WorldWideScience

Sample records for varied approximately inversely

  1. Weighted approximation with varying weight

    CERN Document Server

    Totik, Vilmos

    1994-01-01

    A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

  2. Fast wavelet based sparse approximate inverse preconditioner

    Energy Technology Data Exchange (ETDEWEB)

    Wan, W.L. [Univ. of California, Los Angeles, CA (United States)

    1996-12-31

    Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.

  3. Factorized Approximate Inverses With Adaptive Dropping

    Czech Academy of Sciences Publication Activity Database

    Kopal, Jiří; Rozložník, Miroslav; Tůma, Miroslav

    2016-01-01

    Roč. 38, č. 3 (2016), A1807-A1820 ISSN 1064-8275 R&D Projects: GA ČR GA13-06684S Grant - others:GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : approximate inverses * incomplete factorization * Gram–Schmidt orthogonalization * preconditioned iterative methods Subject RIV: BA - General Mathematics Impact factor: 2.195, year: 2016

  4. Approximate Inverse Preconditioners with Adaptive Dropping

    Czech Academy of Sciences Publication Activity Database

    Kopal, J.; Rozložník, Miroslav; Tůma, Miroslav

    2015-01-01

    Roč. 84, June (2015), s. 13-20 ISSN 0965-9978 R&D Projects: GA ČR(CZ) GAP108/11/0853; GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : approximate inverse * Gram-Schmidt orthogonalization * incomplete decomposition * preconditioned conjugate gradient method * algebraic preconditioning * pivoting Subject RIV: BA - General Mathematics Impact factor: 1.673, year: 2015

  5. Varying prior information in Bayesian inversion

    International Nuclear Information System (INIS)

    Walker, Matthew; Curtis, Andrew

    2014-01-01

    Bayes' rule is used to combine likelihood and prior probability distributions. The former represents knowledge derived from new data, the latter represents pre-existing knowledge; the Bayesian combination is the so-called posterior distribution, representing the resultant new state of knowledge. While varying the likelihood due to differing data observations is common, there are also situations where the prior distribution must be changed or replaced repeatedly. For example, in mixture density neural network (MDN) inversion, using current methods the neural network employed for inversion needs to be retrained every time prior information changes. We develop a method of prior replacement to vary the prior without re-training the network. Thus the efficiency of MDN inversions can be increased, typically by orders of magnitude when applied to geophysical problems. We demonstrate this for the inversion of seismic attributes in a synthetic subsurface geological reservoir model. We also present results which suggest that prior replacement can be used to control the statistical properties (such as variance) of the final estimate of the posterior in more general (e.g., Monte Carlo based) inverse problem solutions. (paper)

  6. Approximation of Bayesian Inverse Problems for PDEs

    OpenAIRE

    Cotter, S. L.; Dashti, M.; Stuart, A. M.

    2010-01-01

    Inverse problems are often ill posed, with solutions that depend sensitively on data.n any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is based on an approach to regularization, employing a Bayesian formulation of the problem, which leads to a notion of well posedness for inverse problems, at the level of probability measures. The stability which results from this well posedness may be used as t...

  7. Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)

    1996-12-31

    A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.

  8. On quasiclassical approximation in the inverse scattering method

    International Nuclear Information System (INIS)

    Geogdzhaev, V.V.

    1985-01-01

    Using as an example quasiclassical limits of the Korteweg-de Vries equation and nonlinear Schroedinger equation, the quasiclassical limiting variant of the inverse scattering problem method is presented. In quasiclassical approximation the inverse scattering problem for the Schroedinger equation is reduced to the classical inverse scattering problem

  9. Frame approximation of pseudo-inverse operators

    DEFF Research Database (Denmark)

    Christensen, Ole

    2001-01-01

    Let T denote an operator on a Hilbert space (H, [.,.]), and let {f(i)}(i=1)(infinity) be a frame for the orthogonal complement of the kernel NT. We construct a sequence of operators {Phi (n)} of the form Phi (n) (.) = Sigma (n)(i=1) [., g(t)(n)]f(i) which converges to the psuedo-inverse T+ of T i...... in the strong operator topology as n --> infinity. The operators {Phi (n)} can be found using finite-dimensional methods. We also prove an adaptive iterative version of the result. (C) 2001 Academic Press....

