Parallel Fast Legendre Transform
Alves de Inda, M.; Bisseling, R.H.; Maslen, D.K.
1998-01-01
We discuss a parallel implementation of a fast algorithm for the discrete polynomial Legendre transform We give an introduction to the DriscollHealy algorithm using polynomial arithmetic and present experimental results on the eciency and accuracy of our implementation The algorithms were
Ntekas, Konstantinos; The ATLAS collaboration
2018-01-01
The upgrade of the ATLAS first-level muon trigger for High- Luminosity LHC foresees incorporating the precise tracking of the Monitored Drift Tubes in the current system based on Resistive Plate Chambers and Thin Gap Chambers to improve the accuracy in the transverse momentum measurement and control the single muon trigger rate by suppressing low quality fake triggers. The core of the MDT trigger algorithm is the segment identification and reconstruction which is performed per MDT chamber. The reconstructed segment positions and directions are then combined to extract the muon candidate’s transverse momentum. A fast pattern recognition segment finding algorithm, called the Legendre transform, is proposed to be used for the MDT trigger, implemented in a FPGA housed on a ATCA blade.
Quadratic Lagrangians and Legendre transformation
International Nuclear Information System (INIS)
Magnano, G.
1988-01-01
In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor
On the efficient parallel computation of Legendre transforms
Inda, M.A.; Bisseling, R.H.; Maslen, D.K.
2001-01-01
In this article, we discuss a parallel implementation of efficient algorithms for computation of Legendre polynomial transforms and other orthogonal polynomial transforms. We develop an approach to the Driscoll-Healy algorithm using polynomial arithmetic and present experimental results on the
On the efficient parallel computation of Legendre transforms
Inda, M.A.; Bisseling, R.H.; Maslen, D.K.
1999-01-01
In this article we discuss a parallel implementation of efficient algorithms for computation of Legendre polynomial transforms and other orthogonal polynomial transforms. We develop an approach to the Driscoll-Healy algorithm using polynomial arithmetic and present experimental results on the
The continous Legendre transform, its inverse transform, and applications
Directory of Open Access Journals (Sweden)
P. L. Butzer
1980-01-01
Full Text Available This paper is concerned with the continuous Legendre transform, derived from the classical discrete Legendre transform by replacing the Legendre polynomial Pk(x by the function Pλ(x with λ real. Another approach to T.M. MacRobert's inversion formula is found; for this purpose an inverse Legendre transform, mapping L1(ℝ+ into L2(−1,1, is defined. Its inversion in turn is naturally achieved by the continuous Legendre transform. One application is devoted to the Shannon sampling theorem in the Legendre frame together with a new type of error estimate. The other deals with a new representation of Legendre functions giving information about their behaviour near the point x=−1.
Ntekas, Konstantinos; The ATLAS collaboration
2018-01-01
Many of the physics goals of ATLAS in the High Luminosity LHC era, including precision studies of the Higgs boson, require an unprescaled single muon trigger with a 20 GeV threshold. The selectivity of the current ATLAS first-level muon trigger is limited by the moderate spatial resolution of the muon trigger chambers. By incorporating the precise tracking of the MDT, the muon transverse momentum can be measured with an accuracy close to that of the offline reconstruction at the trigger level, sharpening the trigger turn-on curves and reducing the single muon trigger rate. A novel algorithm is proposed which reconstructs segments from MDT hits in an FPGA and find tracks within the tight latency constraints of the ATLAS first-level muon trigger. The algorithm represents MDT drift circles as curves in the Legendre space and returns one or more segment lines tangent to the maximum possible number of drift circles. This algorithm is implemented without the need of resource and time consuming hit position calcul...
Legendre transformations and Clairaut-type equations
Energy Technology Data Exchange (ETDEWEB)
Lavrov, Peter M., E-mail: lavrov@tspu.edu.ru [Tomsk State Pedagogical University, Kievskaya St. 60, 634061 Tomsk (Russian Federation); National Research Tomsk State University, Lenin Av. 36, 634050 Tomsk (Russian Federation); Merzlikin, Boris S., E-mail: merzlikin@tspu.edu.ru [National Research Tomsk Polytechnic University, Lenin Av. 30, 634050 Tomsk (Russian Federation)
2016-05-10
It is noted that the Legendre transformations in the standard formulation of quantum field theory have the form of functional Clairaut-type equations. It is shown that in presence of composite fields the Clairaut-type form holds after loop corrections are taken into account. A new solution to the functional Clairaut-type equation appearing in field theories with composite fields is found.
An Algorithm for the Convolution of Legendre Series
Hale, Nicholas; Townsend, Alex
2014-01-01
An O(N2) algorithm for the convolution of compactly supported Legendre series is described. The algorithm is derived from the convolution theorem for Legendre polynomials and the recurrence relation satisfied by spherical Bessel functions. Combining with previous work yields an O(N 2) algorithm for the convolution of Chebyshev series. Numerical results are presented to demonstrate the improved efficiency over the existing algorithm. © 2014 Society for Industrial and Applied Mathematics.
A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula
Hale, Nicholas
2014-02-06
A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(log N)2/ log log N) operations is derived. The fundamental idea of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the discrete cosine transform. Numerical results are provided to demonstrate the efficiency and numerical stability. Since the algorithm evaluates a Legendre expansion at an N +1 Chebyshev grid as an intermediate step, it also provides a fast transform between Legendre coefficients and values on a Chebyshev grid. © 2014 Society for Industrial and Applied Mathematics.
A new representation for ground states and its Legendre transforms
International Nuclear Information System (INIS)
Cedillo, A.
1994-01-01
The ground-state energy of an electronic system is a functional of the number of electrons (N) and the external potential (v): E = E(N,V), this is the energy representation for ground states. In 1982, Nalewajski defined the Legendre transforms of this representation, taking advantage of the strict concavity of E with respect to their variables (concave respect v and convex respect N), and he also constructed a scheme for the reduction of derivatives of his representations. Unfortunately, N and the electronic density (p) were the independent variables of one of these representations, but p depends explicitly on N. In this work, this problem is avoided using the energy per particle (ε) as the basic variables, and the Legendre transformations can be defined. A procedure for the reduction of derivatives is generated for the new four representations and, in contrast to the Nalewajski's procedure, it only includes derivatives of the four representations. Finally, the reduction of derivatives is used to test some relationships between the hardness and softness kernels
A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula
Hale, Nicholas; Townsend, Alex
2014-01-01
-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the discrete cosine transform. Numerical results are provided to demonstrate the efficiency
Transformation formulas for legendre coefficients of double-differential cross sections
International Nuclear Information System (INIS)
Shi Xiangjun; Zhang Jingshang
1989-01-01
Approximate analytical formulas have been derived for the transformation of Legendre coefficients of double-differential continuum cross sections of two-body nuclear reactions from the center-of-mass to the laboratory system. This transformation differs from that of elastic-scattering angular distribution coefficients on its accuracy which depends not only upon the target mass, but also upon outgoing energies. A fast code has been written to transform Legendre coefficients of neutron inelastic scattering cross-sections. The calculations have been carried out using a recently introduced numerical integration method for more complicated problems in which the energy spectrum is either an evaporation spectrum or a spectrum obtained from a (pre-)compound model. The results are quite satisfactory provided that the target mass or the outgoing energy is not sufficiently low
International Nuclear Information System (INIS)
Zhao Yunbin
2010-01-01
While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the condition number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.
Legendre transform structure and extremal properties of the relative Fisher information
Energy Technology Data Exchange (ETDEWEB)
Venkatesan, R.C., E-mail: ravi@systemsresearchcorp.com [Systems Research Corporation, Aundh, Pune 411007 (India); Plastino, A., E-mail: plastino@fisica.unlp.edu.ar [IFLP, National University La Plata and National Research Council (CONICET) C.C., 727 1900 La Plata (Argentina)
2014-04-01
Variational extremization of the relative Fisher information (RFI, hereafter) is performed. Reciprocity relations, akin to those of thermodynamics are derived, employing the extremal results of the RFI expressed in terms of probability amplitudes. A time independent Schrödinger-like equation (Schrödinger-like link) for the RFI is derived. The concomitant Legendre transform structure (LTS, hereafter) is developed by utilizing a generalized RFI-Euler theorem, which shows that the entire mathematical structure of thermodynamics translates into the RFI framework, both for equilibrium and non-equilibrium cases. The qualitatively distinct nature of the present results vis-á-vis those of prior studies utilizing the Shannon entropy and/or the Fisher information measure (FIM, hereafter) is discussed. A principled relationship between the RFI and the FIM frameworks is derived. The utility of this relationship is demonstrated by an example wherein the energy eigenvalues of the Schrödinger-like link for the RFI are inferred solely using the quantum mechanical virial theorem and the LTS of the RFI.
Zhao, G.; Liu, J.; Chen, B.; Guo, R.; Chen, L.
2017-12-01
Forward modeling of gravitational fields at large-scale requires to consider the curvature of the Earth and to evaluate the Newton's volume integral in spherical coordinates. To acquire fast and accurate gravitational effects for subsurface structures, subsurface mass distribution is usually discretized into small spherical prisms (called tesseroids). The gravity fields of tesseroids are generally calculated numerically. One of the commonly used numerical methods is the 3D Gauss-Legendre quadrature (GLQ). However, the traditional GLQ integration suffers from low computational efficiency and relatively poor accuracy when the observation surface is close to the source region. We developed a fast and high accuracy 3D GLQ integration based on the equivalence of kernel matrix, adaptive discretization and parallelization using OpenMP. The equivalence of kernel matrix strategy increases efficiency and reduces memory consumption by calculating and storing the same matrix elements in each kernel matrix just one time. In this method, the adaptive discretization strategy is used to improve the accuracy. The numerical investigations show that the executing time of the proposed method is reduced by two orders of magnitude compared with the traditional method that without these optimized strategies. High accuracy results can also be guaranteed no matter how close the computation points to the source region. In addition, the algorithm dramatically reduces the memory requirement by N times compared with the traditional method, where N is the number of discretization of the source region in the longitudinal direction. It makes the large-scale gravity forward modeling and inversion with a fine discretization possible.
Composite Gauss-Legendre Quadrature with Error Control
Prentice, J. S. C.
2011-01-01
We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)
Prediction of Shanghai Index based on Additive Legendre Neural Network
Directory of Open Access Journals (Sweden)
Yang Bin
2017-01-01
Full Text Available In this paper, a novel Legendre neural network model is proposed, namely additive Legendre neural network (ALNN. A new hybrid evolutionary method besed on binary particle swarm optimization (BPSO algorithm and firefly algorithm is proposed to optimize the structure and parameters of ALNN model. Shanghai stock exchange composite index is used to evaluate the performance of ALNN. Results reveal that ALNN performs better than LNN model.
Fast algorithm for computing complex number-theoretic transforms
Reed, I. S.; Liu, K. Y.; Truong, T. K.
1977-01-01
A high-radix FFT algorithm for computing transforms over FFT, where q is a Mersenne prime, is developed to implement fast circular convolutions. This new algorithm requires substantially fewer multiplications than the conventional FFT.
A fast butterfly algorithm for generalized Radon transforms
Hu, Jingwei; Fomel, Sergey; Demanet, Laurent; Ying, Lexing
2013-01-01
Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We have devised a fast butterfly algorithm
Composite Gauss-Legendre Formulas for Solving Fuzzy Integration
Directory of Open Access Journals (Sweden)
Xiaobin Guo
2014-01-01
Full Text Available Two numerical integration rules based on composition of Gauss-Legendre formulas for solving integration of fuzzy numbers-valued functions are investigated in this paper. The methods' constructions are presented and the corresponding convergence theorems are shown in detail. Two numerical examples are given to illustrate the proposed algorithms finally.
Congruences concerning Legendre polynomials III
Sun, Zhi-Hong
2010-01-01
Let $p>3$ be a prime, and let $R_p$ be the set of rational numbers whose denominator is coprime to $p$. Let $\\{P_n(x)\\}$ be the Legendre polynomials. In this paper we mainly show that for $m,n,t\\in R_p$ with $m\
Inversion algorithms for the spherical Radon and cosine transform
International Nuclear Information System (INIS)
Louis, A K; Riplinger, M; Spiess, M; Spodarev, E
2011-01-01
We consider two integral transforms which are frequently used in integral geometry and related fields, namely the spherical Radon and cosine transform. Fast algorithms are developed which invert the respective transforms in a numerically stable way. So far, only theoretical inversion formulae or algorithms for atomic measures have been derived, which are not so important for applications. We focus on two- and three-dimensional cases, where we also show that our method leads to a regularization. Numerical results are presented and show the validity of the resulting algorithms. First, we use synthetic data for the inversion of the Radon transform. Then we apply the algorithm for the inversion of the cosine transform to reconstruct the directional distribution of line processes from finitely many intersections of their lines with test lines (2D) or planes (3D), respectively. Finally we apply our method to analyse a series of microscopic two- and three-dimensional images of a fibre system
A fast butterfly algorithm for generalized Radon transforms
Hu, Jingwei
2013-06-21
Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We have devised a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to reformulate the transform as an oscillatory integral operator and to construct a blockwise lowrank approximation of the kernel function. The overall structure follows the Fourier integral operator butterfly algorithm. For 2D data, the algorithm runs in complexity O(N2 log N), where N depends on the maximum frequency and offset in the data set and the range of parameters (intercept time and slowness) in the model space. From a series of studies, we found that this algorithm can be significantly more efficient than the conventional time-domain integration. © 2013 Society of Exploration Geophysicists.
Genetic Algorithms Evolve Optimized Transforms for Signal Processing Applications
National Research Council Canada - National Science Library
Moore, Frank; Babb, Brendan; Becke, Steven; Koyuk, Heather; Lamson, Earl, III; Wedge, Christopher
2005-01-01
.... The primary goal of the research described in this final report was to establish a methodology for using genetic algorithms to evolve coefficient sets describing inverse transforms and matched...
Using transformation algorithms to estimate (co)variance ...
African Journals Online (AJOL)
REML) procedures by a diagonalization approach is extended to multiple traits by the use of canonical transformations. A computing strategy is developed for use on large data sets employing two different REML algorithms for the estimation of ...
Matrix form of Legendre polynomials for solving linear integro-differential equations of high order
Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.
2017-04-01
This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.
A general algorithm for computing distance transforms in linear time
Meijster, A.; Roerdink, J.B.T.M.; Hesselink, W.H.; Goutsias, J; Vincent, L; Bloomberg, DS
2000-01-01
A new general algorithm fur computing distance transforms of digital images is presented. The algorithm consists of two phases. Both phases consist of two scans, a forward and a backward scan. The first phase scans the image column-wise, while the second phase scans the image row-wise. Since the
A linear-time algorithm for Euclidean feature transform sets
Hesselink, Wim H.
2007-01-01
The Euclidean distance transform of a binary image is the function that assigns to every pixel the Euclidean distance to the background. The Euclidean feature transform is the function that assigns to every pixel the set of background pixels with this distance. We present an algorithm to compute the
The Watershed Transform : Definitions, Algorithms and Parallelization Strategies
Roerdink, Jos B.T.M.; Meijster, Arnold
2000-01-01
The watershed transform is the method of choice for image segmentation in the field of mathematical morphology. We present a critical review of several definitions of the watershed transform and the associated sequential algorithms, and discuss various issues which often cause confusion in the
Fast numerical algorithm for the linear canonical transform.
Hennelly, Bryan M; Sheridan, John T
2005-05-01
The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an N log N algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.
A difference tracking algorithm based on discrete sine transform
Liu, HaoPeng; Yao, Yong; Lei, HeBing; Wu, HaoKun
2018-04-01
Target tracking is an important field of computer vision. The template matching tracking algorithm based on squared difference matching (SSD) and standard correlation coefficient (NCC) matching is very sensitive to the gray change of image. When the brightness or gray change, the tracking algorithm will be affected by high-frequency information. Tracking accuracy is reduced, resulting in loss of tracking target. In this paper, a differential tracking algorithm based on discrete sine transform is proposed to reduce the influence of image gray or brightness change. The algorithm that combines the discrete sine transform and the difference algorithm maps the target image into a image digital sequence. The Kalman filter predicts the target position. Using the Hamming distance determines the degree of similarity between the target and the template. The window closest to the template is determined the target to be tracked. The target to be tracked updates the template. Based on the above achieve target tracking. The algorithm is tested in this paper. Compared with SSD and NCC template matching algorithms, the algorithm tracks target stably when image gray or brightness change. And the tracking speed can meet the read-time requirement.
Image Retrieval Algorithm Based on Discrete Fractional Transforms
Jindal, Neeru; Singh, Kulbir
2013-06-01
The discrete fractional transforms is a signal processing tool which suggests computational algorithms and solutions to various sophisticated applications. In this paper, a new technique to retrieve the encrypted and scrambled image based on discrete fractional transforms has been proposed. Two-dimensional image was encrypted using discrete fractional transforms with three fractional orders and two random phase masks placed in the two intermediate planes. The significant feature of discrete fractional transforms benefits from its extra degree of freedom that is provided by its fractional orders. Security strength was enhanced (1024!)4 times by scrambling the encrypted image. In decryption process, image retrieval is sensitive for both correct fractional order keys and scrambling algorithm. The proposed approach make the brute force attack infeasible. Mean square error and relative error are the recital parameters to verify validity of proposed method.
Discrete Hadamard transformation algorithm's parallelism analysis and achievement
Hu, Hui
2009-07-01
With respect to Discrete Hadamard Transformation (DHT) wide application in real-time signal processing while limitation in operation speed of DSP. The article makes DHT parallel research and its parallel performance analysis. Based on multiprocessor platform-TMS320C80 programming structure, the research is carried out to achieve two kinds of parallel DHT algorithms. Several experiments demonstrated the effectiveness of the proposed algorithms.
Transformation Algorithm of Dielectric Response in Time-Frequency Domain
Directory of Open Access Journals (Sweden)
Ji Liu
2014-01-01
Full Text Available A transformation algorithm of dielectric response from time domain to frequency domain is presented. In order to shorten measuring time of low or ultralow frequency dielectric response characteristics, the transformation algorithm is used in this paper to transform the time domain relaxation current to frequency domain current for calculating the low frequency dielectric dissipation factor. In addition, it is shown from comparing the calculation results with actual test data that there is a coincidence for both results over a wide range of low frequencies. Meanwhile, the time domain test data of depolarization currents in dry and moist pressboards are converted into frequency domain results on the basis of the transformation. The frequency domain curves of complex capacitance and dielectric dissipation factor at the low frequency range are obtained. Test results of polarization and depolarization current (PDC in pressboards are also given at the different voltage and polarization time. It is demonstrated from the experimental results that polarization and depolarization current are affected significantly by moisture contents of the test pressboards, and the transformation algorithm is effective in ultralow frequency of 10−3 Hz. Data analysis and interpretation of the test results conclude that analysis of time-frequency domain dielectric response can be used for assessing insulation system in power transformer.
An algorithm for the basis of the finite Fourier transform
Santhanam, Thalanayar S.
1995-01-01
The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.
The parallel algorithm for the 2D discrete wavelet transform
Barina, David; Najman, Pavel; Kleparnik, Petr; Kula, Michal; Zemcik, Pavel
2018-04-01
The discrete wavelet transform can be found at the heart of many image-processing algorithms. Until now, the transform on general-purpose processors (CPUs) was mostly computed using a separable lifting scheme. As the lifting scheme consists of a small number of operations, it is preferred for processing using single-core CPUs. However, considering a parallel processing using multi-core processors, this scheme is inappropriate due to a large number of steps. On such architectures, the number of steps corresponds to the number of points that represent the exchange of data. Consequently, these points often form a performance bottleneck. Our approach appropriately rearranges calculations inside the transform, and thereby reduces the number of steps. In other words, we propose a new scheme that is friendly to parallel environments. When evaluating on multi-core CPUs, we consistently overcome the original lifting scheme. The evaluation was performed on 61-core Intel Xeon Phi and 8-core Intel Xeon processors.
Limitations on continuous variable quantum algorithms with Fourier transforms
International Nuclear Information System (INIS)
Adcock, Mark R A; Hoeyer, Peter; Sanders, Barry C
2009-01-01
We study quantum algorithms implemented within a single harmonic oscillator, or equivalently within a single mode of the electromagnetic field. Logical states correspond to functions of the canonical position, and the Fourier transform to canonical momentum serves as the analogue of the Hadamard transform for this implementation. This continuous variable version of quantum information processing has widespread appeal because of advanced quantum optics technology that can create, manipulate and read Gaussian states of light. We show that, contrary to a previous claim, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform, analogous to the famous time-bandwidth theorem of signal processing.
Definite Integrals using Orthogonality and Integral Transforms
Directory of Open Access Journals (Sweden)
Howard S. Cohl
2012-10-01
Full Text Available We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.
A Streaming Distance Transform Algorithm for Neighborhood-Sequence Distances
Directory of Open Access Journals (Sweden)
Nicolas Normand
2014-09-01
Full Text Available We describe an algorithm that computes a “translated” 2D Neighborhood-Sequence Distance Transform (DT using a look up table approach. It requires a single raster scan of the input image and produces one line of output for every line of input. The neighborhood sequence is specified either by providing one period of some integer periodic sequence or by providing the rate of appearance of neighborhoods. The full algorithm optionally derives the regular (centered DT from the “translated” DT, providing the result image on-the-ﬂy, with a minimal delay, before the input image is fully processed. Its efficiency can benefit all applications that use neighborhood- sequence distances, particularly when pipelined processing architectures are involved, or when the size of objects in the source image is limited.
Validation of a numerical algorithm based on transformed equations
International Nuclear Information System (INIS)
Xu, H.; Barron, R.M.; Zhang, C.
2003-01-01
Generally, a typical equation governing a physical process, such as fluid flow or heat transfer, has three types of terms that involve partial derivatives, namely, the transient term, the convective terms and the diffusion terms. The major difficulty in obtaining numerical solutions of these partial differential equations is the discretization of the convective terms. The transient term is usually discretized using the first-order forward or backward differencing scheme. The diffusion terms are usually discretized using the central differencing scheme and no difficulty arises since these terms involve second-order spatial derivatives of the flow variables. The convective terms are non-linear and contain first-order spatial derivatives. The main difference between various numerical algorithms is the discretization of the convective terms. In the present study, an alternative approach to discretizing the governing equations is presented. In this algorithm, the governing equations are first transformed by introducing an exponential function to eliminate the convective terms in the equations. The proposed algorithm is applied to simulate some fluid flows with exact solutions to validate the proposed algorithm. The fluid flows used in this study are a self-designed quasi-fluid flow problem, stagnation in plane flow (Hiemenz flow), and flow between two concentric cylinders. The comparisons with the power-law scheme indicate that the proposed scheme exhibits better performance. (author)
Multi-resolution inversion algorithm for the attenuated radon transform
Barbano, Paolo Emilio
2011-09-01
We present a FAST implementation of the Inverse Attenuated Radon Transform which incorporates accurate collimator response, as well as artifact rejection due to statistical noise and data corruption. This new reconstruction procedure is performed by combining a memory-efficient implementation of the analytical inversion formula (AIF [1], [2]) with a wavelet-based version of a recently discovered regularization technique [3]. The paper introduces all the main aspects of the new AIF, as well numerical experiments on real and simulated data. Those display a substantial improvement in reconstruction quality when compared to linear or iterative algorithms. © 2011 IEEE.
The discrete Fourier transform theory, algorithms and applications
Sundaraajan, D
2001-01-01
This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and
Identification of chaotic memristor systems based on piecewise adaptive Legendre filters
International Nuclear Information System (INIS)
Zhao, Yibo; Zhang, Xiuzai; Xu, Jin; Guo, Yecai
2015-01-01
Memristor is a nonlinear device, which plays an important role in the design and implementation of chaotic systems. In order to be able to understand in-depth the complex nonlinear dynamic behaviors in chaotic memristor systems, modeling or identification of its nonlinear model is very important premise. This paper presents a chaotic memristor system identification method based on piecewise adaptive Legendre filters. The threshold decomposition is carried out for the input vector, and also the input signal subintervals via decomposition satisfy the convergence condition of the adaptive Legendre filters. Then the adaptive Legendre filter structure and adaptive weight update algorithm are derived. Final computer simulation results show the effectiveness as well as fast convergence characteristics.
Discrete fractional solutions of a Legendre equation
Yılmazer, Resat
2018-01-01
One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.
Khan, Sami Ullah; Ali, Ishtiaq
2018-03-01
Explicit solutions to delay differential equation (DDE) and stochastic delay differential equation (SDDE) can rarely be obtained, therefore numerical methods are adopted to solve these DDE and SDDE. While on the other hand due to unstable nature of both DDE and SDDE numerical solutions are also not straight forward and required more attention. In this study, we derive an efficient numerical scheme for DDE and SDDE based on Legendre spectral-collocation method, which proved to be numerical methods that can significantly speed up the computation. The method transforms the given differential equation into a matrix equation by means of Legendre collocation points which correspond to a system of algebraic equations with unknown Legendre coefficients. The efficiency of the proposed method is confirmed by some numerical examples. We found that our numerical technique has a very good agreement with other methods with less computational effort.
Moving boundary - Oxygen diffusion. Two algorithms using Landau transformation
International Nuclear Information System (INIS)
Moyano, E.A.
1991-01-01
A description is made of two algorithms which solve a mathematical model destinated for the study of one-dimensional problems with moving boundaries and implicit boundary conditions. The Landau transformation is used in both methods for each temporal level so as to work all through with the same amount of nodes. Thus, it is necessary to deal with a partial differential equation whose diffusive and convective terms are accompanied by variable coefficients. The partial differential equation is made discrete implicitly, using the Laasonen scheme -which is always stable- instead of the Crank-Nicholson scheme, as performed by Ferris and Hill (5), in the fixed time passing method. The second method employs the tridiagonal algorithm. The first algorithm uses fixed time passing and iterates with variable interface positions, that is to say, it varies δs until it satisfies the boundary condition. The mathematical model describes oxygen diffusion in live tissues. Its numerical solution is obtained by finite differences. An important application of this method could be the estimation of the radiation dose in cancerous tumor treatment. (Author) [es
Development of pattern recognition algorithms for the central drift chamber of the Belle II detector
Energy Technology Data Exchange (ETDEWEB)
Trusov, Viktor
2016-11-04
In this thesis, the development of one of the pattern recognition algorithms for the Belle II experiment based on conformal and Legendre transformations is presented. In order to optimize the performance of the algorithm (CPU time and efficiency) specialized processing steps have been introduced. To show achieved results, Monte-Carlo based efficiency measurements of the tracking algorithms in the Central Drift Chamber (CDC) has been done.
TRANSFORMATION ALGORITHM FOR IMAGES OBTAINED BY OMNIDIRECTIONAL CAMERAS
Directory of Open Access Journals (Sweden)
V. P. Lazarenko
2015-01-01
Full Text Available Omnidirectional optoelectronic systems find their application in areas where a wide viewing angle is critical. However, omnidirectional optoelectronic systems have a large distortion that makes their application more difficult. The paper compares the projection functions of traditional perspective lenses and omnidirectional wide angle fish-eye lenses with a viewing angle not less than 180°. This comparison proves that distortion models of omnidirectional cameras cannot be described as a deviation from the classic model of pinhole camera. To solve this problem, an algorithm for transforming omnidirectional images has been developed. The paper provides a brief comparison of the four calibration methods available in open source toolkits for omnidirectional optoelectronic systems. Geometrical projection model is given used for calibration of omnidirectional optical system. The algorithm consists of three basic steps. At the first step, we calculate he field of view of a virtual pinhole PTZ camera. This field of view is characterized by an array of 3D points in the object space. At the second step the array of corresponding pixels for these three-dimensional points is calculated. Then we make a calculation of the projection function that expresses the relation between a given 3D point in the object space and a corresponding pixel point. In this paper we use calibration procedure providing the projection function for calibrated instance of the camera. At the last step final image is formed pixel-by-pixel from the original omnidirectional image using calculated array of 3D points and projection function. The developed algorithm gives the possibility for obtaining an image for a part of the field of view of an omnidirectional optoelectronic system with the corrected distortion from the original omnidirectional image. The algorithm is designed for operation with the omnidirectional optoelectronic systems with both catadioptric and fish-eye lenses
Adaptive discrete cosine transform coding algorithm for digital mammography
Baskurt, Atilla M.; Magnin, Isabelle E.; Goutte, Robert
1992-09-01
The need for storage, transmission, and archiving of medical images has led researchers to develop adaptive and efficient data compression techniques. Among medical images, x-ray radiographs of the breast are especially difficult to process because of their particularly low contrast and very fine structures. A block adaptive coding algorithm based on the discrete cosine transform to compress digitized mammograms is described. A homogeneous repartition of the degradation in the decoded images is obtained using a spatially adaptive threshold. This threshold depends on the coding error associated with each block of the image. The proposed method is tested on a limited number of pathological mammograms including opacities and microcalcifications. A comparative visual analysis is performed between the original and the decoded images. Finally, it is shown that data compression with rather high compression rates (11 to 26) is possible in the mammography field.
Transformations and algorithms in a computerized brain atlas
International Nuclear Information System (INIS)
Thurfjell, L.; Bohm, C.; Eriksson, L.; Karolinska Institute/Hospital, Stockholm
1993-01-01
The computerized brain atlas constructed at the Karolinska Hospital, Stockholm, Sweden, has been further developed. This atlas was designed to be employed in different fields of neuro imaging such as positron emission tomography (PET), single photon emission tomography (SPECT), computerized tomography (CT) and magnetic resonance imaging (MR). The main objectives with the atlas is to aid the interpretation of functional images by introducing anatomical information, to serve as a tool in the merging of data from different imaging modalities and to facilitate the comparisons of data from different individuals by allowing for anatomical standardization of individual data. The purpose of this paper is to describe the algorithms and transformations used in the implementation of the atlas software
Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
Hale, Nicholas
2013-03-06
An efficient algorithm for the accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton\\'s root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100. © 2013 Society for Industrial and Applied Mathematics.
Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
Hale, Nicholas; Townsend, Alex
2013-01-01
An efficient algorithm for the accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton's root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100. © 2013 Society for Industrial and Applied Mathematics.
The Roadmaker's algorithm for the discrete pulse transform.
Laurie, Dirk P
2011-02-01
The discrete pulse transform (DPT) is a decomposition of an observed signal into a sum of pulses, i.e., signals that are constant on a connected set and zero elsewhere. Originally developed for 1-D signal processing, the DPT has recently been generalized to more dimensions. Applications in image processing are currently being investigated. The time required to compute the DPT as originally defined via the successive application of LULU operators (members of a class of minimax filters studied by Rohwer) has been a severe drawback to its applicability. This paper introduces a fast method for obtaining such a decomposition, called the Roadmaker's algorithm because it involves filling pits and razing bumps. It acts selectively only on those features actually present in the signal, flattening them in order of increasing size by subtracing an appropriate positive or negative pulse, which is then appended to the decomposition. The implementation described here covers 1-D signal as well as two and 3-D image processing in a single framework. This is achieved by considering the signal or image as a function defined on a graph, with the geometry specified by the edges of the graph. Whenever a feature is flattened, nodes in the graph are merged, until eventually only one node remains. At that stage, a new set of edges for the same nodes as the graph, forming a tree structure, defines the obtained decomposition. The Roadmaker's algorithm is shown to be equivalent to the DPT in the sense of obtaining the same decomposition. However, its simpler operators are not in general equivalent to the LULU operators in situations where those operators are not applied successively. A by-product of the Roadmaker's algorithm is that it yields a proof of the so-called Highlight Conjecture, stated as an open problem in 2006. We pay particular attention to algorithmic details and complexity, including a demonstration that in the 1-D case, and also in the case of a complete graph, the Roadmaker
Gog, Simon; Bader, Martin
2008-10-01
The problem of sorting signed permutations by reversals is a well-studied problem in computational biology. The first polynomial time algorithm was presented by Hannenhalli and Pevzner in 1995. The algorithm was improved several times, and nowadays the most efficient algorithm has a subquadratic running time. Simple permutations played an important role in the development of these algorithms. Although the latest result of Tannier et al. does not require simple permutations, the preliminary version of their algorithm as well as the first polynomial time algorithm of Hannenhalli and Pevzner use the structure of simple permutations. More precisely, the latter algorithms require a precomputation that transforms a permutation into an equivalent simple permutation. To the best of our knowledge, all published algorithms for this transformation have at least a quadratic running time. For further investigations on genome rearrangement problems, the existence of a fast algorithm for the transformation could be crucial. Another important task is the back transformation, i.e. if we have a sorting on the simple permutation, transform it into a sorting on the original permutation. Again, the naive approach results in an algorithm with quadratic running time. In this paper, we present a linear time algorithm for transforming a permutation into an equivalent simple permutation, and an O(n log n) algorithm for the back transformation of the sorting sequence.
On computation and use of Fourier coefficients for associated Legendre functions
Gruber, Christian; Abrykosov, Oleh
2016-06-01
The computation of spherical harmonic series in very high resolution is known to be delicate in terms of performance and numerical stability. A major problem is to keep results inside a numerical range of the used data type during calculations as under-/overflow arises. Extended data types are currently not desirable since the arithmetic complexity will grow exponentially with higher resolution levels. If the associated Legendre functions are computed in the spectral domain, then regular grid transformations can be applied to be highly efficient and convenient for derived quantities as well. In this article, we compare three recursive computations of the associated Legendre functions as trigonometric series, thereby ensuring a defined numerical range for each constituent wave number, separately. The results to a high degree and order show the numerical strength of the proposed method. First, the evaluation of Fourier coefficients of the associated Legendre functions has been done with respect to the floating-point precision requirements. Secondly, the numerical accuracy in the cases of standard double and long double precision arithmetic is demonstrated. Following Bessel's inequality the obtained accuracy estimates of the Fourier coefficients are directly transferable to the associated Legendre functions themselves and to derived functionals as well. Therefore, they can provide an essential insight to modern geodetic applications that depend on efficient spherical harmonic analysis and synthesis beyond [5~× ~5] arcmin resolution.
A new fast algorithm for computing a complex number: Theoretic transforms
Reed, I. S.; Liu, K. Y.; Truong, T. K.
1977-01-01
A high-radix fast Fourier transformation (FFT) algorithm for computing transforms over GF(sq q), where q is a Mersenne prime, is developed to implement fast circular convolutions. This new algorithm requires substantially fewer multiplications than the conventional FFT.
A study of Hough Transform-based fingerprint alignment algorithms
CSIR Research Space (South Africa)
Mlambo, CS
2014-10-01
Full Text Available the implementation of each algorithm. The comparison is performed by considering the alignment results computed using each group of algorithms when varying number of minutiae points, rotation angle, and translation. In addition, the memory usage, computing time...
Implementation of Period-Finding Algorithm by Means of Simulating Quantum Fourier Transform
Directory of Open Access Journals (Sweden)
Zohreh Moghareh Abed
2010-01-01
Full Text Available In this paper, we introduce quantum fourier transform as a key ingredient for many useful algorithms. These algorithms make a solution for problems which is considered to be intractable problems on a classical computer. Quantum Fourier transform is propounded as a key for quantum phase estimation algorithm. In this paper our aim is the implementation of period-finding algorithm.Quantum computer solves this problem, exponentially faster than classical one. Quantum phase estimation algorithm is the key for the period-finding problem .Therefore, by means of simulating quantum Fourier transform, we are able to implement the period-finding algorithm. In this paper, the simulation of quantum Fourier transform is carried out by Matlab software.
Multi-stage phase retrieval algorithm based upon the gyrator transform.
Rodrigo, José A; Duadi, Hamootal; Alieva, Tatiana; Zalevsky, Zeev
2010-01-18
The gyrator transform is a useful tool for optical information processing applications. In this work we propose a multi-stage phase retrieval approach based on this operation as well as on the well-known Gerchberg-Saxton algorithm. It results in an iterative algorithm able to retrieve the phase information using several measurements of the gyrator transform power spectrum. The viability and performance of the proposed algorithm is demonstrated by means of several numerical simulations and experimental results.
Multi-stage phase retrieval algorithm based upon the gyrator transform
Rodrigo Martín-Romo, José Augusto; Duadi, Hamootal; Alieva, Tatiana Krasheninnikova; Zalevsky, Zeev
2010-01-01
The gyrator transform is a useful tool for optical information processing applications. In this work we propose a multi-stage phase retrieval approach based on this operation as well as on the well-known Gerchberg-Saxton algorithm. It results in an iterative algorithm able to retrieve the phase information using several measurements of the gyrator transform power spectrum. The viability and performance of the proposed algorithm is demonstrated by means of several numerical simulations and exp...
Adaptive Filtering in the Wavelet Transform Domain via Genetic Algorithms
2004-08-06
wavelet transforms. Whereas the term “evolved” pertains only to the altered wavelet coefficients used during the inverse transform process. 2...words, the inverse transform produces the original signal x(t) from the wavelet and scaling coefficients. )()( ,, tdtx nk n nk k ψ...reconstruct the original signal as accurately as possible. The inverse transform reconstructs an approximation of the original signal (Burrus
Superiority of legendre polynomials to Chebyshev polynomial in ...
African Journals Online (AJOL)
In this paper, we proved the superiority of Legendre polynomial to Chebyshev polynomial in solving first order ordinary differential equation with rational coefficient. We generated shifted polynomial of Chebyshev, Legendre and Canonical polynomials which deal with solving differential equation by first choosing Chebyshev ...
On the analytic continuation of functions defined by Legendre series
International Nuclear Information System (INIS)
Grinstein, F.F.
1981-07-01
An infinite diagonal sequence of Punctual Pade Approximants is considered for the approximate analytical continuation of a function defined by a formal Legendre series. The technique is tested in the case of two series with exactly known analytical sum: the generating function for Legendre polynomials and the Coulombian scattering amplitude. (author)
Higher-Order Hierarchical Legendre Basis Functions in Applications
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Jørgensen, Erik; Meincke, Peter
2007-01-01
The higher-order hierarchical Legendre basis functions have been developed for eﬀective solution of integral equations with the method of moments. They are derived from orthogonal Legendre polynomials modiﬁed to enforce normal continuity between neighboring mesh elements, while preserving a high...
Ogawa, Takahiro; Haseyama, Miki
2013-03-01
A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.
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.
Improved FHT Algorithms for Fast Computation of the Discrete Hartley Transform
Directory of Open Access Journals (Sweden)
M. T. Hamood
2013-05-01
Full Text Available In this paper, by using the symmetrical properties of the discrete Hartley transform (DHT, an improved radix-2 fast Hartley transform (FHT algorithm with arithmetic complexity comparable to that of the real-valued fast Fourier transform (RFFT is developed. It has a simple and regular butterfly structure and possesses the in-place computation property. Furthermore, using the same principles, the development can be extended to more efficient radix-based FHT algorithms. An example for the improved radix-4 FHT algorithm is given to show the validity of the presented method. The arithmetic complexity for the new algorithms are computed and then compared with the existing FHT algorithms. The results of these comparisons have shown that the developed algorithms reduce the number of multiplications and additions considerably.
Fast Algorithm for Computing the Discrete Hartley Transform of Type-II
Directory of Open Access Journals (Sweden)
Mounir Taha Hamood
2016-06-01
Full Text Available The generalized discrete Hartley transforms (GDHTs have proved to be an efficient alternative to the generalized discrete Fourier transforms (GDFTs for real-valued data applications. In this paper, the development of direct computation of radix-2 decimation-in-time (DIT algorithm for the fast calculation of the GDHT of type-II (DHT-II is presented. The mathematical analysis and the implementation of the developed algorithm are derived, showing that this algorithm possesses a regular structure and can be implemented in-place for efficient memory utilization.The performance of the proposed algorithm is analyzed and the computational complexity is calculated for different transform lengths. A comparison between this algorithm and existing DHT-II algorithms shows that it can be considered as a good compromise between the structural and computational complexities.
Healy, John J.
2018-01-01
The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.
Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers
Auteri, F; Quartapelle, L
2003-01-01
A new Galerkin-Legendre direct spectral solver for the Neumann problem associated with Laplace and Helmholtz operators in rectangular domains is presented. The algorithm differs from other Neumann spectral solvers by the high sparsity of the matrices, exploited in conjunction with the direct product structure of the problem. The homogeneous boundary condition is satisfied exactly by expanding the unknown variable into a polynomial basis of functions which are built upon the Legendre polynomials and have a zero slope at the interval extremes. A double diagonalization process is employed pivoting around the eigenstructure of the pentadiagonal mass matrices in both directions, instead of the full stiffness matrices encountered in the classical variational formulation of the problem with a weak natural imposition of the derivative boundary condition. Nonhomogeneous Neumann data are accounted for by means of a lifting. Numerical results are given to illustrate the performance of the proposed spectral elliptic solv...
Multi-resolution inversion algorithm for the attenuated radon transform
Barbano, Paolo Emilio; Fokas, Athanasios S.
2011-01-01
We present a FAST implementation of the Inverse Attenuated Radon Transform which incorporates accurate collimator response, as well as artifact rejection due to statistical noise and data corruption. This new reconstruction procedure is performed
Zhang, Leihong; Liang, Dong; Li, Bei; Kang, Yi; Pan, Zilan; Zhang, Dawei; Gao, Xiumin; Ma, Xiuhua
2016-07-01
On the basis of analyzing the cosine light field with determined analytic expression and the pseudo-inverse method, the object is illuminated by a presetting light field with a determined discrete Fourier transform measurement matrix, and the object image is reconstructed by the pseudo-inverse method. The analytic expression of the algorithm of computational ghost imaging based on discrete Fourier transform measurement matrix is deduced theoretically, and compared with the algorithm of compressive computational ghost imaging based on random measurement matrix. The reconstruction process and the reconstruction error are analyzed. On this basis, the simulation is done to verify the theoretical analysis. When the sampling measurement number is similar to the number of object pixel, the rank of discrete Fourier transform matrix is the same as the one of the random measurement matrix, the PSNR of the reconstruction image of FGI algorithm and PGI algorithm are similar, the reconstruction error of the traditional CGI algorithm is lower than that of reconstruction image based on FGI algorithm and PGI algorithm. As the decreasing of the number of sampling measurement, the PSNR of reconstruction image based on FGI algorithm decreases slowly, and the PSNR of reconstruction image based on PGI algorithm and CGI algorithm decreases sharply. The reconstruction time of FGI algorithm is lower than that of other algorithms and is not affected by the number of sampling measurement. The FGI algorithm can effectively filter out the random white noise through a low-pass filter and realize the reconstruction denoising which has a higher denoising capability than that of the CGI algorithm. The FGI algorithm can improve the reconstruction accuracy and the reconstruction speed of computational ghost imaging.
