either an earth-vertical or an earth-horizontal axis induced orthogonal response components as high as 40-70% of those required for ideal adaptation. Orthogonal response gains were highest at the adapting frequency with phase leads present at lower and phase lags present at higher frequencies. Furthermore, the time course of adaptation, as well as orthogonal response dynamics were similar and relatively independent of the particular visual/vestibular stimulus combination. Low-frequency (0. 05 Hz, vestibular stimulus: +/-60 degrees ; optokinetic stimulus: +/-180 degrees ) adaptation protocols with head movements about an earth-vertical axis induced smaller orthogonal response components that did not exceed 20-40% of the head velocity stimulus (i.e., approximately 10% of that required for ideal adaptation). At the same frequency, adaptation with head movements about an earth-horizontal axis generated large orthogonal responses that reached values as high as 100-120% of head velocity after 2 h of adaptation (i.e., approximately 40% of ideal adaptation gains). The particular spatial and temporal response characteristics after low-frequency, earth-horizontal axis adaptation in both intact and canal-plugged animals strongly suggests that the orienting (and perhaps translational) but not inertial (velocity storage) components of the primate otolith-ocular system exhibit spatial adaptability. Due to the particular nested arrangement of the visual and vestibular stimuli, the optic flow pattern exhibited a significant component about the third spatial axis (i.e., orthogonal to the axes of rotation of the head and visual surround) at twice the oscillation frequency. Accordingly, the adapted VOR was characterized consistently by a third response component (orthogonal to both the axes of head and optokinetic drum rotation) at twice the oscillation frequency after earth-horizontal but not after earth-vertical axis 0.05-Hz adaptation. This suggests that the otolith-ocular (but not the semicircular canal-ocular) system can adaptively change its spatial organization at frequencies different from those of the head movement.

Molecular dynamics simulations of shock waves in oriented nitromethane single crystals: plane-specific effects.

PubMed

He, Lan; Sewell, Thomas D; Thompson, Donald L

2012-01-21

Molecular dynamics simulations of supported shock waves (shock pressure P(s) ∼ 15 GPa) propagating along the [110], [011], [101], and [111] directions in crystalline nitromethane initially at T = 200 K were performed using the nonreactive Sorescu-Rice-Thompson force field [D. C. Sorescu, B. M. Rice, and D. L. Thompson, J. Phys. Chem. B 104, 8406 (2000)]. These simulations, combined with those from a preceding study of shocks propagating along [100], [010], and [001] directions in nitromethane for similar conditions of temperature and shock pressure [L. He, T. D. Sewell, and D. L. Thompson, J. Chem. Phys. 134, 124506 (2011)], have been used to study the post-shock relaxation phenomena. Shocks along [010] and [101] lead to a crystal-crystal structure transformation. Shocks propagating along [011], [110], [111], [100], and [001] exhibit plane-specific disordering, which was characterized by calculating as functions of time the 1D mean square displacement (MSD), 2D radial distribution function (RDF), and 2D orientation order parameter P(2)(θ) in orthogonal planes mutually perpendicular to the shock plane; and by calculating as functions of distance behind the shock front the Cartesian components of intermolecular, intramolecular, and total kinetic energies. The 2D RDF results show that the structural disordering for shocks along [100], [110], and [111] is strongly plane-specific; whereas for shocks along [001] and [011], the loss of crystal structural order is almost equivalent in the orthogonal planes perpendicular to the shock plane. Based on the entire set of simulations, there is a trend for the most extensive disordering to occur in the (010) and (110) planes, less extensive disordering to occur in the (100) plane, and essentially no disordering to occur in the (001) plane. The 2D P(2)(θ) and 1D MSD profiles show, respectively, that the orientational and translational disordering is plane-specific, which results in the plane-specific structural disordering observed in the 2D RDF. By contrast, the kinetic energy partitioning and redistribution do not exhibit plane specificity, as shown by the similarity of spatial profiles of the Cartesian components of the intermolecular, intramolecular, and total kinetic energies in orthogonal planes perpendicular to the shock plane. © 2012 American Institute of Physics

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)

Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices

ERIC Educational Resources Information Center

Glaister, P.