  10. Approximation of the inverse G-frame operator

    Indian Academy of Sciences (India)

    ... projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.

  11. Approximate 2D inversion of airborne TEM data

    DEFF Research Database (Denmark)

    Christensen, N.B.; Wolfgram, Peter

    2006-01-01

    We propose an approximate two-dimensional inversion procedure for transient electromagnetic data. The method is a two-stage procedure, where data are first inverted with 1D multi-layer models. The 1D model section is then considered as data for the next inversion stage that produces the 2D model...... section. For moving platform data there is translational invariance and the second part of the inversion becomes a deconvolution. The convolution kernels are computed by perturbing one model element in an otherwise homogeneous 2D section and calculating full nonlinear responses. These responses...... are then inverted with 1D models to produce a 1D model section. This section is the convolution kernel for the deconvolution. Within its limitations, the approximate 2D inversion performs well. Theoretical modeling shows that it delivers model sections that are a definite improvement over 1D model sections...

  12. An Adaptive Multilevel Factorized Sparse Approximate Inverse Preconditioning

    Czech Academy of Sciences Publication Activity Database

    Kopal, Jiří; Rozložník, Miroslav; Tůma, Miroslav

    2017-01-01

    Roč. 113, November (2017), s. 19-24 ISSN 0965-9978 R&D Projects: GA ČR GA13-06684S Grant - others:GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : approximate inverse * Gram–Schmidt orthogonalization * incomplete factorization * multilevel methods * preconditioned conjugate gradient method Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 3.000, year: 2016

  13. A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems

    Czech Academy of Sciences Publication Activity Database

    Benzi, M.; Tůma, Miroslav

    1998-01-01

    Roč. 19, č. 3 (1998), s. 968-994 ISSN 1064-8275 R&D Projects: GA ČR GA201/93/0067; GA AV ČR IAA230401 Keywords : large sparse systems * interative methods * preconditioning * approximate inverse * sparse linear systems * sparse matrices * incomplete factorizations * conjugate gradient -type methods Subject RIV: BA - General Mathematics Impact factor: 1.378, year: 1998

  14. On rational approximation methods for inverse source problems

    KAUST Repository

    Rundell, William

    2011-02-01

    The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace\\'s equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.

  15. On rational approximation methods for inverse source problems

    KAUST Repository

    Rundell, William; Hanke, Martin

    2011-01-01

    The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace's equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.

  16. Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

    KAUST Repository

    Zhang, Zhendong; Schuster, Gerard T.; Liu, Yike; Hanafy, Sherif M.; Li, Jing

    2016-01-01

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized

  17. Approximation Of Multi-Valued Inverse Functions Using Clustering And Sugeno Fuzzy Inference

    Science.gov (United States)

    Walden, Maria A.; Bikdash, Marwan; Homaifar, Abdollah

    1998-01-01

    Finding the inverse of a continuous function can be challenging and computationally expensive when the inverse function is multi-valued. Difficulties may be compounded when the function itself is difficult to evaluate. We show that we can use fuzzy-logic approximators such as Sugeno inference systems to compute the inverse on-line. To do so, a fuzzy clustering algorithm can be used in conjunction with a discriminating function to split the function data into branches for the different values of the forward function. These data sets are then fed into a recursive least-squares learning algorithm that finds the proper coefficients of the Sugeno approximators; each Sugeno approximator finds one value of the inverse function. Discussions about the accuracy of the approximation will be included.