An Efficient Algorithm for the Discrete Gabor Transform using full length Windows
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2007-01-01
This paper extends the efficient factorization of the Gabor frame operator developed by Strohmer in [1] to the Gabor analysis/synthesis operator. This provides a fast method for computing the discrete Gabor transform (DGT) and several algorithms associated with it. The algorithm is used...
Algorithms for Fast Computing of the 3D-DCT Transform
Directory of Open Access Journals (Sweden)
S. Hanus
2003-04-01
Full Text Available The algorithm for video compression based on the Three-DimensionalDiscrete Cosine Transform (3D-DCT is presented. The original algorithmof the 3D-DCT has high time complexity. We propose several enhancementsto the original algorithm and make the calculation of the DCT algorithmfeasible for future real-time video compression.
Specification of the Fast Fourier Transform algorithm as a term rewriting system
Rodenburg, P.H.; Hoekzema, D.J.
1987-01-01
We specify an algorithm for multiplying polynomials with complex coefficients incorporating, the Fast Fourier Transform algorithm of Cooley and Tukey [CT]. The specification formalism we use is a variant of the formalism ASF described in. [BHK]. The difference with ASF is essentially a matter of
Efficient Algorithms for the Discrete Gabor Transform with a Long Fir Window
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2012-01-01
The Discrete Gabor Transform (DGT) is the most commonly used signal transform for signal analysis and synthesis using a linear frequency scale. The development of the Linear Time-Frequency Analysis Toolbox (LTFAT) has been based on a detailed study of many variants of the relevant algorithms. As ...
Optimization design for the stepped impedance transformer based on the genetic algorithm
International Nuclear Information System (INIS)
Zou Dehui; Lai Wanchang; Qiu Dong
2007-01-01
This paper introduces the basic principium and mathematic model of the stepped impedance transformer, then puts the emphasis on comparing two kinds of design methods of the stepped impedance transformer. The design results are simulated by EDA, which indicates that genetic algorithm design is better than Chebyshev integrated design in the term of the most reflect coefficient's module. (authors)
International Nuclear Information System (INIS)
Yu Guofu; Duan Qihua
2010-01-01
In this paper, based on the Hirota bilinear method, a reliable algorithm for generating the bilinear Baecklund transformation (BT) of integrable hierarchies is described. With the help of Maple symbolic computation the algorithm would be very helpful and powerful for looking for the bilinear BT of integrable systems especially for those high-order integrable hierarchies. The BTs of bilinear Ramani hierarchy are deduced for the first time by using the algorithm.
2018-01-01
ARL-TR-8270 ● JAN 2018 US Army Research Laboratory An Automated Energy Detection Algorithm Based on Morphological Filter...Automated Energy Detection Algorithm Based on Morphological Filter Processing with a Modified Watershed Transform by Kwok F Tom Sensors and Electron...1 October 2016–30 September 2017 4. TITLE AND SUBTITLE An Automated Energy Detection Algorithm Based on Morphological Filter Processing with a
a pyramid algorithm for the haar discrete wavelet packet transform
African Journals Online (AJOL)
PROF EKWUEME
computer-aided signal processing of non-stationary signals, this paper develops a pyramid algorithm for the discrete wavelet packet ... Edith T. Luhanga, School of Computational and Communication Sciences and Engineering, Nelson Mandela African. Institute of ..... Mathematics, Washington University. 134. EDITH T.
Chudnovsky-Ramanujan Type Formulae for the Legendre Family
Chen, Imin; Glebov, Gleb
2017-01-01
We apply the method established in our previous work to derive a Chudnovsky-Ramanujan type formula for the Legendre family of elliptic curves. As a result, we prove two identities for $1/\\pi$ in terms of hypergeometric functions.
Volkov transform generalized projection algorithm for attosecond pulse characterization
International Nuclear Information System (INIS)
Keathley, P D; Bhardwaj, S; Moses, J; Laurent, G; Kärtner, F X
2016-01-01
An algorithm for characterizing attosecond extreme ultraviolet pulses that is not bandwidth-limited, requires no interpolation of the experimental data, and makes no approximations beyond the strong-field approximation is introduced. This approach fully incorporates the dipole transition matrix element into the retrieval process. Unlike attosecond retrieval methods such as phase retrieval by omega oscillation filtering (PROOF), or improved PROOF, it simultaneously retrieves both the attosecond and infrared (IR) pulses, without placing fundamental restrictions on the IR pulse duration, intensity or bandwidth. The new algorithm is validated both numerically and experimentally, and is also found to have practical advantages. These include an increased robustness to noise, and relaxed requirements for the size of the experimental dataset and the intensity of the streaking pulse. (paper)
Extended-Maxima Transform Watershed Segmentation Algorithm for Touching Corn Kernels
Directory of Open Access Journals (Sweden)
Yibo Qin
2013-01-01
Full Text Available Touching corn kernels are usually oversegmented by the traditional watershed algorithm. This paper proposes a modified watershed segmentation algorithm based on the extended-maxima transform. Firstly, a distance-transformed image is processed by the extended-maxima transform in the range of the optimized threshold value. Secondly, the binary image obtained by the preceding process is run through the watershed segmentation algorithm, and watershed ridge lines are superimposed on the original image, so that touching corn kernels are separated into segments. Fifty images which all contain 400 corn kernels were tested. Experimental results showed that the effect of segmentation is satisfactory by the improved algorithm, and the accuracy of segmentation is as high as 99.87%.
Algorithm of parallel: hierarchical transformation and its implementation on FPGA
Timchenko, Leonid I.; Petrovskiy, Mykola S.; Kokryatskay, Natalia I.; Barylo, Alexander S.; Dembitska, Sofia V.; Stepanikuk, Dmytro S.; Suleimenov, Batyrbek; Zyska, Tomasz; Uvaysova, Svetlana; Shedreyeva, Indira
2017-08-01
In this paper considers the algorithm of laser beam spots image classification in atmospheric-optical transmission systems. It discusses the need for images filtering using adaptive methods, using, for example, parallel-hierarchical networks. The article also highlights the need to create high-speed memory devices for such networks. Implementation and simulation results of the developed method based on the PLD are demonstrated, which shows that the presented method gives 15-20% better prediction results than similar methods.
An Image Filter Based on Shearlet Transformation and Particle Swarm Optimization Algorithm
Directory of Open Access Journals (Sweden)
Kai Hu
2015-01-01
Full Text Available Digital image is always polluted by noise and made data postprocessing difficult. To remove noise and preserve detail of image as much as possible, this paper proposed image filter algorithm which combined the merits of Shearlet transformation and particle swarm optimization (PSO algorithm. Firstly, we use classical Shearlet transform to decompose noised image into many subwavelets under multiscale and multiorientation. Secondly, we gave weighted factor to those subwavelets obtained. Then, using classical Shearlet inverse transform, we obtained a composite image which is composed of those weighted subwavelets. After that, we designed fast and rough evaluation method to evaluate noise level of the new image; by using this method as fitness, we adopted PSO to find the optimal weighted factor we added; after lots of iterations, by the optimal factors and Shearlet inverse transform, we got the best denoised image. Experimental results have shown that proposed algorithm eliminates noise effectively and yields good peak signal noise ratio (PSNR.
Gong, Lihua; Deng, Chengzhi; Pan, Shumin; Zhou, Nanrun
2018-07-01
Based on hyper-chaotic system and discrete fractional random transform, an image compression-encryption algorithm is designed. The original image is first transformed into a spectrum by the discrete cosine transform and the resulting spectrum is compressed according to the method of spectrum cutting. The random matrix of the discrete fractional random transform is controlled by a chaotic sequence originated from the high dimensional hyper-chaotic system. Then the compressed spectrum is encrypted by the discrete fractional random transform. The order of DFrRT and the parameters of the hyper-chaotic system are the main keys of this image compression and encryption algorithm. The proposed algorithm can compress and encrypt image signal, especially can encrypt multiple images once. To achieve the compression of multiple images, the images are transformed into spectra by the discrete cosine transform, and then the spectra are incised and spliced into a composite spectrum by Zigzag scanning. Simulation results demonstrate that the proposed image compression and encryption algorithm is of high security and good compression performance.
Directory of Open Access Journals (Sweden)
Vladimir A. Batura
2014-11-01
Full Text Available The efficiency of orthogonal transformations application in the frequency algorithms of the digital watermarking of still images is examined. Discrete Hadamard transform, discrete cosine transform and discrete Haar transform are selected. Their effectiveness is determined by the invisibility of embedded in digital image watermark and its resistance to the most common image processing operations: JPEG-compression, noising, changing of the brightness and image size, histogram equalization. The algorithm for digital watermarking and its embedding parameters remain unchanged at these orthogonal transformations. Imperceptibility of embedding is defined by the peak signal to noise ratio, watermark stability– by Pearson's correlation coefficient. Embedding is considered to be invisible, if the value of the peak signal to noise ratio is not less than 43 dB. Embedded watermark is considered to be resistant to a specific attack, if the Pearson’s correlation coefficient is not less than 0.5. Elham algorithm based on the image entropy is chosen for computing experiment. Computing experiment is carried out according to the following algorithm: embedding of a digital watermark in low-frequency area of the image (container by Elham algorithm, exposure to a harmful influence on the protected image (cover image, extraction of a digital watermark. These actions are followed by quality assessment of cover image and watermark on the basis of which efficiency of orthogonal transformation is defined. As a result of computing experiment it was determined that the choice of the specified orthogonal transformations at identical algorithm and parameters of embedding doesn't influence the degree of imperceptibility for a watermark. Efficiency of discrete Hadamard transform and discrete cosine transformation in relation to the attacks chosen for experiment was established based on the correlation indicators. Application of discrete Hadamard transform increases
Fast parallel algorithms for the x-ray transform and its adjoint.
Gao, Hao
2012-11-01
Iterative reconstruction methods often offer better imaging quality and allow for reconstructions with lower imaging dose than classical methods in computed tomography. However, the computational speed is a major concern for these iterative methods, for which the x-ray transform and its adjoint are two most time-consuming components. The speed issue becomes even notable for the 3D imaging such as cone beam scans or helical scans, since the x-ray transform and its adjoint are frequently computed as there is usually not enough computer memory to save the corresponding system matrix. The purpose of this paper is to optimize the algorithm for computing the x-ray transform and its adjoint, and their parallel computation. The fast and highly parallelizable algorithms for the x-ray transform and its adjoint are proposed for the infinitely narrow beam in both 2D and 3D. The extension of these fast algorithms to the finite-size beam is proposed in 2D and discussed in 3D. The CPU and GPU codes are available at https://sites.google.com/site/fastxraytransform. The proposed algorithm is faster than Siddon's algorithm for computing the x-ray transform. In particular, the improvement for the parallel computation can be an order of magnitude. The authors have proposed fast and highly parallelizable algorithms for the x-ray transform and its adjoint, which are extendable for the finite-size beam. The proposed algorithms are suitable for parallel computing in the sense that the computational cost per parallel thread is O(1).
International Nuclear Information System (INIS)
Ramos Muñoz, Edgar; Razeghi, Ghazal; Zhang, Li; Jabbari, Faryar
2016-01-01
The need to reduce greenhouse gas emissions and fossil fuel consumption has increased the popularity of plug-in electric vehicles. However, a large penetration of plug-in electric vehicles can pose challenges at the grid and local distribution levels. Various charging strategies have been proposed to address such challenges, often separately. In this paper, it is shown that, with uncoordinated charging, distribution transformers and the grid can operate under highly undesirable conditions. Next, several strategies that require modest communication efforts are proposed to mitigate the burden created by high concentrations of plug-in electric vehicles, at the grid and local levels. Existing transformer and battery electric vehicle characteristics are used along with the National Household Travel Survey to simulate various charging strategies. It is shown through the analysis of hot spot temperature and equivalent aging factor that the coordinated strategies proposed here reduce the chances of transformer failure with the addition of plug-in electric vehicle loads, even for an under-designed transformer while uncontrolled and uncoordinated plug-in electric vehicle charging results in increased risk of transformer failure. - Highlights: • Charging algorithm for battery electric vehicles, for high penetration levels. • Algorithm reduces transformer overloading, for grid level valley filling. • Computation and communication requirements are minimal. • The distributed algorithm is implemented without large scale iterations. • Hot spot temperature and loss of life for transformers are evaluated.
Energy Technology Data Exchange (ETDEWEB)
Piovesan, Luis Sergio
1997-07-01
The appliance of two algorithms is evaluated, one based in Fourier analysis and other based in a rectangular transform technique over Fourier analysis, to be used in digital logical circuits (digital protection relays) for the purpose of differential protection of power transformers (ANSI 87T). The first chapter has a brief introduction about electrical protection. The second chapter discusses the general problems of transform protection, the development of digital technology and, with more detail, the differential protection associated to this technology. In this chapter are presented the particular aspects of transformers differential protection concerning sensibility, inrush current situations and harmonic distortions caused by transformer core saturations and the differential protection algorithms and their applications in a specific relay design. In chapter three, a method to make possible testing the protection performance is developed. This work applies digital simulations using EMTP to generate current signal of transformer operation and fault conditions. Digital simulation using Matlab is used to simulate the protection. The EMTP generated field signals are sent to the relay under test, furnishing data of normal operation, internal and external faults. The relay logic simulator at Matlab will work this data and so, it will be possible to verify and evaluate the algorithm behavior and performance. Chapter 4 shows the protection operation over simulations of several of transformer operation and fault conditions. The last chapter presents a conclusion about the protection performance, discussions about all the methods applied in this work and suggestions for further studies. (author)
Improved implementation algorithms of the two-dimensional nonseparable linear canonical transform.
Ding, Jian-Jiun; Pei, Soo-Chang; Liu, Chun-Lin
2012-08-01
The two-dimensional nonseparable linear canonical transform (2D NSLCT), which is a generalization of the fractional Fourier transform and the linear canonical transform, is useful for analyzing optical systems. However, since the 2D NSLCT has 16 parameters and is very complicated, it is a great challenge to implement it in an efficient way. In this paper, we improved the previous work and propose an efficient way to implement the 2D NSLCT. The proposed algorithm can minimize the numerical error arising from interpolation operations and requires fewer chirp multiplications. The simulation results show that, compared with the existing algorithm, the proposed algorithms can implement the 2D NSLCT more accurately and the required computation time is also less.
Hennelly, Bryan M.; Sheridan, John T.
2005-05-01
By use of matrix-based techniques it is shown how the space-bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.
Directory of Open Access Journals (Sweden)
M. I. Fursanov
2014-01-01
Full Text Available This article reflects algorithmization of search methods of effective replacement of consumer transformers in distributed electrical networks. As any electrical equipment of power systems, power transformers have their own limited service duration, which is determined by natural processes of materials degradation and also by unexpected wear under different conditions of overload and overvoltage. According to the standards, adapted by in the Republic of Belarus, rated service life of power transformers is 25 years. But it can be situations that transformers should be better changed till this time – economically efficient. The possibility of such replacement is considered in order to increase efficiency of electrical network operation connected with its physical wear and aging.In this article the faults of early developed mathematical models of transformers replacement were discussed. Early such worked out transformers were not used. But in practice they can be replaced in one substation but they can be successfully used in other substations .Especially if there are limits of financial resources and the replacement needs more detail technical and economical basis.During the research the authors developed the efficient algorithm for determining of optimal location of transformers at substations of distributed electrical networks, based on search of the best solution from all sets of displacement in oriented graph. Suggested algorithm allows considerably reduce design time of optimal placement of transformers using a set of simplifications. The result of algorithm’s work is series displacement of transformers in networks, which allow obtain a great economic effect in comparison with replacement of single transformer.
Directory of Open Access Journals (Sweden)
Hui Huang
2017-01-01
Full Text Available According to the pros and cons of contourlet transform and multimodality medical imaging, here we propose a novel image fusion algorithm that combines nonlinear approximation of contourlet transform with image regional features. The most important coefficient bands of the contourlet sparse matrix are retained by nonlinear approximation. Low-frequency and high-frequency regional features are also elaborated to fuse medical images. The results strongly suggested that the proposed algorithm could improve the visual effects of medical image fusion and image quality, image denoising, and enhancement.
Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
Meyer, Christoph
2018-01-01
The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. This paper presents the Mathematica package CANONICA, which implements a recently developed algorithm to automatize the transformation to a canonical basis. This represents the first publicly available implementation suitable for differential equations depending on multiple scales. In addition to the presentation of the package, this paper extends the description of some aspects of the algorithm, including a proof of the uniqueness of canonical forms up to constant transformations.
Fast and accurate algorithm for the computation of complex linear canonical transforms.
Koç, Aykut; Ozaktas, Haldun M; Hesselink, Lambertus
2010-09-01
A fast and accurate algorithm is developed for the numerical computation of the family of complex linear canonical transforms (CLCTs), which represent the input-output relationship of complex quadratic-phase systems. Allowing the linear canonical transform parameters to be complex numbers makes it possible to represent paraxial optical systems that involve complex parameters. These include lossy systems such as Gaussian apertures, Gaussian ducts, or complex graded-index media, as well as lossless thin lenses and sections of free space and any arbitrary combinations of them. Complex-ordered fractional Fourier transforms (CFRTs) are a special case of CLCTs, and therefore a fast and accurate algorithm to compute CFRTs is included as a special case of the presented algorithm. The algorithm is based on decomposition of an arbitrary CLCT matrix into real and complex chirp multiplications and Fourier transforms. The samples of the output are obtained from the samples of the input in approximately N log N time, where N is the number of input samples. A space-bandwidth product tracking formalism is developed to ensure that the number of samples is information-theoretically sufficient to reconstruct the continuous transform, but not unnecessarily redundant.
Directory of Open Access Journals (Sweden)
Şuayip Yüzbaşı
2017-03-01
Full Text Available In this paper, we suggest a matrix method for obtaining the approximate solutions of the delay linear Fredholm integro-differential equations with constant coefficients using the shifted Legendre polynomials. The problem is considered with mixed conditions. Using the required matrix operations, the delay linear Fredholm integro-differential equation is transformed into a matrix equation. Additionally, error analysis for the method is presented using the residual function. Illustrative examples are given to demonstrate the efficiency of the method. The results obtained in this study are compared with the known results.
Quantum algorithms on Walsh transform and Hamming distance for Boolean functions
Xie, Zhengwei; Qiu, Daowen; Cai, Guangya
2018-06-01
Walsh spectrum or Walsh transform is an alternative description of Boolean functions. In this paper, we explore quantum algorithms to approximate the absolute value of Walsh transform W_f at a single point z0 (i.e., |W_f(z0)|) for n-variable Boolean functions with probability at least 8/π 2 using the number of O(1/|W_f(z_{0)|ɛ }) queries, promised that the accuracy is ɛ , while the best known classical algorithm requires O(2n) queries. The Hamming distance between Boolean functions is used to study the linearity testing and other important problems. We take advantage of Walsh transform to calculate the Hamming distance between two n-variable Boolean functions f and g using O(1) queries in some cases. Then, we exploit another quantum algorithm which converts computing Hamming distance between two Boolean functions to quantum amplitude estimation (i.e., approximate counting). If Ham(f,g)=t≠0, we can approximately compute Ham( f, g) with probability at least 2/3 by combining our algorithm and {Approx-Count(f,ɛ ) algorithm} using the expected number of Θ( √{N/(\\lfloor ɛ t\\rfloor +1)}+√{t(N-t)}/\\lfloor ɛ t\\rfloor +1) queries, promised that the accuracy is ɛ . Moreover, our algorithm is optimal, while the exact query complexity for the above problem is Θ(N) and the query complexity with the accuracy ɛ is O(1/ɛ 2N/(t+1)) in classical algorithm, where N=2n. Finally, we present three exact quantum query algorithms for two promise problems on Hamming distance using O(1) queries, while any classical deterministic algorithm solving the problem uses Ω(2n) queries.
Improvements on the minimax algorithm for the Laplace transformation of orbital energy denominators
Energy Technology Data Exchange (ETDEWEB)
Helmich-Paris, Benjamin, E-mail: b.helmichparis@vu.nl; Visscher, Lucas, E-mail: l.visscher@vu.nl
2016-09-15
We present a robust and non-heuristic algorithm that finds all extremum points of the error distribution function of numerically Laplace-transformed orbital energy denominators. The extremum point search is one of the two key steps for finding the minimax approximation. If pre-tabulation of initial guesses is supposed to be avoided, strategies for a sufficiently robust algorithm have not been discussed so far. We compare our non-heuristic approach with a bracketing and bisection algorithm and demonstrate that 3 times less function evaluations are required altogether when applying it to typical non-relativistic and relativistic quantum chemical systems.
Discrete cosine and sine transforms general properties, fast algorithms and integer approximations
Britanak, Vladimir; Rao, K R; Rao, K R
2006-01-01
The Discrete Cosine Transform (DCT) is used in many applications by the scientific, engineering and research communities and in data compression in particular. Fast algorithms and applications of the DCT Type II (DCT-II) have become the heart of many established international image/video coding standards. Since then other forms of the DCT and Discrete Sine Transform (DST) have been investigated in detail. This new edition presents the complete set of DCT and DST discrete trigonometric transforms, including their definitions, general mathematical properties, and relations to the optimal Karhune
Hegde, Veena; Deekshit, Ravishankar; Satyanarayana, P. S.
2011-12-01
The electrocardiogram (ECG) is widely used for diagnosis of heart diseases. Good quality of ECG is utilized by physicians for interpretation and identification of physiological and pathological phenomena. However, in real situations, ECG recordings are often corrupted by artifacts or noise. Noise severely limits the utility of the recorded ECG and thus needs to be removed, for better clinical evaluation. In the present paper a new noise cancellation technique is proposed for removal of random noise like muscle artifact from ECG signal. A transform domain robust variable step size Griffiths' LMS algorithm (TVGLMS) is proposed for noise cancellation. For the TVGLMS, the robust variable step size has been achieved by using the Griffiths' gradient which uses cross-correlation between the desired signal contaminated with observation or random noise and the input. The algorithm is discrete cosine transform (DCT) based and uses symmetric property of the signal to represent the signal in frequency domain with lesser number of frequency coefficients when compared to that of discrete Fourier transform (DFT). The algorithm is implemented for adaptive line enhancer (ALE) filter which extracts the ECG signal in a noisy environment using LMS filter adaptation. The proposed algorithm is found to have better convergence error/misadjustment when compared to that of ordinary transform domain LMS (TLMS) algorithm, both in the presence of white/colored observation noise. The reduction in convergence error achieved by the new algorithm with desired signal decomposition is found to be lower than that obtained without decomposition. The experimental results indicate that the proposed method is better than traditional adaptive filter using LMS algorithm in the aspects of retaining geometrical characteristics of ECG signal.
Bal, A.; Alam, M. S.; Aslan, M. S.
2006-05-01
Often sensor ego-motion or fast target movement causes the target to temporarily go out of the field-of-view leading to reappearing target detection problem in target tracking applications. Since the target goes out of the current frame and reenters at a later frame, the reentering location and variations in rotation, scale, and other 3D orientations of the target are not known thus complicating the detection algorithm has been developed using Fukunaga-Koontz Transform (FKT) and distance classifier correlation filter (DCCF). The detection algorithm uses target and background information, extracted from training samples, to detect possible candidate target images. The detected candidate target images are then introduced into the second algorithm, DCCF, called clutter rejection module, to determine the target coordinates are detected and tracking algorithm is initiated. The performance of the proposed FKT-DCCF based target detection algorithm has been tested using real-world forward looking infrared (FLIR) video sequences.
Hough transform used on the spot-centroiding algorithm for the Shack-Hartmann wavefront sensor
Chia, Chou-Min; Huang, Kuang-Yuh; Chang, Elmer
2016-01-01
An approach to the spot-centroiding algorithm for the Shack-Hartmann wavefront sensor (SHWS) is presented. The SHWS has a common problem, in that while measuring high-order wavefront distortion, the spots may exceed each of the subapertures, which are used to restrict the displacement of spots. This artificial restriction may limit the dynamic range of the SHWS. When using the SHWS to measure adaptive optics or aspheric lenses, the accuracy of the traditional spot-centroiding algorithm may be uncertain because the spots leave or cross the confined area of the subapertures. The proposed algorithm combines the Hough transform with an artificial neural network, which requires no confined subapertures, to increase the dynamic range of the SHWS. This algorithm is then explored in comprehensive simulations and the results are compared with those of the existing algorithm.
The finite Fourier transform of classical polynomials
Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe
2014-01-01
The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.
Fast heap transform-based QR-decomposition of real and complex matrices: algorithms and codes
Grigoryan, Artyom M.
2015-03-01
In this paper, we describe a new look on the application of Givens rotations to the QR-decomposition problem, which is similar to the method of Householder transformations. We apply the concept of the discrete heap transform, or signal-induced unitary transforms which had been introduced by Grigoryan (2006) and used in signal and image processing. Both cases of real and complex nonsingular matrices are considered and examples of performing QR-decomposition of square matrices are given. The proposed method of QR-decomposition for the complex matrix is novel and differs from the known method of complex Givens rotation and is based on analytical equations for the heap transforms. Many examples illustrated the proposed heap transform method of QR-decomposition are given, algorithms are described in detail, and MATLAB-based codes are included.
Analysis of the Chirplet Transform-Based Algorithm for Radar Detection of Accelerated Targets
Galushko, V. G.; Vavriv, D. M.
2017-06-01
Purpose: Efficiency analysis of an optimal algorithm of chirp signal processing based on the chirplet transform as applied to detection of radar targets in uniformly accelerated motion. Design/methodology/approach: Standard methods of the optimal filtration theory are used to investigate the ambiguity function of chirp signals. Findings: An analytical expression has been derived for the ambiguity function of chirp signals that is analyzed with respect to detection of radar targets moving at a constant acceleration. Sidelobe level and characteristic width of the ambiguity function with respect to the coordinates frequency and rate of its change have been estimated. The gain in the signal-to-noise ratio has been assessed that is provided by the algorithm under consideration as compared with application of the standard Fourier transform to detection of chirp signals against a “white” noise background. It is shown that already with a comparatively small (processing channels (elementary filters with respect to the frequency change rate) the gain in the signal-tonoise ratio exceeds 10 dB. A block diagram of implementation of the algorithm under consideration is suggested on the basis of a multichannel weighted Fourier transform. Recommendations as for selection of the detection algorithm parameters have been developed. Conclusions: The obtained results testify to efficiency of application of the algorithm under consideration to detection of radar targets moving at a constant acceleration. Nevertheless, it seems expedient to perform computer simulations of its operability with account for the noise impact along with trial measurements in real conditions.
Legendre-tau approximations for functional differential equations
Ito, K.; Teglas, R.
1986-01-01
The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.
Finger crease pattern recognition using Legendre moments and principal component analysis
Luo, Rongfang; Lin, Tusheng
2007-03-01
The finger joint lines defined as finger creases and its distribution can identify a person. In this paper, we propose a new finger crease pattern recognition method based on Legendre moments and principal component analysis (PCA). After obtaining the region of interest (ROI) for each finger image in the pre-processing stage, Legendre moments under Radon transform are applied to construct a moment feature matrix from the ROI, which greatly decreases the dimensionality of ROI and can represent principal components of the finger creases quite well. Then, an approach to finger crease pattern recognition is designed based on Karhunen-Loeve (K-L) transform. The method applies PCA to a moment feature matrix rather than the original image matrix to achieve the feature vector. The proposed method has been tested on a database of 824 images from 103 individuals using the nearest neighbor classifier. The accuracy up to 98.584% has been obtained when using 4 samples per class for training. The experimental results demonstrate that our proposed approach is feasible and effective in biometrics.
Sethi, Gaurav; Saini, B S
2015-12-01
This paper presents an abdomen disease diagnostic system based on the flexi-scale curvelet transform, which uses different optimal scales for extracting features from computed tomography (CT) images. To optimize the scale of the flexi-scale curvelet transform, we propose an improved genetic algorithm. The conventional genetic algorithm assumes that fit parents will likely produce the healthiest offspring that leads to the least fit parents accumulating at the bottom of the population, reducing the fitness of subsequent populations and delaying the optimal solution search. In our improved genetic algorithm, combining the chromosomes of a low-fitness and a high-fitness individual increases the probability of producing high-fitness offspring. Thereby, all of the least fit parent chromosomes are combined with high fit parent to produce offspring for the next population. In this way, the leftover weak chromosomes cannot damage the fitness of subsequent populations. To further facilitate the search for the optimal solution, our improved genetic algorithm adopts modified elitism. The proposed method was applied to 120 CT abdominal images; 30 images each of normal subjects, cysts, tumors and stones. The features extracted by the flexi-scale curvelet transform were more discriminative than conventional methods, demonstrating the potential of our method as a diagnostic tool for abdomen diseases.
Szegö Kernels and Asymptotic Expansions for Legendre Polynomials
Directory of Open Access Journals (Sweden)
Roberto Paoletti
2017-01-01
Full Text Available We present a geometric approach to the asymptotics of the Legendre polynomials Pk,n+1, based on the Szegö kernel of the Fermat quadric hypersurface, leading to complete asymptotic expansions holding on expanding subintervals of [-1,1].
Zhang, B.; Sang, Jun; Alam, Mohammad S.
2013-03-01
An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.
Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation
International Nuclear Information System (INIS)
Aldea, N; Pintea, S; Rednic, V; Matei, F; Hu Tiandou; Xie Yaning
2009-01-01
The present work is a comparison study between different algorithms of Fourier transform for obtaining very accurate local structure results using Extended X-ray Absorption Fine Structure technique. In this paper we focus on the local structural characteristics of supported nickel catalysts and Fe 3 O 4 core-shell nanocomposites. The radial distribution function could be efficiently calculated by the fast Fourier transform when the coordination shells are well separated while the Filon quadrature gave remarkable results for close-shell coordination.
Bouganssa, Issam; Sbihi, Mohamed; Zaim, Mounia
2017-07-01
The 2D Discrete Wavelet Transform (DWT) is a computationally intensive task that is usually implemented on specific architectures in many imaging systems in real time. In this paper, a high throughput edge or contour detection algorithm is proposed based on the discrete wavelet transform. A technique for applying the filters on the three directions (Horizontal, Vertical and Diagonal) of the image is used to present the maximum of the existing contours. The proposed architectures were designed in VHDL and mapped to a Xilinx Sparten6 FPGA. The results of the synthesis show that the proposed architecture has a low area cost and can operate up to 100 MHz, which can perform 2D wavelet analysis for a sequence of images while maintaining the flexibility of the system to support an adaptive algorithm.
Energy Technology Data Exchange (ETDEWEB)
He, Hongxing; Fang, Hengrui [Department of Physics and Texas Center for Superconductivity, University of Houston, Houston, Texas 77204 (United States); Miller, Mitchell D. [Department of BioSciences, Rice University, Houston, Texas 77005 (United States); Phillips, George N. Jr [Department of BioSciences, Rice University, Houston, Texas 77005 (United States); Department of Chemistry, Rice University, Houston, Texas 77005 (United States); Department of Biochemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Su, Wu-Pei, E-mail: wpsu@uh.edu [Department of Physics and Texas Center for Superconductivity, University of Houston, Houston, Texas 77204 (United States)
2016-07-15
An iterative transform algorithm is proposed to improve the conventional molecular-replacement method for solving the phase problem in X-ray crystallography. Several examples of successful trial calculations carried out with real diffraction data are presented. An iterative transform method proposed previously for direct phasing of high-solvent-content protein crystals is employed for enhancing the molecular-replacement (MR) algorithm in protein crystallography. Target structures that are resistant to conventional MR due to insufficient similarity between the template and target structures might be tractable with this modified phasing method. Trial calculations involving three different structures are described to test and illustrate the methodology. The relationship of the approach to PHENIX Phaser-MR and MR-Rosetta is discussed.
A Rigid Image Registration Based on the Nonsubsampled Contourlet Transform and Genetic Algorithms
Directory of Open Access Journals (Sweden)
Nasreddine Taleb
2010-09-01
Full Text Available Image registration is a fundamental task used in image processing to match two or more images taken at different times, from different sensors or from different viewpoints. The objective is to find in a huge search space of geometric transformations, an acceptable accurate solution in a reasonable time to provide better registered images. Exhaustive search is computationally expensive and the computational cost increases exponentially with the number of transformation parameters and the size of the data set. In this work, we present an efficient image registration algorithm that uses genetic algorithms within a multi-resolution framework based on the Non-Subsampled Contourlet Transform (NSCT. An adaptable genetic algorithm for registration is adopted in order to minimize the search space. This approach is used within a hybrid scheme applying the two techniques fitness sharing and elitism. Two NSCT based methods are proposed for registration. A comparative study is established between these methods and a wavelet based one. Because the NSCT is a shift-invariant multidirectional transform, the second method is adopted for its search speeding up property. Simulation results clearly show that both proposed techniques are really promising methods for image registration compared to the wavelet approach, while the second technique has led to the best performance results of all. Moreover, to demonstrate the effectiveness of these methods, these registration techniques have been successfully applied to register SPOT, IKONOS and Synthetic Aperture Radar (SAR images. The algorithm has been shown to work perfectly well for multi-temporal satellite images as well, even in the presence of noise.
A rigid image registration based on the nonsubsampled contourlet transform and genetic algorithms.
Meskine, Fatiha; Chikr El Mezouar, Miloud; Taleb, Nasreddine
2010-01-01
Image registration is a fundamental task used in image processing to match two or more images taken at different times, from different sensors or from different viewpoints. The objective is to find in a huge search space of geometric transformations, an acceptable accurate solution in a reasonable time to provide better registered images. Exhaustive search is computationally expensive and the computational cost increases exponentially with the number of transformation parameters and the size of the data set. In this work, we present an efficient image registration algorithm that uses genetic algorithms within a multi-resolution framework based on the Non-Subsampled Contourlet Transform (NSCT). An adaptable genetic algorithm for registration is adopted in order to minimize the search space. This approach is used within a hybrid scheme applying the two techniques fitness sharing and elitism. Two NSCT based methods are proposed for registration. A comparative study is established between these methods and a wavelet based one. Because the NSCT is a shift-invariant multidirectional transform, the second method is adopted for its search speeding up property. Simulation results clearly show that both proposed techniques are really promising methods for image registration compared to the wavelet approach, while the second technique has led to the best performance results of all. Moreover, to demonstrate the effectiveness of these methods, these registration techniques have been successfully applied to register SPOT, IKONOS and Synthetic Aperture Radar (SAR) images. The algorithm has been shown to work perfectly well for multi-temporal satellite images as well, even in the presence of noise.
A wavelet transform algorithm for peak detection and application to powder x-ray diffraction data.
Gregoire, John M; Dale, Darren; van Dover, R Bruce
2011-01-01
Peak detection is ubiquitous in the analysis of spectral data. While many noise-filtering algorithms and peak identification algorithms have been developed, recent work [P. Du, W. Kibbe, and S. Lin, Bioinformatics 22, 2059 (2006); A. Wee, D. Grayden, Y. Zhu, K. Petkovic-Duran, and D. Smith, Electrophoresis 29, 4215 (2008)] has demonstrated that both of these tasks are efficiently performed through analysis of the wavelet transform of the data. In this paper, we present a wavelet-based peak detection algorithm with user-defined parameters that can be readily applied to the application of any spectral data. Particular attention is given to the algorithm's resolution of overlapping peaks. The algorithm is implemented for the analysis of powder diffraction data, and successful detection of Bragg peaks is demonstrated for both low signal-to-noise data from theta-theta diffraction of nanoparticles and combinatorial x-ray diffraction data from a composition spread thin film. These datasets have different types of background signals which are effectively removed in the wavelet-based method, and the results demonstrate that the algorithm provides a robust method for automated peak detection.
Tan, Ru-Chao; Lei, Tong; Zhao, Qing-Min; Gong, Li-Hua; Zhou, Zhi-Hong
2016-12-01
To improve the slow processing speed of the classical image encryption algorithms and enhance the security of the private color images, a new quantum color image encryption algorithm based on a hyper-chaotic system is proposed, in which the sequences generated by the Chen's hyper-chaotic system are scrambled and diffused with three components of the original color image. Sequentially, the quantum Fourier transform is exploited to fulfill the encryption. Numerical simulations show that the presented quantum color image encryption algorithm possesses large key space to resist illegal attacks, sensitive dependence on initial keys, uniform distribution of gray values for the encrypted image and weak correlation between two adjacent pixels in the cipher-image.
Energy Technology Data Exchange (ETDEWEB)
Silveira, L.M.; Kamon, M.; Elfadel, I.; White, J. [Massachusetts Inst. of Technology, Cambridge, MA (United States)
1996-12-31
Model order reduction based on Krylov subspace iterative methods has recently emerged as a major tool for compressing the number of states in linear models used for simulating very large physical systems (VLSI circuits, electromagnetic interactions). There are currently two main methods for accomplishing such a compression: one is based on the nonsymmetric look-ahead Lanczos algorithm that gives a numerically stable procedure for finding Pade approximations, while the other is based on a less well characterized Arnoldi algorithm. In this paper, we show that for certain classes of generalized state-space systems, the reduced-order models produced by a coordinate-transformed Arnoldi algorithm inherit the stability of the original system. Complete Proofs of our results will be given in the final paper.
Directory of Open Access Journals (Sweden)
K. Parvathi
2009-01-01
Full Text Available The watershed transformation is a useful morphological segmentation tool for a variety of grey-scale images. However, over segmentation and under segmentation have become the key problems for the conventional algorithm. In this paper, an efficient segmentation method for high-resolution remote sensing image analysis is presented. Wavelet analysis is one of the most popular techniques that can be used to detect local intensity variation and hence the wavelet transformation is used to analyze the image. Wavelet transform is applied to the image, producing detail (horizontal, vertical, and diagonal and Approximation coefficients. The image gradient with selective regional minima is estimated with the grey-scale morphology for the Approximation image at a suitable resolution, and then the watershed is applied to the gradient image to avoid over segmentation. The segmented image is projected up to high resolutions using the inverse wavelet transform. The watershed segmentation is applied to small subset size image, demanding less computational time. We have applied our new approach to analyze remote sensing images. The algorithm was implemented in MATLAB. Experimental results demonstrated the method to be effective.
On Parameter Differentiation for Integral Representations of Associated Legendre Functions
Directory of Open Access Journals (Sweden)
Howard S. Cohl
2011-05-01
Full Text Available For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-half-integer degrees, for general complex-orders, and derivatives with respect to the order are evaluated at integer-orders, for general complex-degrees. We also discuss the properties of the complex function f: C{−1,1}→C given by f(z=z/((z+1^{1/2}(z−1^{1/2}.
International Nuclear Information System (INIS)
Qi, Zhipeng; Li, Xiu; Lu, Xushan; Zhang, Yingying; Yao, Weihua
2015-01-01
We introduce a new and potentially useful method for wave field inverse transformation and its application in transient electromagnetic method (TEM) 3D interpretation. The diffusive EM field is known to have a unique integral representation in terms of a fictitious wave field that satisfies a wave equation. The continuous imaging of TEM can be accomplished using the imaging methods in seismic interpretation after the diffusion equation is transformed into a fictitious wave equation. The interpretation method based on the imaging of a fictitious wave field could be used as a fast 3D inversion method. Moreover, the fictitious wave field possesses some wave field features making it possible for the application of a wave field interpretation method in TEM to improve the prospecting resolution.Wave field transformation is a key issue in the migration imaging of a fictitious wave field. The equation in the wave field transformation belongs to the first class Fredholm integration equation, which is a typical ill-posed equation. Additionally, TEM has a large dynamic time range, which also facilitates the weakness of this ill-posed problem. The wave field transformation is implemented by using pre-conditioned regularized conjugate gradient method. The continuous imaging of a fictitious wave field is implemented by using Kirchhoff integration. A synthetic aperture and deconvolution algorithm is also introduced to improve the interpretation resolution. We interpreted field data by the method proposed in this paper, and obtained a satisfying interpretation result. (paper)
N-Level Quantum Systems and Legendre Functions
Mazurenko, A. S.; Savva, V. A.
2001-01-01
An excitation dynamics of new quantum systems of N equidistant energy levels in a monochromatic field has been investigated. To obtain exact analytical solutions of dynamic equations an analytical method based on orthogonal functions of a real argument has been proposed. Using the orthogonal Legendre functions we have found an exact analytical expression for a population probability amplitude of the level n. Various initial conditions for the excitation of N-level quantum systems have been co...
