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Topic: Spectral method

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	BioMed Central \| Full text \| Spectral embedding finds meaningful (relevant) structure in image and microarray data
		For the kernel PCA and spectral method from Ng et al., the projection plots were generated with the epsilon terms optimized for QDA (ε = 67,000 for kernel PCA and ε = 20,000 for the spectral method from Ng et al).
		Within these examples, the spectral method from Lafon is demonstrated to extract more meaningful structure, relative to two linear and three nonlinear methods, for calculating low dimensional representations of high dimensional data types, such as image and microarray data, for purposes of determining ordered patterns or classification.
		Methods such as boosting and bagging [24] and the relative distance plane (RDP) [25] may be better suited for certain high dimensional datasets.
	www.biomedcentral.com /1471-2105/7/74 (6074 words)

	Method of characterization of biological entities - Patent 6887711
		The method of claim 6, wherein the indication that a cell is in a cell division stage is the presence of a signal indicating DNA in the infrared absorption spectra.
		The method of claim 10, wherein the indication that a cell is in a cell division stage is the presence of a signal indicating DNA in the infrared absorption spectra.
		The method of claim 25, wherein the indication that a cell is in a cell division stage is the presence of a signal indicating DNA in the infrared absorption spectra.
	www.freepatentsonline.com /6887711.html (6679 words)

	Beth A. Wingate, wingate@lanl.gov, fekete, spectral, element
		spectral methods give exponential convergence rates and have high accuracy for smooth solutions, but are unsuitable for use with complex domains.
		The spectral element method combines the geometric flexibility of the finite element method with the accuracy and efficiency of the spectral method.
		The ill-conditioning of the triangle methods is particularly disconcerting because the finite element method on quadrilaterals doesn't have this problem.
	public.lanl.gov /wingate/spectral.html (502 words)

	Pseudo-spectral method - Wikipedia, the free encyclopedia
		Pseudo-spectral methods are a class of numerical methods used in applied mathematics and scientific computing for the solution of PDEs, such as the direct simulation of a particle with an arbitrary wavefunction interacting with an arbitrary potential.
		They are related to spectral methods and are used extensively in computational fluid dynamics and other areas, but are demonstrated below on an example from quantum physics.
		The error in the pseudo-spectral method is overwhelmingly due to discretization error.
	en.wikipedia.org /wiki/Pseudo-spectral_method (382 words)

	3D Hydro Simulation using Spectral Method and Lattice Boltzmann Method:Accuracy and Performance Analysis
		This method provides the basis for implementation of scalable and efficient spectral method computations of hydrodynamic and magneto-hydrodynamic turbulence on Beowulf clusters assembled from standard commodity components.
		The lattice Boltzmann method is a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporation additional physical complexities.
		This method simulates the motion of the fluid particles trough a distribution of fluid particles function (f).
	www.cis.udel.edu /~pollock/879f00/reports/project5_final.html (3261 words)

	The Lagrange-Galerkin Spectral Element Method on Unstructured Quadrilateral Grids (Site not responding. Last check: 2007-10-29)
		The purpose of this paper is to introduce a new method arrived at by fusing the Lagrange-Galerkin and spectral element methods.
		Spectral element methods are essentially higher order finite element methods that exhibit spectral (exponential) convergence provided that the solution is a smooth function.
		By combining these two methods, a numerical scheme can be constructed that resolves, with extremely high precision, the non-linearities of the advection terms and the smooth regions of the flow generated by the diffusion terms.
	www.nrlmry.navy.mil /~giraldo/papers/sem_slm.html (229 words)

	Coherent Phase Line Enhancer: a Method of Spectral Analysis
		The term "coherent phase line enhancer" (CPLE) refers to a dual-transform method of spectral analysis that enhances the detection of periodic and quasi-periodic signals buried in wide-band noise.
		The CPLE is particularly useful for increasing the signal-to-noise ratios of spectral peaks ("lines") that represent periodic and quasi-periodic components of measurements of vibration, dynamic strain, and/or dynamic pressure in a turbine or other rotating machine.
		The purpose of such measurements, spectral analysis, and enhancement of spectral peaks is to assess machine performance and identify spectral signatures of bearing or gear-train defects.
	www.nasatech.com /Briefs/July01/MFS31426.html (896 words)