2008-01-01

The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.

Limitations of the Porter-Thomas distribution

NASA Astrophysics Data System (ADS)

Weidenmüller, Hans A.

2017-12-01

Data on the distribution of reduced partial neutron widths and on the distribution of total gamma decay widths disagree with the Porter-Thomas distribution (PTD) for reduced partial widths or with predictions of the statistical model. We recall why the disagreement is important: The PTD is a direct consequence of the orthogonal invariance of the Gaussian Orthogonal Ensemble (GOE) of random matrices. The disagreement is reviewed. Two possible causes for violation of orthogonal invariance of the GOE are discussed, and their consequences explored. The disagreement of the distribution of total gamma decay widths with theoretical predictions cannot be blamed on the statistical model.

Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights

NASA Astrophysics Data System (ADS)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2009-12-01

We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.

Numerical simulation on semi-solid die-casting of magnesium matrix composite based on orthogonal experiment

NASA Astrophysics Data System (ADS)

Liu, Huihui; He, Xiongwei; Guo, Peng

2017-04-01

Three factors (pouring temperature, injection speed and mold temperature) were selected to do three levels L9 (33)orthogonal experiment, then simulate processing of semi-solid die-casting of magnesium matrix composite by Flow-3D software. The stress distribution, temperature field and defect distribution of filling process were analyzed to find the optimized processing parameter with the help of orthogonal experiment. The results showed that semi-solid has some advantages of well-proportioned stress and temperature field, less defect concentrated in the surface. The results of simulation were the same as the experimental results.

A simple X-ray source of two orthogonal beams for small samples imaging

NASA Astrophysics Data System (ADS)

Hrdý, J.

2018-04-01

A simple method for simultaneous imaging of small samples by two orthogonal beams is proposed. The method is based on one channel-cut crystal which is oriented such that the beam is diffracted on two crystallographic planes simultaneously. These planes are symmetrically inclined to the crystal surface. The beams are three times diffracted. After the first diffraction the beam is split. After the second diffraction the split beams become parallel. Finally, after the third diffraction the beams become convergent and may be used for imaging. The corresponding angular relations to obtain orthogonal beams are derived.

Selective posttranslational modification of phage-displayed polypeptides

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

Tsao, Meng-Lin; Tian, Feng; Schultz, Peter

The invention relates to posttranslational modification of phage-displayed polypeptides. These displayed polypeptides comprise at least one unnatural amino acid, e.g., an aryl-azide amino acid such as p-azido-L-phenylalanine, or an alkynyl-amino acid such as para-propargyloxyphenylalanine, which are incorporated into the phage-displayed fusion polypeptide at a selected position by using an in vivo orthogonal translation system comprising a suitable orthogonal aminoacyl-tRNA synthetase and a suitable orthogonal tRNA species. These unnatural amino acids advantageously provide targets for posttranslational modifications such as azide-alkyne [3+2] cycloaddition reactions and Staudinger modifications.

Selective posttranslational modification of phage-displayed polypeptides

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

Tsao, Meng-Lin; Tian, Feng; Schultz, Peter

The invention relates to posttranslational modification of phage-displayed polypeptides. These displayed polypeptides comprise at least one unnatural amino acid, e.g., an aryl-azide amino acid such as p-azido-L-phenylalanine, or an alkynyl-amino acid such as para-propargyloxyphenylalanine, which are incorporated into the phage-displayed fusion polypeptide at a selected position by using an in vivo orthogonal translation system comprising a suitable orthogonal aminoacyl-tRNA synthetase and a suitable orthogonal tRNA species. These unnatural amino acids advantageously provide targets for posttranslational modifications such as azide-alkyne [3+2]cycloaddition reactions and Staudinger modifications.