International Nuclear Information System (INIS)
Chouakri, S A; Djaafri, O; Taleb-Ahmed, A
2013-01-01
We present in this work an algorithm for electrocardiogram (ECG) signal compression aimed to its transmission via telecommunication channel. Basically, the proposed ECG compression algorithm is articulated on the use of wavelet transform, leading to low/high frequency components separation, high order statistics based thresholding, using level adjusted kurtosis value, to denoise the ECG signal, and next a linear predictive coding filter is applied to the wavelet coefficients producing a lower variance signal. This latter one will be coded using the Huffman encoding yielding an optimal coding length in terms of average value of bits per sample. At the receiver end point, with the assumption of an ideal communication channel, the inverse processes are carried out namely the Huffman decoding, inverse linear predictive coding filter and inverse discrete wavelet transform leading to the estimated version of the ECG signal. The proposed ECG compression algorithm is tested upon a set of ECG records extracted from the MIT-BIH Arrhythmia Data Base including different cardiac anomalies as well as the normal ECG signal. The obtained results are evaluated in terms of compression ratio and mean square error which are, respectively, around 1:8 and 7%. Besides the numerical evaluation, the visual perception demonstrates the high quality of ECG signal restitution where the different ECG waves are recovered correctly
Multiple Harmonics Fitting Algorithms Applied to Periodic Signals Based on Hilbert-Huang Transform
Directory of Open Access Journals (Sweden)
Hui Wang
2013-01-01
Full Text Available A new generation of multipurpose measurement equipment is transforming the role of computers in instrumentation. The new features involve mixed devices, such as kinds of sensors, analog-to-digital and digital-to-analog converters, and digital signal processing techniques, that are able to substitute typical discrete instruments like multimeters and analyzers. Signal-processing applications frequently use least-squares (LS sine-fitting algorithms. Periodic signals may be interpreted as a sum of sine waves with multiple frequencies: the Fourier series. This paper describes a new sine fitting algorithm that is able to fit a multiharmonic acquired periodic signal. By means of a “sinusoidal wave” whose amplitude and phase are both transient, the “triangular wave” can be reconstructed on the basis of Hilbert-Huang transform (HHT. This method can be used to test effective number of bits (ENOBs of analog-to-digital converter (ADC, avoiding the trouble of selecting initial value of the parameters and working out the nonlinear equations. The simulation results show that the algorithm is precise and efficient. In the case of enough sampling points, even under the circumstances of low-resolution signal with the harmonic distortion existing, the root mean square (RMS error between the sampling data of original “triangular wave” and the corresponding points of fitting “sinusoidal wave” is marvelously small. That maybe means, under the circumstances of any periodic signal, that ENOBs of high-resolution ADC can be tested accurately.
Qian, Jinfang; Zhang, Changjiang
2014-11-01
An efficient algorithm based on continuous wavelet transform combining with pre-knowledge, which can be used to detect the defect of glass bottle mouth, is proposed. Firstly, under the condition of ball integral light source, a perfect glass bottle mouth image is obtained by Japanese Computar camera through the interface of IEEE-1394b. A single threshold method based on gray level histogram is used to obtain the binary image of the glass bottle mouth. In order to efficiently suppress noise, moving average filter is employed to smooth the histogram of original glass bottle mouth image. And then continuous wavelet transform is done to accurately determine the segmentation threshold. Mathematical morphology operations are used to get normal binary bottle mouth mask. A glass bottle to be detected is moving to the detection zone by conveyor belt. Both bottle mouth image and binary image are obtained by above method. The binary image is multiplied with normal bottle mask and a region of interest is got. Four parameters (number of connected regions, coordinate of centroid position, diameter of inner cycle, and area of annular region) can be computed based on the region of interest. Glass bottle mouth detection rules are designed by above four parameters so as to accurately detect and identify the defect conditions of glass bottle. Finally, the glass bottles of Coca-Cola Company are used to verify the proposed algorithm. The experimental results show that the proposed algorithm can accurately detect the defect conditions of the glass bottles and have 98% detecting accuracy.
A Novel Robust Audio Watermarking Algorithm by Modifying the Average Amplitude in Transform Domain
Directory of Open Access Journals (Sweden)
Qiuling Wu
2018-05-01
Full Text Available In order to improve the robustness and imperceptibility in practical application, a novel audio watermarking algorithm with strong robustness is proposed by exploring the multi-resolution characteristic of discrete wavelet transform (DWT and the energy compaction capability of discrete cosine transform (DCT. The human auditory system is insensitive to the minor changes in the frequency components of the audio signal, so the watermarks can be embedded by slightly modifying the frequency components of the audio signal. The audio fragments segmented from the cover audio signal are decomposed by DWT to obtain several groups of wavelet coefficients with different frequency bands, and then the fourth level detail coefficient is selected to be divided into the former packet and the latter packet, which are executed for DCT to get two sets of transform domain coefficients (TDC respectively. Finally, the average amplitudes of the two sets of TDC are modified to embed the binary image watermark according to the special embedding rule. The watermark extraction is blind without the carrier audio signal. Experimental results confirm that the proposed algorithm has good imperceptibility, large payload capacity and strong robustness when resisting against various attacks such as MP3 compression, low-pass filtering, re-sampling, re-quantization, amplitude scaling, echo addition and noise corruption.
Wei, B. G.; Huo, K. X.; Yao, Z. F.; Lou, J.; Li, X. Y.
2018-03-01
It is one of the difficult problems encountered in the research of condition maintenance technology of transformers to recognize partial discharge (PD) pattern. According to the main physical characteristics of PD, three models of oil-paper insulation defects were set up in laboratory to study the PD of transformers, and phase resolved partial discharge (PRPD) was constructed. By using least square method, the grey-scale images of PRPD were constructed and features of each grey-scale image were 28 box dimensions and 28 information dimensions. Affinity propagation algorithm based on manifold distance (AP-MD) for transformers PD pattern recognition was established, and the data of box dimension and information dimension were clustered based on AP-MD. Study shows that clustering result of AP-MD is better than the results of affinity propagation (AP), k-means and fuzzy c-means algorithm (FCM). By choosing different k values of k-nearest neighbor, we find clustering accuracy of AP-MD falls when k value is larger or smaller, and the optimal k value depends on sample size.
Iris Location Algorithm Based on the CANNY Operator and Gradient Hough Transform
Zhong, L. H.; Meng, K.; Wang, Y.; Dai, Z. Q.; Li, S.
2017-12-01
In the iris recognition system, the accuracy of the localization of the inner and outer edges of the iris directly affects the performance of the recognition system, so iris localization has important research meaning. Our iris data contain eyelid, eyelashes, light spot and other noise, even the gray transformation of the images is not obvious, so the general methods of iris location are unable to realize the iris location. The method of the iris location based on Canny operator and gradient Hough transform is proposed. Firstly, the images are pre-processed; then, calculating the gradient information of images, the inner and outer edges of iris are coarse positioned using Canny operator; finally, according to the gradient Hough transform to realize precise localization of the inner and outer edge of iris. The experimental results show that our algorithm can achieve the localization of the inner and outer edges of the iris well, and the algorithm has strong anti-interference ability, can greatly reduce the location time and has higher accuracy and stability.
Searching for continuous gravitational wave signals. The hierarchical Hough transform algorithm
International Nuclear Information System (INIS)
Papa, M.; Schutz, B.F.; Sintes, A.M.
2001-01-01
It is well known that matched filtering techniques cannot be applied for searching extensive parameter space volumes for continuous gravitational wave signals. This is the reason why alternative strategies are being pursued. Hierarchical strategies are best at investigating a large parameter space when there exist computational power constraints. Algorithms of this kind are being implemented by all the groups that are developing software for analyzing the data of the gravitational wave detectors that will come online in the next years. In this talk I will report about the hierarchical Hough transform method that the GEO 600 data analysis team at the Albert Einstein Institute is developing. The three step hierarchical algorithm has been described elsewhere [8]. In this talk I will focus on some of the implementational aspects we are currently concerned with. (author)
NDT applications of the 3D radon transform algorithm for cone beam reconstruction
International Nuclear Information System (INIS)
Sire, P.; Grangeat, P.; Lemasson, P.; Molennec, P.; Rizo, P.
1990-01-01
The paper describes the authors' 3D X-ray CT algorithm RADON using attenuation measurements acquired with a bidimensional detector. The authors' inversion diagram uses the first derivative of the Radon transform synthesis then its inversion. The potentiality of that new method, particularly for the large aperture, prompted us to develop an optimized software offering convenience and high performances on a modern scientific computer. After a brief recall of the basic principle of X-ray imaging processing, the authors introduce theoretical developments resulting in the present inversion diagram. A general algorithm structure will be proposed afterwards. As a conclusion the authors present the performances and the results obtained with ceramic rotors examination
Qin, Jin; Tang, Siqi; Han, Congying; Guo, Tiande
2018-04-01
Partial fingerprint identification technology which is mainly used in device with small sensor area like cellphone, U disk and computer, has taken more attention in recent years with its unique advantages. However, owing to the lack of sufficient minutiae points, the conventional method do not perform well in the above situation. We propose a new fingerprint matching technique which utilizes ridges as features to deal with partial fingerprint images and combines the modified generalized Hough transform and scoring strategy based on machine learning. The algorithm can effectively meet the real-time and space-saving requirements of the resource constrained devices. Experiments on in-house database indicate that the proposed algorithm have an excellent performance.
[A peak recognition algorithm designed for chromatographic peaks of transformer oil].
Ou, Linjun; Cao, Jian
2014-09-01
In the field of the chromatographic peak identification of the transformer oil, the traditional first-order derivative requires slope threshold to achieve peak identification. In terms of its shortcomings of low automation and easy distortion, the first-order derivative method was improved by applying the moving average iterative method and the normalized analysis techniques to identify the peaks. Accurate identification of the chromatographic peaks was realized through using multiple iterations of the moving average of signal curves and square wave curves to determine the optimal value of the normalized peak identification parameters, combined with the absolute peak retention times and peak window. The experimental results show that this algorithm can accurately identify the peaks and is not sensitive to the noise, the chromatographic peak width or the peak shape changes. It has strong adaptability to meet the on-site requirements of online monitoring devices of dissolved gases in transformer oil.
Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets
International Nuclear Information System (INIS)
Stanek, Jan; Kozminski, Wiktor
2010-01-01
Spectra obtained by application of multidimensional Fourier Transformation (MFT) to sparsely sampled nD NMR signals are usually corrupted due to missing data. In the present paper this phenomenon is investigated on simulations and experiments. An effective iterative algorithm for artifact suppression for sparse on-grid NMR data sets is discussed in detail. It includes automated peak recognition based on statistical methods. The results enable one to study NMR spectra of high dynamic range of peak intensities preserving benefits of random sampling, namely the superior resolution in indirectly measured dimensions. Experimental examples include 3D 15 N- and 13 C-edited NOESY-HSQC spectra of human ubiquitin.
Scheduling Two-Sided Transformations Using Tile Algorithms on Multicore Architectures
Directory of Open Access Journals (Sweden)
Hatem Ltaief
2010-01-01
Full Text Available The objective of this paper is to describe, in the context of multicore architectures, three different scheduler implementations for the two-sided linear algebra transformations, in particular the Hessenberg and Bidiagonal reductions which are the first steps for the standard eigenvalue problems and the singular value decompositions respectively. State-of-the-art dense linear algebra softwares, such as the LAPACK and ScaLAPACK libraries, suffer performance losses on multicore processors due to their inability to fully exploit thread-level parallelism. At the same time the fine-grain dataflow model gains popularity as a paradigm for programming multicore architectures. Buttari et al. (Parellel Comput. Syst. Appl. 35 (2009, 38–53 introduced the concept of tile algorithms in which parallelism is no longer hidden inside Basic Linear Algebra Subprograms but is brought to the fore to yield much better performance. Along with efficient scheduling mechanisms for data-driven execution, these tile two-sided reductions achieve high performance computing by reaching up to 75% of the DGEMM peak on a 12000×12000 matrix with 16 Intel Tigerton 2.4 GHz processors. The main drawback of the tile algorithms approach for two-sided transformations is that the full reduction cannot be obtained in one stage. Other methods have to be considered to further reduce the band matrices to the required forms.
Can we use the known fast spherical fourier transforms in numerical meterology?
Sprengel, F.
2001-01-01
In numerical meteorology, there are many solvers using spectral methods. Most of the computing time is spent computing the discrete Legendre function transforms. The aim of this paper is to clarify whether the recently published fast Legendre function transforms can be used here.
Efficient Algorithm and Architecture of Critical-Band Transform for Low-Power Speech Applications
Directory of Open Access Journals (Sweden)
Gan Woon-Seng
2007-01-01
Full Text Available An efficient algorithm and its corresponding VLSI architecture for the critical-band transform (CBT are developed to approximate the critical-band filtering of the human ear. The CBT consists of a constant-bandwidth transform in the lower frequency range and a Brown constant- transform (CQT in the higher frequency range. The corresponding VLSI architecture is proposed to achieve significant power efficiency by reducing the computational complexity, using pipeline and parallel processing, and applying the supply voltage scaling technique. A 21-band Bark scale CBT processor with a sampling rate of 16 kHz is designed and simulated. Simulation results verify its suitability for performing short-time spectral analysis on speech. It has a better fitting on the human ear critical-band analysis, significantly fewer computations, and therefore is more energy-efficient than other methods. With a 0.35 m CMOS technology, it calculates a 160-point speech in 4.99 milliseconds at 234 kHz. The power dissipation is 15.6 W at 1.1 V. It achieves 82.1 power reduction as compared to a benchmark 256-point FFT processor.
Legendre Duality of Spherical and Gaussian Spin Glasses
International Nuclear Information System (INIS)
Genovese, Giuseppe; Tantari, Daniele
2015-01-01
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model
Legendre Duality of Spherical and Gaussian Spin Glasses
Energy Technology Data Exchange (ETDEWEB)
Genovese, Giuseppe, E-mail: giuseppe.genovese@math.uzh.ch [Universität Zürich, Institut für Mathematik (Switzerland); Tantari, Daniele, E-mail: daniele.tantari@sns.it [Scuola Normale Superiore di Pisa, Centro Ennio de Giorgi (Italy)
2015-12-15
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model.
Directory of Open Access Journals (Sweden)
Shin'ya Nakano
2014-05-01
Full Text Available A hybrid algorithm that combines the ensemble transform Kalman filter (ETKF and the importance sampling approach is proposed. Since the ETKF assumes a linear Gaussian observation model, the estimate obtained by the ETKF can be biased in cases with nonlinear or non-Gaussian observations. The particle filter (PF is based on the importance sampling technique, and is applicable to problems with nonlinear or non-Gaussian observations. However, the PF usually requires an unrealistically large sample size in order to achieve a good estimation, and thus it is computationally prohibitive. In the proposed hybrid algorithm, we obtain a proposal distribution similar to the posterior distribution by using the ETKF. A large number of samples are then drawn from the proposal distribution, and these samples are weighted to approximate the posterior distribution according to the importance sampling principle. Since the importance sampling provides an estimate of the probability density function (PDF without assuming linearity or Gaussianity, we can resolve the bias due to the nonlinear or non-Gaussian observations. Finally, in the next forecast step, we reduce the sample size to achieve computational efficiency based on the Gaussian assumption, while we use a relatively large number of samples in the importance sampling in order to consider the non-Gaussian features of the posterior PDF. The use of the ETKF is also beneficial in terms of the computational simplicity of generating a number of random samples from the proposal distribution and in weighting each of the samples. The proposed algorithm is not necessarily effective in case that the ensemble is located distant from the true state. However, monitoring the effective sample size and tuning the factor for covariance inflation could resolve this problem. In this paper, the proposed hybrid algorithm is introduced and its performance is evaluated through experiments with non-Gaussian observations.
International Nuclear Information System (INIS)
Collins, David
2010-01-01
A general framework for regarding oracle-assisted quantum algorithms as tools for discriminating among unitary transformations is described. This framework is applied to the Deutsch-Jozsa problem and all possible quantum algorithms which solve the problem with certainty using oracle unitaries in a particular form are derived. It is also used to show that any quantum algorithm that solves the Deutsch-Jozsa problem starting with a quantum system in a particular class of initial, thermal equilibrium-based states of the type encountered in solution-state NMR can only succeed with greater probability than a classical algorithm when the problem size n exceeds ∼10 5 .
Energy Technology Data Exchange (ETDEWEB)
Eldin, A.A. Hossam; Refaey, M.A. [Electrical Engineering Department, Alexandria University, Alexandria (Egypt)
2011-01-15
This paper proposes a novel methodology for transformer differential protection, based on wave shape recognition of the discriminating criterion extracted of the instantaneous differential currents. Discrete wavelet transform has been applied to the differential currents due to internal fault and inrush currents. The diagnosis criterion is based on median absolute deviation (MAD) of wavelet coefficients over a specified frequency band. The proposed algorithm is examined using various simulated inrush and internal fault current cases on a power transformer that has been modeled using electromagnetic transients program EMTDC software. Results of evaluation study show that, proposed wavelet based differential protection scheme can discriminate internal faults from inrush currents. (author)
Sum of top-hat transform based algorithm for vessel enhancement in MRA images
Ouazaa, Hibet-Allah; Jlassi, Hajer; Hamrouni, Kamel
2018-04-01
The Magnetic Resonance Angiography (MRA) is rich with information's. But, they suffer from poor contrast, illumination and noise. Thus, it is required to enhance the images. But, these significant information can be lost if improper techniques are applied. Therefore, in this paper, we propose a new method of enhancement. We applied firstly the CLAHE method to increase the contrast of the image. Then, we applied the sum of Top-Hat Transform to increase the brightness of vessels. It is performed with the structuring element oriented in different angles. The methodology is tested and evaluated on the publicly available database BRAINIX. And, we used the measurement methods MSE (Mean Square Error), PSNR (Peak Signal to Noise Ratio) and SNR (Signal to Noise Ratio) for the evaluation. The results demonstrate that the proposed method could efficiently enhance the image details and is comparable with state of the art algorithms. Hence, the proposed method could be broadly used in various applications.
Binol, Hamidullah; Bal, Abdullah; Cukur, Huseyin
2015-10-01
The performance of the kernel based techniques depends on the selection of kernel parameters. That's why; suitable parameter selection is an important problem for many kernel based techniques. This article presents a novel technique to learn the kernel parameters in kernel Fukunaga-Koontz Transform based (KFKT) classifier. The proposed approach determines the appropriate values of kernel parameters through optimizing an objective function constructed based on discrimination ability of KFKT. For this purpose we have utilized differential evolution algorithm (DEA). The new technique overcomes some disadvantages such as high time consumption existing in the traditional cross-validation method, and it can be utilized in any type of data. The experiments for target detection applications on the hyperspectral images verify the effectiveness of the proposed method.
Parallel algorithms for quantum chemistry. I. Integral transformations on a hypercube multiprocessor
International Nuclear Information System (INIS)
Whiteside, R.A.; Binkley, J.S.; Colvin, M.E.; Schaefer, H.F. III
1987-01-01
For many years it has been recognized that fundamental physical constraints such as the speed of light will limit the ultimate speed of single processor computers to less than about three billion floating point operations per second (3 GFLOPS). This limitation is becoming increasingly restrictive as commercially available machines are now within an order of magnitude of this asymptotic limit. A natural way to avoid this limit is to harness together many processors to work on a single computational problem. In principle, these parallel processing computers have speeds limited only by the number of processors one chooses to acquire. The usefulness of potentially unlimited processing speed to a computationally intensive field such as quantum chemistry is obvious. If these methods are to be applied to significantly larger chemical systems, parallel schemes will have to be employed. For this reason we have developed distributed-memory algorithms for a number of standard quantum chemical methods. We are currently implementing these on a 32 processor Intel hypercube. In this paper we present our algorithm and benchmark results for one of the bottleneck steps in quantum chemical calculations: the four index integral transformation
Directory of Open Access Journals (Sweden)
Mahin K. Atiq
2013-09-01
Full Text Available Measurement of the active, reactive, and apparent power is one of the most fundamental tasks of smart meters in energy systems. Recently, a number of studies have employed the discrete wavelet transform (DWT for power measurement in smart meters. The most common way to implement DWT is the pyramid algorithm; however, this is not feasible for practical DWT computation because it requires either a log N cascaded filter or O (N word size memory storage for an input signal of the N-point. Both solutions are too expensive for practical applications of smart meters. It is proposed that the recursive pyramid algorithm is more suitable for smart meter implementation because it requires only word size storage of L × Log (N-L, where L is the length of filter. We also investigated the effect of varying different system parameters, such as the sampling rate, dc offset, phase offset, linearity error in current and voltage sensors, analog to digital converter resolution, and number of harmonics in a non-sinusoidal system, on the reactive energy measurement using DWT. The error analysis is depicted in the form of the absolute difference between the measured and the true value of the reactive energy.
Algorithm, applications and evaluation for protein comparison by Ramanujan Fourier transform.
Zhao, Jian; Wang, Jiasong; Hua, Wei; Ouyang, Pingkai
2015-12-01
The amino acid sequence of a protein determines its chemical properties, chain conformation and biological functions. Protein sequence comparison is of great importance to identify similarities of protein structures and infer their functions. Many properties of a protein correspond to the low-frequency signals within the sequence. Low frequency modes in protein sequences are linked to the secondary structures, membrane protein types, and sub-cellular localizations of the proteins. In this paper, we present Ramanujan Fourier transform (RFT) with a fast algorithm to analyze the low-frequency signals of protein sequences. The RFT method is applied to similarity analysis of protein sequences with the Resonant Recognition Model (RRM). The results show that the proposed fast RFT method on protein comparison is more efficient than commonly used discrete Fourier transform (DFT). RFT can detect common frequencies as significant feature for specific protein families, and the RFT spectrum heat-map of protein sequences demonstrates the information conservation in the sequence comparison. The proposed method offers a new tool for pattern recognition, feature extraction and structural analysis on protein sequences. Copyright © 2015 Elsevier Ltd. All rights reserved.
Multirate-based fast parallel algorithms for 2-D DHT-based real-valued discrete Gabor transform.
Tao, Liang; Kwan, Hon Keung
2012-07-01
Novel algorithms for the multirate and fast parallel implementation of the 2-D discrete Hartley transform (DHT)-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented in this paper. A 2-D multirate-based analysis convolver bank is designed for the 2-D RDGT, and a 2-D multirate-based synthesis convolver bank is designed for the 2-D inverse RDGT. The parallel channels in each of the two convolver banks have a unified structure and can apply the 2-D fast DHT algorithm to speed up their computations. The computational complexity of each parallel channel is low and is independent of the Gabor oversampling rate. All the 2-D RDGT coefficients of an image are computed in parallel during the analysis process and can be reconstructed in parallel during the synthesis process. The computational complexity and time of the proposed parallel algorithms are analyzed and compared with those of the existing fastest algorithms for 2-D discrete Gabor transforms. The results indicate that the proposed algorithms are the fastest, which make them attractive for real-time image processing.
Correa Monteiro, Luis Fernando; Aredes, Mauricio; Pinto, J. G.; Exposto, Bruno; Afonso, João L.
2016-01-01
This study presents control algorithms for a new unified power quality conditioner (UPQC) without the series transformers that are frequently used to make the insertion of the series converter of the UPQC between the power supply and the load. The behaviour of the proposed UPQC is evaluated in presence of voltage imbalances, as well as under non-sinusoidal voltage-and current conditions. The presented algorithms derive from the concepts involving the active and non-active currents, together w...
Cheng, Jun; Zhang, Jun; Tian, Jinwen
2015-12-01
Based on deep analysis of the LiveWire interactive boundary extraction algorithm, a new algorithm focusing on improving the speed of LiveWire algorithm is proposed in this paper. Firstly, the Haar wavelet transform is carried on the input image, and the boundary is extracted on the low resolution image obtained by the wavelet transform of the input image. Secondly, calculating LiveWire shortest path is based on the control point set direction search by utilizing the spatial relationship between the two control points users provide in real time. Thirdly, the search order of the adjacent points of the starting node is set in advance. An ordinary queue instead of a priority queue is taken as the storage pool of the points when optimizing their shortest path value, thus reducing the complexity of the algorithm from O[n2] to O[n]. Finally, A region iterative backward projection method based on neighborhood pixel polling has been used to convert dual-pixel boundary of the reconstructed image to single-pixel boundary after Haar wavelet inverse transform. The algorithm proposed in this paper combines the advantage of the Haar wavelet transform and the advantage of the optimal path searching method based on control point set direction search. The former has fast speed of image decomposition and reconstruction and is more consistent with the texture features of the image and the latter can reduce the time complexity of the original algorithm. So that the algorithm can improve the speed in interactive boundary extraction as well as reflect the boundary information of the image more comprehensively. All methods mentioned above have a big role in improving the execution efficiency and the robustness of the algorithm.
Indian Academy of Sciences (India)
polynomial) division have been found in Vedic Mathematics which are dated much before Euclid's algorithm. A programming language Is used to describe an algorithm for execution on a computer. An algorithm expressed using a programming.
Energy Technology Data Exchange (ETDEWEB)
Bang, Jeongho [Seoul National University, Seoul (Korea, Republic of); Hanyang University, Seoul (Korea, Republic of); Yoo, Seokwon [Hanyang University, Seoul (Korea, Republic of)
2014-12-15
We propose a genetic-algorithm-based method to find the unitary transformations for any desired quantum computation. We formulate a simple genetic algorithm by introducing the 'genetic parameter vector' of the unitary transformations to be found. In the genetic algorithm process, all components of the genetic parameter vectors are supposed to evolve to the solution parameters of the unitary transformations. We apply our method to find the optimal unitary transformations and to generalize the corresponding quantum algorithms for a realistic problem, the one-bit oracle decision problem, or the often-called Deutsch problem. By numerical simulations, we can faithfully find the appropriate unitary transformations to solve the problem by using our method. We analyze the quantum algorithms identified by the found unitary transformations and generalize the variant models of the original Deutsch's algorithm.
Modified Legendre Wavelets Technique for Fractional Oscillation Equations
Directory of Open Access Journals (Sweden)
Syed Tauseef Mohyud-Din
2015-10-01
Full Text Available Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s we recommend a new method. In the proposed method, Picard’s iteration is used to convert the nonlinear fractional order oscillation equation into a fractional order recurrence relation and then Legendre wavelets method is applied on the converted problem. In order to check the efficiency and accuracy of the suggested modification, we have considered three problems namely: fractional order force-free Duffing–van der Pol oscillator, forced Duffing–van der Pol oscillator and higher order fractional Duffing equations. The obtained results are compared with the results obtained via other techniques.
Yang, Xue; Li, Xue-You; Li, Jia-Guo; Ma, Jun; Zhang, Li; Yang, Jan; Du, Quan-Ye
2014-02-01
Fast Fourier transforms (FFT) is a basic approach to remote sensing image processing. With the improvement of capacity of remote sensing image capture with the features of hyperspectrum, high spatial resolution and high temporal resolution, how to use FFT technology to efficiently process huge remote sensing image becomes the critical step and research hot spot of current image processing technology. FFT algorithm, one of the basic algorithms of image processing, can be used for stripe noise removal, image compression, image registration, etc. in processing remote sensing image. CUFFT function library is the FFT algorithm library based on CPU and FFTW. FFTW is a FFT algorithm developed based on CPU in PC platform, and is currently the fastest CPU based FFT algorithm function library. However there is a common problem that once the available memory or memory is less than the capacity of image, there will be out of memory or memory overflow when using the above two methods to realize image FFT arithmetic. To address this problem, a CPU and partitioning technology based Huge Remote Fast Fourier Transform (HRFFT) algorithm is proposed in this paper. By improving the FFT algorithm in CUFFT function library, the problem of out of memory and memory overflow is solved. Moreover, this method is proved rational by experiment combined with the CCD image of HJ-1A satellite. When applied to practical image processing, it improves effect of the image processing, speeds up the processing, which saves the time of computation and achieves sound result.
International Nuclear Information System (INIS)
Bueno, Josiane M.; Traina, Agma Juci M.; Cruvinel, Paulo E.
1995-01-01
This work presents an algorithm for three-dimensional digital image reconstruction. Such algorithms based on the combination of both a Fast Fourier Transform method with Hamming Window and the use of a tri-linear interpolation function. The algorithm allows not only the generation of three-dimensional spatial spin distribution maps for Magnetic Resonance Tomography data but also X and Y-rays linear attenuation coefficient maps for CT scanners. Results demonstrates the usefulness of the algorithm in three-dimensional image reconstruction by doing first two-dimensional reconstruction and rather after interpolation. The algorithm was developed in C++ language, and there are two available versions: one under the DOS environment, and the other under the UNIX/Sun environment. (author)
Schaffrin, Burkhard; Felus, Yaron A.
2008-06-01
The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model ( Y- E Y = ( X- E X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E Y and E X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler-Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335-342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.
Wormeester, Herbert; Sasse, A.G.B.M.; van Silfhout, Arend
1988-01-01
One of the main problems in the analysis of measured spectra is how to reduce the influence of noise in data processing. We show a deconvolution, a differentiation and a Fourier Transform algorithm that can be run on a small computer (64 K RAM) and suffer less from noise than commonly used routines.
Wei, B. G.; Wu, X. Y.; Yao, Z. F.; Huang, H.
2017-11-01
Transformers are essential devices of the power system. The accurate computation of the highest temperature (HST) of a transformer’s windings is very significant, as for the HST is a fundamental parameter in controlling the load operation mode and influencing the life time of the insulation. Based on the analysis of the heat transfer processes and the thermal characteristics inside transformers, there is taken into consideration the influence of factors like the sunshine, external wind speed etc. on the oil-immersed transformers. Experimental data and the neural network are used for modeling and protesting of the HST, and furthermore, investigations are conducted on the optimization of the structure and algorithms of neutral network are conducted. Comparison is made between the measured values and calculated values by using the recommended algorithm of IEC60076 and by using the neural network algorithm proposed by the authors; comparison that shows that the value computed with the neural network algorithm approximates better the measured value than the value computed with the algorithm proposed by IEC60076.
Liu, Hua-Long; Liu, Hua-Dong
2014-10-01
Partial discharge (PD) in power transformers is one of the prime reasons resulting in insulation degradation and power faults. Hence, it is of great importance to study the techniques of the detection and localization of PD in theory and practice. The detection and localization of PD employing acoustic emission (AE) techniques, as a kind of non-destructive testing, plus due to the advantages of powerful capability of locating and high precision, have been paid more and more attention. The localization algorithm is the key factor to decide the localization accuracy in AE localization of PD. Many kinds of localization algorithms exist for the PD source localization adopting AE techniques including intelligent and non-intelligent algorithms. However, the existed algorithms possess some defects such as the premature convergence phenomenon, poor local optimization ability and unsuitability for the field applications. To overcome the poor local optimization ability and easily caused premature convergence phenomenon of the fundamental genetic algorithm (GA), a new kind of improved GA is proposed, namely the sequence quadratic programming-genetic algorithm (SQP-GA). For the hybrid optimization algorithm, SQP-GA, the sequence quadratic programming (SQP) algorithm which is used as a basic operator is integrated into the fundamental GA, so the local searching ability of the fundamental GA is improved effectively and the premature convergence phenomenon is overcome. Experimental results of the numerical simulations of benchmark functions show that the hybrid optimization algorithm, SQP-GA, is better than the fundamental GA in the convergence speed and optimization precision, and the proposed algorithm in this paper has outstanding optimization effect. At the same time, the presented SQP-GA in the paper is applied to solve the ultrasonic localization problem of PD in transformers, then the ultrasonic localization method of PD in transformers based on the SQP-GA is proposed. And
A Fast Algorithm of Generalized Radon-Fourier Transform for Weak Maneuvering Target Detection
Directory of Open Access Journals (Sweden)
Weijie Xia
2016-01-01
Full Text Available The generalized Radon-Fourier transform (GRFT has been proposed to detect radar weak maneuvering targets by realizing coherent integration via jointly searching in motion parameter space. Two main drawbacks of GRFT are the heavy computational burden and the blind speed side lobes (BSSL which will cause serious false alarms. The BSSL learning-based particle swarm optimization (BPSO has been proposed before to reduce the computational burden of GRFT and solve the BSSL problem simultaneously. However, the BPSO suffers from an apparent loss in detection performance compared with GRFT. In this paper, a fast implementation algorithm of GRFT using the BSSL learning-based modified wind-driven optimization (BMWDO is proposed. In the BMWDO, the BSSL learning procedure is also used to deal with the BSSL phenomenon. Besides, the MWDO adjusts the coefficients in WDO with Levy distribution and uniform distribution, and it outperforms PSO in a noisy environment. Compared with BPSO, the proposed method can achieve better detection performance with a similar computational cost. Several numerical experiments are also provided to demonstrate the effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Abhijeet Ravankar
2016-05-01
Full Text Available Line detection is an important problem in computer vision, graphics and autonomous robot navigation. Lines detected using a laser range sensor (LRS mounted on a robot can be used as features to build a map of the environment, and later to localize the robot in the map, in a process known as Simultaneous Localization and Mapping (SLAM. We propose an efficient algorithm for line detection from LRS data using a novel hopping-points Singular Value Decomposition (SVD and Hough transform-based algorithm, in which SVD is applied to intermittent LRS points to accelerate the algorithm. A reverse-hop mechanism ensures that the end points of the line segments are accurately extracted. Line segments extracted from the proposed algorithm are used to form a map and, subsequently, LRS data points are matched with the line segments to localize the robot. The proposed algorithm eliminates the drawbacks of point-based matching algorithms like the Iterative Closest Points (ICP algorithm, the performance of which degrades with an increasing number of points. We tested the proposed algorithm for mapping and localization in both simulated and real environments, and found it to detect lines accurately and build maps with good self-localization.
Comment on 'Analytical results for a Bessel function times Legendre polynomials class integrals'
International Nuclear Information System (INIS)
Cregg, P J; Svedlindh, P
2007-01-01
A result is obtained, stemming from Gegenbauer, where the products of certain Bessel functions and exponentials are expressed in terms of an infinite series of spherical Bessel functions and products of associated Legendre functions. Closed form solutions for integrals involving Bessel functions times associated Legendre functions times exponentials, recently elucidated by Neves et al (J. Phys. A: Math. Gen. 39 L293), are then shown to result directly from the orthogonality properties of the associated Legendre functions. This result offers greater flexibility in the treatment of classical Heisenberg chains and may do so in other problems such as occur in electromagnetic diffraction theory. (comment)
Indian Academy of Sciences (India)
to as 'divide-and-conquer'. Although there has been a large effort in realizing efficient algorithms, there are not many universally accepted algorithm design paradigms. In this article, we illustrate algorithm design techniques such as balancing, greedy strategy, dynamic programming strategy, and backtracking or traversal of ...
Peng, Jiangtao; Peng, Silong; Xie, Qiong; Wei, Jiping
2011-04-01
In order to eliminate the lower order polynomial interferences, a new quantitative calibration algorithm "Baseline Correction Combined Partial Least Squares (BCC-PLS)", which combines baseline correction and conventional PLS, is proposed. By embedding baseline correction constraints into PLS weights selection, the proposed calibration algorithm overcomes the uncertainty in baseline correction and can meet the requirement of on-line attenuated total reflectance Fourier transform infrared (ATR-FTIR) quantitative analysis. The effectiveness of the algorithm is evaluated by the analysis of glucose and marzipan ATR-FTIR spectra. BCC-PLS algorithm shows improved prediction performance over PLS. The root mean square error of cross-validation (RMSECV) on marzipan spectra for the prediction of the moisture is found to be 0.53%, w/w (range 7-19%). The sugar content is predicted with a RMSECV of 2.04%, w/w (range 33-68%). Copyright © 2011 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Padmavathi Kora
2017-06-01
Full Text Available Electrocardiogram (ECG, a non-invasive diagnostic technique, used for detecting cardiac arrhythmia. From last decade industry dealing with biomedical instrumentation and research, demanding an advancement in its ability to distinguish different cardiac arrhythmia. Atrial Fibrillation (AF is an irregular rhythm of the human heart. During AF, the atrial moments are quicker than the normal rate. As blood is not completely ejected out of atria, chances for the formation of blood clots in atrium. These abnormalities in the heart can be identified by the changes in the morphology of the ECG. The first step in the detection of AF is preprocessing of ECG, which removes noise using filters. Feature extraction is the next key process in this research. Recent feature extraction methods, such as Auto Regressive (AR modeling, Magnitude Squared Coherence (MSC and Wavelet Coherence (WTC using standard database (MIT-BIH, yielded a lot of features. Many of these features might be insignificant containing some redundant and non-discriminatory features that introduce computational burden and loss of performance. This paper presents fast Conjugate Symmetric Sequency Ordered Complex Hadamard Transform (CS-SCHT for extracting relevant features from the ECG signal. The sparse matrix factorization method is used for developing fast and efficient CS-SCHT algorithm and its computational performance is examined and compared to that of the HT and NCHT. The applications of the CS-SCHT in the ECG-based AF detection is also discussed. These fast CS-SCHT features are optimized using Hybrid Firefly and Particle Swarm Optimization (FFPSO to increase the performance of the classifier.
National Research Council Canada - National Science Library
Franke, Richard
2001-01-01
.... It was found that for all levels the approximation of the covariance data for pressure height innovations by Legendre functions led to positive coefficients for up to 25 terms except at the some low and high levels...
International Nuclear Information System (INIS)
Li Tianduo; Xiao Gang; Di Yuming; Han Feng; Qiu Xiaoling
1999-01-01
The γ energy spectrum is expanded in allied energy-frequency space. By the different characterization of the evolution of wavelet transform modulus maxima across scales between energy spectrum and noise, the algorithm for removing the noise from γ energy spectrum by analyzing the evolution of the wavelet transform maxima across scales is presented. The results show, in contrast to the methods in energy space or in frequency space, the method has the advantages that the peak of energy spectrum can be indicated accurately and the energy spectrum can be reconstructed with a good approximation
A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems
Directory of Open Access Journals (Sweden)
A. Karimi Dizicheh
2013-01-01
wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate.
Transform Decoding of Reed-Solomon Codes. Volume I. Algorithm and Signal Processing Structure
1982-11-01
systematic channel co.’e. 1. lake the inverse transform of the r- ceived se, - nee. 2. Isolate the error syndrome from the inverse transform and use... inverse transform is identic l with interpolation of the polynomial a(z) from its n values. In order to generate a Reed-Solomon (n,k) cooce, we let the set...in accordance with the transform of equation (4). If we were to apply the inverse transform of equa- tion (6) to the coefficient sequence of A(z), we
Computation of temperature-dependent legendre moments of a double-differential elastic cross section
International Nuclear Information System (INIS)
Arbanas, G.; Dunn, M.E.; Larson, N.M.; Leal, L.C.; Williams, M.L.; Becker, B.; Dagan, R.
2011-01-01
A general expression for temperature-dependent Legendre moments of a double-differential elastic scattering cross section was derived by Ouisloumen and Sanchez [Nucl. Sci. Eng. 107, 189-200 (1991)]. Attempts to compute this expression are hindered by the three-fold nested integral, limiting their practical application to just the zeroth Legendre moment of an isotropic scattering. It is shown that the two innermost integrals could be evaluated analytically to all orders of Legendre moments, and for anisotropic scattering, by a recursive application of the integration by parts method. For this method to work, the anisotropic angular distribution in the center of mass is expressed as an expansion in Legendre polynomials. The first several Legendre moments of elastic scattering of neutrons on 238 U are computed at T=1000 K at incoming energy 6.5 eV for isotropic scattering in the center of mass frame. Legendre moments of the anisotropic angular distribution given via Blatt-Biedenharn coefficients are computed at 1 keV. The results are in agreement with those computed by the Monte Carlo method. (author)
Pal, Suvra; Balakrishnan, Narayanaswamy
2018-05-01
In this paper, we develop likelihood inference based on the expectation maximization algorithm for the Box-Cox transformation cure rate model assuming the lifetimes to follow a Weibull distribution. A simulation study is carried out to demonstrate the performance of the proposed estimation method. Through Monte Carlo simulations, we also study the effect of model misspecification on the estimate of cure rate. Finally, we analyze a well-known data on melanoma with the model and the inferential method developed here.
Graph Transformation and Designing Parallel Sparse Matrix Algorithms beyond Data Dependence Analysis
Directory of Open Access Journals (Sweden)
H.X. Lin
2004-01-01
Full Text Available Algorithms are often parallelized based on data dependence analysis manually or by means of parallel compilers. Some vector/matrix computations such as the matrix-vector products with simple data dependence structures (data parallelism can be easily parallelized. For problems with more complicated data dependence structures, parallelization is less straightforward. The data dependence graph is a powerful means for designing and analyzing parallel algorithms. However, for sparse matrix computations, parallelization based on solely exploiting the existing parallelism in an algorithm does not always give satisfactory results. For example, the conventional Gaussian elimination algorithm for the solution of a tri-diagonal system is inherently sequential, so algorithms specially for parallel computation has to be designed. After briefly reviewing different parallelization approaches, a powerful graph formalism for designing parallel algorithms is introduced. This formalism will be discussed using a tri-diagonal system as an example. Its application to general matrix computations is also discussed. Its power in designing parallel algorithms beyond the ability of data dependence analysis is shown by means of a new algorithm called ACER (Alternating Cyclic Elimination and Reduction algorithm.
Indian Academy of Sciences (India)
ticians but also forms the foundation of computer science. Two ... with methods of developing algorithms for solving a variety of problems but ... applications of computers in science and engineer- ... numerical calculus are as important. We will ...
Directory of Open Access Journals (Sweden)
Nan YU
2014-09-01
Full Text Available The interference signal in magneto-hydro-dynamics (MHD may be the disturbance from the power supply, the equipment itself, or the electromagnetic radiation. Interference signal mixed in normal signal, brings difficulties for signal analysis and processing. Recently proposed S-Transform algorithm combines advantages of short time Fourier transform and wavelet transform. It uses Fourier kernel and wavelet like Gauss window whose width is inversely proportional to the frequency. Therefore, S-Transform algorithm not only preserves the phase information of the signals but also has variable resolution like wavelet transform. This paper proposes a new method to establish a MHD signal classifier using S-transform algorithm and radial basis function neural network (RBFNN. Because RBFNN centers ascertained by k-means clustering algorithm probably are the local optimum, this paper analyzes the characteristics of k-means clustering algorithm and proposes an improved k-means clustering algorithm called GCW (Group-cluster-weight k-means clustering algorithm to improve the centers distribution. The experiment results show that the improvement greatly enhances the RBFNN performance.