	USGS OGW, BG: Spectral Gamma Borehole Tool
		Spectral gamma borehole geophysical methods measure natural-gamma energy spectra, which are caused by the decay of uranium, thorium, potassium-40, and anthropogenic radioactive isotopes.
		Spectral gamma data can be used to identify and quantify the amount of uranium, thorium, and potassium-40 isotopes detected in boreholes.
		Careful calibration of the spectral gamma probe in a test pit of known isotope concentrations permits the process of spectral stripping to be done.
	water.usgs.gov /ogw/bgas/spectral_gamma (981 words)

	Thomson's method of spectral estimation (Site not responding. Last check: 2007-10-29)
		The spectral estimate is formulated by averaging together, with appropriately chosen weightings (the eigenvalues), multiple power spectral estimates, each computed with a different window.
		It should be stressed that while other methods of spectral estimation (such as the Welchoppenheim method) exist, the Thomson method is particularly noteworthy for its precisely defined rectangular frequency bins.
		Generally, the Thomson method is thought of as a multiple window method, but another way of thinking of the Thomson method is by the way that the energy in each frequency bin is calculated.
	wearcam.org /chirplet/node12.html (327 words)

	SPECTRAL METHODS AND THEIR APPLICATIONS
		Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other fields.
		It includes Fourier spectral method, Legendre spectral method, Chebyshev spectral method, spectral penalty method, spectral vanishing viscosity method, spectral approximation of isolated solutions, multi-dimensional spectral method, spectral method for high-order equations, spectral-domain decomposition method and spectral multigrid method.
		The third part is devoted to some recent developments of spectral methods, such as mixed spectral methods, combined spectral methods and spectral methods on the surface.
	www.worldscibooks.com /mathematics/3662.html (195 words)

	Thermo Scientific - Algorithms - Discriminant Analysis, The PCA/MDR Method
		In this method, both the Mahalanobis distance and the SIMCA test on the spectral residual had to pass in order for a sample to be classified as a match.
		The main benefit of this method is that all of the data in the sample spectrum is included in the calculations, and not just the PCA-modeled data (as with PCA/MD) and the spectral residual data that is left over (as with SIMCA).
		Another method that is used to improve the sensitivity on the analysis is to normalize the predicted distances by the Root Mean Squared Group size (RMSG).
	www.thermo.com /com/cda/resources/resources_detail/1,2166,13325,00.html (1671 words)

	Spectral method - Wikipedia, the free encyclopedia
		Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain partial differential equations, often involving the use of the Fast Fourier Transform.
		For well-behaved problems, spectral methods have excellent error properties: The more differentiable the solution is, the better the accuracy of the method.
		Spectral method can also mean the use of high-order polynomials to approximate the solution to a PDE. It is known as the spectral element method when combined with the finite element method.
	en.wikipedia.org /wiki/Spectral_method (438 words)

	Regularized Method of Spectral Curve Deconvolution (Site not responding. Last check: 2007-10-29)
		A regularized method of spectral curves, deconvolution is proposed.
		The regularized method of deconvolution permits the acquisition of an approximately stable solution for the deconvolution problem of spectral curves, which moves toward an exact solution by with the decrease of the experimental spectrum error.
		Examples are given of application of the regularized method of deconvolution to simulated and experimental IR spectra.
	www.s-a-s.org /journal/97/asv51n5/ASv51n5_sp6.html (103 words)

	Citations: Solution of the equations of dynamic elasticity by a Chebyshev spectral method - Kosloff, Kessler, Filho, ...
		A Pseudospectral Chebychev method for the 2D Wave Equation..
		....the pseudospectral Fourier method applied to forward modelling so that the acoustic wave equation is modified by a damping term, non zero only in a damping region at the boundary.
		These methods have been used for a wide variety of applications, see for example the recent papers by Kosloff et al.
	citeseer.ist.psu.edu /context/303701/0 (413 words)