  18. Fitting Social Network Models Using Varying Truncation Stochastic Approximation MCMC Algorithm

    KAUST Repository

    Jin, Ick Hoon

    2013-10-01

    The exponential random graph model (ERGM) plays a major role in social network analysis. However, parameter estimation for the ERGM is a hard problem due to the intractability of its normalizing constant and the model degeneracy. The existing algorithms, such as Monte Carlo maximum likelihood estimation (MCMLE) and stochastic approximation, often fail for this problem in the presence of model degeneracy. In this article, we introduce the varying truncation stochastic approximation Markov chain Monte Carlo (SAMCMC) algorithm to tackle this problem. The varying truncation mechanism enables the algorithm to choose an appropriate starting point and an appropriate gain factor sequence, and thus to produce a reasonable parameter estimate for the ERGM even in the presence of model degeneracy. The numerical results indicate that the varying truncation SAMCMC algorithm can significantly outperform the MCMLE and stochastic approximation algorithms: for degenerate ERGMs, MCMLE and stochastic approximation often fail to produce any reasonable parameter estimates, while SAMCMC can do; for nondegenerate ERGMs, SAMCMC can work as well as or better than MCMLE and stochastic approximation. The data and source codes used for this article are available online as supplementary materials. © 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

  19. Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

    KAUST Repository

    Zhang, Zhendong

    2016-07-26

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.

  20. Iterative Multiparameter Elastic Waveform Inversion Using Prestack Time Imaging and Kirchhoff approximation

    Science.gov (United States)

    Khaniani, Hassan

    This thesis proposes a "standard strategy" for iterative inversion of elastic properties from the seismic reflection data. The term "standard" refers to the current hands-on commercial techniques that are used for the seismic imaging and inverse problem. The method is established to reduce the computation time associated with elastic Full Waveform Inversion (FWI) methods. It makes use of AVO analysis, prestack time migration and corresponding forward modeling in an iterative scheme. The main objective is to describe the iterative inversion procedure used in seismic reflection data using simplified mathematical expression and their numerical applications. The frame work of the inversion is similar to (FWI) method but with less computational costs. The reduction of computational costs depends on the data conditioning (with or without multiple data), the level of the complexity of geological model and acquisition condition such as Signal to Noise Ratio (SNR). Many processing methods consider multiple events as noise and remove it from the data. This is the motivation for reducing the computational cost associated with Finite Difference Time Domain (FDTD) forward modeling and Reverse Time Migration (RTM)-based techniques. Therefore, a one-way solution of the wave equation for inversion is implemented. While less computationally intensive depth imaging methods are available by iterative coupling of ray theory and the Born approximation, it is shown that we can further reduce the cost of inversion by dropping the cost of ray tracing for traveltime estimation in a way similar to standard Prestack Time Migration (PSTM) and the corresponding forward modeling. This requires the model to have smooth lateral variations in elastic properties, so that the traveltime of the scatterpoints can be approximated by a Double Square Root (DSR) equation. To represent a more realistic and stable solution of the inverse problem, while considering the phase of supercritical angles, the

  1. Multidisciplinary Inverse Reliability Analysis Based on Collaborative Optimization with Combination of Linear Approximations

    Directory of Open Access Journals (Sweden)

    Xin-Jia Meng

    2015-01-01

    Full Text Available Multidisciplinary reliability is an important part of the reliability-based multidisciplinary design optimization (RBMDO. However, it usually has a considerable amount of calculation. The purpose of this paper is to improve the computational efficiency of multidisciplinary inverse reliability analysis. A multidisciplinary inverse reliability analysis method based on collaborative optimization with combination of linear approximations (CLA-CO is proposed in this paper. In the proposed method, the multidisciplinary reliability assessment problem is first transformed into a problem of most probable failure point (MPP search of inverse reliability, and then the process of searching for MPP of multidisciplinary inverse reliability is performed based on the framework of CLA-CO. This method improves the MPP searching process through two elements. One is treating the discipline analyses as the equality constraints in the subsystem optimization, and the other is using linear approximations corresponding to subsystem responses as the replacement of the consistency equality constraint in system optimization. With these two elements, the proposed method realizes the parallel analysis of each discipline, and it also has a higher computational efficiency. Additionally, there are no difficulties in applying the proposed method to problems with nonnormal distribution variables. One mathematical test problem and an electronic packaging problem are used to demonstrate the effectiveness of the proposed method.

  2. Inverse scattering problem for a magnetic field in the Glauber approximation

    International Nuclear Information System (INIS)

    Bogdanov, I.V.