Directory of Open Access Journals (Sweden)
R. Hajiabadi
2016-10-01
Full Text Available Introduction One reason for the complexity of hydrological phenomena prediction, especially time series is existence of features such as trend, noise and high-frequency oscillations. These complex features, especially noise, can be detected or removed by preprocessing. Appropriate preprocessing causes estimation of these phenomena become easier. Preprocessing in the data driven models such as artificial neural network, gene expression programming, support vector machine, is more effective because the quality of data in these models is important. Present study, by considering diagnosing and data transformation as two different preprocessing, tries to improve the results of intelligent models. In this study two different intelligent models, Artificial Neural Network and Gene Expression Programming, are applied to estimation of daily suspended sediment load. Wavelet transforms and logarithmic transformation is used for diagnosing and data transformation, respectively. Finally, the impacts of preprocessing on the results of intelligent models are evaluated. Materials and Methods In this study, Gene Expression Programming and Artificial Neural Network are used as intelligent models for suspended sediment load estimation, then the impacts of diagnosing and logarithmic transformations approaches as data preprocessor are evaluated and compared to the result improvement. Two different logarithmic transforms are considered in this research, LN and LOG. Wavelet transformation is used to time series denoising. In order to denoising by wavelet transforms, first, time series can be decomposed at one level (Approximation part and detail part and second, high-frequency part (detail will be removed as noise. According to the ability of gene expression programming and artificial neural network to analysis nonlinear systems; daily values of suspended sediment load of the Skunk River in USA, during a 5-year period, are investigated and then estimated.4 years of
Algorithm comparison and benchmarking using a parallel spectra transform shallow water model
Energy Technology Data Exchange (ETDEWEB)
Worley, P.H. [Oak Ridge National Lab., TN (United States); Foster, I.T.; Toonen, B. [Argonne National Lab., IL (United States)
1995-04-01
In recent years, a number of computer vendors have produced supercomputers based on a massively parallel processing (MPP) architecture. These computers have been shown to be competitive in performance with conventional vector supercomputers for some applications. As spectral weather and climate models are heavy users of vector supercomputers, it is interesting to determine how these models perform on MPPS, and which MPPs are best suited to the execution of spectral models. The benchmarking of MPPs is complicated by the fact that different algorithms may be more efficient on different architectures. Hence, a comprehensive benchmarking effort must answer two related questions: which algorithm is most efficient on each computer and how do the most efficient algorithms compare on different computers. In general, these are difficult questions to answer because of the high cost associated with implementing and evaluating a range of different parallel algorithms on each MPP platform.
Iterative-Transform Phase Diversity: An Object and Wavefront Recovery Algorithm
Smith, J. Scott
2011-01-01
Presented is a solution for recovering the wavefront and an extended object. It builds upon the VSM architecture and deconvolution algorithms. Simulations are shown for recovering the wavefront and extended object from noisy data.
A splitting algorithm for the wavelet transform of cubic splines on a nonuniform grid
Sulaimanov, Z. M.; Shumilov, B. M.
2017-10-01
For cubic splines with nonuniform nodes, splitting with respect to the even and odd nodes is used to obtain a wavelet expansion algorithm in the form of the solution to a three-diagonal system of linear algebraic equations for the coefficients. Computations by hand are used to investigate the application of this algorithm for numerical differentiation. The results are illustrated by solving a prediction problem.
International Nuclear Information System (INIS)
Pang Chaoyang; Hu Benqiong
2008-01-01
The discrete Fourier transform (DFT) is the base of modern signal processing. 1-dimensional fast Fourier transform (ID FFT) and 2D FFT have time complexity O (N log N) and O (N 2 log N) respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. One-dimensional quantum DFT (ID QDFT) and two-dimensional quantum DFT (2D QDFT) are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, ID and 2D QDFT have time complexity O(√N) and O (N) respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible. (general)
DEFF Research Database (Denmark)
Bock, Lars Nicolai
2011-01-01
Artiklen diskuterer ordet "transformation" med udgangspunkt i dels hvorledes ordet bruges i arkitektfaglig terminologi og dels med fokus på ordets potentielle indhold og egnethed i samme teminologi.......Artiklen diskuterer ordet "transformation" med udgangspunkt i dels hvorledes ordet bruges i arkitektfaglig terminologi og dels med fokus på ordets potentielle indhold og egnethed i samme teminologi....
Energy Technology Data Exchange (ETDEWEB)
LACKS,S.A.
2003-10-09
Transformation, which alters the genetic makeup of an individual, is a concept that intrigues the human imagination. In Streptococcus pneumoniae such transformation was first demonstrated. Perhaps our fascination with genetics derived from our ancestors observing their own progeny, with its retention and assortment of parental traits, but such interest must have been accelerated after the dawn of agriculture. It was in pea plants that Gregor Mendel in the late 1800s examined inherited traits and found them to be determined by physical elements, or genes, passed from parents to progeny. In our day, the material basis of these genetic determinants was revealed to be DNA by the lowly bacteria, in particular, the pneumococcus. For this species, transformation by free DNA is a sexual process that enables cells to sport new combinations of genes and traits. Genetic transformation of the type found in S. pneumoniae occurs naturally in many species of bacteria (70), but, initially only a few other transformable species were found, namely, Haemophilus influenzae, Neisseria meningitides, Neisseria gonorrheae, and Bacillus subtilis (96). Natural transformation, which requires a set of genes evolved for the purpose, contrasts with artificial transformation, which is accomplished by shocking cells either electrically, as in electroporation, or by ionic and temperature shifts. Although such artificial treatments can introduce very small amounts of DNA into virtually any type of cell, the amounts introduced by natural transformation are a million-fold greater, and S. pneumoniae can take up as much as 10% of its cellular DNA content (40).
Directory of Open Access Journals (Sweden)
Byambaa Dorj
2016-01-01
Full Text Available The next promising key issue of the automobile development is a self-driving technique. One of the challenges for intelligent self-driving includes a lane-detecting and lane-keeping capability for advanced driver assistance systems. This paper introduces an efficient and lane detection method designed based on top view image transformation that converts an image from a front view to a top view space. After the top view image transformation, a Hough transformation technique is integrated by using a parabolic model of a curved lane in order to estimate a parametric model of the lane in the top view space. The parameters of the parabolic model are estimated by utilizing a least-square approach. The experimental results show that the newly proposed lane detection method with the top view transformation is very effective in estimating a sharp and curved lane leading to a precise self-driving capability.
Indian Academy of Sciences (India)
algorithm design technique called 'divide-and-conquer'. One of ... Turtle graphics, September. 1996. 5. ... whole list named 'PO' is a pointer to the first element of the list; ..... Program for computing matrices X and Y and placing the result in C *).
Indian Academy of Sciences (India)
algorithm that it is implicitly understood that we know how to generate the next natural ..... Explicit comparisons are made in line (1) where maximum and minimum is ... It can be shown that the function T(n) = 3/2n -2 is the solution to the above ...
Healy, John J; Sheridan, John T
2011-05-01
The product of the spatial and spatial frequency extents of a wave field has proven useful in the analysis of the sampling requirements of numerical simulations. We propose that the ratio of these quantities is also illuminating. We have shown that the distance at which the so-called "direct method" becomes more efficient than the so-called "spectral method" for simulations of Fresnel transforms may be written in terms of this space-bandwidth ratio. We have proposed generalizations of these algorithms for numerical simulations of general ABCD systems and derived expressions for the "transition space-bandwidth ratio," above which the generalization of the spectral method is the more efficient algorithm and below which the generalization of the direct method is preferable.
Baker, W.R.
1959-08-25
Transformers of a type adapted for use with extreme high power vacuum tubes where current requirements may be of the order of 2,000 to 200,000 amperes are described. The transformer casing has the form of a re-entrant section being extended through an opening in one end of the cylinder to form a coaxial terminal arrangement. A toroidal multi-turn primary winding is disposed within the casing in coaxial relationship therein. In a second embodiment, means are provided for forming the casing as a multi-turn secondary. The transformer is characterized by minimized resistance heating, minimized external magnetic flux, and an economical construction.
Xu, Shaoping; Zeng, Xiaoxia; Jiang, Yinnan; Tang, Yiling
2018-01-01
We proposed a noniterative principal component analysis (PCA)-based noise level estimation (NLE) algorithm that addresses the problem of estimating the noise level with a two-step scheme. First, we randomly extracted a number of raw patches from a given noisy image and took the smallest eigenvalue of the covariance matrix of the raw patches as the preliminary estimation of the noise level. Next, the final estimation was directly obtained with a nonlinear mapping (rectification) function that was trained on some representative noisy images corrupted with different known noise levels. Compared with the state-of-art NLE algorithms, the experiment results show that the proposed NLE algorithm can reliably infer the noise level and has robust performance over a wide range of image contents and noise levels, showing a good compromise between speed and accuracy in general.
Mulyadi, Y.; Sucita, T.; Sumarto; Alpani, M.
2018-02-01
Electricity supply demand is increasing every year. It makes PT. PLN (Persero) is required to provide optimal customer service and satisfaction. Optimal service depends on the performance of the equipment of the power system owned, especially the transformer. Power transformer is an electrical equipment that transforms electricity from high voltage to low voltage or vice versa. However, in the electrical power system, is inseparable from interference included in the transformer. But, the disturbance can be minimized by the protection system. The main protection transformer is differential relays. Differential relays working system using Kirchoff law where inflows equal outflows. If there are excessive currents that interfere then the relays will work. But, the relay can also experience decreased performance. Therefore, this final project aims to analyze the reliability of the differential relay on the transformer in three different substations. Referring to the standard applied by the transmission line protection officer, the differential relay shall have slope characteristics of 30% in the first slope and 80% in the second slope when using two slopes and 80% when using one slope with an instant time and the corresponding ratio. So, the results obtained on the Siemens differential release have a reliable slope characteristic with a value of 30 on the fuzzy logic system. In a while, ABB a differential relay is only 80% reliable because two experiments are not reliable. For the time, all the differential relays are instant with a value of 0.06 on the fuzzy logic system. For ratios, the differential relays ABB have a better value than others brand with a value of 151 on the fuzzy logic system.
Indian Academy of Sciences (India)
will become clear in the next article when we discuss a simple logo like programming language. ... Rod B may be used as an auxiliary store. The problem is to find an algorithm which performs this task. ... No disks are moved from A to Busing C as auxiliary rod. • move _disk (A, C);. (No + l)th disk is moved from A to C directly ...
We describe the development and evaluation of two new model algorithms for NOx chemistry in the R-LINE near-road dispersion model for traffic sources. With increased urbanization, there is increased mobility leading to higher amount of traffic related activity on a global scale. ...
Osler, James Edward
2013-01-01
This paper discusses the implementation of the Tri-Squared Test as an advanced statistical measure used to verify and validate the research outcomes of Educational Technology software. A mathematical and epistemological rational is provided for the transformative process of qualitative data into quantitative outcomes through the Tri-Squared Test…
Institute of Scientific and Technical Information of China (English)
G.Ya(n)ez-Navarro; Guo-Hua Sun; Dong-Sheng Sun; Chang-Yuan Chen; Shi-Hai Dong
2017-01-01
A few important integrals involving the product of two universal associated Legendre polynomials Pl'm'(x),Pk'n'(x) and x2a(1-x2)-p-1,xb(1 ±x)-p-1 and xc(1-x2)-p-1 (1 ±-x) are evaluated using the operator form of Taylor's theorem and an integral over a single universal associated Legendre polynomial.These integrals are more general since the quantum numbers are unequal,i.e.l'≠ k'and m'≠ n'.Their selection rules are also given.We also verify the correctness of those integral formulas numerically.
Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation
Directory of Open Access Journals (Sweden)
S. Balaji
2014-01-01
Full Text Available A Legendre wavelet operational matrix method (LWM is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.
Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions
Farrell, Orin J
2013-01-01
Nearly 200 problems, each with a detailed, worked-out solution, deal with the properties and applications of the gamma and beta functions, Legendre polynomials, and Bessel functions. The first two chapters examine gamma and beta functions, including applications to certain geometrical and physical problems such as heat-flow in a straight wire. The following two chapters treat Legendre polynomials, addressing applications to specific series expansions, steady-state heat-flow temperature distribution, gravitational potential of a circular lamina, and application of Gauss's mechanical quadrature
Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method
Sohaib, Muhammad; Haq, Sirajul; Mukhtar, Safyan; Khan, Imad
2018-03-01
An efficient method is proposed to approximate sixth order boundary value problems. The proposed method is based on Legendre wavelet in which Legendre polynomial is used. The mechanism of the method is to use collocation points that converts the differential equation into a system of algebraic equations. For validation two test problems are discussed. The results obtained from proposed method are quite accurate, also close to exact solution, and other different methods. The proposed method is computationally more effective and leads to more accurate results as compared to other methods from literature.
Ito, K.
1983-01-01
Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.
Schneider, Barry I.; Segura, Javier; Gil, Amparo; Guan, Xiaoxu; Bartschat, Klaus
2018-04-01
This is a revised and updated version of a modern Fortran 90 code to compute the regular Plm (x) and irregular Qlm (x) associated Legendre functions for all x ∈(- 1 , + 1) (on the cut) and | x | > 1 and integer degree (l) and order (m). The necessity to revise the code comes as a consequence of some comments of Prof. James Bremer of the UC//Davis Mathematics Department, who discovered that there were errors in the code for large integer degree and order for the normalized regular Legendre functions on the cut.
Directory of Open Access Journals (Sweden)
HE Manyun
2017-09-01
Full Text Available Classification of building and vegetation is difficult solely by LiDAR data and vegetation in shadows can't be eliminated only by aerial images. The improved top-hat transformations and local binary patterns (LBP elevation texture analysis for building extraction are proposed based on the fusion of aerial images and LiDAR data. Firstly, LiDAR data is reorganized into grid cell, the algorithm removes ground points through top-hat transform. Then, the vegetation points are extracted by normalized difference vegetation index (NDVI. Thirdly, according to the elevation information of LiDAR points, LBP elevation texture is calculated and achieving precise elimination of vegetation in shadows or surrounding to the buildings. At last, morphological operations are used to fill the holes of building roofs, and region growing for complete building edges. The simulation is based on the complex urban area in Vaihingen benchmark provided by ISPRS, the results show that the algorithm affording higher classification accuracy.
Rezaee, Kh; Haddadnia, J
2013-09-01
Breast cancer is currently one of the leading causes of death among women worldwide. The diagnosis and separation of cancerous tumors in mammographic images require accuracy, experience and time, and it has always posed itself as a major challenge to the radiologists and physicians. This paper proposes a new algorithm which draws on discrete wavelet transform and adaptive K-means techniques to transmute the medical images implement the tumor estimation and detect breast cancer tumors in mammograms in early stages. It also allows the rapid processing of the input data. In the first step, after designing a filter, the discrete wavelet transform is applied to the input images and the approximate coefficients of scaling components are constructed. Then, the different parts of image are classified in continuous spectrum. In the next step, by using adaptive K-means algorithm for initializing and smart choice of clusters' number, the appropriate threshold is selected. Finally, the suspicious cancerous mass is separated by implementing the image processing techniques. We Received 120 mammographic images in LJPEG format, which had been scanned in Gray-Scale with 50 microns size, 3% noise and 20% INU from clinical data taken from two medical databases (mini-MIAS and DDSM). The proposed algorithm detected tumors at an acceptable level with an average accuracy of 92.32% and sensitivity of 90.24%. Also, the Kappa coefficient was approximately 0.85, which proved the suitable reliability of the system performance. The exact positioning of the cancerous tumors allows the radiologist to determine the stage of disease progression and suggest an appropriate treatment in accordance with the tumor growth. The low PPV and high NPV of the system is a warranty of the system and both clinical specialists and patients can trust its output.
Wei, Xiuyan; Song, Xinyue; Dong, Dong; Keyhani, Nemat O; Yao, Lindan; Zang, Xiangyun; Dong, Lili; Gu, Zijian; Fu, Delai; Liu, Xingzhong; Qiu, Junzhi; Guan, Xiong
2016-07-01
The insect pathogenic fungus Aschersonia placenta is a highly effective pathogen of whiteflies and scale insects. However, few genetic tools are currently available for studying this organism. Here we report on the conditions for the production of transformable A. placenta protoplasts using an optimized protocol based on the response surface method (RSM). Critical parameters for protoplast production were modelled by using a Box-Behnken design (BBD) involving 3 levels of 3 variables that was subsequently tested to verify its ability to predict protoplast production (R(2) = 0.9465). The optimized conditions resulted in the highest yield of protoplasts ((4.41 ± 0.02) × 10(7) cells/mL of culture, mean ± SE) when fungal cells were treated with 26.1 mg/mL of lywallzyme for 4 h of digestion, and subsequently allowed to recover for 64.6 h in 0.7 mol/L NaCl-Tris buffer. The latter was used as an osmotic stabilizer. The yield of protoplasts was approximately 10-fold higher than that of the nonoptimized conditions. Generated protoplasts were transformed with vector PbarGPE containing the bar gene as the selection marker. Transformation efficiency was 300 colonies/(μg DNA·10(7) protoplasts), and integration of the vector DNA was confirmed by PCR. The results show that rational design strategies (RSM and BBD methods) are useful to increase the production of fungal protoplasts for a variety of downstream applications.
National Research Council Canada - National Science Library
Moon, II, Ron L
2005-01-01
...) development environment into an FPGA-based embedded-platform development board. Research at the Naval Postgraduate School has produced a revolutionary time-optimal spacecraft control algorithm based upon the Legendre Pseudospectral method...
Khoje, Suchitra
2018-02-01
Images of four qualities of mangoes and guavas are evaluated for color and textural features to characterize and classify them, and to model the fruit appearance grading. The paper discusses three approaches to identify most discriminating texture features of both the fruits. In the first approach, fruit's color and texture features are selected using Mahalanobis distance. A total of 20 color features and 40 textural features are extracted for analysis. Using Mahalanobis distance and feature intercorrelation analyses, one best color feature (mean of a* [L*a*b* color space]) and two textural features (energy a*, contrast of H*) are selected as features for Guava while two best color features (R std, H std) and one textural features (energy b*) are selected as features for mangoes with the highest discriminate power. The second approach studies some common wavelet families for searching the best classification model for fruit quality grading. The wavelet features extracted from five basic mother wavelets (db, bior, rbior, Coif, Sym) are explored to characterize fruits texture appearance. In third approach, genetic algorithm is used to select only those color and wavelet texture features that are relevant to the separation of the class, from a large universe of features. The study shows that image color and texture features which were identified using a genetic algorithm can distinguish between various qualities classes of fruits. The experimental results showed that support vector machine classifier is elected for Guava grading with an accuracy of 97.61% and artificial neural network is elected from Mango grading with an accuracy of 95.65%. The proposed method is nondestructive fruit quality assessment method. The experimental results has proven that Genetic algorithm along with wavelet textures feature has potential to discriminate fruit quality. Finally, it can be concluded that discussed method is an accurate, reliable, and objective tool to determine fruit
A time-dependent semiclassical wavepacket method using a fast Fourier transform (FFT) algorithm
International Nuclear Information System (INIS)
Gauss, J.; Heller, E.J.
1991-01-01
A new semiclassical propagator based on a local expansion of the potential up to second order around the moving center of the wavepackt is proposed. Formulas for the propagator are derived and the implementation using grid and fast Fourier transform (FFT) methods is discussed. The semiclassical propagator can be improved up to the exact quantum mechanical limit by including anharmonic corrections using a split operator approach. Preliminary applications to the CH 3 I photodissociation problem show the applicability and accuracy of the proposed method. (orig.)D
Generalizations of an integral for Legendre polynomials by Persson and Strang
Diekema, E.; Koornwinder, T.H.
2012-01-01
Persson and Strang (2003) evaluated the integral over [−1,1] of a squared odd degree Legendre polynomial divided by x2 as being equal to 2. We consider a similar integral for orthogonal polynomials with respect to a general even orthogonality measure, with Gegenbauer and Hermite polynomials as
A kinetic theory for nonanalog Monte Carlo algorithms: Exponential transform with angular biasing
International Nuclear Information System (INIS)
Ueki, T.; Larsen, E.W.
1998-01-01
A new Boltzmann Monte Carlo (BMC) equation is proposed to describe the transport of Monte Carlo particles governed by a set of nonanalog rules for the transition of space, velocity, and weight. The BMC equation is a kinetic equation that includes weight as an extra independent variable. The solution of the BMC equation is the pointwise distribution of velocity and weight throughout the physical system. The BMC equation is derived for the simulation of a transmitted current, utilizing the exponential transform with angular biasing. The weight moments of the solution of the BMC equation are used to predict the score moments of the transmission current. (Also, it is shown that an adjoint BMC equation can be used for this purpose.) Integrating the solution of the forward BMC equation over space, velocity, and weight, the mean number of flights per history is obtained. This is used to determine theoretically the figure of merit for any choice of biasing parameters. Also, a maximum safe value of the exponential transform parameter is proposed, which ensure the finite variance of variance estimate (sample variance) for any penetration distance. Finally, numerical results that validate the new theory are provided
On the derivative of the Legendre function of the first kind with respect to its degree
International Nuclear Information System (INIS)
Szmytkowski, Radoslaw
2006-01-01
We study the derivative of the Legendre function of the first kind, P ν (z), with respect to its degree ν. At first, we provide two contour integral representations for ∂P ν (z)/∂ν. Then, we proceed to investigate the case of [∂P ν (z)/∂ν] ν=n , with n being an integer; this case is met in some physical and engineering problems. Since it holds that [∂P ν' (z)/∂ν'] ν'==ν-1 -[∂P ν' (z0/∂ν'] ν'=ν , we focus on the sub-case of n being a non-negative integer. We show that ∂P ν (z)/∂ν vertical bar ν=n = P n (z) ln((z+1)/2) + R n (z) (n element of N) where R n (z) is a polynomial in z of degree n. We present alternative derivations of several known explicit expressions for R n (z) and also add some new. A generating function for R n (z) is also constructed. Properties of the polynomials V n (z) = [R n (z) + (-1) n R n (-z)]/2 and W n-1 (z) = -[R n (z) - (-1) n R n (-z)]/2 are also investigated. It is found that W n-1 (z) is the Christoffel polynomial, well known from the theory of the Legendre function of the second kind, Q n (z). As examples of applications of the results obtained, we present non-standard derivations of some representations of Q n (z), sum to closed forms some Legendre series, evaluate some definite integrals involving Legendre polynomials and also derive an explicit representation of the indefinite integral of the Legendre polynomial squared
Directory of Open Access Journals (Sweden)
Mohd Tahir Ismail
2016-06-01
Full Text Available The daily returns of four African countries' stock market indices for the period January 2, 2000, to December 31, 2014, were employed to compare the GARCH(1,1 model and a newly proposed Maximal Overlap Discreet Wavelet Transform (MODWT-GARCH(1,1 model. The results showed that although both models fit the returns data well, the forecast produced by the GARCH(1,1 model underestimates the observed returns whereas the newly proposed MODWT-GARCH(1,1 model generates an accurate forecast value of the observed returns. The results generally showed that the newly proposed MODWT-GARCH(1,1 model best fits returns series for these African countries. Hence the proposed MODWT-GARCH should be applied on other context to further verify its validity.
Trusiak, Maciej; Patorski, Krzysztof; Wielgus, Maciej
2012-10-08
Presented method for fringe pattern enhancement has been designed for processing and analyzing low quality fringe patterns. It uses a modified fast and adaptive bidimensional empirical mode decomposition (FABEMD) for the extraction of bidimensional intrinsic mode functions (BIMFs) from an interferogram. Fringe pattern is then selectively reconstructed (SR) taking the regions of selected BIMFs with high modulation values only. Amplitude demodulation and normalization of the reconstructed image is conducted using the spiral phase Hilbert transform (HS). It has been tested using computer generated interferograms and real data. The performance of the presented SR-FABEMD-HS method is compared with other normalization techniques. Its superiority, potential and robustness to high fringe density variations and the presence of noise, modulation and background illumination defects in analyzed fringe patterns has been corroborated.
Parallelizing the spectral transform method: A comparison of alternative parallel algorithms
International Nuclear Information System (INIS)
Foster, I.; Worley, P.H.
1993-01-01
The spectral transform method is a standard numerical technique for solving partial differential equations on the sphere and is widely used in global climate modeling. In this paper, we outline different approaches to parallelizing the method and describe experiments that we are conducting to evaluate the efficiency of these approaches on parallel computers. The experiments are conducted using a testbed code that solves the nonlinear shallow water equations on a sphere, but are designed to permit evaluation in the context of a global model. They allow us to evaluate the relative merits of the approaches as a function of problem size and number of processors. The results of this study are guiding ongoing work on PCCM2, a parallel implementation of the Community Climate Model developed at the National Center for Atmospheric Research
Lin, H.; Zhang, X.; Wu, X.; Tarnas, J. D.; Mustard, J. F.
2018-04-01
Quantitative analysis of hydrated minerals from hyperspectral remote sensing data is fundamental for understanding Martian geologic process. Because of the difficulties for selecting endmembers from hyperspectral images, a sparse unmixing algorithm has been proposed to be applied to CRISM data on Mars. However, it's challenge when the endmember library increases dramatically. Here, we proposed a new methodology termed Target Transformation Constrained Sparse Unmixing (TTCSU) to accurately detect hydrous minerals on Mars. A new version of target transformation technique proposed in our recent work was used to obtain the potential detections from CRISM data. Sparse unmixing constrained with these detections as prior information was applied to CRISM single-scattering albedo images, which were calculated using a Hapke radiative transfer model. This methodology increases success rate of the automatic endmember selection of sparse unmixing and could get more accurate abundances. CRISM images with well analyzed in Southwest Melas Chasma was used to validate our methodology in this study. The sulfates jarosite was detected from Southwest Melas Chasma, the distribution is consistent with previous work and the abundance is comparable. More validations will be done in our future work.
Directory of Open Access Journals (Sweden)
Erik Cuevas
2015-01-01
Full Text Available In this paper, a new method for robustly estimating multiple view relations from point correspondences is presented. The approach combines the popular random sampling consensus (RANSAC algorithm and the evolutionary method harmony search (HS. With this combination, the proposed method adopts a different sampling strategy than RANSAC to generate putative solutions. Under the new mechanism, at each iteration, new candidate solutions are built taking into account the quality of the models generated by previous candidate solutions, rather than purely random as it is the case of RANSAC. The rules for the generation of candidate solutions (samples are motivated by the improvisation process that occurs when a musician searches for a better state of harmony. As a result, the proposed approach can substantially reduce the number of iterations still preserving the robust capabilities of RANSAC. The method is generic and its use is illustrated by the estimation of homographies, considering synthetic and real images. Additionally, in order to demonstrate the performance of the proposed approach within a real engineering application, it is employed to solve the problem of position estimation in a humanoid robot. Experimental results validate the efficiency of the proposed method in terms of accuracy, speed, and robustness.
An algorithm to transform natural language into SQL queries for relational databases
Directory of Open Access Journals (Sweden)
Garima Singh
2016-09-01
Full Text Available Intelligent interface, to enhance efficient interactions between user and databases, is the need of the database applications. Databases must be intelligent enough to make the accessibility faster. However, not every user familiar with the Structured Query Language (SQL queries as they may not aware of structure of the database and they thus require to learn SQL. So, non-expert users need a system to interact with relational databases in their natural language such as English. For this, Database Management System (DBMS must have an ability to understand Natural Language (NL. In this research, an intelligent interface is developed using semantic matching technique which translates natural language query to SQL using set of production rules and data dictionary. The data dictionary consists of semantics sets for relations and attributes. A series of steps like lower case conversion, tokenization, speech tagging, database element and SQL element extraction is used to convert Natural Language Query (NLQ to SQL Query. The transformed query is executed and the results are obtained by the user. Intelligent Interface is the need of database applications to enhance efficient interaction between user and DBMS.
Kumar, Gaurav; Kumar, Ashok
2017-11-01
Structural control has gained significant attention in recent times. The standalone issue of power requirement during an earthquake has already been solved up to a large extent by designing semi-active control systems using conventional linear quadratic control theory, and many other intelligent control algorithms such as fuzzy controllers, artificial neural networks, etc. In conventional linear-quadratic regulator (LQR) theory, it is customary to note that the values of the design parameters are decided at the time of designing the controller and cannot be subsequently altered. During an earthquake event, the response of the structure may increase or decrease, depending the quasi-resonance occurring between the structure and the earthquake. In this case, it is essential to modify the value of the design parameters of the conventional LQR controller to obtain optimum control force to mitigate the vibrations due to the earthquake. A few studies have been done to sort out this issue but in all these studies it was necessary to maintain a database of the earthquake. To solve this problem and to find the optimized design parameters of the LQR controller in real time, a fast Fourier transform and particle swarm optimization based modified linear quadratic regulator method is presented here. This method comprises four different algorithms: particle swarm optimization (PSO), the fast Fourier transform (FFT), clipped control algorithm and the LQR. The FFT helps to obtain the dominant frequency for every time window. PSO finds the optimum gain matrix through the real-time update of the weighting matrix R, thereby, dispensing with the experimentation. The clipped control law is employed to match the magnetorheological (MR) damper force with the desired force given by the controller. The modified Bouc-Wen phenomenological model is taken to recognize the nonlinearities in the MR damper. The assessment of the advised method is done by simulation of a three-story structure
The Generalized Legendre transform and its applications to inverse spectral problems
Guillemin, Victor; Wang, Zuoqin
2015-01-01
Let $M$ be a Riemannian manifold, $\\tau: G \\times M \\to M$ an isometric action on $M$ of an $n$-torus $G$ and $V: M \\to \\mathbb R$ a bounded $G$-invariant smooth function. By $G$-invariance the Schr\\"odinger operator, $P=-\\hbar^2 \\Delta_M+V$, restricts to a self-adjoint operator on $L^2(M)_{\\alpha/\\hbar}$, $\\alpha$ being a weight of $G$ and $1/\\hbar$ a large positive integer. Let $[c_\\alpha, \\infty)$ be the asymptotic support of the spectrum of this operator. We will show that $c_\\alpha$ exte...
Experimental analysis of shape deformation of evaporating droplet using Legendre polynomials
International Nuclear Information System (INIS)
Sanyal, Apratim; Basu, Saptarshi; Kumar, Ranganathan
2014-01-01
Experiments involving heating of liquid droplets which are acoustically levitated, reveal specific modes of oscillations. For a given radiation flux, certain fluid droplets undergo distortion leading to catastrophic bag type breakup. The voltage of the acoustic levitator has been kept constant to operate at a nominal acoustic pressure intensity, throughout the experiments. Thus the droplet shape instabilities are primarily a consequence of droplet heating through vapor pressure, surface tension and viscosity. A novel approach is used by employing Legendre polynomials for the mode shape approximation to describe the thermally induced instabilities. The two dominant Legendre modes essentially reflect (a) the droplet size reduction due to evaporation, and (b) the deformation around the equilibrium shape. Dissipation and inter-coupling of modal energy lead to stable droplet shape while accumulation of the same ultimately results in droplet breakup.
Experimental analysis of shape deformation of evaporating droplet using Legendre polynomials
Energy Technology Data Exchange (ETDEWEB)
Sanyal, Apratim [Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012 (India); Basu, Saptarshi, E-mail: sbasu@mecheng.iisc.ernet.in [Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012 (India); Kumar, Ranganathan [Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816 (United States)
2014-01-24
Experiments involving heating of liquid droplets which are acoustically levitated, reveal specific modes of oscillations. For a given radiation flux, certain fluid droplets undergo distortion leading to catastrophic bag type breakup. The voltage of the acoustic levitator has been kept constant to operate at a nominal acoustic pressure intensity, throughout the experiments. Thus the droplet shape instabilities are primarily a consequence of droplet heating through vapor pressure, surface tension and viscosity. A novel approach is used by employing Legendre polynomials for the mode shape approximation to describe the thermally induced instabilities. The two dominant Legendre modes essentially reflect (a) the droplet size reduction due to evaporation, and (b) the deformation around the equilibrium shape. Dissipation and inter-coupling of modal energy lead to stable droplet shape while accumulation of the same ultimately results in droplet breakup.
International Nuclear Information System (INIS)
Almeida Ferreira, A.C. de.
1984-01-01
For problems with azimuthal symmetry in velocity space, the distribution function depends only on the speed and on the pitch angle. The angular dependence of the distribution function is expanded in Legendre polynomials, and the expansions of the collision integrals describing two-body Coulomb interactions in a plasma are determined through the use of the Rosenbluth potentials. The electron distribution function is written as a Maxwellian plus a deviation, and the representation in Legendre polynomials of the electron-electron collision term is given for both its linear and nonlinear part. To determine the representation of the electron-ion collision term it is assumed that the ion distribution is much narrower in velocity space than the electron distribution, and shifted from the origin by a flow velocity. The equations are presented in a form that is suitable for their use in a computer. (Author) [pt
Modified rational Legendre approach to laminar viscous flow over a semi-infinite flat plate
International Nuclear Information System (INIS)
Tajvidi, T.; Razzaghi, M.; Dehghan, M.
2008-01-01
A numerical method for solving the classical Blasius' equation is proposed. The Blasius' equation is a third order nonlinear ordinary differential equation , which arises in the problem of the two-dimensional laminar viscous flow over a semi-infinite flat plane. The approach is based on a modified rational Legendre tau method. The operational matrices for the derivative and product of the modified rational Legendre functions are presented. These matrices together with the tau method are utilized to reduce the solution of Blasius' equation to the solution of a system of algebraic equations. A numerical evaluation is included to demonstrate the validity and applicability of the method and a comparison is made with existing results
International Nuclear Information System (INIS)
Kiknadze, N.A.; Khelashvili, A.A.
1990-01-01
The problem on stability of classical soliton solutions is studied from the unique point of view: the Legendre condition - necessary condition of existence of weak local minimum for energy functional (term soliton is used here in the wide sense) is used. Limits to parameters of the model Lagrangians are obtained; it is shown that there is no soliton stabilization in some of them despite the phenomenological achievements. The Jacoby sufficient condition is discussed
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav
2007-01-01
The problem of electromagnetic scattering by composite metallic and dielectric objects is solved using the coupled volume-surface integral equation (VSIE). The method of moments (MoM) based on higher-order hierarchical Legendre basis functions and higher-order curvilinear geometrical elements...... with the analytical Mie series solution. Scattering by more complex metal-dielectric objects are also considered to compare the presented technique with other numerical methods....
Ito, Kazufumi; Teglas, Russell
1987-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
Ito, K.; Teglas, R.
1984-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
Directory of Open Access Journals (Sweden)
Byung Eun Lee
2014-09-01
Full Text Available This paper proposes an algorithm for fault detection, faulted phase and winding identification of a three-winding power transformer based on the induced voltages in the electrical power system. The ratio of the induced voltages of the primary-secondary, primary-tertiary and secondary-tertiary windings is the same as the corresponding turns ratio during normal operating conditions, magnetic inrush, and over-excitation. It differs from the turns ratio during an internal fault. For a single phase and a three-phase power transformer with wye-connected windings, the induced voltages of each pair of windings are estimated. For a three-phase power transformer with delta-connected windings, the induced voltage differences are estimated to use the line currents, because the delta winding currents are practically unavailable. Six detectors are suggested for fault detection. An additional three detectors and a rule for faulted phase and winding identification are presented as well. The proposed algorithm can not only detect an internal fault, but also identify the faulted phase and winding of a three-winding power transformer. The various test results with Electromagnetic Transients Program (EMTP-generated data show that the proposed algorithm successfully discriminates internal faults from normal operating conditions including magnetic inrush and over-excitation. This paper concludes by implementing the algorithm into a prototype relay based on a digital signal processor.
Mixed Legendre moments and discrete scattering cross sections for anisotropy representation
International Nuclear Information System (INIS)
Calloo, A.; Vidal, J. F.; Le Tellier, R.; Rimpault, G.
2012-01-01
This paper deals with the resolution of the integro-differential form of the Boltzmann transport equation for neutron transport in nuclear reactors. In multigroup theory, deterministic codes use transfer cross sections which are expanded on Legendre polynomials. This modelling leads to negative values of the transfer cross section for certain scattering angles, and hence, the multigroup scattering source term is wrongly computed. The first part compares the convergence of 'Legendre-expanded' cross sections with respect to the order used with the method of characteristics (MOC) for Pressurised Water Reactor (PWR) type cells. Furthermore, the cross section is developed using piecewise-constant functions, which better models the multigroup transfer cross section and prevents the occurrence of any negative value for it. The second part focuses on the method of solving the transport equation with the above-mentioned piecewise-constant cross sections for lattice calculations for PWR cells. This expansion thereby constitutes a 'reference' method to compare the conventional Legendre expansion to, and to determine its pertinence when applied to reactor physics calculations. (authors)
Siddeq, M. M.; Rodrigues, M. A.
2015-09-01
Image compression techniques are widely used on 2D image 2D video 3D images and 3D video. There are many types of compression techniques and among the most popular are JPEG and JPEG2000. In this research, we introduce a new compression method based on applying a two level discrete cosine transform (DCT) and a two level discrete wavelet transform (DWT) in connection with novel compression steps for high-resolution images. The proposed image compression algorithm consists of four steps. (1) Transform an image by a two level DWT followed by a DCT to produce two matrices: DC- and AC-Matrix, or low and high frequency matrix, respectively, (2) apply a second level DCT on the DC-Matrix to generate two arrays, namely nonzero-array and zero-array, (3) apply the Minimize-Matrix-Size algorithm to the AC-Matrix and to the other high-frequencies generated by the second level DWT, (4) apply arithmetic coding to the output of previous steps. A novel decompression algorithm, Fast-Match-Search algorithm (FMS), is used to reconstruct all high-frequency matrices. The FMS-algorithm computes all compressed data probabilities by using a table of data, and then using a binary search algorithm for finding decompressed data inside the table. Thereafter, all decoded DC-values with the decoded AC-coefficients are combined in one matrix followed by inverse two levels DCT with two levels DWT. The technique is tested by compression and reconstruction of 3D surface patches. Additionally, this technique is compared with JPEG and JPEG2000 algorithm through 2D and 3D root-mean-square-error following reconstruction. The results demonstrate that the proposed compression method has better visual properties than JPEG and JPEG2000 and is able to more accurately reconstruct surface patches in 3D.
International Nuclear Information System (INIS)
Bakhos, Tania; Saibaba, Arvind K.; Kitanidis, Peter K.
2015-01-01
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method
Energy Technology Data Exchange (ETDEWEB)
Du Weiliang; Yang, James [Department of Radiation Physics, University of Texas M D Anderson Cancer Center, 1515 Holcombe Blvd, Unit 94, Houston, TX 77030 (United States)], E-mail: wdu@mdanderson.org
2009-02-07
Uncertainty in localizing the radiation field center is among the major components that contribute to the overall positional error and thus must be minimized. In this study, we developed a Hough transform (HT)-based computer algorithm to localize the radiation center of a circular or rectangular field with subpixel accuracy. We found that the HT method detected the centers of the test circular fields with an absolute error of 0.037 {+-} 0.019 pixels. On a typical electronic portal imager with 0.5 mm image resolution, this mean detection error was translated to 0.02 mm, which was much finer than the image resolution. It is worth noting that the subpixel accuracy described here does not include experimental uncertainties such as linac mechanical instability or room laser inaccuracy. The HT method was more accurate and more robust to image noise and artifacts than the traditional center-of-mass method. Application of the HT method in Winston-Lutz tests was demonstrated to measure the ball-radiation center alignment with subpixel accuracy. Finally, the method was applied to quantitative evaluation of the radiation center wobble during collimator rotation.
Energy Technology Data Exchange (ETDEWEB)
Bakhos, Tania, E-mail: taniab@stanford.edu [Institute for Computational and Mathematical Engineering, Stanford University (United States); Saibaba, Arvind K. [Department of Electrical and Computer Engineering, Tufts University (United States); Kitanidis, Peter K. [Institute for Computational and Mathematical Engineering, Stanford University (United States); Department of Civil and Environmental Engineering, Stanford University (United States)
2015-10-15
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.
Momeni, Saba; Pourghassem, Hossein
2014-08-01
Recently image fusion has prominent role in medical image processing and is useful to diagnose and treat many diseases. Digital subtraction angiography is one of the most applicable imaging to diagnose brain vascular diseases and radiosurgery of brain. This paper proposes an automatic fuzzy-based multi-temporal fusion algorithm for 2-D digital subtraction angiography images. In this algorithm, for blood vessel map extraction, the valuable frames of brain angiography video are automatically determined to form the digital subtraction angiography images based on a novel definition of vessel dispersion generated by injected contrast material. Our proposed fusion scheme contains different fusion methods for high and low frequency contents based on the coefficient characteristic of wrapping second generation of curvelet transform and a novel content selection strategy. Our proposed content selection strategy is defined based on sample correlation of the curvelet transform coefficients. In our proposed fuzzy-based fusion scheme, the selection of curvelet coefficients are optimized by applying weighted averaging and maximum selection rules for the high frequency coefficients. For low frequency coefficients, the maximum selection rule based on local energy criterion is applied to better visual perception. Our proposed fusion algorithm is evaluated on a perfect brain angiography image dataset consisting of one hundred 2-D internal carotid rotational angiography videos. The obtained results demonstrate the effectiveness and efficiency of our proposed fusion algorithm in comparison with common and basic fusion algorithms.
De la glosa a la publicidad. Notas para una lectura de Pierre Legendre
Directory of Open Access Journals (Sweden)
Bellido, José
2008-12-01
Full Text Available By emphasizing the singular experience of the act of reading, this paper presents the work of a French legal philosopher and psychoanalyst: Pierre Legendre. Whereas this attempt could be simultaneously an impossible and irritating venture, its aim is to emphasize something that is not so often seen in legal theory: an inquiry into the nuances of the legal unconscious. In doing so, the paper opens with some references to his particular understanding of love and the spectacular as a legal resource to dominate its subjects. It continues to be peppered with several attractive spaces in which Legendre’s ecounters the binding force in the imaginary of the legal institution.
Señalando la experiencia singular del acto de leer, este trabajo presenta la obra de un filósofo del derecho y psicoanalista francés: Pierre Legendre. A pesar de que tal proyecto pudiera constituir una empresa tan imposible como irritante, el propósito principal es resaltar un elemento que no suele observarse con frecuencia en la teoría del derecho: un recorrido por los diversos matices del inconsciente jurídico. El trabajo comienza con algunas referencias a su concepción particular del amor y del espectáculo como recursos legales para dominar a los sujetos. Y continúa con algunos espacios sugerentes donde Legendre encuentra la fuerza vinculante en el imaginario de la institución jurídica.