	The Discontinuous Spectral Element Method
		In FE methods, the basis functions are usually constructed for one specific order of the scheme (they are derived from Lagrange interpolators on regular grids inside each element).
		And, contrary to the spectral method for which Gibbs oscillations are prone to occur in under-resolved regions, in the SE method, one can easily increase the polynomial order (p-refinement) or the number of elements (h-refinement) in the underesolved regions.
		For FE methods using linear basis functions, it is usually recommended to estimate the local second order derivatives of the fields and put more resolution where these derivatives are the largest (Zienkiewicz and Taylor, 1991, p.571).
	frederic.dupont8.free.fr /science/thesis/node9.html (2878 words)

	A NEW METHOD OF SPECTRAL ANALYSIS OF DNA/RNA AND PROTEIN SEQUENCES (Site not responding. Last check: 2007-10-29)
		It is based on a combined application of spectral analysis and artificial neural networks for extraction of common spectral characterization of a group of sequences that have the same or similar biological functions.
		The nature of the method allows possible applications to a number of relevant problems such as recognition of membership of a particular sequence to a specific functional group or localization of an unknown sequence of a specific functional group within a longer sequence.
		The method is aimed to find the spectral characterization, the so-called consensus spectrum (CS), of a group of sequences that have the same or similar type of biological functions.
	www.bionet.nsc.ru /bgrs/thesis/30 (1965 words)

	Spectral method (Site not responding. Last check: 2007-10-29)
		Moreover, the method makes inefficient use of available data, as only a few summary statistics are used in the fitting.
		This method uses the sample Fourier coefficients rather than the original data, and makes use of the fact that, for large samples, small collections of the Fourier coefficients have a joint distribution which is approximately multivariate normal [Brillinger and Rosenblatt1967].
		In both cases, the only theoretical properties required from the model are the mean and second-order spectral density of the process; the required expressions (corresponding both to the underlying model and to the aggregated domain of observation) have been derived for wide classes of models in both cases.
	www.ucl.ac.uk /stats/research/Resrprts/rr176/node13.html (292 words)

	Using the Coupled Method of Spectral Elements and Modal Solution to study the D'' layer.
		The coupled method of Spectral Elements and Modal Solution is very well adapted to such a problem by allowing to restrict the 3D model in the D" layer and to use a spherically symmetric model is enough in the rest of the Earth.
		Within the spectral element method, the coupling is introduced via a dynamic interface operator, a Dirichlet-to-Neumann (DtN) operator which can be explicitly constructed in the frequency and generalized spherical harmonics domain using modal solutions in the inner sphere and outer shell.
		The accuracy of the method is checked against the mode summation method in simple spherically symmetric models and shows very good agreement for all type of waves, including diffracted waves traveling on the coupling boundary.
	seismo.berkeley.edu /annual_report/ar01_02/node41.html (816 words)

	Springer Online Reference Works
		Trigonometric pseudo-spectral methods) used to solve differential and integral equations.
		The Fourier pseudo-spectral method is used for problems in which there is a natural periodicity.
		In non-periodic directions, Chebyshev methods, finite element or difference methods of high order should be used.
	eom.springer.de /F/f130190.htm (372 words)

	(WO/2003/079045) SYSTEM AND METHOD FOR SPECTRAL GENERATION IN RADAR (Site not responding. Last check: 2007-10-29)
		This invention relates to a spectral generator and a spectral generation method for receiving pre-processed range-doppler-sensor data and generating at least one noise-reduced high-resolution spectrum therefrom.
		The spectral generator further comprises a covariance matrix calculator that is in communication with the window generator to receive the range-doppler-sensor data within the window and calculate a covariance matrix estimate for a range-doppler cell of interest in the window.
		The spectral generator also includes a spectral calculator that is in communication with the covariance matrix calculator to calculate a high-resolution spectral vector based on a location matrix and a noise subspace matrix estimate.
	www.wipo.int /pctdb/en/wo.jsp?KEY=03/79045.031204 (318 words)