    1985-01-01

    New results in the general theory of scattering are obtained. An inverse problem at fixed energy for an axisymmetric magnetic field is formulated and solved within the frames of the quantum-mechanical Glauber approximation. The solution is found in quadratures in the form of an explicit inversion algorithm reproducing a vector potential by the angular dependence of the scattering amplitude. Extreme transitions from the eikonal inversion method to the classical and Born ones are investigated. Integral and differential equations are derived for the eikonal amplitude that ensure the real value of the vector potential and its energy independence. Magnetoelectric analogies the existence of equivalent axisymmetric electric and magnetic fields scattering charged particles in the same manner both in the Glauber and Born approximation are established. The mentioned analogies permit to simulate ion-potential scattering by potential one that is of interest from the practical viewpoint. Three-dimensional (excentral) eikonal inverse problems for the electric and magnetic fields are discussed. The results of the paper can be used in electron optics

  3. Stabilized and Block Approximate Inverse Preconditioners for Problems in Solid and Structural Mechanics

    Czech Academy of Sciences Publication Activity Database

    Benzi, M.; Kouhia, R.; Tůma, Miroslav

    2001-01-01

    Roč. 190, - (2001), s. 6533-6554 ISSN 0045-7825 R&D Projects: GA AV ČR IAA2030801; GA ČR GA201/00/0080 Institutional research plan: AV0Z1030915 Keywords : preconditioning * conjugate gradient * factorized sparse approximate inverse * block algorithms * finite elements * shells Subject RIV: BA - General Mathematics Impact factor: 0.913, year: 2001

  4. Efficient approximations of dispersion relations in optical waveguides with varying refractive-index profiles.

    Science.gov (United States)

    Li, Yutian; Zhu, Jianxin

    2015-05-04

    In this paper we consider the problem of computing the eigen-modes for the varying refractive-index profile in an open waveguide. We first approximate the refractive-index by a piecewise polynomial of degree two, and the corresponding Sturm-Liouville problem (eigenvalue problem) of the Helmholtz operator in each layer can be solved analytically by the Kummer functions. Then, analytical approximate dispersion equations are established for both TE and TM cases. Furthermore, the approximate dispersion equations converge fast to the exact ones for the continuous refractive-index function as the maximum value of the subinterval sizes tends to zero. Suitable numerical methods, such as Müller's method or the chord secant method, may be applied to the dispersion relations to compute the eigenmodes. Numerical simulations show that our method is very practical and efficient for computing eigenmodes.

  5. Seismic Imaging and Velocity Analysis Using a Pseudo Inverse to the Extended Born Approximation

    KAUST Repository

    Alali, Abdullah A.

    2018-05-01

    extension, makes it possible to compute the derivative without applying the extension. I also verify the newly proposed inversion formula on a laterally variant velocity model. In addition, I test the effect of the computed derivative and compare its contribution with the full formula. This additional term has overall limited influence on conventional images. Its largest impact is on vertical reflectors such as salt flanks, granted the velocity is varying laterally in the background as often is in this case. Otherwise, for most applications, we can obtain good quality extended images without this additional term.

  6. Energy spectrum inverse problem of q -deformed harmonic oscillator and WBK approximation

    International Nuclear Information System (INIS)

    Sang, Nguyen Anh; Thuy, Do Thi Thu; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai

    2016-01-01

    Using the connection between q-deformed harmonic oscillator and Morse-like anharmonic potential we investigate the energy spectrum inverse problem. Consider some energy levels of energy spectrum of q -deformed harmonic oscillator are known, we construct the corresponding Morse-like potential then find out the deform parameter q . The application possibility of using the WKB approximation in the energy spectrum inverse problem was discussed for the cases of parabolic potential (harmonic oscillator), Morse-like potential ( q -deformed harmonic oscillator). so we consider our deformed-three-levels simple model, where the set-parameters of Morse potential and the corresponding set-parameters of level deformations are easily and explicitly defined. For practical problems, we propose the deformed- three-levels simple model, where the set-parameters of Morse potential and the corresponding set-parameters of level deformations are easily and explicitly defined. (paper)

  7. The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting

    International Nuclear Information System (INIS)