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Jørgensen, Erik; Meincke, Peter
2004-01-01
An efficient higher-order method of moments (MoM) solution of volume integral equations is presented. The higher-order MoM solution is based on higher-order hierarchical Legendre basis functions and higher-order geometry modeling. An unstructured mesh composed of 8-node trilinear and/or curved 27...... of magnitude in comparison to existing higher-order hierarchical basis functions. Consequently, an iterative solver can be applied even for high expansion orders. Numerical results demonstrate excellent agreement with the analytical Mie series solution for a dielectric sphere as well as with results obtained...
Characterizing the Lyα forest flux probability distribution function using Legendre polynomials
Energy Technology Data Exchange (ETDEWEB)
Cieplak, Agnieszka M.; Slosar, Anže, E-mail: acieplak@bnl.gov, E-mail: anze@bnl.gov [Brookhaven National Laboratory, Bldg 510, Upton, NY, 11973 (United States)
2017-10-01
The Lyman-α forest is a highly non-linear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the n -th Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation over mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of well-measured quantities. We find that the amount of recoverable information is a very non-linear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.
Cieplak, Agnieszka; Slosar, Anze
2018-01-01
The Lyman-alpha forest has become a powerful cosmological probe at intermediate redshift. It is a highly non-linear field with much information present beyond the power spectrum. The flux probability flux distribution (PDF) in particular has been a successful probe of small scale physics. However, it is also sensitive to pixel noise, spectrum resolution, and continuum fitting, all of which lead to possible biased estimators. Here we argue that measuring the coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. Since the n-th Legendre coefficient can be expressed as a linear combination of the first n moments of the field, this allows for the coefficients to be measured in the presence of noise and allows for a clear route towards marginalization over the mean flux. Additionally, in the presence of noise, a finite number of these coefficients are well measured with a very sharp transition into noise dominance. This compresses the information into a small amount of well-measured quantities. Finally, we find that measuring fewer quasars with high signal-to-noise produces a higher amount of recoverable information.
Characterizing the Lyα forest flux probability distribution function using Legendre polynomials
Cieplak, Agnieszka M.; Slosar, Anže
2017-10-01
The Lyman-α forest is a highly non-linear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the n-th Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation over mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of well-measured quantities. We find that the amount of recoverable information is a very non-linear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.
Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint
Energy Technology Data Exchange (ETDEWEB)
Wang, Q.; Sprague, M. A.; Jonkman, J.; Johnson, N.
2014-01-01
This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context of LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.
Lieb, Florian; Stark, Hans-Georg; Thielemann, Christiane
2017-06-01
Spike detection from extracellular recordings is a crucial preprocessing step when analyzing neuronal activity. The decision whether a specific part of the signal is a spike or not is important for any kind of other subsequent preprocessing steps, like spike sorting or burst detection in order to reduce the classification of erroneously identified spikes. Many spike detection algorithms have already been suggested, all working reasonably well whenever the signal-to-noise ratio is large enough. When the noise level is high, however, these algorithms have a poor performance. In this paper we present two new spike detection algorithms. The first is based on a stationary wavelet energy operator and the second is based on the time-frequency representation of spikes. Both algorithms are more reliable than all of the most commonly used methods. The performance of the algorithms is confirmed by using simulated data, resembling original data recorded from cortical neurons with multielectrode arrays. In order to demonstrate that the performance of the algorithms is not restricted to only one specific set of data, we also verify the performance using a simulated publicly available data set. We show that both proposed algorithms have the best performance under all tested methods, regardless of the signal-to-noise ratio in both data sets. This contribution will redound to the benefit of electrophysiological investigations of human cells. Especially the spatial and temporal analysis of neural network communications is improved by using the proposed spike detection algorithms.
Lieb, Florian; Stark, Hans-Georg; Thielemann, Christiane
2017-06-01
Objective. Spike detection from extracellular recordings is a crucial preprocessing step when analyzing neuronal activity. The decision whether a specific part of the signal is a spike or not is important for any kind of other subsequent preprocessing steps, like spike sorting or burst detection in order to reduce the classification of erroneously identified spikes. Many spike detection algorithms have already been suggested, all working reasonably well whenever the signal-to-noise ratio is large enough. When the noise level is high, however, these algorithms have a poor performance. Approach. In this paper we present two new spike detection algorithms. The first is based on a stationary wavelet energy operator and the second is based on the time-frequency representation of spikes. Both algorithms are more reliable than all of the most commonly used methods. Main results. The performance of the algorithms is confirmed by using simulated data, resembling original data recorded from cortical neurons with multielectrode arrays. In order to demonstrate that the performance of the algorithms is not restricted to only one specific set of data, we also verify the performance using a simulated publicly available data set. We show that both proposed algorithms have the best performance under all tested methods, regardless of the signal-to-noise ratio in both data sets. Significance. This contribution will redound to the benefit of electrophysiological investigations of human cells. Especially the spatial and temporal analysis of neural network communications is improved by using the proposed spike detection algorithms.
Energy Technology Data Exchange (ETDEWEB)
Sanchez Miro, J J; Sanz Martin, J C
1994-07-01
Obtaining polynomial fittings from observational data in two and three dimensions is an interesting and practical task. Such an arduous problem suggests the development of an automatic code. The main novelty we provide lies in the generalization of the classical least squares method in three FORTRAN 77 programs usable in any sampling problem. Furthermore, we introduce the orthogonal 2D-Legendre function in the fitting process. These FORTRAN 77 programs are equipped with the options to calculate the approximation quality standard indicators, obviously generalized to two and three dimensions (correlation nonlinear factor, confidence intervals, cuadratic mean error, and so on). The aim of this paper is to rectify the absence of fitting algorithms for more than one independent variable in mathematical libraries. (Author) 10 refs.
Unaldi, Numan; Temel, Samil; Asari, Vijayan K.
2012-01-01
One of the most critical issues of Wireless Sensor Networks (WSNs) is the deployment of a limited number of sensors in order to achieve maximum coverage on a terrain. The optimal sensor deployment which enables one to minimize the consumed energy, communication time and manpower for the maintenance of the network has attracted interest with the increased number of studies conducted on the subject in the last decade. Most of the studies in the literature today are proposed for two dimensional (2D) surfaces; however, real world sensor deployments often arise on three dimensional (3D) environments. In this paper, a guided wavelet transform (WT) based deployment strategy (WTDS) for 3D terrains, in which the sensor movements are carried out within the mutation phase of the genetic algorithms (GAs) is proposed. The proposed algorithm aims to maximize the Quality of Coverage (QoC) of a WSN via deploying a limited number of sensors on a 3D surface by utilizing a probabilistic sensing model and the Bresenham's line of sight (LOS) algorithm. In addition, the method followed in this paper is novel to the literature and the performance of the proposed algorithm is compared with the Delaunay Triangulation (DT) method as well as a standard genetic algorithm based method and the results reveal that the proposed method is a more powerful and more successful method for sensor deployment on 3D terrains. PMID:22666078
Tests of a numerical algorithm for the linear instability study of flows on a sphere
Energy Technology Data Exchange (ETDEWEB)
Perez Garcia, Ismael; Skiba, Yuri N [Univerisidad Nacional Autonoma de Mexico, Mexico, D.F. (Mexico)
2001-04-01
A numerical algorithm for the normal mode instability of a steady nondivergent flow on a rotating sphere is developed. The algorithm accuracy is tested with zonal solutions of the nonlinear barotropic vorticity equation (Legendre polynomials, zonal Rossby-Harwitz waves and monopole modons). [Spanish] Ha sido desarrollado un algoritmo numerico para estudiar la inestabilidad lineal de un flujo estacionario no divergente en una esfera en rotacion. La precision del algoritmo se prueba con soluciones zonales de la ecuacion no lineal de vorticidad barotropica (polinomios de Legendre, ondas zonales Rossby-Harwitz y modones monopolares).
Directory of Open Access Journals (Sweden)
Maria Gabriela Campolina Diniz Peixoto
2014-05-01
Full Text Available The objective of this work was to compare random regression models for the estimation of genetic parameters for Guzerat milk production, using orthogonal Legendre polynomials. Records (20,524 of test-day milk yield (TDMY from 2,816 first-lactation Guzerat cows were used. TDMY grouped into 10-monthly classes were analyzed for additive genetic effect and for environmental and residual permanent effects (random effects, whereas the contemporary group, calving age (linear and quadratic effects and mean lactation curve were analized as fixed effects. Trajectories for the additive genetic and permanent environmental effects were modeled by means of a covariance function employing orthogonal Legendre polynomials ranging from the second to the fifth order. Residual variances were considered in one, four, six, or ten variance classes. The best model had six residual variance classes. The heritability estimates for the TDMY records varied from 0.19 to 0.32. The random regression model that used a second-order Legendre polynomial for the additive genetic effect, and a fifth-order polynomial for the permanent environmental effect is adequate for comparison by the main employed criteria. The model with a second-order Legendre polynomial for the additive genetic effect, and that with a fourth-order for the permanent environmental effect could also be employed in these analyses.
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Ishibashi, Hideo
1978-01-01
A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)
Spherical space Bessel-Legendre-Fourier mode solver for Maxwell's wave equations
Alzahrani, Mohammed A.; Gauthier, Robert C.
2015-02-01
For spherically symmetric dielectric structures, a basis set composed of Bessel, Legendre and Fourier functions, BLF, are used to cast Maxwell's wave equations into an eigenvalue problem from which the localized modes can be determined. The steps leading to the eigenmatrix are reviewed and techniques used to reduce the order of matrix and tune the computations for particular mode types are detailed. The BLF basis functions are used to expand the electric and magnetic fields as well as the inverse relative dielectric profile. Similar to the common plane wave expansion technique, the BLF matrix returns the eigen-frequencies and eigenvectors, but in BLF only steady states, non-propagated, are obtained. The technique is first applied to a air filled spherical structure with perfectly conducting outer surface and then to a spherical microsphere located in air. Results are compared published values were possible.
Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping
Smith, Timothy; Pantano, Carlos
2017-11-01
We present a new method to enforce field bounds in high-order Legendre-WENO finite volume schemes. The strategy consists of reconstructing each field through an intermediate mapping, which by design satisfies realizability constraints. Determination of the coefficients of the polynomial reconstruction involves nonlinear equations that are solved using Newton's method. The selection between the original or mapped reconstruction is implemented dynamically to minimize computational cost. The method has also been generalized to fields that exhibit interdependencies, requiring multi-dimensional mappings. Further, the method does not depend on the existence of a numerical flux function. We will discuss details of the proposed scheme and show results for systems in conservation and non-conservation form. This work was funded by the NSF under Grant DMS 1318161.
Directory of Open Access Journals (Sweden)
D. Galán Martínez
2000-07-01
Full Text Available Una de las herramientas matemáticas más utilizadas en ingeniería en el estudio de los denominados sistemas de control dedatos muestreados es la transformada Z. La transformada Z como método operacional puede ser utilizada en la resoluciónde ecuaciones en diferencias finitas; las cuales formulan la dinámica de los sistemas de control de datos muestreados. Estatransformada juega un papel similar que el de la transformada de Laplace en el análisis de los sistemas de control de tiempocontinuo.El presente trabajo tiene como objetivo la confección de un programa para computadora digital, utilizando el asistentematemático DERIVE, para la determinación de la transformada Z inversa de una función algebraica racional, las cualesmodelan matemáticamente los sistemas de control de datos muestreados lineales que aparecen con mucha frecuencia en elestudio de los procesos de ingeniería.Palabras claves: Algoritmo, transformada Z, DERIVE, función algebraica racional, modelo matemático._______________________________________________________________________AbstractOne of the mathematical tools more used in engineering in the study of the denominated systems of data control samples isthe transformed Z. The transformed Z like as an operational method can be used in the resolution of equations in finitedifferences; which formulate the dynamics of the systems of data control samples. This transformed plays a similar paperthat the Laplace transformed in the analysis of the systems of control in continuous time.The present work has as objective the confection of a program for digital computer, using the mathematical assistantDERIVES, for the determination of the Z inverse transformed of a rational algebraic function, which model mathematicallythe systems of lineal data control samples that appear very frecuently in the study of the engineering processesKey words: algorithm, Z inverse transformed, Derives, Digital computer program, Rational
Directory of Open Access Journals (Sweden)
Wei Sun
2015-01-01
Full Text Available Electric power is a kind of unstorable energy concerning the national welfare and the people’s livelihood, the stability of which is attracting more and more attention. Because the short-term power load is always interfered by various external factors with the characteristics like high volatility and instability, a single model is not suitable for short-term load forecasting due to low accuracy. In order to solve this problem, this paper proposes a new model based on wavelet transform and the least squares support vector machine (LSSVM which is optimized by fruit fly algorithm (FOA for short-term load forecasting. Wavelet transform is used to remove error points and enhance the stability of the data. Fruit fly algorithm is applied to optimize the parameters of LSSVM, avoiding the randomness and inaccuracy to parameters setting. The result of implementation of short-term load forecasting demonstrates that the hybrid model can be used in the short-term forecasting of the power system.
Directory of Open Access Journals (Sweden)
Wenzhu Huang
2015-04-01
Full Text Available Static strain can be detected by measuring a cross-correlation of reflection spectra from two fiber Bragg gratings (FBGs. However, the static-strain measurement resolution is limited by the dominant Gaussian noise source when using this traditional method. This paper presents a novel static-strain demodulation algorithm for FBG-based Fabry-Perot interferometers (FBG-FPs. The Hilbert transform is proposed for changing the Gaussian distribution of the two FBG-FPs’ reflection spectra, and a cross third-order cumulant is used to use the results of the Hilbert transform and get a group of noise-vanished signals which can be used to accurately calculate the wavelength difference of the two FBG-FPs. The benefit by these processes is that Gaussian noise in the spectra can be suppressed completely in theory and a higher resolution can be reached. In order to verify the precision and flexibility of this algorithm, a detailed theory model and a simulation analysis are given, and an experiment is implemented. As a result, a static-strain resolution of 0.9 nε under laboratory environment condition is achieved, showing a higher resolution than the traditional cross-correlation method.
Akkoç, Betül; Arslan, Ahmet; Kök, Hatice
2017-05-01
One of the first stages in the identification of an individual is gender determination. Through gender determination, the search spectrum can be reduced. In disasters such as accidents or fires, which can render identification somewhat difficult, durable teeth are an important source for identification. This study proposes a smart system that can automatically determine gender using 3D digital maxillary tooth plaster models. The study group was composed of 40 Turkish individuals (20 female, 20 male) between the ages of 21 and 24. Using the iterative closest point (ICP) algorithm, tooth models were aligned, and after the segmentation process, models were transformed into depth images. The local discrete cosine transform (DCT) was used in the process of feature extraction, and the random forest (RF) algorithm was used for the process of classification. Classification was performed using 30 different seeds for random generator values and 10-fold cross-validation. A value of 85.166% was obtained for average classification accuracy (CA) and a value of 91.75% for the area under the ROC curve (AUC). A multi-disciplinary study is performed here that includes computer sciences, medicine and dentistry. A smart system is proposed for the determination of gender from 3D digital models of maxillary tooth plaster models. This study has the capacity to extend the field of gender determination from teeth. Copyright © 2017 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
D. Jabari Sabeg
2016-10-01
Full Text Available In this paper, we present a new computational method for solving nonlinear singular boundary value problems of fractional order arising in biology. To this end, we apply the operational matrices of derivatives of shifted Legendre polynomials to reduce such problems to a system of nonlinear algebraic equations. To demonstrate the validity and applicability of the presented method, we present some numerical examples.
Vaidya, Bhargav; Prasad, Deovrat; Mignone, Andrea; Sharma, Prateek; Rickler, Luca
2017-12-01
An important ingredient in numerical modelling of high temperature magnetized astrophysical plasmas is the anisotropic transport of heat along magnetic field lines from higher to lower temperatures. Magnetohydrodynamics typically involves solving the hyperbolic set of conservation equations along with the induction equation. Incorporating anisotropic thermal conduction requires to also treat parabolic terms arising from the diffusion operator. An explicit treatment of parabolic terms will considerably reduce the simulation time step due to its dependence on the square of the grid resolution (Δx) for stability. Although an implicit scheme relaxes the constraint on stability, it is difficult to distribute efficiently on a parallel architecture. Treating parabolic terms with accelerated super-time-stepping (STS) methods has been discussed in literature, but these methods suffer from poor accuracy (first order in time) and also have difficult-to-choose tuneable stability parameters. In this work, we highlight a second-order (in time) Runge-Kutta-Legendre (RKL) scheme (first described by Meyer, Balsara & Aslam 2012) that is robust, fast and accurate in treating parabolic terms alongside the hyperbolic conversation laws. We demonstrate its superiority over the first-order STS schemes with standard tests and astrophysical applications. We also show that explicit conduction is particularly robust in handling saturated thermal conduction. Parallel scaling of explicit conduction using RKL scheme is demonstrated up to more than 104 processors.
Dynamics of one-dimensional self-gravitating systems using Hermite-Legendre polynomials
Barnes, Eric I.; Ragan, Robert J.
2014-01-01
The current paradigm for understanding galaxy formation in the Universe depends on the existence of self-gravitating collisionless dark matter. Modelling such dark matter systems has been a major focus of astrophysicists, with much of that effort directed at computational techniques. Not surprisingly, a comprehensive understanding of the evolution of these self-gravitating systems still eludes us, since it involves the collective non-linear dynamics of many particle systems interacting via long-range forces described by the Vlasov equation. As a step towards developing a clearer picture of collisionless self-gravitating relaxation, we analyse the linearized dynamics of isolated one-dimensional systems near thermal equilibrium by expanding their phase-space distribution functions f(x, v) in terms of Hermite functions in the velocity variable, and Legendre functions involving the position variable. This approach produces a picture of phase-space evolution in terms of expansion coefficients, rather than spatial and velocity variables. We obtain equations of motion for the expansion coefficients for both test-particle distributions and self-gravitating linear perturbations of thermal equilibrium. N-body simulations of perturbed equilibria are performed and found to be in excellent agreement with the expansion coefficient approach over a time duration that depends on the size of the expansion series used.
Kuligowski, J; Quintás, G; Garrigues, S; de la Guardia, M
2010-03-15
A new background correction method for the on-line coupling of gradient liquid chromatography and Fourier transform infrared spectrometry has been developed. It is based on the use of a point-to-point matching algorithm that compares the absorption spectra of the sample data set with those of a previously recorded reference data set in order to select an appropriate reference spectrum. The spectral range used for the point-to-point comparison is selected with minimal user-interaction, thus facilitating considerably the application of the whole method. The background correction method has been successfully tested on a chromatographic separation of four nitrophenols running acetonitrile (0.08%, v/v TFA):water (0.08%, v/v TFA) gradients with compositions ranging from 35 to 85% (v/v) acetonitrile, giving accurate results for both, baseline resolved and overlapped peaks. Copyright (c) 2009 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Abdallah Bengueddoudj
2017-05-01
Full Text Available In this paper, we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform (2D-SMCWT. The fusion of the detail 2D-SMCWT coefficients is performed via a Bayesian Maximum a Posteriori (MAP approach by considering a trivariate statistical model for the local neighboring of 2D-SMCWT coefficients. For the approximation coefficients, a new fusion rule based on the Principal Component Analysis (PCA is applied. We conduct several experiments using three different groups of multimodal medical images to evaluate the performance of the proposed method. The obtained results prove the superiority of the proposed method over the state of the art fusion methods in terms of visual quality and several commonly used metrics. Robustness of the proposed method is further tested against different types of noise. The plots of fusion metrics establish the accuracy of the proposed fusion method.
International Nuclear Information System (INIS)
Khayat, O.; Ghergherehchi, M.; Afarideh, H.; Durrani, S.A.; Pouyan, Ali A.; Kim, Y.S.
2013-01-01
A computer program named ATMS written in MATLAB and running with a friendly interface has been developed for recognition and parametric measurements of etched tracks in images captured from the surface of Solid State Nuclear Track Detectors. The program, using image analysis tools, counts the number of etched tracks and depending on the current working mode classifies them according to their radii (small object removal) or their axis (non-perpendicular or non-circular etched tracks), their mean intensity value and their orientation through the minor and major axes. Images of the detectors' surfaces are input to the code, which generates text and figure files as output, including the number of counted etched tracks with the associated track parameters, histograms and a figure showing edge and center of detected etched tracks. ATMS code is running hierarchically as calibration, testing and measurement modes to demonstrate the reliability, repeatability and adaptability. Fuzzy Hough Transform is used for the estimation of the number of etched tracks and their parameters, providing results even in cases that overlapping and orientation occur. ATMS code is finally converted to a standalone file which makes it able to run out of MATLAB environment. - Highlights: ► Presenting a novel code named ATMS for nuclear track measurements. ► Execution in three modes for generality, adaptability and reliability. ► Using Fuzzy Hough Transform for overlapping detection and orientation recognition. ► Using DFT as a filter for noise removal process in track images. ► Processing the noisy track images and demonstration of the presented code
Sui, Liansheng; Lu, Haiwei; Ning, Xiaojuan; Wang, Yinghui
2014-02-01
A double-image encryption scheme is proposed based on an asymmetric technique, in which the encryption and decryption processes are different and the encryption keys are not identical to the decryption ones. First, a phase-only function (POF) of each plain image is retrieved by using an iterative process and then encoded into an interim matrix. Two interim matrices are directly modulated into a complex image by using the convolution operation in the fractional Fourier transform (FrFT) domain. Second, the complex image is encrypted into the gray scale ciphertext with stationary white-noise distribution by using the FrFT. In the encryption process, three random phase functions are used as encryption keys to retrieve the POFs of plain images. Simultaneously, two decryption keys are generated in the encryption process, which make the optical implementation of the decryption process convenient and efficient. The proposed encryption scheme has high robustness to various attacks, such as brute-force attack, known plaintext attack, cipher-only attack, and specific attack. Numerical simulations demonstrate the validity and security of the proposed method.
International Nuclear Information System (INIS)
Sanchez Miro, J. J.; Sanz Martin, J. C.
1994-01-01
Obtaining polynomial fittings from observational data in two and three dimensions is an interesting and practical task. Such an arduous problem suggests the development of an automatic code. The main novelty we provide lies in the generalization of the classical least squares method in three FORTRAN 77 programs usable in any sampling problem. Furthermore, we introduce the orthogonal 2D-Legendre function in the fitting process. These FORTRAN 77 programs are equipped with the options to calculate the approximation quality standard indicators, obviously generalized to two and three dimensions (correlation nonlinear factor, confidence intervals, cuadratic mean error, and so on). The aim of this paper is to rectify the absence of fitting algorithms for more than one independent variable in mathematical libraries. (Author) 10 refs
The Mehler-Fock transform of general order and arbitrary index and its inversion
Directory of Open Access Journals (Sweden)
Cyril Nasim
1984-01-01
Full Text Available An integral transform involving the associated Legendre function of zero order, P−12+iτ(x, x∈[1,∞, as the kernel (considered as a function of τ, is called Mehler-Fock transform. Some generalizations, involving the function P−12+iτμ(x, where the order μ is an arbitrary complex number, including the case when μ=0,1,2,… have been known for some time. In this present note, we define a general Mehler-Fock transform involving, as the kernel, the Legendre function P−12+tμ(x, of general order μ and an arbitrary index −12+t, t=σ+iτ, −∞<τ<∞. Then we develop a symmetric inversion formulae for these transforms. Many well-known results are derived as special cases of this general form. These transforms are widely used for solving many axisymmetric potential problems.
International Nuclear Information System (INIS)
Aghajani, Afshin; Kazemzadeh, Rasool; Ebrahimi, Afshin
2016-01-01
Highlights: • Proposing a novel hybrid method for short-term prediction of wind farms with high accuracy. • Investigating the prediction accuracy for proposed method in comparison with other methods. • Investigating the effect of six types of parameters as input data on predictions. • Comparing results for 6 & 4 types of the input parameters – addition of pressure and air humidity. - Abstract: This paper proposes a novel hybrid approach to forecast electric power production in wind farms. Wavelet transform (WT) is employed to filter input data of wind power, while radial basis function (RBF) neural network is utilized for primary prediction. For better predictions the main forecasting engine is comprised of three multilayer perceptron (MLP) neural networks by different learning algorithms of Levenberg–Marquardt (LM), Broyden–Fletcher–Goldfarb–Shanno (BFGS), and Bayesian regularization (BR). Meta-heuristic technique Imperialist Competitive Algorithm (ICA) is used to optimize neural networks’ weightings in order to escape from local minima. In the forecast process, the real data of wind farms located in the southern part of Alberta, Canada, are used to train and test the proposed model. The data are a complete set of six meteorological and technical characteristics, including wind speed, wind power, wind direction, temperature, pressure, and air humidity. In order to demonstrate the efficiency of the proposed method, it is compared with several other wind power forecast techniques. Results of optimizations indicate the superiority of the proposed method over the other mentioned techniques; and, forecasting error is remarkably reduced. For instance, the average normalized root mean square error (NRMSE) and average mean absolute percentage error (MAPE) are respectively 11% and 14% lower for the proposed method in 1-h-ahead forecasts over a 24-h period with six types of input than those for the best of the compared models.
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.
International Nuclear Information System (INIS)
Rashid, M.A.
1984-08-01
Integrals involving powers of (1-x 2 ) and two associated Legendre functions or two Gegenbauer polynomials are evaluated as finite sums which can be expressed in terms of terminating hypergeometric function 4 F 3 . The integrals which are evaluated are ∫sub(-1)sup(1)[Psub(l)sup(m)(x)Psub(k)sup(n)(x)]/[(1-x 2 )sup(p+1)]dx and ∫sub(-1)sup(1)Csub(l)sup(α)(x)Csub(k)sup(β)(x)[(1-x 2 )sup[(α+β-3)/2-p
Liu, Yongliang; Kim, Hee-Jin
2017-06-22
With cotton fiber growth or maturation, cellulose content in cotton fibers markedly increases. Traditional chemical methods have been developed to determine cellulose content, but it is time-consuming and labor-intensive, mostly owing to the slow hydrolysis process of fiber cellulose components. As one approach, the attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopy technique has also been utilized to monitor cotton cellulose formation, by implementing various spectral interpretation strategies of both multivariate principal component analysis (PCA) and 1-, 2- or 3-band/-variable intensity or intensity ratios. The main objective of this study was to compare the correlations between cellulose content determined by chemical analysis and ATR FT-IR spectral indices acquired by the reported procedures, among developmental Texas Marker-1 (TM-1) and immature fiber ( im ) mutant cotton fibers. It was observed that the R value, CI IR , and the integrated intensity of the 895 cm -1 band exhibited strong and linear relationships with cellulose content. The results have demonstrated the suitability and utility of ATR FT-IR spectroscopy, combined with a simple algorithm analysis, in assessing cotton fiber cellulose content, maturity, and crystallinity in a manner which is rapid, routine, and non-destructive.
Directory of Open Access Journals (Sweden)
Carlos Andres Perez-Ramirez
2017-01-01
Full Text Available Nowadays, the accurate identification of natural frequencies and damping ratios play an important role in smart civil engineering, since they can be used for seismic design, vibration control, and condition assessment, among others. To achieve it in practical way, it is required to instrument the structure and apply techniques which are able to deal with noise-corrupted and non-linear signals, as they are common features in real-life civil structures. In this article, a two-step strategy is proposed for performing accurate modal parameters identification in an automated manner. In the first step, it is obtained and decomposed the measured signals using the natural excitation technique and the synchrosqueezed wavelet transform, respectively. Then, the second step estimates the modal parameters by solving an optimization problem employing a genetic algorithm-based approach, where the micropopulation concept is used to improve the speed convergence as well as the accuracy of the estimated values. The accuracy and effectiveness of the proposal are tested using both the simulated response of a benchmark structure and the measurements of a real eight-story building. The obtained results show that the proposed strategy can estimate the modal parameters accurately, indicating than the proposal can be considered as an alternative to perform the abovementioned task.
International Nuclear Information System (INIS)
Saharian, A A
2009-01-01
By using the generalized Abel-Plana formula, we derive a summation formula for the series over the zeros of a combination of the associated Legendre functions with respect to the degree. The summation formula for the series over the zeros of the combination of the Bessel functions, previously discussed in the literature, is obtained as a limiting case. As an application we evaluate the Wightman function for a scalar field with a general curvature coupling parameter in the region between concentric spherical shells on a background of constant negative curvature space. For the Dirichlet boundary conditions the corresponding mode-sum contains the series over the zeros of the combination of the associated Legendre functions. The application of the summation formula allows us to present the Wightman function in the form of the sum of two integrals. The first one corresponds to the Wightman function for the geometry of a single spherical shell and the second one is induced by the presence of the second shell. The boundary-induced part in the vacuum expectation value of the field squared is investigated. For points away from the boundaries the corresponding renormalization procedure is reduced to that for the boundary-free part.
Transformer Protection Using the Wavelet Transform
ÖZGÖNENEL, Okan; ÖNBİLGİN, Güven; KOCAMAN, Çağrı
2014-01-01
This paper introduces a novel approach for power transformer protection algorithm. Power system signals such as current and voltage have traditionally been analysed by the Fast Fourier Transform. This paper aims to prove that the Wavelet Transform is a reliable and computationally efficient tool for distinguishing between the inrush currents and fault currents. The simulated results presented clearly show that the proposed technique for power transformer protection facilitates the a...
International Nuclear Information System (INIS)
Fernandes, A.
1991-01-01
A method to solve three dimensional neutron transport equation and it is based on the original work suggested by J.K. Fletcher (42, 43). The angular dependence of the flux is approximated by associated Legendre functions and the finite element method is applied to the space components is presented. When the angular flux, the scattering cross section and the neutrons source are expanded in associated Legendre functions, the first order neutron transport equation is reduced to a coupled set of second order diffusion like equations. These equations are solved in an iterative way by the finite element method to the moments. (author)
Directory of Open Access Journals (Sweden)
Wei Li
2017-01-01
Full Text Available We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. Its generating function is applied to obtain an analytical result for a class of interesting integrals involving complicated argument, that is, ∫-11Pl′m′xt-1/1+t2-2xtPk′m′(x/(1+t2-2tx(l′+1/2dx, where t∈(0,1. The present method can in principle be generalizable to the integrals involving other special functions. As an illustration we also study a typical Bessel integral with a complicated argument ∫0∞Jn(αx2+z2/(x2+z2nx2m+1dx.
Parallel implementation of geometric transformations
Energy Technology Data Exchange (ETDEWEB)
Clarke, K A; Ip, H H.S.
1982-10-01
An implementation of digitized picture rotation and magnification based on Weiman's algorithm is presented. In a programmable array machine routines to perform small transformations code efficiently. The method illustrates the interpolative nature of the algorithm. 6 references.
Feature Extraction Using the Hough Transform
Ferguson, Tara; Baker, Doran
2002-01-01
This paper contains a brief literature survey of applications and improvements of the Hough transform, a description of the Hough transform and a few of its algorithms, and simulation examples of line and curve detection using the Hough transform.
A Novel Radiation Transport Algorithm for Radiography Simulations
International Nuclear Information System (INIS)
Inanc, Feyzi
2004-01-01
The simulations used in the NDE community are becoming more realistic with the introduction of more physics. In this work, we have developed a new algorithm that is capable of representing photon and charged particle fluxes through spherical harmonic expansions in a manner similar to well known discrete ordinates method with the exception that Boltzmann operator is treated through exact integration rather than conventional Legendre expansions. This approach provides a mean to include radiation interactions for higher energy regimes where there are additional physical mechanisms for photons and charged particles
Open-path Fourier transform infrared (OP/FTIR) spectrometry was used to measure the concentrations of ammonia, methane, and other atmospheric gases at an integrated swine production facility. The concentration-pathlength products of the target gases at this site often exceeded th...
International Nuclear Information System (INIS)
Ueki, T.; Larsen, E.W.
1998-01-01
The authors show that Monte Carlo simulations of neutral particle transport in planargeometry anisotropically scattering media, using the exponential transform with angular biasing as a variance reduction device, are governed by a new Boltzman Monte Carlo (BMC) equation, which includes particle weight as an extra independent variable. The weight moments of the solution of the BMC equation determine the moments of the score and the mean number of collisions per history in the nonanalog Monte Carlo simulations. Therefore, the solution of the BMC equation predicts the variance of the score and the figure of merit in the simulation. Also, by (1) using an angular biasing function that is closely related to the ''asymptotic'' solution of the linear Boltzman equation and (2) requiring isotropic weight changes as collisions, they derive a new angular biasing scheme. Using the BMC equation, they propose a universal ''safe'' upper limit of the transform parameter, valid for any type of exponential transform. In numerical calculations, they demonstrate that the behavior of the Monte Carlo simulations and the performance predicted by deterministically solving the BMC equation agree well, and that the new angular biasing scheme is always advantageous
Discrete fourier transform (DFT) analysis for applications using iterative transform methods
Dean, Bruce H. (Inventor)
2012-01-01
According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.
Foundations of genetic algorithms 1991
1991-01-01
Foundations of Genetic Algorithms 1991 (FOGA 1) discusses the theoretical foundations of genetic algorithms (GA) and classifier systems.This book compiles research papers on selection and convergence, coding and representation, problem hardness, deception, classifier system design, variation and recombination, parallelization, and population divergence. Other topics include the non-uniform Walsh-schema transform; spurious correlations and premature convergence in genetic algorithms; and variable default hierarchy separation in a classifier system. The grammar-based genetic algorithm; condition
Institute of Scientific and Technical Information of China (English)
徐涛; 李冠章
2011-01-01
A novel adaptive detail enhancement algorithm aiming at colour image is proposed in this paper based on wavelet transform. The first step is to select appropriate colour space, and then the luminance components of the image are being implemented wavelet transform while the chroma components are hold on. The detail wavelet coefficients are adjusted adaptively considering the contrasts of discomposed approximate images on each level while the approximate coefficients are increased properly to boost the average luminance of colour image, there is no extra adjustment parameters setting in the process of treatment. Experiments confirm that the algorithm preserves the brighter details of the image and improves the darker details in it too. Meanwhile the image colour distortion does not appear.%针对彩色图像,提出了一种基于小波变换的自适应细节增强算法.首先选择了合适的彩色空间,保持图像的彩色分量不变,对其亮度分量进行小波变换,然后按照分解后的各级近似图像对比度自适应地调整小波细节系数,同时适当地增强近似系数以提高彩色图像的平均亮度,在处理过程中不需要设定额外的调整参数.实验证明,算法不但保留了图像较亮的细节,而且增强了较暗的细节,同时达到了图像色彩不失真的目的.
Directory of Open Access Journals (Sweden)
Mojtaba Rasouli Gandomani
2016-06-01
Full Text Available In this paper, the model of HIV infection of CD4+ T cells is considered as a system of fractional differential equations. Then, a numerical method by using collocation method based on the Müntz-Legendre polynomials to approximate solution of the model is presented. The application of the proposed numerical method causes fractional differential equations system to convert into the algebraic equations system. The new system can be solved by one of the existing methods. Finally, we compare the result of this numerical method with the result of the methods have already been presented in the literature.
Kunenkov, Erast V; Kononikhin, Alexey S; Perminova, Irina V; Hertkorn, Norbert; Gaspar, Andras; Schmitt-Kopplin, Philippe; Popov, Igor A; Garmash, Andrew V; Nikolaev, Evgeniy N
2009-12-15
The ultrahigh-resolution Fourier transform ion cyclotron resonance (FTICR) mass spectrum of natural organic matter (NOM) contains several thousand peaks with dozens of molecules matching the same nominal mass. Such a complexity poses a significant challenge for automatic data interpretation, in which the most difficult task is molecular formula assignment, especially in the case of heavy and/or multielement ions. In this study, a new universal algorithm for automatic treatment of FTICR mass spectra of NOM and humic substances based on total mass difference statistics (TMDS) has been developed and implemented. The algorithm enables a blind search for unknown building blocks (instead of a priori known ones) by revealing repetitive patterns present in spectra. In this respect, it differs from all previously developed approaches. This algorithm was implemented in designing FIRAN-software for fully automated analysis of mass data with high peak density. The specific feature of FIRAN is its ability to assign formulas to heavy and/or multielement molecules using "virtual elements" approach. To verify the approach, it was used for processing mass spectra of sodium polystyrene sulfonate (PSS, M(w) = 2200 Da) and polymethacrylate (PMA, M(w) = 3290 Da) which produce heavy multielement and multiply-charged ions. Application of TMDS identified unambiguously monomers present in the polymers consistent with their structure: C(8)H(7)SO(3)Na for PSS and C(4)H(6)O(2) for PMA. It also allowed unambiguous formula assignment to all multiply-charged peaks including the heaviest peak in PMA spectrum at mass 4025.6625 with charge state 6- (mass bias -0.33 ppm). Application of the TMDS-algorithm to processing data on the Suwannee River FA has proven its unique capacities in analysis of spectra with high peak density: it has not only identified the known small building blocks in the structure of FA such as CH(2), H(2), C(2)H(2)O, O but the heavier unit at 154.027 amu. The latter was
DEFF Research Database (Denmark)
Mahnke, Martina; Uprichard, Emma
2014-01-01
Imagine sailing across the ocean. The sun is shining, vastness all around you. And suddenly [BOOM] you’ve hit an invisible wall. Welcome to the Truman Show! Ever since Eli Pariser published his thoughts on a potential filter bubble, this movie scenario seems to have become reality, just with slight...... changes: it’s not the ocean, it’s the internet we’re talking about, and it’s not a TV show producer, but algorithms that constitute a sort of invisible wall. Building on this assumption, most research is trying to ‘tame the algorithmic tiger’. While this is a valuable and often inspiring approach, we...
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1975-01-01
A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de
KAM Tori Construction Algorithms
Wiesel, W.
In this paper we evaluate and compare two algorithms for the calculation of KAM tori in Hamiltonian systems. The direct fitting of a torus Fourier series to a numerically integrated trajectory is the first method, while an accelerated finite Fourier transform is the second method. The finite Fourier transform, with Hanning window functions, is by far superior in both computational loading and numerical accuracy. Some thoughts on applications of KAM tori are offered.
Approximating the Analytic Fourier Transform with the Discrete Fourier Transform
Axelrod, Jeremy
2015-01-01
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.
The Kustaanheimo-Stiefel transformation and certain special functions
International Nuclear Information System (INIS)
Kibler, M.; Negadi, T.; Ronveaux, A.
1984-10-01
The Kustaanheimo-Stiefel transformation is briefly described in various frameworks. This transformation is used to convert the R 3 harmonics into R 4 harmonics. Then, the Schroedinger equation for an hydrogen-like atom is transformed into the set of a coupled pair of Schroedinger equations for two R 2 isotropic harmonic oscillators and a coupled pair of constraint relations. This connection between two famous quantization cases is tackled in terms of both eigenvalues and eigenvectors corresponding to the discrete spectrum of the hydrogen atom. This leads to an integral involving Laguerre, Legendre, and Hermite polynomials. A program has been realized in the algebraic and symbolic programming system macsyma to cover the various computing aspects of this work
Energy Technology Data Exchange (ETDEWEB)
Othmani, Cherif, E-mail: othmanicheriffss@gmail.com; Takali, Farid; Njeh, Anouar; Ben Ghozlen, Mohamed Hédi
2016-09-01
The propagation of Rayleigh–Lamb waves in bi-layered structures is studied. For this purpose, an extension of the Legendre polynomial (LP) method is proposed to formulate the acoustic wave equation in the bi-layered structures induced by thin film Gallium Antimonide (GaSb) and with Aluminum Antimonide (AlSb) substrate in moderate thickness. Acoustic modes propagating along a bi-layer plate are shown to be quite different than classical Lamb modes, contrary to most of the multilayered structures. The validation of the LP method is illustrated by a comparison between the associated numerical results and those obtained using the ordinary differential equation (ODE) method. The convergency of the LP method is discussed through a numerical example. Moreover, the influences of thin film GaSb parameters on the characteristics Rayleigh–Lamb waves propagation has been studied in detail. Finally, the advantages of the Legendre polynomial (LP) method to analyze the multilayered structures are described. All the developments performed in this work were implemented in Matlab software.
International Nuclear Information System (INIS)
Othmani, Cherif; Takali, Farid; Njeh, Anouar; Ben Ghozlen, Mohamed Hédi
2016-01-01
The propagation of Rayleigh–Lamb waves in bi-layered structures is studied. For this purpose, an extension of the Legendre polynomial (LP) method is proposed to formulate the acoustic wave equation in the bi-layered structures induced by thin film Gallium Antimonide (GaSb) and with Aluminum Antimonide (AlSb) substrate in moderate thickness. Acoustic modes propagating along a bi-layer plate are shown to be quite different than classical Lamb modes, contrary to most of the multilayered structures. The validation of the LP method is illustrated by a comparison between the associated numerical results and those obtained using the ordinary differential equation (ODE) method. The convergency of the LP method is discussed through a numerical example. Moreover, the influences of thin film GaSb parameters on the characteristics Rayleigh–Lamb waves propagation has been studied in detail. Finally, the advantages of the Legendre polynomial (LP) method to analyze the multilayered structures are described. All the developments performed in this work were implemented in Matlab software.
Directory of Open Access Journals (Sweden)
Francesca Musiani
2013-08-01
Full Text Available Algorithms are increasingly often cited as one of the fundamental shaping devices of our daily, immersed-in-information existence. Their importance is acknowledged, their performance scrutinised in numerous contexts. Yet, a lot of what constitutes 'algorithms' beyond their broad definition as “encoded procedures for transforming input data into a desired output, based on specified calculations” (Gillespie, 2013 is often taken for granted. This article seeks to contribute to the discussion about 'what algorithms do' and in which ways they are artefacts of governance, providing two examples drawing from the internet and ICT realm: search engine queries and e-commerce websites’ recommendations to customers. The question of the relationship between algorithms and rules is likely to occupy an increasingly central role in the study and the practice of internet governance, in terms of both institutions’ regulation of algorithms, and algorithms’ regulation of our society.