	Improved Spectral Method for Variable Amplitude Fatigue Prediction (Site not responding. Last check: 2007-10-29)
		The dependence of fatigue damage accumulation on power spectral density (psd) is investigated for several types of random processes relevant to the stresses in offshore structures.
		These data are used to test the accuracy of spectral approximation methods in which the damage predictions are made from fairly simple calculational operations on the psd function.
		Primary emphasis is placed on the commonly used Rayleigh approximation method and a new method that involves calculation of only one spectral moment (i.e., one integral of the psd).
	www.pubs.asce.org /WWWdisplay.cgi?9001186 (157 words)

	Spectral method (FFT scheme)
		With the methods that we have used so far, we have been interested mainly in calculating the new value of the function in the same space as the solution exists in.
		Spectral methods use these ideas by Fourier transforming the problem and performing the calculation in Fourier space, it being easier in some cases for the solution to be calculated there than in position space.
		The process that spectral methods use is to take an evolving function in some space, transform it into Fourier space, calculate the evolution of the function in Fourier space, and then transform back to the original space by taking the inverse Fourier transform.
	www.physics.uq.edu.au /people/cochrane/phys3071/phys3071Notes/node12.html (751 words)

	3.7 The Spectral Method for Function Minimization
		The spectral method (SM) is a minimization iteration, which has as main goal to avoid saddle points.
		A saddle point is a point, where the function has zero gradient, a minimum in some directions and a maximum in other directions.
		Methods like Newton cannot differentiate between a minimum, a maximum or a saddle point.
	linneus20.ethz.ch:8080 /3_7.html (406 words)

	Comparison of the Rain Flow Algorithm and the Spectral Method for Fatigue Life Determination Under Uniaxial and ...
		The first method is based on schematization of energy parameter histories with the rain flow algorithm.
		The other one is based on moments of the power spectral density function of the energy parameter.
		The experimental data of fatigue tests of 10HNAP steel under constant amplitude and random uniaxial loading with non-gaussion probability distribution, zero mean value, and wide-band frequency spectrum used for comparison of the rain flow algorithm and the spectral method gave satisfactory results.
	www.astm.org /DIGITAL_LIBRARY/JOURNALS/JAI/PAGES/118.htm (286 words)

	A mortar spectral element method for 3D Maxwell's equations -- Boulmezaoud and El Rhabi, 10.1093/imanum/dri010 -- IMA ...
		A mortar spectral element method for 3D Maxwell's equations -- Boulmezaoud and El Rhabi, 10.1093/imanum/dri010 -- IMA Journal of Numerical Analysis
		A mortar spectral element method for 3D Maxwell's equations
		Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues.
	imanum.oxfordjournals.org /cgi/content/abstract/dri010v1 (219 words)

	Citations: Elastic modeling with surface topography by a Chebychev spectral method - Tessmer, Kosloff (ResearchIndex)
		Tessmer and D. Kosloff, 3-D Elastic modeling with surface topography by a Chebychev spectral method, Geophysics 59, 3, 464-473, (1994).
		....method applied to forward modelling so that the acoustic wave equation is modified by a damping term, non zero only in a damping region at the boundary.
		The solution, however, maintains the periodicity induced by the Fourier method, and therefore the damping layer has to be large enough to prevent reentrant waves at the physical boundary.
	citeseer.ist.psu.edu /context/928018/0 (194 words)

	Solution of ODEs and Eigenvalue Problems with a Chebyshev Polynomial Spectral Method -- from Mathematica Information ...
		Solution of ODEs and Eigenvalue Problems with a Chebyshev Polynomial Spectral Method -- from Mathematica Information Center
		This notebook demonstrates the Orszag-tau (a modification of the Galerkin) spectral method for a simple ODE and an ODE eigenvalue problem.
		It is intended as a first introduction to solving these problems with a spectral numerical method.
	library.wolfram.com /infocenter/MathSource/443 (132 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		ddcon2d - Double-Diffusive Convection Code Using a Pseudo-Spectral Method
		ddcon2d solves the two-dimensional Navier-Stokes equations for Boussinesq convection by Fourier Galerkin + Collocation method.
		The current set-up models the occurence of various waves (standing and traveling convection waves)
	www.netlib.org /utk/misc/sw_survey/urc/118.urc (96 words)

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