    Schuster, T; Schöpfer, F; Rieder, A

    2012-01-01

    This article concerns the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search for a solution in an infinite-dimensional Banach space having only a finite number of data available. In this sense the situation is applicable to a large variety of applications where a measurement process delivers a discretization of an infinite-dimensional data space. The method of approximate inverse computes scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The convergence, approximation power and regularization property of this method when applied to semi-discrete operator equations in Hilbert spaces has been investigated in three prequels to this paper. Here we extend these results to a Banach space setting. We prove convergence and stability for general Banach spaces and reproduce the results specifically for the integration operator acting on the space of continuous functions. (paper)

  8. Approximate inverse for the common offset acquisition geometry in 2D seismic imaging

    Science.gov (United States)

    Grathwohl, Christine; Kunstmann, Peer; Quinto, Eric Todd; Rieder, Andreas

    2018-01-01

    We explore how the concept of approximate inverse can be used and implemented to recover singularities in the sound speed from common offset measurements in two space dimensions. Numerical experiments demonstrate the performance of the method. We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173. Quinto additionally thanks the Otto Mønsteds Fond and U.S. National Science Foundation (under grants DMS 1311558 and DMS 1712207) for their support. He thanks colleagues at DTU and KIT for their warm hospitality while this research was being done.

  9. A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

    Energy Technology Data Exchange (ETDEWEB)

    Li, Jinglai, E-mail: jinglaili@sjtu.edu.cn [Institute of Natural Sciences, Department of Mathematics, and MOE Key Laboratory of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240 (China); Lin, Guang, E-mail: lin491@purdue.edu [Department of Mathematics, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 (United States); Computational Sciences and Mathematics Division, Pacific Northwest National Laboratory, Richland, WA 99352 (United States); Yang, Xu, E-mail: xuyang@math.ucsb.edu [Department of Mathematics, University of California, Santa Barbara, CA 93106 (United States)

    2015-09-01

    In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by three steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.

  10. Approximation in generalized Hardy classes and resolution of inverse problems for tokamaks

    International Nuclear Information System (INIS)

    Fisher, Y.

    2011-11-01

    This thesis concerns both the theoretical and constructive resolution of inverse problems for isotropic diffusion equation in planar domains, simply and doubly connected. From partial Cauchy boundary data (potential, flux), we look for those quantities on the remaining part of the boundary, where no information is available, as well as inside the domain. The proposed approach proceeds by considering solutions to the diffusion equation as real parts of complex valued solutions to some conjugated Beltrami equation. These particular generalized analytic functions allow to introduce Hardy classes, where the inverse problem is stated as a best constrained approximation issue (bounded extrema problem), and thereby is regularized. Hence, existence and smoothness properties, together with density results of traces on the boundary, ensure well-posedness. An application is studied, to a free boundary problem for a magnetically confined plasma in the tokamak Tore Supra (CEA Cadarache France). The resolution of the approximation problem on a suitable basis of functions (toroidal harmonics) leads to a qualification criterion for the estimated plasma boundary. A descent algorithm makes it decrease, and refines the estimations. The method does not require any integration of the solution in the overall domain. It furnishes very accurate numerical results, and could be extended to other devices, like JET or ITER. (author)

  11. Inverse bremsstrahlung heating beyond the first Born approximation for dense plasmas in laser fields

    International Nuclear Information System (INIS)

    Moll, M; Schlanges, M; Bornath, Th; Krainov, V P

    2012-01-01

    Inverse bremsstrahlung (IB) heating, an important process in the laser-matter interaction, involves two different kinds of interaction—the interaction of the electrons with the external laser field and the electron-ion interaction. This makes analytical approaches very difficult. In a quantum perturbative approach to the IB heating rate in strong laser fields, usually the first Born approximation with respect to the electron-ion potential is considered, whereas the influence of the electric field is taken exactly in the Volkov wave functions. In this paper, a perturbative treatment is presented adopting a screened electron-ion interaction potential. As a new result, we derive the momentum-dependent, angle-averaged heating rate in the first Born approximation. Numerical results are discussed for a broad range of field strengths, and the conditions for the applicability of a linear approximation for the heating rate are analyzed in detail. Going a step further in the perturbation series, we consider the transition amplitude in the second Born approximation, which enables us to calculate the heating rate up to the third order of the interaction strength. (paper)