Energy Technology Data Exchange (ETDEWEB)
Bueno, Josiane M.; Traina, Agma Juci M. [Sao Paulo Univ., Sao Carlos, SP (Brazil). Inst. de Ciencias Matematicas; Cruvinel, Paulo E. [EMBRAPA, Sao Carlos, SP (Brazil). CNPDIA
1995-12-31
This work presents an algorithm for three-dimensional digital image reconstruction. Such algorithms based on the combination of both a Fast Fourier Transform method with Hamming Window and the use of a tri-linear interpolation function. The algorithm allows not only the generation of three-dimensional spatial spin distribution maps for Magnetic Resonance Tomography data but also X and Y-rays linear attenuation coefficient maps for CT scanners. Results demonstrates the usefulness of the algorithm in three-dimensional image reconstruction by doing first two-dimensional reconstruction and rather after interpolation. The algorithm was developed in C++ language, and there are two available versions: one under the DOS environment, and the other under the UNIX/Sun environment. (author) 10 refs., 5 figs.
Maser-like transformations using the lie transform
International Nuclear Information System (INIS)
Michelotti, L.
1985-01-01
The Deprit-Hori-Kamel recursive algorithm is presented for carrying out canonical transformations that eliminate non-secular terms of a Hamiltonian. The method is illustrated in the context of accelerator theory by application to three sample problems. (author)
A Fast Mellin and Scale Transform
Directory of Open Access Journals (Sweden)
Davide Rocchesso
2007-01-01
Full Text Available A fast algorithm for the discrete-scale (and β-Mellin transform is proposed. It performs a discrete-time discrete-scale approximation of the continuous-time transform, with subquadratic asymptotic complexity. The algorithm is based on a well-known relation between the Mellin and Fourier transforms, and it is practical and accurate. The paper gives some theoretical background on the Mellin, β-Mellin, and scale transforms. Then the algorithm is presented and analyzed in terms of computational complexity and precision. The effects of different interpolation procedures used in the algorithm are discussed.
A Fast Mellin and Scale Transform
Directory of Open Access Journals (Sweden)
Rocchesso Davide
2007-01-01
Full Text Available A fast algorithm for the discrete-scale (and -Mellin transform is proposed. It performs a discrete-time discrete-scale approximation of the continuous-time transform, with subquadratic asymptotic complexity. The algorithm is based on a well-known relation between the Mellin and Fourier transforms, and it is practical and accurate. The paper gives some theoretical background on the Mellin, -Mellin, and scale transforms. Then the algorithm is presented and analyzed in terms of computational complexity and precision. The effects of different interpolation procedures used in the algorithm are discussed.
International Nuclear Information System (INIS)
Meyer, Chad D.; Balsara, Dinshaw S.; Aslam, Tariq D.
2014-01-01
Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s 2 times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful
A Parallel Butterfly Algorithm
Poulson, Jack; Demanet, Laurent; Maxwell, Nicholas; Ying, Lexing
2014-01-01
The butterfly algorithm is a fast algorithm which approximately evaluates a discrete analogue of the integral transform (Equation Presented.) at large numbers of target points when the kernel, K(x, y), is approximately low-rank when restricted to subdomains satisfying a certain simple geometric condition. In d dimensions with O(Nd) quasi-uniformly distributed source and target points, when each appropriate submatrix of K is approximately rank-r, the running time of the algorithm is at most O(r2Nd logN). A parallelization of the butterfly algorithm is introduced which, assuming a message latency of α and per-process inverse bandwidth of β, executes in at most (Equation Presented.) time using p processes. This parallel algorithm was then instantiated in the form of the open-source DistButterfly library for the special case where K(x, y) = exp(iΦ(x, y)), where Φ(x, y) is a black-box, sufficiently smooth, real-valued phase function. Experiments on Blue Gene/Q demonstrate impressive strong-scaling results for important classes of phase functions. Using quasi-uniform sources, hyperbolic Radon transforms, and an analogue of a three-dimensional generalized Radon transform were, respectively, observed to strong-scale from 1-node/16-cores up to 1024-nodes/16,384-cores with greater than 90% and 82% efficiency, respectively. © 2014 Society for Industrial and Applied Mathematics.
A Parallel Butterfly Algorithm
Poulson, Jack
2014-02-04
The butterfly algorithm is a fast algorithm which approximately evaluates a discrete analogue of the integral transform (Equation Presented.) at large numbers of target points when the kernel, K(x, y), is approximately low-rank when restricted to subdomains satisfying a certain simple geometric condition. In d dimensions with O(Nd) quasi-uniformly distributed source and target points, when each appropriate submatrix of K is approximately rank-r, the running time of the algorithm is at most O(r2Nd logN). A parallelization of the butterfly algorithm is introduced which, assuming a message latency of α and per-process inverse bandwidth of β, executes in at most (Equation Presented.) time using p processes. This parallel algorithm was then instantiated in the form of the open-source DistButterfly library for the special case where K(x, y) = exp(iΦ(x, y)), where Φ(x, y) is a black-box, sufficiently smooth, real-valued phase function. Experiments on Blue Gene/Q demonstrate impressive strong-scaling results for important classes of phase functions. Using quasi-uniform sources, hyperbolic Radon transforms, and an analogue of a three-dimensional generalized Radon transform were, respectively, observed to strong-scale from 1-node/16-cores up to 1024-nodes/16,384-cores with greater than 90% and 82% efficiency, respectively. © 2014 Society for Industrial and Applied Mathematics.
De Götzen , Amalia; Mion , Luca; Tache , Olivier
2007-01-01
International audience; We call sound algorithms the categories of algorithms that deal with digital sound signal. Sound algorithms appeared in the very infancy of computer. Sound algorithms present strong specificities that are the consequence of two dual considerations: the properties of the digital sound signal itself and its uses, and the properties of auditory perception.
Wang, Lui; Bayer, Steven E.
1991-01-01
Genetic algorithms are mathematical, highly parallel, adaptive search procedures (i.e., problem solving methods) based loosely on the processes of natural genetics and Darwinian survival of the fittest. Basic genetic algorithms concepts are introduced, genetic algorithm applications are introduced, and results are presented from a project to develop a software tool that will enable the widespread use of genetic algorithm technology.
Energy Technology Data Exchange (ETDEWEB)
Nosrati, R [Reyrson University, Toronto, Ontario (Canada); Sunnybrook Health Sciences Centre, Toronto, Ontario (Canada); Soliman, A; Owrangi, A [Sunnybrook Research Institute, Toronto, Ontario (Canada); Sunnybrook Health Sciences Centre, Toronto, Ontario (Canada); Ghugre, N [Sunnybrook Research Institute, Toronto, Ontario (Canada); University of Toronto, Toronto, ON (Canada); Morton, G [Sunnybrook Health Sciences Centre, Toronto, Ontario (Canada); University of Toronto, Toronto, ON (Canada); Pejovic-Milic, A [Reyrson University, Toronto, Ontario (Canada); Song, W [Reyrson University, Toronto, Ontario (Canada); Sunnybrook Research Institute, Toronto, Ontario (Canada); Sunnybrook Health Sciences Centre, Toronto, Ontario (Canada); University of Toronto, Toronto, ON (Canada)
2016-06-15
Purpose: This study aims at developing an MRI-only workflow for post-implant dosimetry of the prostate LDR brachytherapy seeds. The specific goal here is to develop a post-processing algorithm to produce positive contrast for the seeds and prostatic calcifications and differentiate between them on MR images. Methods: An agar-based phantom incorporating four dummy seeds (I-125) and five calcifications of different sizes (from sheep cortical bone) was constructed. Seeds were placed arbitrarily in the coronal plane. The phantom was scanned with 3T Philips Achieva MR scanner using an 8-channel head coil array. Multi-echo turbo spin echo (ME-TSE) and multi-echo gradient recalled echo (ME-GRE) sequences were acquired. Due to minimal susceptibility artifacts around seeds, ME-GRE sequence (flip angle=15; TR/TE=20/2.3/2.3; resolution=0.7×0.7×2mm3) was further processed.The induced field inhomogeneity due to the presence of titaniumencapsulated seeds was corrected using a B0 field map. B0 map was calculated using the ME-GRE sequence by calculating the phase difference at two different echo times. Initially, the product of the first echo and B0 map was calculated. The features corresponding to the seeds were then extracted in three steps: 1) the edge pixels were isolated using “Prewitt” operator; 2) the Hough transform was employed to detect ellipses approximately matching the dimensions of the seeds and 3) at the position and orientation of the detected ellipses an ellipse was drawn on the B0-corrected image. Results: The proposed B0-correction process produced positive contrast for the seeds and calcifications. The Hough transform based on Prewitt edge operator successfully identified all the seeds according to their ellipsoidal shape and dimensions in the edge image. Conclusion: The proposed post-processing algorithm successfully visualized the seeds and calcifications with positive contrast and differentiates between them according to their shapes. Further
International Nuclear Information System (INIS)
Hallenga, K.
1991-01-01
This paper discusses the concept of Fourier transformation one of the many precious legacies of the French mathematician Jean Baptiste Joseph Fourier, essential for understanding the link between continuous-wave (CW) and Fourier transform (FT) NMR. Although in modern FT NMR the methods used to obtain a frequency spectrum from the time-domain signal may vary greatly, from the efficient Cooley-Tukey algorithm to very elaborate iterative least-square methods based other maximum entropy method or on linear prediction, the principles for Fourier transformation are unchanged and give invaluable insight into the interconnection of many pairs of physical entities called Fourier pairs
One improved LSB steganography algorithm
Song, Bing; Zhang, Zhi-hong
2013-03-01
It is easy to be detected by X2 and RS steganalysis with high accuracy that using LSB algorithm to hide information in digital image. We started by selecting information embedded location and modifying the information embedded method, combined with sub-affine transformation and matrix coding method, improved the LSB algorithm and a new LSB algorithm was proposed. Experimental results show that the improved one can resist the X2 and RS steganalysis effectively.
Adaption of optical Fresnel transform to optical Wigner transform
International Nuclear Information System (INIS)
Lv Cuihong; Fan Hongyi
2010-01-01
Enlightened by the algorithmic isomorphism between the rotation of the Wigner distribution function (WDF) and the αth fractional Fourier transform, we show that the optical Fresnel transform performed on the input through an ABCD system makes the output naturally adapting to the associated Wigner transform, i.e. there exists algorithmic isomorphism between ABCD transformation of the WDF and the optical Fresnel transform. We prove this adaption in the context of operator language. Both the single-mode and the two-mode Fresnel operators as the image of classical Fresnel transform are introduced in our discussions, while the two-mode Wigner operator in the entangled state representation is introduced for fitting the two-mode Fresnel operator.
Joux, Antoine
2009-01-01
Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applic
Hougardy, Stefan
2016-01-01
Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.
Integral transformations applied to image encryption
International Nuclear Information System (INIS)
Vilardy, Juan M.; Torres, Cesar O.; Perez, Ronal
2017-01-01
In this paper we consider the application of the integral transformations for image encryption through optical systems, a mathematical algorithm under Matlab platform using fractional Fourier transform (FrFT) and Random Phase Mask (RPM) for digital images encryption is implemented. The FrFT can be related to others integral transforms, such as: Fourier transform, Sine and Cosine transforms, Radial Hilbert transform, fractional Sine transform, fractional Cosine transform, fractional Hartley transform, fractional Wavelet transform and Gyrator transform, among other transforms. The encryption scheme is based on the use of the FrFT, the joint transform correlator and two RPMs, which provide security and robustness to the implemented security system. One of the RPMs used during encryption-decryption and the fractional order of the FrFT are the keys to improve security and make the system more resistant against security attacks. (paper)
Tel, G.
We define the notion of total algorithms for networks of processes. A total algorithm enforces that a "decision" is taken by a subset of the processes, and that participation of all processes is required to reach this decision. Total algorithms are an important building block in the design of
An algorithm for reduct cardinality minimization
AbouEisha, Hassan M.
2013-12-01
This is devoted to the consideration of a new algorithm for reduct cardinality minimization. This algorithm transforms the initial table to a decision table of a special kind, simplify this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. Results of computer experiments with decision tables from UCI ML Repository are discussed. © 2013 IEEE.
An algorithm for reduct cardinality minimization
AbouEisha, Hassan M.; Al Farhan, Mohammed; Chikalov, Igor; Moshkov, Mikhail
2013-01-01
This is devoted to the consideration of a new algorithm for reduct cardinality minimization. This algorithm transforms the initial table to a decision table of a special kind, simplify this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. Results of computer experiments with decision tables from UCI ML Repository are discussed. © 2013 IEEE.
Wang, Victor C. X.; Cranton, Patricia
2011-01-01
The theory of transformative learning has been explored by different theorists and scholars. However, few scholars have made an attempt to make a comparison between transformative learning and Confucianism or between transformative learning and andragogy. The authors of this article address these comparisons to develop new and different insights…
Multisensor data fusion algorithm development
Energy Technology Data Exchange (ETDEWEB)
Yocky, D.A.; Chadwick, M.D.; Goudy, S.P.; Johnson, D.K.
1995-12-01
This report presents a two-year LDRD research effort into multisensor data fusion. We approached the problem by addressing the available types of data, preprocessing that data, and developing fusion algorithms using that data. The report reflects these three distinct areas. First, the possible data sets for fusion are identified. Second, automated registration techniques for imagery data are analyzed. Third, two fusion techniques are presented. The first fusion algorithm is based on the two-dimensional discrete wavelet transform. Using test images, the wavelet algorithm is compared against intensity modulation and intensity-hue-saturation image fusion algorithms that are available in commercial software. The wavelet approach outperforms the other two fusion techniques by preserving spectral/spatial information more precisely. The wavelet fusion algorithm was also applied to Landsat Thematic Mapper and SPOT panchromatic imagery data. The second algorithm is based on a linear-regression technique. We analyzed the technique using the same Landsat and SPOT data.
Backlund transformations as canonical transformations
International Nuclear Information System (INIS)
Villani, A.; Zimerman, A.H.
1977-01-01
Toda and Wadati as well as Kodama and Wadati have shown that the Backlund transformations, for the exponential lattice equation, sine-Gordon equation, K-dV (Korteweg de Vries) equation and modifies K-dV equation, are canonical transformation. It is shown that the Backlund transformation for the Boussinesq equation, for a generalized K-dV equation, for a model equation for shallow water waves and for the nonlinear Schroedinger equation are also canonical transformations [pt
The fractional Fourier transform and applications
Bailey, David H.; Swarztrauber, Paul N.
1991-01-01
This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
International Nuclear Information System (INIS)
Alberty, R.A.; Oppenheim, I.
1993-01-01
When temperature, pressure, and the partial pressure of a reactant are fixed, the criterion of chemical equilibrium can be expressed in terms of the transformed Gibbs energy G' that is obtained by using a Legendre transform involving the chemical potential of the reactant that is fixed. For reactions of ideal gases, the most natural variables to use in the fundamental equation are T, P', and P B , where P' is the partial pressure of the reactants other than the one that is fixed and P B is the partial pressure of the reactant that is fixed. The fundamental equation for G' yields the expression for the transformed entropy S', and a transformed enthalpy can be defined by the additional Legendre transform H'=G'+TS'. This leads to an additional form of the fundamental equation. The calculation of transformed thermodynamic properties and equilibrium compositions is discussed for a simple system and for a general multireaction system. The change, in a reaction, of the binding of the reactant that is at a specified pressure can be calculated using one of the six Maxwell equations of the fundamental equation in G'
The Mehler-Fock Transform in Signal Processing
Directory of Open Access Journals (Sweden)
Reiner Lenz
2017-06-01
Full Text Available Many signals can be described as functions on the unit disk (ball. In the framework of group representations it is well-known how to construct Hilbert-spaces containing these functions that have the groups SU(1,N as their symmetry groups. One illustration of this construction is three-dimensional color spaces in which chroma properties are described by points on the unit disk. A combination of principal component analysis and the Perron-Frobenius theorem can be used to show that perspective projections map positive signals (i.e., functions with positive values to a product of the positive half-axis and the unit ball. The representation theory (harmonic analysis of the group SU(1,1 leads to an integral transform, the Mehler-Fock-transform (MFT, that decomposes functions, depending on the radial coordinate only, into combinations of associated Legendre functions. This transformation is applied to kernel density estimators of probability distributions on the unit disk. It is shown that the transform separates the influence of the data and the measured data. The application of the transform is illustrated by studying the statistical distribution of RGB vectors obtained from a common set of object points under different illuminants.
International Nuclear Information System (INIS)
Boyd, John P.
2003-01-01
If the dispersion in a nonlinear hyperbolic wave equation is weak in the sense that the frequency ω(k) of cos(kx) is bounded as k→∞, it is common that (i) travelling waves exist up to a limiting amplitude with wave-breaking for higher amplitudes, and (ii) the limiting wave has a corner, that is, a discontinuity in slope. Because 'corner' waves are not smooth, standard numerical methods converge poorly as the number of grid points is increased. However, the corner wave is important because, at least in some systems, it is the attractor for all large amplitude initial conditions. Here we devise a Legendre-pseudospectral method which is uncorrupted by the singularity. The symmetric (u(X)=u(-X)) wave can be computed on an interval spanning only half the spatial period; since u is smooth on this domain which does not include the corner except as an endpoint, all numerical difficulties are avoided. A key step is to derive an extra boundary condition which uniquely identifies the corner wave. With both the grid point values of u(x) and phase speed c as unknowns, the discretized equations, imposing three boundary conditions on a second order differential equation, are solved by a Newton-Raphson iteration. Although our method is illustrated by the so-called 'Whitham's equation', u t +uu x =∫Du dx ' where D is a very general linear operator, the ideas are widely applicable
Agaian, Sos; Egiazarian, Karen; Astola, Jaakko
2011-01-01
The Hadamard matrix and Hadamard transform are fundamental problem-solving tools in a wide spectrum of scientific disciplines and technologies, such as communication systems, signal and image processing (signal representation, coding, filtering, recognition, and watermarking), digital logic (Boolean function analysis and synthesis), and fault-tolerant system design. Hadamard Transforms intends to bring together different topics concerning current developments in Hadamard matrices, transforms, and their applications. Each chapter begins with the basics of the theory, progresses to more advanced
APPLICATION OF NATURAL TRANSFORM IN CRYPTOGRAPHY
Chindhe, Anil Dhondiram; Kiwne, Sakharam
2017-01-01
Abstaract−The newly defined integral transform ”Natural transform” has many application in the field of science and engineering.In this paper we described the application of Natural transform to Cryptography.This provide the algorithm for cryptography in which we use the natural transform of the exponential function for encryption of the plain text and corresponding inverse natural transform for decryption
Algorithmic Verification of Linearizability for Ordinary Differential Equations
Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Michels, Dominik L.
2017-01-01
one by a point transformation of the dependent and independent variables. The first algorithm is based on a construction of the Lie point symmetry algebra and on the computation of its derived algebra. The second algorithm exploits the differential
Array architectures for iterative algorithms
Jagadish, Hosagrahar V.; Rao, Sailesh K.; Kailath, Thomas
1987-01-01
Regular mesh-connected arrays are shown to be isomorphic to a class of so-called regular iterative algorithms. For a wide variety of problems it is shown how to obtain appropriate iterative algorithms and then how to translate these algorithms into arrays in a systematic fashion. Several 'systolic' arrays presented in the literature are shown to be specific cases of the variety of architectures that can be derived by the techniques presented here. These include arrays for Fourier Transform, Matrix Multiplication, and Sorting.
Dependency Parsing with Transformed Feature
Directory of Open Access Journals (Sweden)
Fuxiang Wu
2017-01-01
Full Text Available Dependency parsing is an important subtask of natural language processing. In this paper, we propose an embedding feature transforming method for graph-based parsing, transform-based parsing, which directly utilizes the inner similarity of the features to extract information from all feature strings including the un-indexed strings and alleviate the feature sparse problem. The model transforms the extracted features to transformed features via applying a feature weight matrix, which consists of similarities between the feature strings. Since the matrix is usually rank-deficient because of similar feature strings, it would influence the strength of constraints. However, it is proven that the duplicate transformed features do not degrade the optimization algorithm: the margin infused relaxed algorithm. Moreover, this problem can be alleviated by reducing the number of the nearest transformed features of a feature. In addition, to further improve the parsing accuracy, a fusion parser is introduced to integrate transformed and original features. Our experiments verify that both transform-based and fusion parser improve the parsing accuracy compared to the corresponding feature-based parser.
DEFF Research Database (Denmark)
Pedersen, Pia
2012-01-01
Transformation, defined as the step of extracting, arranging and simplifying data into visual form (M. Neurath, 1974), was developed in connection with ISOTYPE (International System Of TYpographic Picture Education) and might well be the most important legacy of Isotype to the field of graphic...... design. Recently transformation has attracted renewed interest because of the book The Transformer written by Robin Kinross and Marie Neurath. My on-going research project, summarized in this paper, identifies and depicts the essential principles of data visualization underlying the process...... of transformation with reference to Marie Neurath’s sketches on the Bilston Project. The material has been collected at the Otto and Marie Neurath Collection housed at the University of Reading, UK. By using data visualization as a research method to look directly into the process of transformation, the project...
A New Formula for the Inverse Wavelet Transform
Sun, Wenchang
2010-01-01
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
Dirichlet Characters, Gauss Sums, and Inverse Z Transform
Gao, Jing; Liu, Huaning
2012-01-01
A generalized Möbius transform is presented. It is based on Dirichlet characters. A general algorithm is developed to compute the inverse $Z$ transform on the unit circle, and an error estimate is given for the truncated series representation.
International Nuclear Information System (INIS)
Creutz, M.
1987-11-01
A large variety of Monte Carlo algorithms are being used for lattice gauge simulations. For purely bosonic theories, present approaches are generally adequate; nevertheless, overrelaxation techniques promise savings by a factor of about three in computer time. For fermionic fields the situation is more difficult and less clear. Algorithms which involve an extrapolation to a vanishing step size are all quite closely related. Methods which do not require such an approximation tend to require computer time which grows as the square of the volume of the system. Recent developments combining global accept/reject stages with Langevin or microcanonical updatings promise to reduce this growth to V/sup 4/3/
Hu, T C
2002-01-01
Newly enlarged, updated second edition of a valuable text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discusses binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. 153 black-and-white illus. 23 tables.Newly enlarged, updated second edition of a valuable, widely used text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: Chapter 9
Image Registration Using Redundant Wavelet Transforms
National Research Council Canada - National Science Library
Brown, Richard
2001-01-01
.... In our research, we present a fundamentally new wavelet-based registration algorithm utilizing redundant transforms and a masking process to suppress the adverse effects of noise and improve processing efficiency...
National Research Council Canada - National Science Library
Metz, Steven
2003-01-01
... adjustment. With American military forces engaged around the world in both combat and stabilization operations, the need for rigorous and critical analysis of security transformation has never been greater...
Group-invariant finite Fourier transforms
International Nuclear Information System (INIS)
Shenefelt, M.H.
1988-01-01
The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible
DEFF Research Database (Denmark)
Munck Petersen, Rikke
2005-01-01
Seminaroplæg fra forskere. Faglige seminarer på KA, forår 2005. Belyser transformation af det danske landskab fysisk som holdningsmæssigt, samt hvordan phd-arbejdets egen proces håndterer den.......Seminaroplæg fra forskere. Faglige seminarer på KA, forår 2005. Belyser transformation af det danske landskab fysisk som holdningsmæssigt, samt hvordan phd-arbejdets egen proces håndterer den....
Kisil, Vladimir V.
2010-01-01
The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not admissible. Covariant transform extends an applicability of the popular wavelets construction to classic examples like the Hardy space H_2, Banach spaces, covariant functional calculus and many others. Keywords: Wavelets, cohe...
Hall, Anndee
2017-01-01
Abstract: Transforming Anatomy Studying historic books allows people to witness the transformation of the world right before their very eyes. The Bruxellensis Icones Anatomicae[1] by Andreas Vesalius is a vital piece of evidence in the movement from a more rudimentary understanding of the human body into the more complex and accurate development of modern anatomy. Vesalius’ research worked to both refute and confirm findings of his predecessor, the great historical Greek philosopher, Galen...
Inversion of the star transform
International Nuclear Information System (INIS)
Zhao, Fan; Schotland, John C; Markel, Vadim A
2014-01-01
We define the star transform as a generalization of the broken ray transform introduced by us in previous work. The advantages of using the star transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium separately and simultaneously (from the same data) and the possibility to utilize scattered radiation which, in the case of conventional x-ray tomography, is discarded. In this paper, we derive the star transform from physical principles, discuss its mathematical properties and analyze numerical stability of inversion. In particular, it is shown that stable inversion of the star transform can be obtained only for configurations involving odd number of rays. Several computationally-efficient inversion algorithms are derived and tested numerically. (paper)
WAVELET TRANSFORM AND LIP MODEL
Directory of Open Access Journals (Sweden)
Guy Courbebaisse
2011-05-01
Full Text Available The Fourier transform is well suited to the study of stationary functions. Yet, it is superseded by the Wavelet transform for the powerful characterizations of function features such as singularities. On the other hand, the LIP (Logarithmic Image Processing model is a mathematical framework developed by Jourlin and Pinoli, dedicated to the representation and processing of gray tones images called hereafter logarithmic images. This mathematically well defined model, comprising a Fourier Transform "of its own", provides an effective tool for the representation of images obtained by transmitted light, such as microscope images. This paper presents a Wavelet transform within the LIP framework, with preservation of the classical Wavelet Transform properties. We show that the fast computation algorithm due to Mallat can be easily used. An application is given for the detection of crests.
Road Detection by Using a Generalized Hough Transform
Directory of Open Access Journals (Sweden)
Weifeng Liu
2017-06-01
Full Text Available Road detection plays key roles for remote sensing image analytics. Hough transform (HT is one very typical method for road detection, especially for straight line road detection. Although many variants of Hough transform have been reported, it is still a great challenge to develop a low computational complexity and time-saving Hough transform algorithm. In this paper, we propose a generalized Hough transform (i.e., Radon transform implementation for road detection in remote sensing images. Specifically, we present a dictionary learning method to approximate the Radon transform. The proposed approximation method treats a Radon transform as a linear transform, which then facilitates parallel implementation of the Radon transform for multiple images. To evaluate the proposed algorithm, we conduct extensive experiments on the popular RSSCN7 database for straight road detection. The experimental results demonstrate that our method is superior to the traditional algorithms in terms of accuracy and computing complexity.
A Sweepline Algorithm for Generalized Delaunay Triangulations
DEFF Research Database (Denmark)
Skyum, Sven
We give a deterministic O(n log n) sweepline algorithm to construct the generalized Voronoi diagram for n points in the plane or rather its dual the generalized Delaunay triangulation. The algorithm uses no transformations and it is developed solely from the sweepline paradigm together...
Quantum entanglement and quantum computational algorithms
Indian Academy of Sciences (India)
We demonstrate that the one- and the two-bit Deutsch-Jozsa algorithm does not require entanglement and can be mapped onto a classical optical scheme. It is only for three and more input bits that the DJ algorithm requires the implementation of entangling transformations and in these cases it is impossible to implement ...
Directory of Open Access Journals (Sweden)
Anna Bourmistrova
2011-02-01
Full Text Available The autodriver algorithm is an intelligent method to eliminate the need of steering by a driver on a well-defined road. The proposed method performs best on a four-wheel steering (4WS vehicle, though it is also applicable to two-wheel-steering (TWS vehicles. The algorithm is based on coinciding the actual vehicle center of rotation and road center of curvature, by adjusting the kinematic center of rotation. The road center of curvature is assumed prior information for a given road, while the dynamic center of rotation is the output of dynamic equations of motion of the vehicle using steering angle and velocity measurements as inputs. We use kinematic condition of steering to set the steering angles in such a way that the kinematic center of rotation of the vehicle sits at a desired point. At low speeds the ideal and actual paths of the vehicle are very close. With increase of forward speed the road and tire characteristics, along with the motion dynamics of the vehicle cause the vehicle to turn about time-varying points. By adjusting the steering angles, our algorithm controls the dynamic turning center of the vehicle so that it coincides with the road curvature center, hence keeping the vehicle on a given road autonomously. The position and orientation errors are used as feedback signals in a closed loop control to adjust the steering angles. The application of the presented autodriver algorithm demonstrates reliable performance under different driving conditions.
Unconventional Algorithms: Complementarity of Axiomatics and Construction
Directory of Open Access Journals (Sweden)
Gordana Dodig Crnkovic
2012-10-01
Full Text Available In this paper, we analyze axiomatic and constructive issues of unconventional computations from a methodological and philosophical point of view. We explain how the new models of algorithms and unconventional computations change the algorithmic universe, making it open and allowing increased flexibility and expressive power that augment creativity. At the same time, the greater power of new types of algorithms also results in the greater complexity of the algorithmic universe, transforming it into the algorithmic multiverse and demanding new tools for its study. That is why we analyze new powerful tools brought forth by local mathematics, local logics, logical varieties and the axiomatic theory of algorithms, automata and computation. We demonstrate how these new tools allow efficient navigation in the algorithmic multiverse. Further work includes study of natural computation by unconventional algorithms and constructive approaches.
A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms
Directory of Open Access Journals (Sweden)
Mingli Jing
2010-01-01
Full Text Available An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition (SVD of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible matrices (TERMs, which map integers to integers by rounding arithmetic. The cost of factorizing block matrix into TERMs does not increase with the increase of the dimension of transform matrix, and the proposed algorithm is in-place calculation and without allocating auxiliary memory. Examples of integer multiwavelet transform using DGHM and CL are given, which verify that the proposed algorithm is an executable algorithm and outperforms the existing algorithm for orthogonal 4-tap integer multiwavelet transform.
Research on Palmprint Identification Method Based on Quantum Algorithms
Directory of Open Access Journals (Sweden)
Hui Li
2014-01-01
Full Text Available Quantum image recognition is a technology by using quantum algorithm to process the image information. It can obtain better effect than classical algorithm. In this paper, four different quantum algorithms are used in the three stages of palmprint recognition. First, quantum adaptive median filtering algorithm is presented in palmprint filtering processing. Quantum filtering algorithm can get a better filtering result than classical algorithm through the comparison. Next, quantum Fourier transform (QFT is used to extract pattern features by only one operation due to quantum parallelism. The proposed algorithm exhibits an exponential speed-up compared with discrete Fourier transform in the feature extraction. Finally, quantum set operations and Grover algorithm are used in palmprint matching. According to the experimental results, quantum algorithm only needs to apply square of N operations to find out the target palmprint, but the traditional method needs N times of calculation. At the same time, the matching accuracy of quantum algorithm is almost 100%.
A coordinate transform method for one-speed neutron transport in composite slabs
International Nuclear Information System (INIS)
Haidar, N.H.S.
1988-01-01
The optical path transformation is applied to reduce the one-speed neutron transport equation for a class of composite subcritical slabs to single-region problems. The class idealises, within the uncertainty of the one-speed model, a variety of practical situations such as U-D 2 O-C-Zr-Pb or Pu-U-Na-Fe symmetric reactor assemblies; which may possibly contain a symmetrically anisotropic neutron source. A closed form double series solution, which turns out to be quite convenient for design and optimisation purposes, has been obtained, in terms of discontinuous functions for the multi-regional angular flux by application of a double finite Legendre transform. Disadvantage factor evaluations for a U-C lattice cell resulting from a low-order P 0 P 1 approximation of this method are found to be in full agreement with hybrid diffusion-transport estimates. (author)
Fast compact algorithms and software for spline smoothing
Weinert, Howard L
2012-01-01
Fast Compact Algorithms and Software for Spline Smoothing investigates algorithmic alternatives for computing cubic smoothing splines when the amount of smoothing is determined automatically by minimizing the generalized cross-validation score. These algorithms are based on Cholesky factorization, QR factorization, or the fast Fourier transform. All algorithms are implemented in MATLAB and are compared based on speed, memory use, and accuracy. An overall best algorithm is identified, which allows very large data sets to be processed quickly on a personal computer.
Fast Unitary Transforms - Benefits and Restrictions.
1980-04-01
transformation kernel, and u assumes values in the range 0, 1, ... , N-i. Similarly, the inverse transform is given by the relation N-1 f(x) E T(u)h(x...function to obtain T(u,v). Similar comments hold for the inverse transform if h(x,y,u,v) is separable. If the kernel g(xy,u,v) is separable and symmetric...the forward transform can be used directly to obtain the inverse transform simply by multiplying the result of the algorithm by N. 12 The forward and
Hough transform search for continuous gravitational waves
International Nuclear Information System (INIS)
Krishnan, Badri; Papa, Maria Alessandra; Sintes, Alicia M.; Schutz, Bernard F.; Frasca, Sergio; Palomba, Cristiano
2004-01-01
This paper describes an incoherent method to search for continuous gravitational waves based on the Hough transform, a well-known technique used for detecting patterns in digital images. We apply the Hough transform to detect patterns in the time-frequency plane of the data produced by an earth-based gravitational wave detector. Two different flavors of searches will be considered, depending on the type of input to the Hough transform: either Fourier transforms of the detector data or the output of a coherent matched-filtering type search. We present the technical details for implementing the Hough transform algorithm for both kinds of searches, their statistical properties, and their sensitivities
DEFF Research Database (Denmark)
Markham, Annette
This paper takes an actor network theory approach to explore some of the ways that algorithms co-construct identity and relational meaning in contemporary use of social media. Based on intensive interviews with participants as well as activity logging and data tracking, the author presents a richly...... layered set of accounts to help build our understanding of how individuals relate to their devices, search systems, and social network sites. This work extends critical analyses of the power of algorithms in implicating the social self by offering narrative accounts from multiple perspectives. It also...... contributes an innovative method for blending actor network theory with symbolic interaction to grapple with the complexity of everyday sensemaking practices within networked global information flows....
Bäcklund transformations and divisor doubling
Tsiganov, A. V.
2018-03-01
In classical mechanics well-known cryptographic algorithms and protocols can be very useful for construction of canonical transformations preserving form of Hamiltonians. We consider application of a standard generic divisor doubling for construction of new auto Bäcklund transformations for the Lagrange top and Hénon-Heiles system separable in parabolic coordinates.
DEFF Research Database (Denmark)
Andersen, Nicolai Bo
This paper is about sustainable transformation with a particular focus on listed buildings. It is based on the notion that sustainability is not just a question of energy conditions, but also about the building being robust. Robust architecture means that the building can be maintained and rebuilt......, that it can be adapted to changing functional needs, and that it has an architectural and cultural value. A specific proposal for a transformation that enhances the architectural qualities and building heritage values of an existing building forms the empirical material, which is discussed using different...... theoretical lenses. It is proposed that three parameters concerning the ꞌtransformabilityꞌ of the building can contribute to a more nuanced understanding of sustainable transformation: technical aspects, programmatic requirements and narrative value. It is proposed that the concept of ꞌsustainable...
DEFF Research Database (Denmark)
Neergaard, Helle; Robinson, Sarah; Jones, Sally
, as well as the resources they have when they come to the classroom. It also incorporates perspectives from (ii) transformational learning and explores the concept of (iii) nudging from a pedagogical viewpoint, proposing it as an important tool in entrepreneurship education. The study incorporates......This paper develops the concept of ‘pedagogical nudging’ and examines four interventions in an entrepreneurship classroom and the potential it has for student identity transformation. Pedagogical nudging is positioned as a tool, which in the hands of a reflective, professional......) assists students in straddling the divide between identities, the emotions and tensions this elicits, and (iv) transform student understanding. We extend nudging theory into a new territory. Pedagogical nudging techniques may be able to unlock doors and bring our students beyond the unacknowledged...
Legendre's and Kummer's Theorems Again
Indian Academy of Sciences (India)
tember 1895. Gazeta Mate- matica was a true school of math- ematics, that contributed to the formation of many generations of young math enthusiasts. Al- most all romanian mathemati- cians were collaborators of. Gazeta. 2.3 A Useful Inequality. From vp(n!) = n¡sp(n) p¡1 the following useful inequality immediately follows:.
Improved autonomous star identification algorithm
International Nuclear Information System (INIS)
Luo Li-Yan; Xu Lu-Ping; Zhang Hua; Sun Jing-Rong
2015-01-01
The log–polar transform (LPT) is introduced into the star identification because of its rotation invariance. An improved autonomous star identification algorithm is proposed in this paper to avoid the circular shift of the feature vector and to reduce the time consumed in the star identification algorithm using LPT. In the proposed algorithm, the star pattern of the same navigation star remains unchanged when the stellar image is rotated, which makes it able to reduce the star identification time. The logarithmic values of the plane distances between the navigation and its neighbor stars are adopted to structure the feature vector of the navigation star, which enhances the robustness of star identification. In addition, some efforts are made to make it able to find the identification result with fewer comparisons, instead of searching the whole feature database. The simulation results demonstrate that the proposed algorithm can effectively accelerate the star identification. Moreover, the recognition rate and robustness by the proposed algorithm are better than those by the LPT algorithm and the modified grid algorithm. (paper)
DEFF Research Database (Denmark)
Andersen, Nicolai Bo
This paper is about sustainable transformation with a particular focus on listed buildings. It is based on the notion that sustainability is not just a question of energy conditions, but also about the building being robust. Robust architecture means that the building can be maintained and rebuil...
Mehendale, A.; Hagedoorn, Wouter; Lötters, Joost Conrad
2008-01-01
A transformer core includes a stack of a plurality of planar core plates of a magnetically permeable material, which plates each consist of a first and a second sub-part that together enclose at least one opening. The sub-parts can be fitted together via contact faces that are located on either side
Mehendale, A.; Hagedoorn, Wouter; Lötters, Joost Conrad
2010-01-01
A transformer core includes a stack of a plurality of planar core plates of a magnetically permeable material, which plates each consist of a first and a second sub-part that together enclose at least one opening. The sub-parts can be fitted together via contact faces that are located on either side
International Nuclear Information System (INIS)
Murphy, J.H.
1982-01-01
A superconducting transformer having a winding arrangement that provides for current limitation when subjected to a current transient as well as more efficient utilization of radial spacing and winding insulation. Structural innovations disclosed include compressed conical shaped winding layers and a resistive matrix to promote rapid switching of current between parallel windings
Transformation & Metamorphosis
Lott, Debra
2009-01-01
The sculptures of Canadian artist Brian Jungen are a great inspiration for a lesson on creating new forms. Jungen transforms found objects into unique creations without fully concealing their original form or purpose. Frank Stella's sculpture series, including "K.132,2007" made of stainless steel and spray paint, is another great example of…
DEFF Research Database (Denmark)
Enemark, Stig; Dahl Højgaard, Pia
2017-01-01
, was a result of transforming society from a feudal system to a capitalistic and market based economy. This story is interesting in itself - but it also provides a key to understanding the cadastral system of today. The system has evolved over time and now serves a whole range of functions in society. The paper...
Optimized nonorthogonal transforms for image compression.
Guleryuz, O G; Orchard, M T
1997-01-01
The transform coding of images is analyzed from a common standpoint in order to generate a framework for the design of optimal transforms. It is argued that all transform coders are alike in the way they manipulate the data structure formed by transform coefficients. A general energy compaction measure is proposed to generate optimized transforms with desirable characteristics particularly suited to the simple transform coding operation of scalar quantization and entropy coding. It is shown that the optimal linear decoder (inverse transform) must be an optimal linear estimator, independent of the structure of the transform generating the coefficients. A formulation that sequentially optimizes the transforms is presented, and design equations and algorithms for its computation provided. The properties of the resulting transform systems are investigated. In particular, it is shown that the resulting basis are nonorthogonal and complete, producing energy compaction optimized, decorrelated transform coefficients. Quantization issues related to nonorthogonal expansion coefficients are addressed with a simple, efficient algorithm. Two implementations are discussed, and image coding examples are given. It is shown that the proposed design framework results in systems with superior energy compaction properties and excellent coding results.
A Direct Search Algorithm for Global Optimization
Directory of Open Access Journals (Sweden)
Enrique Baeyens
2016-06-01
Full Text Available A direct search algorithm is proposed for minimizing an arbitrary real valued function. The algorithm uses a new function transformation and three simplex-based operations. The function transformation provides global exploration features, while the simplex-based operations guarantees the termination of the algorithm and provides global convergence to a stationary point if the cost function is differentiable and its gradient is Lipschitz continuous. The algorithm’s performance has been extensively tested using benchmark functions and compared to some well-known global optimization algorithms. The results of the computational study show that the algorithm combines both simplicity and efficiency and is competitive with the heuristics-based strategies presently used for global optimization.
Casanova, Henri; Robert, Yves
2008-01-01
""…The authors of the present book, who have extensive credentials in both research and instruction in the area of parallelism, present a sound, principled treatment of parallel algorithms. … This book is very well written and extremely well designed from an instructional point of view. … The authors have created an instructive and fascinating text. The book will serve researchers as well as instructors who need a solid, readable text for a course on parallelism in computing. Indeed, for anyone who wants an understandable text from which to acquire a current, rigorous, and broad vi
DEFF Research Database (Denmark)
Gustavson, Fred G.; Reid, John K.; Wasniewski, Jerzy
2007-01-01
We present subroutines for the Cholesky factorization of a positive-definite symmetric matrix and for solving corresponding sets of linear equations. They exploit cache memory by using the block hybrid format proposed by the authors in a companion article. The matrix is packed into n(n + 1)/2 real...... variables, and the speed is usually better than that of the LAPACK algorithm that uses full storage (n2 variables). Included are subroutines for rearranging a matrix whose upper or lower-triangular part is packed by columns to this format and for the inverse rearrangement. Also included is a kernel...
International Nuclear Information System (INIS)
Hazou, I.A.
1986-01-01
In emission computed tomography one wants to determine the location and intensity of radiation emitted by sources in the presence of an attenuating medium. If the attenuation is known everywhere and equals a constant α in a convex neighborhood of the support of f, then the problem reduces to that of inverting the exponential x-ray transform P/sub α/. The exponential x-ray transform P/sub μ/ with the attenuation μ variable, is of interest mathematically. For the exponential x-ray transform in two dimensions, it is shown that for a large class of approximate δ functions E, convolution kernels K exist for use in the convolution backprojection algorithm. For the case where the attenuation is constant, exact formulas are derived for calculating the convolution kernels from radial point spread functions. From these an exact inversion formula for the constantly attenuated transform is obtained
Watermarking on 3D mesh based on spherical wavelet transform.
Jin, Jian-Qiu; Dai, Min-Ya; Bao, Hu-Jun; Peng, Qun-Sheng
2004-03-01
In this paper we propose a robust watermarking algorithm for 3D mesh. The algorithm is based on spherical wavelet transform. Our basic idea is to decompose the original mesh into a series of details at different scales by using spherical wavelet transform; the watermark is then embedded into the different levels of details. The embedding process includes: global sphere parameterization, spherical uniform sampling, spherical wavelet forward transform, embedding watermark, spherical wavelet inverse transform, and at last resampling the mesh watermarked to recover the topological connectivity of the original model. Experiments showed that our algorithm can improve the capacity of the watermark and the robustness of watermarking against attacks.
Efficient algorithms of multidimensional γ-ray spectra compression
International Nuclear Information System (INIS)
Morhac, M.; Matousek, V.
2006-01-01
The efficient algorithms to compress multidimensional γ-ray events are presented. Two alternative kinds of compression algorithms based on both the adaptive orthogonal and randomizing transforms are proposed. In both algorithms we employ the reduction of data volume due to the symmetry of the γ-ray spectra
Schilders, W.H.A.; Meijer, P.B.L.; Ciggaar, E.
2008-01-01
In this paper we discuss the use of the state-space modelling MOESP algorithm to generate precise information about the number of neurons and hidden layers in dynamic neural networks developed for the behavioural modelling of electronic circuits. The Bartels–Stewart algorithm is used to transform
Firth, Jean M
1992-01-01
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...
Directory of Open Access Journals (Sweden)
Felician ALECU
2012-04-01
Full Text Available XSLT style sheets are designed to transform the XML documents into something else. The two most popular parsers of the moment are the Document Object Model (DOM and the Simple API for XML (SAX. DOM is an official recommendation of the W3C (available at http://www.w3.org/TR/REC-DOM-Level-1, while SAX is a de facto standard. A good parser should be fast, space efficient, rich in functionality and easy to use.
Smith, James L.; Helenberg, Harold W.; Kilsdonk, Dennis J.
1979-01-01
There is provided an improved RF transformer having a single-turn secondary of cylindrical shape and a coiled encapsulated primary contained within the secondary. The coil is tapered so that the narrowest separation between the primary and the secondary is at one end of the coil. The encapsulated primary is removable from the secondary so that a variety of different capacity primaries can be utilized with one secondary.
DEFF Research Database (Denmark)
Majgaard, Klaus
The purpose of this paper is to enhance the conceptual understanding of the mediatory relationship between paradoxes on an organizational and an individual level. It presents a concept of agency that comprises and mediates between a structural and individual pole. The constitution of this agency ...... is achieved through narrative activity that oscillates between the poles and transforms paradoxes through the configuration of plots and metaphors. Empirical cases are introduced in order to illustrate the implications of this understanding....
Hinchey, Michael G. (Inventor); Margaria, Tiziana (Inventor); Rash, James L. (Inventor); Rouff, Christopher A. (Inventor); Steffen, Bernard (Inventor)
2010-01-01
Systems, methods and apparatus are provided through which in some embodiments, automata learning algorithms and techniques are implemented to generate a more complete set of scenarios for requirements based programming. More specifically, a CSP-based, syntax-oriented model construction, which requires the support of a theorem prover, is complemented by model extrapolation, via automata learning. This may support the systematic completion of the requirements, the nature of the requirement being partial, which provides focus on the most prominent scenarios. This may generalize requirement skeletons by extrapolation and may indicate by way of automatically generated traces where the requirement specification is too loose and additional information is required.
General entanglement-assisted transformation for bipartite pure quantum states
Song, Wei; Huang, Yan; Nai-LeLiu; Chen, Zeng-Bing
2007-01-01
We introduce the general catalysts for pure entanglement transformations under local operations and classical communications in such a way that we disregard the profit and loss of entanglement of the catalysts per se. As such, the possibilities of pure entanglement transformations are greatly expanded. We also design an efficient algorithm to detect whether a k × k general catalyst exists for a given entanglement transformation. This algorithm can also be exploited to witness the existence of standard catalysts.
A discrete Fourier transform for virtual memory machines
Galant, David C.
1992-01-01
An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.
BOX-COX transformation and random regression models for fecal egg count data
Directory of Open Access Journals (Sweden)
Marcos Vinicius Silva
2012-01-01
Full Text Available Accurate genetic evaluation of livestock is based on appropriate modeling of phenotypic measurements. In ruminants fecal egg count (FEC is commonly used to measure resistance to nematodes. FEC values are not normally distributed and logarithmic transformations have been used to achieve normality before analysis. However, the transformed data are often not normally distributed, especially when data are extremely skewed. A series of repeated FEC measurements may provide information about the population dynamics of a group or individual. A total of 6,375 FEC measures were obtained for 410 animals between 1992 and 2003 from the Beltsville Agricultural Research Center Angus herd. Original data were transformed using an extension of the Box-Cox transformation to approach normality and to estimate (covariance components. We also proposed using random regression models (RRM for genetic and non-genetic studies of FEC. Phenotypes were analyzed using RRM and restricted maximum likelihood. Within the different orders of Legendre polynomials used, those with more parameters (order 4 adjusted FEC data best. Results indicated that the transformation of FEC data utilizing the Box-Cox transformation family was effective in reducing the skewness and kurtosis, and dramatically increased estimates of heritability, and measurements of FEC obtained in the period between 12 and 26 weeks in a 26-week experimental challenge period are genetically correlated.
Box-Cox Transformation and Random Regression Models for Fecal egg Count Data.
da Silva, Marcos Vinícius Gualberto Barbosa; Van Tassell, Curtis P; Sonstegard, Tad S; Cobuci, Jaime Araujo; Gasbarre, Louis C
2011-01-01
Accurate genetic evaluation of livestock is based on appropriate modeling of phenotypic measurements. In ruminants, fecal egg count (FEC) is commonly used to measure resistance to nematodes. FEC values are not normally distributed and logarithmic transformations have been used in an effort to achieve normality before analysis. However, the transformed data are often still not normally distributed, especially when data are extremely skewed. A series of repeated FEC measurements may provide information about the population dynamics of a group or individual. A total of 6375 FEC measures were obtained for 410 animals between 1992 and 2003 from the Beltsville Agricultural Research Center Angus herd. Original data were transformed using an extension of the Box-Cox transformation to approach normality and to estimate (co)variance components. We also proposed using random regression models (RRM) for genetic and non-genetic studies of FEC. Phenotypes were analyzed using RRM and restricted maximum likelihood. Within the different orders of Legendre polynomials used, those with more parameters (order 4) adjusted FEC data best. Results indicated that the transformation of FEC data utilizing the Box-Cox transformation family was effective in reducing the skewness and kurtosis, and dramatically increased estimates of heritability, and measurements of FEC obtained in the period between 12 and 26 weeks in a 26-week experimental challenge period are genetically correlated.
Electrical transformer handbook
Energy Technology Data Exchange (ETDEWEB)
Hurst, R.W.; Horne, D. (eds.)
2005-07-01
This handbook is a valuable user guide intended for electrical engineering and maintenance personnel, electrical contractors and electrical engineering students. It provides current information on techniques and technologies that can help extend the life of transformers. It discusses transformer testing, monitoring, design, commissioning, retrofitting and other elements involved in keeping electrical transformers in safe and efficient operation. It demonstrates how a power transformer can be put to use and common problems faced by owners. In addition to covering control techniques, testing and maintenance procedures, this handbook covers the power transformer; control electrical power transformer; electrical power transformer; electrical theory transformer; used electrical transformer; down electrical step transformer; electrical manufacturer transformer; electrical picture transformer; electrical transformer work; electrical surplus transformer; current transformer; step down transformer; voltage transformer; step up transformer; isolation transformer; low voltage transformer; toroidal transformer; high voltage transformer; and control power transformer. The handbook includes articles from leading experts on overcurrent protection of transformers; ventilated dry-type transformers; metered load factors for low-voltage, and dry-type transformers in buildings. The maintenance of both dry-type or oil-filled transformers was discussed with reference to sealing, gaskets, oils, moisture and testing. The adoption of dynamic load practices was also discussed along with the reclamation or recycling of used lube oil, transformer dielectric fluids and aged solid insulation. A buyer's guide and directory of transformer manufacturers and suppliers was also included. refs., tabs., figs.
Algorithmic Reflections on Choreography
Directory of Open Access Journals (Sweden)
Pablo Ventura
2016-11-01
Full Text Available In 1996, Pablo Ventura turned his attention to the choreography software Life Forms to find out whether the then-revolutionary new tool could lead to new possibilities of expression in contemporary dance. During the next 2 decades, he devised choreographic techniques and custom software to create dance works that highlight the operational logic of computers, accompanied by computer-generated dance and media elements. This article provides a firsthand account of how Ventura’s engagement with algorithmic concepts guided and transformed his choreographic practice. The text describes the methods that were developed to create computer-aided dance choreographies. Furthermore, the text illustrates how choreography techniques can be applied to correlate formal and aesthetic aspects of movement, music, and video. Finally, the text emphasizes how Ventura’s interest in the wider conceptual context has led him to explore with choreographic means fundamental issues concerning the characteristics of humans and machines and their increasingly profound interdependencies.
Baecklund transformations for discrete Painleve equations: Discrete PII-PV
International Nuclear Information System (INIS)
Sakka, A.; Mugan, U.
2006-01-01
Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations
Homotopy Algorithm for Optimal Control Problems with a Second-order State Constraint
International Nuclear Information System (INIS)
Hermant, Audrey
2010-01-01
This paper deals with optimal control problems with a regular second-order state constraint and a scalar control, satisfying the strengthened Legendre-Clebsch condition. We study the stability of structure of stationary points. It is shown that under a uniform strict complementarity assumption, boundary arcs are stable under sufficiently smooth perturbations of the data. On the contrary, nonreducible touch points are not stable under perturbations. We show that under some reasonable conditions, either a boundary arc or a second touch point may appear. Those results allow us to design an homotopy algorithm which automatically detects the structure of the trajectory and initializes the shooting parameters associated with boundary arcs and touch points.
Wang, Chang; Qin, Xin; Liu, Yan; Zhang, Wenchao
2016-06-01
An adaptive inertia weight particle swarm algorithm is proposed in this study to solve the local optimal problem with the method of traditional particle swarm optimization in the process of estimating magnetic resonance(MR)image bias field.An indicator measuring the degree of premature convergence was designed for the defect of traditional particle swarm optimization algorithm.The inertia weight was adjusted adaptively based on this indicator to ensure particle swarm to be optimized globally and to avoid it from falling into local optimum.The Legendre polynomial was used to fit bias field,the polynomial parameters were optimized globally,and finally the bias field was estimated and corrected.Compared to those with the improved entropy minimum algorithm,the entropy of corrected image was smaller and the estimated bias field was more accurate in this study.Then the corrected image was segmented and the segmentation accuracy obtained in this research was 10% higher than that with improved entropy minimum algorithm.This algorithm can be applied to the correction of MR image bias field.
Quantum walks and search algorithms
Portugal, Renato
2013-01-01
This book addresses an interesting area of quantum computation called quantum walks, which play an important role in building quantum algorithms, in particular search algorithms. Quantum walks are the quantum analogue of classical random walks. It is known that quantum computers have great power for searching unsorted databases. This power extends to many kinds of searches, particularly to the problem of finding a specific location in a spatial layout, which can be modeled by a graph. The goal is to find a specific node knowing that the particle uses the edges to jump from one node to the next. This book is self-contained with main topics that include: Grover's algorithm, describing its geometrical interpretation and evolution by means of the spectral decomposition of the evolution operater Analytical solutions of quantum walks on important graphs like line, cycles, two-dimensional lattices, and hypercubes using Fourier transforms Quantum walks on generic graphs, describing methods to calculate the limiting d...
Usher, P. D.
1997-12-01
William Shakespeare's Hamlet has much evidence to suggest that the Bard was aware of the cosmological models of his time, specifically the geocentric bounded Ptolemaic and Tychonic models, and the infinite Diggesian. Moreover, Shakespeare describes how the Ptolemaic model is to be transformed to the Diggesian. Hamlet's "transformation" is the reason that Claudius, who personifies the Ptolemaic model, summons Rosencrantz and Guildenstern, who personify the Tychonic. Pantometria, written by Leonard Digges and his son Thomas in 1571, contains the first technical use of the word "transformation." At age thirty, Thomas Digges went on to propose his Perfit Description, as alluded to in Act Five where Hamlet's age is given as thirty. In Act Five as well, the words "bore" and "arms" refer to Thomas' vocation as muster-master and his scientific interest in ballistics. England's leading astronomer was also the father of the poet whose encomium introduced the First Folio of 1623. His oldest child Dudley became a member of the Virginia Company and facilitated the writing of The Tempest. Taken as a whole, such manifold connections to Thomas Digges support Hotson's contention that Shakespeare knew the Digges family. Rosencrantz and Guildenstern in Hamlet bear Danish names because they personify the Danish model, while the king's name is latinized like that of Claudius Ptolemaeus. The reason Shakespeare anglicized "Amleth" to "Hamlet" was because he saw a parallel between Book Three of Saxo Grammaticus and the eventual triumph of the Diggesian model. But Shakespeare eschewed Book Four, creating this particular ending from an infinity of other possibilities because it "suited his purpose," viz. to celebrate the concept of a boundless universe of stars like the Sun.
Wolfgang, F.; Nicol, J.
1962-11-01
Transformer apparatus is designed for measuring the amount of a paramagnetic substance dissolved or suspended in a diamagnetic liquid. The apparatus consists of a cluster of tubes, some of which are closed and have sealed within the diamagnetic substance without any of the paramagnetic material. The remaining tubes are open to flow of the mix- ture. Primary and secondary conductors are wrapped around the tubes in such a way as to cancel noise components and also to produce a differential signal on the secondaries based upon variations of the content of the paramagnetic material. (AEC)
McLyman, Colonel Wm. T.
1996-01-01
None given. From first Par: Many spacecraft (S/C) and surface rovers require the transfer of signals and power across rotating interfaces. Science instruments, antennas and solar arrays are elements needing rotary power transfer for certain (S/C) configurations. Delivery of signal and power has mainly been done by using the simplest means, the slip ring approach. This approach, although simple, leaves debris generating noise over a period of time...The rotary transformer is a good alternative to slip rings for signal and power transfer.
On the Cooley-Turkey Fast Fourier algorithm for arbitrary factors ...
African Journals Online (AJOL)
Atonuje and Okonta in [1] developed the Cooley-Turkey Fast Fourier transform algorithm and its application to the Fourier transform of discretely sampled data points N, expressed in terms of a power y of 2. In this paper, we extend the formalism of [1] Cookey-Turkey Fast Fourier transform algorithm. The method is developed ...
Complex nonlinear Fourier transform and its inverse
International Nuclear Information System (INIS)
Saksida, Pavle
2015-01-01
We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)
Combined Sparsifying Transforms for Compressive Image Fusion
Directory of Open Access Journals (Sweden)
ZHAO, L.
2013-11-01
Full Text Available In this paper, we present a new compressive image fusion method based on combined sparsifying transforms. First, the framework of compressive image fusion is introduced briefly. Then, combined sparsifying transforms are presented to enhance the sparsity of images. Finally, a reconstruction algorithm based on the nonlinear conjugate gradient is presented to get the fused image. The simulations demonstrate that by using the combined sparsifying transforms better results can be achieved in terms of both the subjective visual effect and the objective evaluation indexes than using only a single sparsifying transform for compressive image fusion.
Parallel Monte Carlo Search for Hough Transform
Lopes, Raul H. C.; Franqueira, Virginia N. L.; Reid, Ivan D.; Hobson, Peter R.
2017-10-01
We investigate the problem of line detection in digital image processing and in special how state of the art algorithms behave in the presence of noise and whether CPU efficiency can be improved by the combination of a Monte Carlo Tree Search, hierarchical space decomposition, and parallel computing. The starting point of the investigation is the method introduced in 1962 by Paul Hough for detecting lines in binary images. Extended in the 1970s to the detection of space forms, what came to be known as Hough Transform (HT) has been proposed, for example, in the context of track fitting in the LHC ATLAS and CMS projects. The Hough Transform transfers the problem of line detection, for example, into one of optimization of the peak in a vote counting process for cells which contain the possible points of candidate lines. The detection algorithm can be computationally expensive both in the demands made upon the processor and on memory. Additionally, it can have a reduced effectiveness in detection in the presence of noise. Our first contribution consists in an evaluation of the use of a variation of the Radon Transform as a form of improving theeffectiveness of line detection in the presence of noise. Then, parallel algorithms for variations of the Hough Transform and the Radon Transform for line detection are introduced. An algorithm for Parallel Monte Carlo Search applied to line detection is also introduced. Their algorithmic complexities are discussed. Finally, implementations on multi-GPU and multicore architectures are discussed.
Energy Technology Data Exchange (ETDEWEB)
Fontana, W.
1990-12-13
In this paper complex adaptive systems are defined by a self- referential loop in which objects encode functions that act back on these objects. A model for this loop is presented. It uses a simple recursive formal language, derived from the lambda-calculus, to provide a semantics that maps character strings into functions that manipulate symbols on strings. The interaction between two functions, or algorithms, is defined naturally within the language through function composition, and results in the production of a new function. An iterated map acting on sets of functions and a corresponding graph representation are defined. Their properties are useful to discuss the behavior of a fixed size ensemble of randomly interacting functions. This function gas'', or Turning gas'', is studied under various conditions, and evolves cooperative interaction patterns of considerable intricacy. These patterns adapt under the influence of perturbations consisting in the addition of new random functions to the system. Different organizations emerge depending on the availability of self-replicators.
Algorithms as fetish: Faith and possibility in algorithmic work
Directory of Open Access Journals (Sweden)
Suzanne L Thomas
2018-01-01
Full Text Available Algorithms are powerful because we invest in them the power to do things. With such promise, they can transform the ordinary, say snapshots along a robotic vacuum cleaner’s route, into something much more, such as a clean home. Echoing David Graeber’s revision of fetishism, we argue that this easy slip from technical capabilities to broader claims betrays not the “magic” of algorithms but rather the dynamics of their exchange. Fetishes are not indicators of false thinking, but social contracts in material form. They mediate emerging distributions of power often too nascent, too slippery or too disconcerting to directly acknowledge. Drawing primarily on 2016 ethnographic research with computer vision professionals, we show how faith in what algorithms can do shapes the social encounters and exchanges of their production. By analyzing algorithms through the lens of fetishism, we can see the social and economic investment in some people’s labor over others. We also see everyday opportunities for social creativity and change. We conclude that what is problematic about algorithms is not their fetishization but instead their stabilization into full-fledged gods and demons – the more deserving objects of critique.
International Nuclear Information System (INIS)
Beer, G.
2003-01-01
State forestry company Lesy, s.p., Banska Bystrica have chosen Austrian state forestry company to operate as their restructuring advisor. 20 million Sk (0.142 mn Euro) were assigned to transformation of Lesy SR from a state enterprise to a state-owned joint-stock company. The whole process should take two years. The joint-stock company should be established at the beginning of next year. 'What we have to do first is to define the objectives and perspectives of this restructuring,' claims new director, Karol Vins. The new boss recalled all directors of the 26 branches. They were given a lot of freedom to trade with wood. The new management wants to establish a profit-making company. At the moment the company has total claims of 600 million Sk (14.59 million Eur) it will have to provision for
Jones, Patricia S; Zhang, Xinwei Esther; Meleis, Afaf I
2003-11-01
Asian American immigrant women engaged in filial caregiving are at special risk for health problems due to complex contextual factors related to immigration, cultural traditions, and role transition. This study examines the experience of two groups of immigrant Asian American women who are caring for older parents. A total of 41 women (22 Chinese American and 19 Filipino American) were interviewed in a study based on Strauss and Corbin's grounded theory methodology. The women were determined to be loyal to their traditional culture, which included strong filial values, while adapting to a new culture. Through the struggle of meeting role expectations and coping with paradox, the women mobilized personal and family resources to transform vulnerability into strength and well-being.
Rutherford, Ernest
2012-01-01
Radioactive Transformations describes Ernest Rutherford's Nobel Prize-winning investigations into the mysteries of radioactive matter. In this historic work, Rutherford outlines the scientific investigations that led to and coincided with his own research--including the work of Wilhelm Rӧntgen, J. J. Thomson, and Marie Curie--and explains in detail the experiments that provided a glimpse at special relativity, quantum mechanics, and other concepts that would shape modern physics. This new edition features a comprehensive introduction by Nobel Laureate Frank Wilczek which engagingly explains how Rutherford's early research led to a better understanding of topics as diverse as the workings of the atom's nucleus, the age of our planet, and the fusion in stars.
Entanglement-continuous unitary transformations
Energy Technology Data Exchange (ETDEWEB)
Sahin, Serkan; Orus, Roman [Institute of Physics, Johannes Gutenberg University, 55099 Mainz (Germany)
2016-07-01
In this talk we present a new algorithm for quantum many-body systems using continuous unitary transformations (CUT) and tensor networks (TNs). With TNs we are able to approximate the solution to the flow equations that lie at the heart of continuous unitary transformations. We call this method Entanglement-Continuous Unitary Transformations (eCUT). It allows us to compute expectation values of local observables as well as tensor network representations of ground states and low-energy excited states. An implementation of the method is shown for 1d systems using matrix product operators. We show preliminary results for the 1d transverse-field Ising model to demonstrate the feasibility of the method.
Theoretical Provision of Tax Transformation
Directory of Open Access Journals (Sweden)
Feofanova Iryna V.
2016-05-01
Full Text Available The article is aimed at defining the questions, giving answers to which is necessary for scientific substantiation of the tax transformation in Ukraine. The article analyzes the structural-logical relationships of the theories, providing substantiation of tax systems and transformation of them. Various views on the level of both the tax burden and the distribution of the tax burden between big and small business have been systematized. The issues that require theoretical substantiation when choosing a model of tax system have been identified. It is determined that shares of both indirect and direct taxes and their rates can be substantiated by calculations on the basis of statistical data. The results of the presented research can be used to develop the algorithm for theoretical substantiation of tax transformation
Hegazy, Maha A.; Lotfy, Hayam M.; Mowaka, Shereen; Mohamed, Ekram Hany
2016-07-01
Wavelets have been adapted for a vast number of signal-processing applications due to the amount of information that can be extracted from a signal. In this work, a comparative study on the efficiency of continuous wavelet transform (CWT) as a signal processing tool in univariate regression and a pre-processing tool in multivariate analysis using partial least square (CWT-PLS) was conducted. These were applied to complex spectral signals of ternary and quaternary mixtures. CWT-PLS method succeeded in the simultaneous determination of a quaternary mixture of drotaverine (DRO), caffeine (CAF), paracetamol (PAR) and p-aminophenol (PAP, the major impurity of paracetamol). While, the univariate CWT failed to simultaneously determine the quaternary mixture components and was able to determine only PAR and PAP, the ternary mixtures of DRO, CAF, and PAR and CAF, PAR, and PAP. During the calculations of CWT, different wavelet families were tested. The univariate CWT method was validated according to the ICH guidelines. While for the development of the CWT-PLS model a calibration set was prepared by means of an orthogonal experimental design and their absorption spectra were recorded and processed by CWT. The CWT-PLS model was constructed by regression between the wavelet coefficients and concentration matrices and validation was performed by both cross validation and external validation sets. Both methods were successfully applied for determination of the studied drugs in pharmaceutical formulations.
Electrocardiogram ST-Segment Morphology Delineation Method Using Orthogonal Transformations.
Directory of Open Access Journals (Sweden)
Miha Amon
Full Text Available 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
Directory of Open Access Journals (Sweden)
Johnn Alejandro Quintero Salazar
2012-08-01
Full Text Available Este documento presenta una metodología basada en algoritmos genéticos que permite adelantar el reordenamiento del parque de transformadores existente en el nivel de tensión I de los sistemas de distribución de Bogotá D.C., Colombia, con el fin de maximizar el reconocimiento de activos que el ente regulador CREG (Comisión Reguladora de Energía y Gas realiza a los distintos operadores de red, según lo establecido en la resolución 097 de 2008. Para la aplicación del algoritmo se obtuvieron mediciones de potencia activa máxima para cada hora del año 2009 en un conjunto de 94 transformadores de diferentes capacidades, escogidos de forma aleatoria, instalados en el sistema de distribución de CODENSA S.A. ESP, empresa encargada de prestar el servicio de energía eléctrica en la ciudad de Bogotá D.C. Con esta información se construyeron curvas de carga diarias representativas y se elaboró una base de datos que contiene los costos operativos del movimiento de los equipos y de las tarifas, a partir de los cuales fue posible modelar la función objetivo y las restricciones del problema, obteniéndose un elevado número de combinaciones posibles (alrededor de 1*10(134 debido al gran número de nodos y de transformadores presentes en el sistema de distribución. La búsqueda convencional de una solución en la anterior situación implicaría el empleo de tiempos prohibitivos, por lo cual se implementó un algoritmo genético clásico, obteniéndose de esta manera una solución óptima que ofrece una ganancia económica en el primer año, asociada al incremento en el cargo por uso, de $ 253.446.362,47 (COP, ganancias que podrían verse incrementadas considerablemente al ejecutar el algoritmo en parques de transformadores más grandes.This paper presents a methodology based on genetic algorithms that allows the reordering of the existing park transformers voltage level I of the distribution systems of Bogotá city, Colombia, in order to
Mobile robot motion estimation using Hough transform
Aldoshkin, D. N.; Yamskikh, T. N.; Tsarev, R. Yu
2018-05-01
This paper proposes an algorithm for estimation of mobile robot motion. The geometry of surrounding space is described with range scans (samples of distance measurements) taken by the mobile robot’s range sensors. A similar sample of space geometry in any arbitrary preceding moment of time or the environment map can be used as a reference. The suggested algorithm is invariant to isotropic scaling of samples or map that allows using samples measured in different units and maps made at different scales. The algorithm is based on Hough transform: it maps from measurement space to a straight-line parameters space. In the straight-line parameters, space the problems of estimating rotation, scaling and translation are solved separately breaking down a problem of estimating mobile robot localization into three smaller independent problems. The specific feature of the algorithm presented is its robustness to noise and outliers inherited from Hough transform. The prototype of the system of mobile robot orientation is described.
The derivation of distributed termination detection algorithms from garbage collection schemes
Tel, G.; Mattern, F.
1990-01-01
It is shown that the termination detection problem for distributed computations can be modelled as an instance of the garbage collection problem. Consequently, algorithms for the termination detection problem are obtained by applying transformations to garbage collection algorithms. The
CSIR Research Space (South Africa)
Mlambo, CS
2015-01-01
Full Text Available In this paper, implementations of three Hough Transform based fingerprint alignment algorithms are analyzed with respect to time complexity on Java Card environment. Three algorithms are: Local Match Based Approach (LMBA), Discretized Rotation Based...
GPU-Vote: A Framework for Accelerating Voting Algorithms on GPU.
Braak, van den G.J.W.; Nugteren, C.; Mesman, B.; Corporaal, H.; Kaklamanis, C.; Papatheodorou, T.; Spirakis, P.G.
2012-01-01
Voting algorithms, such as histogram and Hough transforms, are frequently used algorithms in various domains, such as statistics and image processing. Algorithms in these domains may be accelerated using GPUs. Implementing voting algorithms efficiently on a GPU however is far from trivial due to
An optical Fourier transform coprocessor with direct phase determination.
Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D
2017-10-20
The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.
Studying entanglement-assisted entanglement transformation
International Nuclear Information System (INIS)
Hsu Liyi
2004-01-01
In this paper, we study catalysis of entanglement transformations for n-level pure entangled states. We propose an algorithm of finding the required catalystic entanglement. We introduce several examples by way of demonstration. We evaluate the lower and upper bound of the required inequalities for deciding whether there are m-level appropriate catalyst states for entanglement transformations for two n-level pure entangled states
Pseudo-deterministic Algorithms
Goldwasser , Shafi
2012-01-01
International audience; In this talk we describe a new type of probabilistic algorithm which we call Bellagio Algorithms: a randomized algorithm which is guaranteed to run in expected polynomial time, and to produce a correct and unique solution with high probability. These algorithms are pseudo-deterministic: they can not be distinguished from deterministic algorithms in polynomial time by a probabilistic polynomial time observer with black box access to the algorithm. We show a necessary an...
Multidimensional Scaling Localization Algorithm in Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Zhang Dongyang
2014-02-01
Full Text Available Due to the localization algorithm in large-scale wireless sensor network exists shortcomings both in positioning accuracy and time complexity compared to traditional localization algorithm, this paper presents a fast multidimensional scaling location algorithm. By positioning algorithm for fast multidimensional scaling, fast mapping initialization, fast mapping and coordinate transform can get schematic coordinates of node, coordinates Initialize of MDS algorithm, an accurate estimate of the node coordinates and using the PRORUSTES to analysis alignment of the coordinate and final position coordinates of nodes etc. There are four steps, and the thesis gives specific implementation steps of the algorithm. Finally, compared with stochastic algorithms and classical MDS algorithm experiment, the thesis takes application of specific examples. Experimental results show that: the proposed localization algorithm has fast multidimensional scaling positioning accuracy in ensuring certain circumstances, but also greatly improves the speed of operation.
Kanter, Rosabeth Moss
2008-01-01
Large corporations have long been seen as lumbering, inflexible, bureaucratic--and clueless about global developments. But recently some multinationals seem to be transforming themselves: They're engaging employees, moving quickly, and introducing innovations that show true connection with the world. Harvard Business School's Kanter ventured with a research team inside a dozen global giants--including IBM, Procter & Gamble, Omron, CEMEX, Cisco, and Banco Real--to discover what has been driving the change. After conducting more than 350 interviews on five continents, she and her colleagues came away with a strong sense that we are witnessing the dawn of a new model of corporate power: The coordination of actions and decisions on the front lines now appears to stem from widely shared values and a sturdy platform of common processes and technology, not from top-down decrees. In particular, the values that engage the passions of far-flung workforces stress openness, inclusion, and making the world a better place. Through this shift in what might be called their guidance systems, the companies have become as creative and nimble as much smaller ones, even while taking on social and environmental challenges of a scale that only large enterprises could attempt. IBM, for instance, has created a nonprofit partnership, World Community Grid, through which any organization or individual can donate unused computing power to research projects and see what is being done with the donation in real time. IBM has gained an inspiring showcase for its new technology, helped business partners connect with the company in a positive way, and offered individuals all over the globe the chance to contribute to something big.
[A new peak detection algorithm of Raman spectra].
Jiang, Cheng-Zhi; Sun, Qiang; Liu, Ying; Liang, Jing-Qiu; An, Yan; Liu, Bing
2014-01-01
The authors proposed a new Raman peak recognition method named bi-scale correlation algorithm. The algorithm uses the combination of the correlation coefficient and the local signal-to-noise ratio under two scales to achieve Raman peak identification. We compared the performance of the proposed algorithm with that of the traditional continuous wavelet transform method through MATLAB, and then tested the algorithm with real Raman spectra. The results show that the average time for identifying a Raman spectrum is 0.51 s with the algorithm, while it is 0.71 s with the continuous wavelet transform. When the signal-to-noise ratio of Raman peak is greater than or equal to 6 (modern Raman spectrometers feature an excellent signal-to-noise ratio), the recognition accuracy with the algorithm is higher than 99%, while it is less than 84% with the continuous wavelet transform method. The mean and the standard deviations of the peak position identification error of the algorithm are both less than that of the continuous wavelet transform method. Simulation analysis and experimental verification prove that the new algorithm possesses the following advantages: no needs of human intervention, no needs of de-noising and background removal operation, higher recognition speed and higher recognition accuracy. The proposed algorithm is operable in Raman peak identification.
Direct numerical reconstruction of conductivities in three dimensions using scattering transforms
DEFF Research Database (Denmark)
Bikowski, Jutta; Knudsen, Kim; Mueller, Jennifer L
2011-01-01
A direct three-dimensional EIT reconstruction algorithm based on complex geometrical optics solutions and a nonlinear scattering transform is presented and implemented for spherically symmetric conductivity distributions. The scattering transform is computed both with a Born approximation and from...
Super-Encryption Implementation Using Monoalphabetic Algorithm and XOR Algorithm for Data Security
Rachmawati, Dian; Andri Budiman, Mohammad; Aulia, Indra
2018-03-01
The exchange of data that occurs offline and online is very vulnerable to the threat of data theft. In general, cryptography is a science and art to maintain data secrecy. An encryption is a cryptography algorithm in which data is transformed into cipher text, which is something that is unreadable and meaningless so it cannot be read or understood by other parties. In super-encryption, two or more encryption algorithms are combined to make it more secure. In this work, Monoalphabetic algorithm and XOR algorithm are combined to form a super- encryption. Monoalphabetic algorithm works by changing a particular letter into a new letter based on existing keywords while the XOR algorithm works by using logic operation XOR Since Monoalphabetic algorithm is a classical cryptographic algorithm and XOR algorithm is a modern cryptographic algorithm, this scheme is expected to be both easy-to-implement and more secure. The combination of the two algorithms is capable of securing the data and restoring it back to its original form (plaintext), so the data integrity is still ensured.
Fast parallel approach for 2-D DHT-based real-valued discrete Gabor transform.
Tao, Liang; Kwan, Hon Keung
2009-12-01
Two-dimensional fast Gabor transform algorithms are useful for real-time applications due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT). This paper presents two block time-recursive algorithms for 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform and develops a fast parallel approach for the implementation of the two algorithms. The computational complexity of the proposed parallel approach is analyzed and compared with that of the existing 2-D CDGT algorithms. The results indicate that the proposed parallel approach is attractive for real time image processing.
Complementing SRCNN by Transformed Self-Exemplars
DEFF Research Database (Denmark)
Aakerberg, Andreas; Rasmussen, Christoffer Bøgelund; Nasrollahi, Kamal
2017-01-01
, namelythe one found in Single Image Super-Resolution from Transformed Self-Exemplars [7] and the Super-Resolution Convolutional Neural Networkfrom [4]. The combination of these two, through an alpha-blending, hasresulted in a system that outperforms state-of-the-art super-resolutionalgorithms on public......Super-resolution algorithms are used to improve the qualityand resolution of low-resolution images. These algorithms can be dividedinto two classes of hallucination- and reconstruction-based ones. Theimprovement factors of these algorithms are limited, however, previousresearch [10], [9] has shown...
Fourier-transforming with quantum annealers
Directory of Open Access Journals (Sweden)
Itay eHen
2014-07-01
Full Text Available We introduce a set of quantum adiabatic evolutions that we argue may be used as `building blocks', or subroutines, in the onstruction of an adiabatic algorithm that executes Quantum Fourier Transform (QFT with the same complexity and resources as its gate-model counterpart. One implication of the above construction is the theoretical feasibility of implementing Shor's algorithm for integer factorization in an optimal manner, and any other algorithm that makes use of QFT, on quantum annealing devices. We discuss the possible advantages, as well as the limitations, of the proposed approach as well as its relation to traditional adiabatic quantum computation.
Impact of data transformation and preprocessing in supervised ...
African Journals Online (AJOL)
Impact of data transformation and preprocessing in supervised learning ... Nowadays, the ideas of integrating machine learning techniques in power system has ... The proposed algorithm used Python-based split train and k-fold model ...
Hamiltonian Algorithm Sound Synthesis
大矢, 健一
2013-01-01
Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.
Progressive geometric algorithms
Alewijnse, S.P.A.; Bagautdinov, T.M.; de Berg, M.T.; Bouts, Q.W.; ten Brink, Alex P.; Buchin, K.A.; Westenberg, M.A.
2015-01-01
Progressive algorithms are algorithms that, on the way to computing a complete solution to the problem at hand, output intermediate solutions that approximate the complete solution increasingly well. We present a framework for analyzing such algorithms, and develop efficient progressive algorithms
Progressive geometric algorithms
Alewijnse, S.P.A.; Bagautdinov, T.M.; Berg, de M.T.; Bouts, Q.W.; Brink, ten A.P.; Buchin, K.; Westenberg, M.A.
2014-01-01
Progressive algorithms are algorithms that, on the way to computing a complete solution to the problem at hand, output intermediate solutions that approximate the complete solution increasingly well. We present a framework for analyzing such algorithms, and develop efficient progressive algorithms
Medical image compression with fast Hartley transform
International Nuclear Information System (INIS)
Paik, C.H.; Fox, M.D.
1988-01-01
The purpose of data compression is storage and transmission of images with minimization of memory for storage and bandwidth for transmission, while maintaining robustness in the presence of transmission noise or storage medium errors. Here, the fast Hartley transform (FHT) is used for transformation and a new thresholding method is devised. The FHT is used instead of the fast Fourier transform (FFT), thus providing calculation at least as fast as that of the fastest algorithm of FFT. This real numbered transform requires only half the memory array space for saving of transform coefficients and allows for easy implementation on very large-scale integrated circuits because of the use of the same formula for both forward and inverse transformation and the conceptually straightforward algorithm. Threshold values were adaptively selected according to the correlation factor of each block of equally divided blocks of the image. Therefore, this approach provided a coding scheme that included maximum information with minimum image bandwidth. Overall, the results suggested that the Hartley transform adaptive thresholding approach results in improved fidelity, shorter decoding time, and greater robustness in the presence of noise than previous approaches
DEFF Research Database (Denmark)
Bucher, Taina
2017-01-01
the notion of the algorithmic imaginary. It is argued that the algorithmic imaginary – ways of thinking about what algorithms are, what they should be and how they function – is not just productive of different moods and sensations but plays a generative role in moulding the Facebook algorithm itself...... of algorithms affect people's use of these platforms, if at all? To help answer these questions, this article examines people's personal stories about the Facebook algorithm through tweets and interviews with 25 ordinary users. To understand the spaces where people and algorithms meet, this article develops...
Energy Technology Data Exchange (ETDEWEB)
Geist, G.A. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.; Howell, G.W. [Florida Inst. of Tech., Melbourne, FL (United States). Dept. of Applied Mathematics; Watkins, D.S. [Washington State Univ., Pullman, WA (United States). Dept. of Pure and Applied Mathematics
1997-11-01
The BR algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. It is a bulge-chasing algorithm like the QR algorithm, but, unlike the QR algorithm, it is well adapted to computing the eigenvalues of the narrowband, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes the BR algorithm and gives numerical evidence that it works well in conjunction with the Lanczos process. On the biggest problems run so far, the BR algorithm beats the QR algorithm by a factor of 30--60 in computing time and a factor of over 100 in matrix storage space.
The Bargmann transform and canonical transformations
International Nuclear Information System (INIS)
Villegas-Blas, Carlos
2002-01-01
This paper concerns a relationship between the kernel of the Bargmann transform and the corresponding canonical transformation. We study this fact for a Bargmann transform introduced by Thomas and Wassell [J. Math. Phys. 36, 5480-5505 (1995)]--when the configuration space is the two-sphere S 2 and for a Bargmann transform that we introduce for the three-sphere S 3 . It is shown that the kernel of the Bargmann transform is a power series in a function which is a generating function of the corresponding canonical transformation (a classical analog of the Bargmann transform). We show in each case that our canonical transformation is a composition of two other canonical transformations involving the complex null quadric in C 3 or C 4 . We also describe quantizations of those two other canonical transformations by dealing with spaces of holomorphic functions on the aforementioned null quadrics. Some of these quantizations have been studied by Bargmann and Todorov [J. Math. Phys. 18, 1141-1148 (1977)] and the other quantizations are related to the work of Guillemin [Integ. Eq. Operator Theory 7, 145-205 (1984)]. Since suitable infinite linear combinations of powers of the generating functions are coherent states for L 2 (S 2 ) or L 2 (S 3 ), we show finally that the studied Bargmann transforms are actually coherent states transforms
Quantitative Comparison of Tolerance-Based Feature Transforms
Reniers, Dennie; Telea, Alexandru
2006-01-01
Tolerance-based feature transforms (TFTs) assign to each pixel in an image not only the nearest feature pixels on the boundary (origins), but all origins from the minimum distance up to a user-defined tolerance. In this paper, we compare four simple-to-implement methods for computing TFTs for binary images. Of these, two are novel methods and two extend existing distance transform algorithms. We quantitatively and qualitatively compare all algorithms on speed and accuracy of both distance and...
Cryptanalysis of Application of Laplace Transform for Cryptography
Gençoğlu Muharrem Tuncay
2017-01-01
Although Laplace Transform is a good application field in the design of cryptosystems, many cryptographic algorithm proposals become unsatisfactory for secure communication. In this cryptanalysis study, one of the significant disadvantages of the proposed algorithm is performed with only statistical test of security analysis. In this study, Explaining what should be considered when performing security analysis of Laplace Transform based encryption systems and using basic mathematical rules, p...
Algorithmically specialized parallel computers
Snyder, Lawrence; Gannon, Dennis B
1985-01-01
Algorithmically Specialized Parallel Computers focuses on the concept and characteristics of an algorithmically specialized computer.This book discusses the algorithmically specialized computers, algorithmic specialization using VLSI, and innovative architectures. The architectures and algorithms for digital signal, speech, and image processing and specialized architectures for numerical computations are also elaborated. Other topics include the model for analyzing generalized inter-processor, pipelined architecture for search tree maintenance, and specialized computer organization for raster
A Motion Estimation Algorithm Using DTCWT and ARPS
Directory of Open Access Journals (Sweden)
Unan Y. Oktiawati
2013-09-01
Full Text Available In this paper, a hybrid motion estimation algorithm utilizing the Dual Tree Complex Wavelet Transform (DTCWT and the Adaptive Rood Pattern Search (ARPS block is presented. The proposed algorithm first transforms each video sequence with DTCWT. The frame n of the video sequence is used as a reference input and the frame n+2 is used to find the motion vector. Next, the ARPS block search algorithm is carried out and followed by an inverse DTCWT. The motion compensation is then carried out on each inversed frame n and motion vector. The results show that PSNR can be improved for mobile device without depriving its quality. The proposed algorithm also takes less memory usage compared to the DCT-based algorithm. The main contribution of this work is a hybrid wavelet-based motion estimation algorithm for mobile devices. Other contribution is the visual quality scoring system as used in section 6.
Modeling of austenite to ferrite transformation
Indian Academy of Sciences (India)
395–398. c Indian Academy of Sciences. Modeling of austenite to ferrite transformation. MOHSEN KAZEMINEZHAD. ∗. Department of Materials Science and Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran. MS received 17 January 2011; revised 9 July 2011. Abstract. In this research, an algorithm ...
Improved transformer protection using probabilistic neural network ...
African Journals Online (AJOL)
This article presents a novel technique to distinguish between magnetizing inrush current and internal fault current of power transformer. An algorithm has been developed around the theme of the conventional differential protection method in which parallel combination of Probabilistic Neural Network (PNN) and Power ...
Computation of watersheds based on parallel graph algorithms
Meijster, A.; Roerdink, J.B.T.M.; Maragos, P; Schafer, RW; Butt, MA
1996-01-01
In this paper the implementation of a parallel watershed algorithm is described. The algorithm has been implemented on a Cray J932, which is a shared memory architecture with 32 processors. The watershed transform has generally been considered to be inherently sequential, but recently a few research
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory foll...... follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure....
Directory of Open Access Journals (Sweden)
Ümit Budak
2017-12-01
Full Text Available Hough transform (HT is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its shape detection performance, in this paper, we proposed neutrosophic Hough transform (NHT. As it was proved earlier, neutrosophy theory based image processing applications were successful in noisy environments. To this end, the Hough space is initially transferred into the NS domain by calculating the NS membership triples (T, I, and F. An indeterminacy filtering is constructed where the neighborhood information is used in order to remove the indeterminacy in the spatial neighborhood of neutrosophic Hough space. The potential peaks are detected based on thresholding on the neutrosophic Hough space, and these peak locations are then used to detect the lines in the image domain. Extensive experiments on noisy and noise-free images are performed in order to show the efficiency of the proposed NHT algorithm. We also compared our proposed NHT with traditional HT and fuzzy HT methods on variety of images. The obtained results showed the efficiency of the proposed NHT on noisy images.
Army Maintenance System Transformation
National Research Council Canada - National Science Library
Gilbertson, Frank V
2006-01-01
.... Used in conjunction with pertinent historical data and developed with Army transformation goals in mind, General Systems thinking can provide the framework for guiding maintenance transformation...
Graph Creation, Visualisation and Transformation
Directory of Open Access Journals (Sweden)
Maribel Fernández
2010-03-01
Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.
A Novel Parallel Algorithm for Edit Distance Computation
Directory of Open Access Journals (Sweden)
Muhammad Murtaza Yousaf
2018-01-01
Full Text Available The edit distance between two sequences is the minimum number of weighted transformation-operations that are required to transform one string into the other. The weighted transformation-operations are insert, remove, and substitute. Dynamic programming solution to find edit distance exists but it becomes computationally intensive when the lengths of strings become very large. This work presents a novel parallel algorithm to solve edit distance problem of string matching. The algorithm is based on resolving dependencies in the dynamic programming solution of the problem and it is able to compute each row of edit distance table in parallel. In this way, it becomes possible to compute the complete table in min(m,n iterations for strings of size m and n whereas state-of-the-art parallel algorithm solves the problem in max(m,n iterations. The proposed algorithm also increases the amount of parallelism in each of its iteration. The algorithm is also capable of exploiting spatial locality while its implementation. Additionally, the algorithm works in a load balanced way that further improves its performance. The algorithm is implemented for multicore systems having shared memory. Implementation of the algorithm in OpenMP shows linear speedup and better execution time as compared to state-of-the-art parallel approach. Efficiency of the algorithm is also proven better in comparison to its competitor.
Quantum Computation and Algorithms
International Nuclear Information System (INIS)
Biham, O.; Biron, D.; Biham, E.; Grassi, M.; Lidar, D.A.
1999-01-01
It is now firmly established that quantum algorithms provide a substantial speedup over classical algorithms for a variety of problems, including the factorization of large numbers and the search for a marked element in an unsorted database. In this talk I will review the principles of quantum algorithms, the basic quantum gates and their operation. The combination of superposition and interference, that makes these algorithms efficient, will be discussed. In particular, Grover's search algorithm will be presented as an example. I will show that the time evolution of the amplitudes in Grover's algorithm can be found exactly using recursion equations, for any initial amplitude distribution
A practical Hadamard transform spectrometer for astronomical application
Tai, M. H.
1977-01-01
The mathematical properties of Hadamard matrices and their application to spectroscopy are discussed. A comparison is made between Fourier and Hadamard transform encoding in spectrometry. The spectrometer is described and its laboratory performance evaluated. The algorithm and programming of inverse transform are given. A minicomputer is used to recover the spectrum.
MANAGER PRINCIPLES AS BASIS OF MANAGEMENT STYLE TRANSFORMATION
R. A. Kopytov
2011-01-01
The paper considers an approach which is based on non-conventional mechanisms of management style formation. The preset level of sustainable management is maintained by self-organized environment created in the process of management style transformation in efficient management principles. Their efficiency is checked within an adaptive algorithm. The algorithm is developed on the basis of combination of evaluative tools and base of operational proves. The operating algorithm capability is te...
Cyclic transformation of orbital angular momentum modes
International Nuclear Information System (INIS)
Schlederer, Florian; Krenn, Mario; Fickler, Robert; Malik, Mehul; Zeilinger, Anton
2016-01-01
The spatial modes of photons are one realization of a QuDit, a quantum system that is described in a D-dimensional Hilbert space. In order to perform quantum information tasks with QuDits, a general class of D-dimensional unitary transformations is needed. Among these, cyclic transformations are an important special case required in many high-dimensional quantum communication protocols. In this paper, we experimentally demonstrate a cyclic transformation in the high-dimensional space of photonic orbital angular momentum (OAM). Using simple linear optical components, we show a successful four-fold cyclic transformation of OAM modes. Interestingly, our experimental setup was found by a computer algorithm. In addition to the four-cyclic transformation, the algorithm also found extensions to higher-dimensional cycles in a hybrid space of OAM and polarization. Besides being useful for quantum cryptography with QuDits, cyclic transformations are key for the experimental production of high-dimensional maximally entangled Bell-states. (paper)
Negotiated Grammar Transformation
V. Zaytsev (Vadim)
2012-01-01
htmlabstractIn this paper, we study controlled adaptability of metamodel transformations. We consider one of the most rigid metamodel transformation formalisms — automated grammar transformation with operator suites, where a transformation script is built in such a way that it is essentially meant
International Nuclear Information System (INIS)
Kibler, M.; Hage Hassan, M.
1991-04-01
A bibliography on the Hurwitz transformations is given. We deal here, with some details, with two particular Hurwitz transformations, viz, the R 4 → R 3 Kustaanheimo-Stiefel transformation and its R 8 → R 5 compact extension. These transformations are derived in the context of Fock-Bargmann-Schwinger calculus with special emphasis on angular momentum theory
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...
a pyramid algorithm for the haar discrete wavelet packet transform
African Journals Online (AJOL)
PROF EKWUEME
GLOBAL JOURNAL OF PURE AND APPLIED SCIENCES VOL. 20, 2014: ..... In moving from Level 1 to Level 2 of Fig.2, the mathematical operations just described are repeated but now the .... Banks, Wellesley-Cambridge Press, Welleysley.
An algorithm for learning sparsifying transforms of multidimensional signals
Directory of Open Access Journals (Sweden)
Oscar Enrique Hurtado-Camacho
2017-01-01
Full Text Available Las señales multidimensionales contienen información de un objeto en más de una dimensión y, comúnmente, su procesamiento requiere métodos de mayor complejidad que las señales unidimensionales. En procesamiento de señales, la representación escasa de una señal es de gran importancia para fines de compresión. Convencionalmente, transformaciones analíticas como las transformadas de Fourier, Coseno o Wavelet, han sido utilizadas. Recientemente, se ha popularizado el uso de diccionarios entrenados, que se adaptan a una señal dada, en aplicaciones como clasificación de imágenes, eliminación de ruido, separación espectral, y reconstrucción de imágenes médicas. Este artículo presenta un algoritmo para entrenar bases de transformación para representación escasa de señales multidimensionales. El algoritmo propuesto alterna entre una codificación escasa que se resuelve por umbralización, y la actualización del diccionario que se resuelve mediante el método de gradiente conjugado. Además, el artículo incluye una comparación entre parches bidimensionales y tridimensionales en términos del nivel de escasez que ofrecen en diferentes tipos de señales multidimensionales como: imágenes hiperespectrales, imágenes de tomografía computarizada, e imágenes de resonancia magnética. Los resultados obtenidos son comparados contra transformaciones analíticas tradicionales y contra el método de entrenamiento de diccionarios más conocido en el estado del arte: K-SVD.
Fast Hankel Transform Algorithms for Optical Beam Propagation
National Research Council Canada - National Science Library
Pritchett, Timothy
2001-01-01
.... This problem may be solved numerically with the well-known 'split-step' procedure, in which the effects of propagation are computed separately from those arising from nonlinear absorption and refraction...
Basic Theoretical Principles Pertaining to Thermal Protection of Oil Transformer
Directory of Open Access Journals (Sweden)
O. G. Shirokov
2008-01-01
Full Text Available The paper contains formulation of basic theoretical principles pertaining to thermal protection of an oil transformer in accordance with classical theory of relay protection and theory of diagnostics with the purpose of unification of terminological and analytical information which is presently available in respect of this problem. Classification of abnormal thermal modes of an oil transformer and also algorithms and methods for operation of diagnostic thermal protection of a transformer have been proposed.
Stereo matching using epipolar distance transform.
Yang, Qingxiong; Ahuja, Narendra
2012-10-01
In this paper, we propose a simple but effective image transform, called the epipolar distance transform, for matching low-texture regions. It converts image intensity values to a relative location inside a planar segment along the epipolar line, such that pixels in the low-texture regions become distinguishable. We theoretically prove that the transform is affine invariant, thus the transformed images can be directly used for stereo matching. Any existing stereo algorithms can be directly used with the transformed images to improve reconstruction accuracy for low-texture regions. Results on real indoor and outdoor images demonstrate the effectiveness of the proposed transform for matching low-texture regions, keypoint detection, and description for low-texture scenes. Our experimental results on Middlebury images also demonstrate the robustness of our transform for highly textured scenes. The proposed transform has a great advantage, its low computational complexity. It was tested on a MacBook Air laptop computer with a 1.8 GHz Core i7 processor, with a speed of about 9 frames per second for a video graphics array-sized image.
International Nuclear Information System (INIS)
Chandrasekharan, Shailesh
2000-01-01
Cluster algorithms have been recently used to eliminate sign problems that plague Monte-Carlo methods in a variety of systems. In particular such algorithms can also be used to solve sign problems associated with the permutation of fermion world lines. This solution leads to the possibility of designing fermion cluster algorithms in certain cases. Using the example of free non-relativistic fermions we discuss the ideas underlying the algorithm
Autonomous Star Tracker Algorithms
DEFF Research Database (Denmark)
Betto, Maurizio; Jørgensen, John Leif; Kilsgaard, Søren
1998-01-01
Proposal, in response to an ESA R.f.P., to design algorithms for autonomous star tracker operations.The proposal also included the development of a star tracker breadboard to test the algorithms performances.......Proposal, in response to an ESA R.f.P., to design algorithms for autonomous star tracker operations.The proposal also included the development of a star tracker breadboard to test the algorithms performances....
Fourier transform and controlling of flux in scalar hysteresis measurement
International Nuclear Information System (INIS)
Kuczmann, Miklos
2008-01-01
The paper deals with a possible realization of eliminating the effect of noise in scalar hysteresis measurements. The measured signals have been transformed into the frequency domain, and, after applying digital filter, the spectrums of the filtered signals have been transformed back to the time domain. The proposed technique results in an accurate noise-removal algorithm. The paper illustrates a fast controlling algorithm applying the inverse of the actually measured hysteresis loop, and another proportional one to measure distorted flux pattern. By developing the mentioned algorithms, it aims at the controlling of a more complicated phenomena, i.e. measuring the vector hysteresis characteristics
Fast Exact Euclidean Distance (FEED): A new class of adaptable distance transforms
Schouten, Theo E.; van den Broek, Egon
2014-01-01
A new unique class of foldable distance transforms of digital images (DT) is introduced, baptized: Fast Exact Euclidean Distance (FEED) transforms. FEED class algorithms calculate the DT starting directly from the definition or rather its inverse. The principle of FEED class algorithms is
Fast Exact Euclidean Distance (FEED) : A new class of adaptable distance transforms
Schouten, Theo E.; van den Broek, Egon L.
2014-01-01
A new unique class of foldable distance transforms of digital images (DT) is introduced, baptized: Fast Exact Euclidean Distance (FEED) transforms. FEED class algorithms calculate the DT startingdirectly from the definition or rather its inverse. The principle of FEED class algorithms is introduced,
Energy Technology Data Exchange (ETDEWEB)
Walstrom, Peter Lowell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-08-24
A numerical algorithm for computing the field components B_{r} and B_{z} and their r and z derivatives with open boundaries in cylindrical coordinates for circular current loops is described. An algorithm for computing the vector potential is also described. For the convenience of the reader, derivations of the final expressions from their defining integrals are given in detail, since their derivations (especially for the field derivatives) are not all easily found in textbooks. Numerical calculations are based on evaluation of complete elliptic integrals using the Bulirsch algorithm cel. Since cel can evaluate complete elliptic integrals of a fairly general type, in some cases the elliptic integrals can be evaluated without first reducing them to forms containing standard Legendre forms. The algorithms avoid the numerical difficulties that many of the textbook solutions have for points near the axis because of explicit factors of 1=r or 1=r^{2} in the some of the expressions.
Divasón, Jose; Joosten, Sebastiaan; Thiemann, René; Yamada, Akihisa
2018-01-01
The Lenstra-Lenstra-Lovász basis reduction algorithm, also known as LLL algorithm, is an algorithm to find a basis with short, nearly orthogonal vectors of an integer lattice. Thereby, it can also be seen as an approximation to solve the shortest vector problem (SVP), which is an NP-hard problem,
Cryptanalysis of Application of Laplace Transform for Cryptography
Directory of Open Access Journals (Sweden)
Gençoğlu Muharrem Tuncay
2017-01-01
Full Text Available Although Laplace Transform is a good application field in the design of cryptosystems, many cryptographic algorithm proposals become unsatisfactory for secure communication. In this cryptanalysis study, one of the significant disadvantages of the proposed algorithm is performed with only statistical test of security analysis. In this study, Explaining what should be considered when performing security analysis of Laplace Transform based encryption systems and using basic mathematical rules, password has broken without knowing secret key. Under the skin; This study is a refutation for the article titled Application of Laplace Transform for Cryptography written by Hiwerakar[3].
MRI reconstruction with joint global regularization and transform learning.
Tanc, A Korhan; Eksioglu, Ender M
2016-10-01
Sparsity based regularization has been a popular approach to remedy the measurement scarcity in image reconstruction. Recently, sparsifying transforms learned from image patches have been utilized as an effective regularizer for the Magnetic Resonance Imaging (MRI) reconstruction. Here, we infuse additional global regularization terms to the patch-based transform learning. We develop an algorithm to solve the resulting novel cost function, which includes both patchwise and global regularization terms. Extensive simulation results indicate that the introduced mixed approach has improved MRI reconstruction performance, when compared to the algorithms which use either of the patchwise transform learning or global regularization terms alone. Copyright © 2016 Elsevier Ltd. All rights reserved.
Interpolation algorithm for asynchronous ADC-data
Directory of Open Access Journals (Sweden)
S. Bramburger
2017-09-01
Full Text Available This paper presents a modified interpolation algorithm for signals with variable data rate from asynchronous ADCs. The Adaptive weights Conjugate gradient Toeplitz matrix (ACT algorithm is extended to operate with a continuous data stream. An additional preprocessing of data with constant and linear sections and a weighted overlap of step-by-step into spectral domain transformed signals improve the reconstruction of the asycnhronous ADC signal. The interpolation method can be used if asynchronous ADC data is fed into synchronous digital signal processing.
Speckle imaging algorithms for planetary imaging
Energy Technology Data Exchange (ETDEWEB)
Johansson, E. [Lawrence Livermore National Lab., CA (United States)
1994-11-15
I will discuss the speckle imaging algorithms used to process images of the impact sites of the collision of comet Shoemaker-Levy 9 with Jupiter. The algorithms use a phase retrieval process based on the average bispectrum of the speckle image data. High resolution images are produced by estimating the Fourier magnitude and Fourier phase of the image separately, then combining them and inverse transforming to achieve the final result. I will show raw speckle image data and high-resolution image reconstructions from our recent experiment at Lick Observatory.
Algorithmic foundation of multi-scale spatial representation
Li, Zhilin
2006-01-01
With the widespread use of GIS, multi-scale representation has become an important issue in the realm of spatial data handling. However, no book to date has systematically tackled the different aspects of this discipline. Emphasizing map generalization, Algorithmic Foundation of Multi-Scale Spatial Representation addresses the mathematical basis of multi-scale representation, specifically, the algorithmic foundation.Using easy-to-understand language, the author focuses on geometric transformations, with each chapter surveying a particular spatial feature. After an introduction to the essential operations required for geometric transformations as well as some mathematical and theoretical background, the book describes algorithms for a class of point features/clusters. It then examines algorithms for individual line features, such as the reduction of data points, smoothing (filtering), and scale-driven generalization, followed by a discussion of algorithms for a class of line features including contours, hydrog...
Integrating Data Transformation in Principal Components Analysis
Maadooliat, Mehdi
2015-01-02
Principal component analysis (PCA) is a popular dimension reduction method to reduce the complexity and obtain the informative aspects of high-dimensional datasets. When the data distribution is skewed, data transformation is commonly used prior to applying PCA. Such transformation is usually obtained from previous studies, prior knowledge, or trial-and-error. In this work, we develop a model-based method that integrates data transformation in PCA and finds an appropriate data transformation using the maximum profile likelihood. Extensions of the method to handle functional data and missing values are also developed. Several numerical algorithms are provided for efficient computation. The proposed method is illustrated using simulated and real-world data examples.
Linear canonical transforms theory and applications
Kutay, M; Ozaktas, Haldun; Sheridan, John
2016-01-01
This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.
Nature-inspired optimization algorithms
Yang, Xin-She
2014-01-01
Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorithm introduction, theoretical background and practical implementation, complements extensive literature with well-chosen case studies to illustrate how these algorithms work. Topics include particle swarm optimization, ant and bee algorithms, simulated annealing, cuckoo search, firefly algorithm, bat algorithm, flower algorithm, harmony search, algorithm analysis, constraint handling, hybrid methods, parameter tuning
Human Motion Capture Data Tailored Transform Coding.
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.
VISUALIZATION OF PAGERANK ALGORITHM
Perhaj, Ervin
2013-01-01
The goal of the thesis is to develop a web application that help users understand the functioning of the PageRank algorithm. The thesis consists of two parts. First we develop an algorithm to calculate PageRank values of web pages. The input of algorithm is a list of web pages and links between them. The user enters the list through the web interface. From the data the algorithm calculates PageRank value for each page. The algorithm repeats the process, until the difference of PageRank va...
Akl, Selim G
1985-01-01
Parallel Sorting Algorithms explains how to use parallel algorithms to sort a sequence of items on a variety of parallel computers. The book reviews the sorting problem, the parallel models of computation, parallel algorithms, and the lower bounds on the parallel sorting problems. The text also presents twenty different algorithms, such as linear arrays, mesh-connected computers, cube-connected computers. Another example where algorithm can be applied is on the shared-memory SIMD (single instruction stream multiple data stream) computers in which the whole sequence to be sorted can fit in the
Pyramid algorithms as models of human cognition
Pizlo, Zygmunt; Li, Zheng
2003-06-01
There is growing body of experimental evidence showing that human perception and cognition involves mechanisms that can be adequately modeled by pyramid algorithms. The main aspect of those mechanisms is hierarchical clustering of information: visual images, spatial relations, and states as well as transformations of a problem. In this paper we review prior psychophysical and simulation results on visual size transformation, size discrimination, speed-accuracy tradeoff, figure-ground segregation, and the traveling salesman problem. We also present our new results on graph search and on the 15-puzzle.
Transforming the Way We Teach Function Transformations
Faulkenberry, Eileen Durand; Faulkenberry, Thomas J.
2010-01-01
In this article, the authors discuss "function," a well-defined rule that relates inputs to outputs. They have found that by using the input-output definition of "function," they can examine transformations of functions simply by looking at changes to input or output and the respective changes to the graph. Applying transformations to the input…
Modified Clipped LMS Algorithm
Directory of Open Access Journals (Sweden)
Lotfizad Mojtaba
2005-01-01
Full Text Available Abstract A new algorithm is proposed for updating the weights of an adaptive filter. The proposed algorithm is a modification of an existing method, namely, the clipped LMS, and uses a three-level quantization ( scheme that involves the threshold clipping of the input signals in the filter weight update formula. Mathematical analysis shows the convergence of the filter weights to the optimum Wiener filter weights. Also, it can be proved that the proposed modified clipped LMS (MCLMS algorithm has better tracking than the LMS algorithm. In addition, this algorithm has reduced computational complexity relative to the unmodified one. By using a suitable threshold, it is possible to increase the tracking capability of the MCLMS algorithm compared to the LMS algorithm, but this causes slower convergence. Computer simulations confirm the mathematical analysis presented.
Forest FIRE and FIRE wood : tools for tree automata and tree algorithms
Cleophas, L.G.W.A.; Piskorski, J.; Watson, B.W.; Yli-Jyrä, A.
2009-01-01
Pattern matching, acceptance, and parsing algorithms on node-labeled, ordered, ranked trees ('tree algorithms') are important for applications such as instruction selection and tree transformation/term rewriting. Many such algorithms have been developed. They often are based on results from such
Three dimensional canonical transformations
International Nuclear Information System (INIS)
Tegmen, A.
2010-01-01
A generic construction of canonical transformations is given in three-dimensional phase spaces on which Nambu bracket is imposed. First, the canonical transformations are defined as based on cannonade transformations. Second, it is shown that determination of the generating functions and the transformation itself for given generating function is possible by solving correspondent Pfaffian differential equations. Generating functions of type are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed as the complementary subject. Finally, it is shown that decomposition of canonical transformations is also possible in three-dimensional phase spaces as in the usual two-dimensional ones.
z-transform DFT filters and FFT's
DEFF Research Database (Denmark)
Bruun, G.
1978-01-01
The paper shows how discrete Fourier transformation can be implemented as a filter bank in a way which reduces the number of filter coefficients. A particular implementation of such a filter bank is directly related to the normal complex FFT algorithm. The principle developed further leads to types...... of DFT filter banks which utilize a minimum of complex coefficients. These implementations lead to new forms of FFT's, among which is acos/sinFFT for a real signal which only employs real coefficients. The new FFT algorithms use only half as many real multiplications as does the classical FFT....
Semioptimal practicable algorithmic cooling
International Nuclear Information System (INIS)
Elias, Yuval; Mor, Tal; Weinstein, Yossi
2011-01-01
Algorithmic cooling (AC) of spins applies entropy manipulation algorithms in open spin systems in order to cool spins far beyond Shannon's entropy bound. Algorithmic cooling of nuclear spins was demonstrated experimentally and may contribute to nuclear magnetic resonance spectroscopy. Several cooling algorithms were suggested in recent years, including practicable algorithmic cooling (PAC) and exhaustive AC. Practicable algorithms have simple implementations, yet their level of cooling is far from optimal; exhaustive algorithms, on the other hand, cool much better, and some even reach (asymptotically) an optimal level of cooling, but they are not practicable. We introduce here semioptimal practicable AC (SOPAC), wherein a few cycles (typically two to six) are performed at each recursive level. Two classes of SOPAC algorithms are proposed and analyzed. Both attain cooling levels significantly better than PAC and are much more efficient than the exhaustive algorithms. These algorithms are shown to bridge the gap between PAC and exhaustive AC. In addition, we calculated the number of spins required by SOPAC in order to purify qubits for quantum computation. As few as 12 and 7 spins are required (in an ideal scenario) to yield a mildly pure spin (60% polarized) from initial polarizations of 1% and 10%, respectively. In the latter case, about five more spins are sufficient to produce a highly pure spin (99.99% polarized), which could be relevant for fault-tolerant quantum computing.
Laplace Transforms without Integration
Robertson, Robert L.
2017-01-01
Calculating Laplace transforms from the definition often requires tedious integrations. This paper provides an integration-free technique for calculating Laplace transforms of many familiar functions. It also shows how the technique can be applied to probability theory.
On Poisson Nonlinear Transformations
Directory of Open Access Journals (Sweden)
Nasir Ganikhodjaev
2014-01-01
Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.
Chemical Transformation Simulator
The Chemical Transformation Simulator (CTS) is a web-based, high-throughput screening tool that automates the calculation and collection of physicochemical properties for an organic chemical of interest and its predicted products resulting from transformations in environmental sy...
Diffusionless phase transformations
International Nuclear Information System (INIS)
Vejman, K.M.
1987-01-01
Diffusionless phase transformations in metals and alloys in the process of which atomic displacements occur at the distances lower than interatomic ones and relative correspondence of neighbour atoms is preserved, are considered. Special attention is paid to the mechanism of martensitic transformations. Phenomenologic crystallographical theory of martensitic transformations are presented. Two types of martensitic transformations different from the energy viewpoint are pointed out - thermoelastic and non-thermoelastic ones - which are characterized by transformation hysteresis and ways of martensite - initial phase reverse transformation realization. Mechanical effect in the martensitic transformations have been analyzed. The problem of diffusionless formation of ω-phases and the effect of impurities and vacancies on the process are briefly discussed. The role of charge density waves in phase transformations of the second type (transition of initial phase into noncommensurate one) and of the first type (transition of noncommensurate phase into commensurate one) is considered
Equations For Rotary Transformers
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
Novel Simplex Unscented Transform and Filter
Institute of Scientific and Technical Information of China (English)
Wan-Chun Li; Ping Wei; Xian-Ci Xiao
2008-01-01
In this paper, a new simplex unscented transform (UT) based Schmidt orthogonal algorithm and a new filter method based on this transform are proposed. This filter has less computation consumption than UKF (unscented Kalman filter), SUKF (simplex unscented Kalman filter) and EKF (extended Kalman filter). Computer simulation shows that this filter has the same performance as UKF and SUKF, and according to the analysis of the computational requirements of EKF, UKF and SUKF, this filter has preferable practicality value. Finally, the appendix shows the efficiency for this UT.
On the effect of response transformations in sequential parameter optimization.
Wagner, Tobias; Wessing, Simon
2012-01-01
Parameter tuning of evolutionary algorithms (EAs) is attracting more and more interest. In particular, the sequential parameter optimization (SPO) framework for the model-assisted tuning of stochastic optimizers has resulted in established parameter tuning algorithms. In this paper, we enhance the SPO framework by introducing transformation steps before the response aggregation and before the actual modeling. Based on design-of-experiments techniques, we empirically analyze the effect of integrating different transformations. We show that in particular, a rank transformation of the responses provides significant improvements. A deeper analysis of the resulting models and additional experiments with adaptive procedures indicates that the rank and the Box-Cox transformation are able to improve the properties of the resultant distributions with respect to symmetry and normality of the residuals. Moreover, model-based effect plots document a higher discriminatory power obtained by the rank transformation.
Entropy of Baker's Transformation
Institute of Scientific and Technical Information of China (English)
栾长福
2003-01-01
Four theorems about four different kinds of entropies for Baker's transformation are presented. The Kolmogorov entropy of Baker's transformation is sensitive to the initial flips by the time. The topological entropy of Baker's transformation is found to be log k. The conditions for the state of Baker's transformation to be forbidden are also derived. The relations among the Shanonn, Kolmogorov, topological and Boltzmann entropies are discussed in details.
Almagest, a new trackless ring finding algorithm
Energy Technology Data Exchange (ETDEWEB)
Lamanna, G., E-mail: gianluca.lamanna@cern.ch
2014-12-01
A fast ring finding algorithm is a crucial point to allow the use of RICH in on-line trigger selection. The present algorithms are either too slow (with respect to the incoming data rate) or need the information coming from a tracking system. Digital image techniques, assuming limited computing power (as for example Hough transform), are not perfectly robust for what concerns the noise immunity. We present a novel technique based on Ptolemy's theorem for multi-ring pattern recognition. Starting from purely geometrical considerations, this algorithm (also known as “Almagest”) allows fast and trackless rings reconstruction, with spatial resolution comparable with other offline techniques. Almagest is particularly suitable for parallel implementation on multi-cores machines. Preliminary tests on GPUs (multi-cores video card processors) show that, thanks to an execution time smaller than 10 μs per event, this algorithm could be employed for on-line selection in trigger systems. The user case of the NA62 RICH trigger, based on GPU, will be discussed. - Highlights: • A new algorithm for fast multiple ring searching in RICH detectors is presented. • The Almagest algorithm exploits the computing power of Graphics processers (GPUs). • A preliminary implementation for on-line triggering in the NA62 experiment shows encouraging results.
Electrostatic shielding of transformers
Energy Technology Data Exchange (ETDEWEB)
De Leon, Francisco
2017-11-28
Toroidal transformers are currently used only in low-voltage applications. There is no published experience for toroidal transformer design at distribution-level voltages. Toroidal transformers are provided with electrostatic shielding to make possible high voltage applications and withstand the impulse test.
Defense Business Transformation
2009-12-01
Defense Business Transformation by Jacques S. Gansler and William Lucyshyn The Center for Technology and National...REPORT TYPE 3. DATES COVERED 00-00-2009 to 00-00-2009 4. TITLE AND SUBTITLE Defense Business Transformation 5a. CONTRACT NUMBER 5b. GRANT NUMBER...vii Part One: DoD Business Transformation
Energy functions for regularization algorithms
Delingette, H.; Hebert, M.; Ikeuchi, K.
1991-01-01
Regularization techniques are widely used for inverse problem solving in computer vision such as surface reconstruction, edge detection, or optical flow estimation. Energy functions used for regularization algorithms measure how smooth a curve or surface is, and to render acceptable solutions these energies must verify certain properties such as invariance with Euclidean transformations or invariance with parameterization. The notion of smoothness energy is extended here to the notion of a differential stabilizer, and it is shown that to void the systematic underestimation of undercurvature for planar curve fitting, it is necessary that circles be the curves of maximum smoothness. A set of stabilizers is proposed that meet this condition as well as invariance with rotation and parameterization.
Transforming the Force and Logistics Transformation
National Research Council Canada - National Science Library
Cook, Katherine M
2006-01-01
U.S. Army transformation strategy addresses the imperative to change the Army from a Cold War-oriented design to one that is more responsive, agile, and adaptable to present and emerging threats across...
Introduction to Evolutionary Algorithms
Yu, Xinjie
2010-01-01
Evolutionary algorithms (EAs) are becoming increasingly attractive for researchers from various disciplines, such as operations research, computer science, industrial engineering, electrical engineering, social science, economics, etc. This book presents an insightful, comprehensive, and up-to-date treatment of EAs, such as genetic algorithms, differential evolution, evolution strategy, constraint optimization, multimodal optimization, multiobjective optimization, combinatorial optimization, evolvable hardware, estimation of distribution algorithms, ant colony optimization, particle swarm opti
Recursive forgetting algorithms
DEFF Research Database (Denmark)
Parkum, Jens; Poulsen, Niels Kjølstad; Holst, Jan
1992-01-01
In the first part of the paper, a general forgetting algorithm is formulated and analysed. It contains most existing forgetting schemes as special cases. Conditions are given ensuring that the basic convergence properties will hold. In the second part of the paper, the results are applied...... to a specific algorithm with selective forgetting. Here, the forgetting is non-uniform in time and space. The theoretical analysis is supported by a simulation example demonstrating the practical performance of this algorithm...
Explaining algorithms using metaphors
Forišek, Michal
2013-01-01
There is a significant difference between designing a new algorithm, proving its correctness, and teaching it to an audience. When teaching algorithms, the teacher's main goal should be to convey the underlying ideas and to help the students form correct mental models related to the algorithm. This process can often be facilitated by using suitable metaphors. This work provides a set of novel metaphors identified and developed as suitable tools for teaching many of the 'classic textbook' algorithms taught in undergraduate courses worldwide. Each chapter provides exercises and didactic notes fo
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
Woo, Andrew
2012-01-01
Digital shadow generation continues to be an important aspect of visualization and visual effects in film, games, simulations, and scientific applications. This resource offers a thorough picture of the motivations, complexities, and categorized algorithms available to generate digital shadows. From general fundamentals to specific applications, it addresses shadow algorithms and how to manage huge data sets from a shadow perspective. The book also examines the use of shadow algorithms in industrial applications, in terms of what algorithms are used and what software is applicable.
Spectral Decomposition Algorithm (SDA)
National Aeronautics and Space Administration — Spectral Decomposition Algorithm (SDA) is an unsupervised feature extraction technique similar to PCA that was developed to better distinguish spectral features in...
Quick fuzzy backpropagation algorithm.
Nikov, A; Stoeva, S
2001-03-01
A modification of the fuzzy backpropagation (FBP) algorithm called QuickFBP algorithm is proposed, where the computation of the net function is significantly quicker. It is proved that the FBP algorithm is of exponential time complexity, while the QuickFBP algorithm is of polynomial time complexity. Convergence conditions of the QuickFBP, resp. the FBP algorithm are defined and proved for: (1) single output neural networks in case of training patterns with different targets; and (2) multiple output neural networks in case of training patterns with equivalued target vector. They support the automation of the weights training process (quasi-unsupervised learning) establishing the target value(s) depending on the network's input values. In these cases the simulation results confirm the convergence of both algorithms. An example with a large-sized neural network illustrates the significantly greater training speed of the QuickFBP rather than the FBP algorithm. The adaptation of an interactive web system to users on the basis of the QuickFBP algorithm is presented. Since the QuickFBP algorithm ensures quasi-unsupervised learning, this implies its broad applicability in areas of adaptive and adaptable interactive systems, data mining, etc. applications.
Portfolios of quantum algorithms.
Maurer, S M; Hogg, T; Huberman, B A
2001-12-17
Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can find the solution of hard problems only probabilistically. Thus the efficiency of the algorithms has to be characterized by both the expected time to completion and the associated variance. In order to minimize both the running time and its uncertainty, we show that portfolios of quantum algorithms analogous to those of finance can outperform single algorithms when applied to the NP-complete problems such as 3-satisfiability.
Fractional finite Fourier transform.
Khare, Kedar; George, Nicholas
2004-07-01
We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.
Computational complexity in entanglement transformations
Chitambar, Eric A.
In physics, systems having three parts are typically much more difficult to analyze than those having just two. Even in classical mechanics, predicting the motion of three interacting celestial bodies remains an insurmountable challenge while the analogous two-body problem has an elementary solution. It is as if just by adding a third party, a fundamental change occurs in the structure of the problem that renders it unsolvable. In this thesis, we demonstrate how such an effect is likewise present in the theory of quantum entanglement. In fact, the complexity differences between two-party and three-party entanglement become quite conspicuous when comparing the difficulty in deciding what state changes are possible for these systems when no additional entanglement is consumed in the transformation process. We examine this entanglement transformation question and its variants in the language of computational complexity theory, a powerful subject that formalizes the concept of problem difficulty. Since deciding feasibility of a specified bipartite transformation is relatively easy, this task belongs to the complexity class P. On the other hand, for tripartite systems, we find the problem to be NP-Hard, meaning that its solution is at least as hard as the solution to some of the most difficult problems humans have encountered. One can then rigorously defend the assertion that a fundamental complexity difference exists between bipartite and tripartite entanglement since unlike the former, the full range of forms realizable by the latter is incalculable (assuming P≠NP). However, similar to the three-body celestial problem, when one examines a special subclass of the problem---invertible transformations on systems having at least one qubit subsystem---we prove that the problem can be solved efficiently. As a hybrid of the two questions, we find that the question of tripartite to bipartite transformations can be solved by an efficient randomized algorithm. Our results are
Numerical calculation of the Fresnel transform.
Kelly, Damien P
2014-04-01
In this paper, we address the problem of calculating Fresnel diffraction integrals using a finite number of uniformly spaced samples. General and simple sampling rules of thumb are derived that allow the user to calculate the distribution for any propagation distance. It is shown how these rules can be extended to fast-Fourier-transform-based algorithms to increase calculation efficiency. A comparison with other theoretical approaches is made.
Quantum Fourier Transform Over Galois Rings
Zhang, Yong
2009-01-01
Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorit...
Efficient Computer Implementations of Fast Fourier Transforms.
1980-12-01
fit in computer? Yes, continue (9) Determine fastest algorithm between WFTA and PFA from Table 4.6. For N=420, WFTA PFA Mult 1296 2528 Add 11352 10956...real adds = 24tN/4 + 2(3tN/4) = 15tN/2 (G.8) 260 All odd prime C<ictors ciual to or (,rater than 5 iso the general transform section. Based on the
Nonsynchronous Noncommensurate Impedance Transformers
DEFF Research Database (Denmark)
Zhurbenko, Vitaliy; Kim, K
2012-01-01
Nonsynchronous noncommensurate impedance transformers consist of a combination of two types of transmission lines: transmission lines with a characteristic impedance equal to the impedance of the source, and transmission lines with a characteristic impedance equal to the load. The practical...... advantage of such transformers is that they can be constructed using sections of transmission lines with a limited variety of characteristic impedances. These transformers also provide comparatively compact size in applications where a wide transformation ratio is required. This paper presents the data...... matrix approach and experimentally verified by synthesizing a 12-section nonsynchronous noncommensurate impedance transformer. The measured characteristics of the transformer are compared to the characteristics of a conventional tapered line transformer....
Algorithm 426 : Merge sort algorithm [M1
Bron, C.
1972-01-01
Sorting by means of a two-way merge has a reputation of requiring a clerically complicated and cumbersome program. This ALGOL 60 procedure demonstrates that, using recursion, an elegant and efficient algorithm can be designed, the correctness of which is easily proved [2]. Sorting n objects gives
Optimization and experimental realization of the quantum permutation algorithm
Yalçınkaya, I.; Gedik, Z.
2017-12-01
The quantum permutation algorithm provides computational speed-up over classical algorithms for determining the parity of a given cyclic permutation. For its n -qubit implementations, the number of required quantum gates scales quadratically with n due to the quantum Fourier transforms included. We show here for the n -qubit case that the algorithm can be simplified so that it requires only O (n ) quantum gates, which theoretically reduces the complexity of the implementation. To test our results experimentally, we utilize IBM's 5-qubit quantum processor to realize the algorithm by using the original and simplified recipes for the 2-qubit case. It turns out that the latter results in a significantly higher success probability which allows us to verify the algorithm more precisely than the previous experimental realizations. We also verify the algorithm for the first time for the 3-qubit case with a considerable success probability by taking the advantage of our simplified scheme.
Composite Differential Search Algorithm
Directory of Open Access Journals (Sweden)
Bo Liu
2014-01-01
Full Text Available Differential search algorithm (DS is a relatively new evolutionary algorithm inspired by the Brownian-like random-walk movement which is used by an organism to migrate. It has been verified to be more effective than ABC, JDE, JADE, SADE, EPSDE, GSA, PSO2011, and CMA-ES. In this paper, we propose four improved solution search algorithms, namely “DS/rand/1,” “DS/rand/2,” “DS/current to rand/1,” and “DS/current to rand/2” to search the new space and enhance the convergence rate for the global optimization problem. In order to verify the performance of different solution search methods, 23 benchmark functions are employed. Experimental results indicate that the proposed algorithm performs better than, or at least comparable to, the original algorithm when considering the quality of the solution obtained. However, these schemes cannot still achieve the best solution for all functions. In order to further enhance the convergence rate and the diversity of the algorithm, a composite differential search algorithm (CDS is proposed in this paper. This new algorithm combines three new proposed search schemes including “DS/rand/1,” “DS/rand/2,” and “DS/current to rand/1” with three control parameters using a random method to generate the offspring. Experiment results show that CDS has a faster convergence rate and better search ability based on the 23 benchmark functions.
Algorithms and Their Explanations
Benini, M.; Gobbo, F.; Beckmann, A.; Csuhaj-Varjú, E.; Meer, K.
2014-01-01
By analysing the explanation of the classical heapsort algorithm via the method of levels of abstraction mainly due to Floridi, we give a concrete and precise example of how to deal with algorithmic knowledge. To do so, we introduce a concept already implicit in the method, the ‘gradient of
Finite lattice extrapolation algorithms
International Nuclear Information System (INIS)
Henkel, M.; Schuetz, G.
1987-08-01
Two algorithms for sequence extrapolation, due to von den Broeck and Schwartz and Bulirsch and Stoer are reviewed and critically compared. Applications to three states and six states quantum chains and to the (2+1)D Ising model show that the algorithm of Bulirsch and Stoer is superior, in particular if only very few finite lattice data are available. (orig.)
Recursive automatic classification algorithms
Energy Technology Data Exchange (ETDEWEB)
Bauman, E V; Dorofeyuk, A A
1982-03-01
A variational statement of the automatic classification problem is given. The dependence of the form of the optimal partition surface on the form of the classification objective functional is investigated. A recursive algorithm is proposed for maximising a functional of reasonably general form. The convergence problem is analysed in connection with the proposed algorithm. 8 references.
DEFF Research Database (Denmark)
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...
8. Algorithm Design Techniques
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 8. Algorithms - Algorithm Design Techniques. R K Shyamasundar. Series Article Volume 2 ... Author Affiliations. R K Shyamasundar1. Computer Science Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India ...
Geometric approximation algorithms
Har-Peled, Sariel
2011-01-01
Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.