  12. Solution of the point kinetics equations in the presence of Newtonian temperature feedback by Pade approximations via the analytical inversion method

    International Nuclear Information System (INIS)

    Aboanber, A E; Nahla, A A

    2002-01-01

    A method based on the Pade approximations is applied to the solution of the point kinetics equations with a time varying reactivity. The technique consists of treating explicitly the roots of the inhour formula. A significant improvement has been observed by treating explicitly the most dominant roots of the inhour equation, which usually would make the Pade approximation inaccurate. Also the analytical inversion method which permits a fast inversion of polynomials of the point kinetics matrix is applied to the Pade approximations. Results are presented for several cases of Pade approximations using various options of the method with different types of reactivity. The formalism is applicable equally well to non-linear problems, where the reactivity depends on the neutron density through temperature feedback. It was evident that the presented method is particularly good for cases in which the reactivity can be represented by a series of steps and performed quite well for more general cases

  13. One-dimensional free-electron laser equations without the slowly varying envelope approximation

    Directory of Open Access Journals (Sweden)

    C. Maroli

    2011-07-01

    Full Text Available A set of one-dimensional equations has been deduced in the time domain from the Maxwell-Lorentz system with the aim of describing the free-electron laser radiation without using the slowly varying envelope approximation (SVEA. These equations are valid even in the case of arbitrarily short electron bunches and of current distributions with ripples on the scale of or shorter than the wavelength. Numerical examples are presented, showing that for long homogeneous bunches the new set of equations gives results in agreement with the SVEA free-electron laser theory and that the use of short or prebunched electron beams leads to a decrease of the emission lethargy. Furthermore, we demonstrate that in all cases in which the backward low frequency wave has negligible effects, these equations can be reduced to a form similar to the usual 1D SVEA equations but with a different definition of the bunching term.

  14. Scattering of particles with inclusions. Modeling and inverse problem solution in the Rayleigh-Gans approximation

    International Nuclear Information System (INIS)

    Otero, F A; Frontini, G L; Elicabe, G E

    2011-01-01

    An analytic model for the scattering of a spherical particle with spherical inclusions has been proposed under the RG approximation. The model can be used without limitations to describe an X-ray scattering experiment. However, for light scattering several conditions must be fulfilled. Based on this model an inverse methodology is proposed to estimate the radii of host particle and inclusions, the number of inclusions and the Distance Distribution Functions (DDF's) of the distances between inclusions and the distances between inclusions and the origin of coordinates. The methodology is numerically tested in a light scattering example in which the host particle is eliminated by matching the refractive indices of host particle and medium. The results obtained for this cluster particle are very satisfactory.

  15. Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization

    Science.gov (United States)

    Zhang, Li-qiang; Ma, Ting-ting; Yu, Chang-shui

    2018-03-01

    The computability of the quantifier of a given quantum resource is the essential challenge in the resource theory and the inevitable bottleneck for its application. Here we focus on the measurement-induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the noncontractivity of the measurement-induced nonlocality and has analytic expressions for pure states, (2 ⊗d )-dimensional quantum states, and some particular high-dimensional quantum states. Most importantly, an inverse approximate joint diagonalization algorithm, due to its simplicity, high efficiency, stability, and state independence, is presented to provide almost-analytic expressions for any quantum state, which can also shed light on other aspects in physics. To illustrate applications as well as demonstrate the validity of the algorithm, we compare the analytic and numerical expressions of various examples and show their perfect consistency.

  16. Inverse periodic problem for the discrete approximation of the Schroedinger nonlinear equation

    International Nuclear Information System (INIS)

    Bogolyubov, N.N.; Prikarpatskij, A.K.; AN Ukrainskoj SSR, Lvov. Inst. Prikladnykh Problem Mekhaniki i Matematiki)

    1982-01-01

    The problem of numerical solution of the Schroedinger nonlinear equation (1) iPSIsub(t) = PSIsub(xx)+-2(PSI)sup(2)PSI. The numerical solution of nonlinear differential equation supposes its discrete approximation is required for the realization of the computer calculation process. Tor the equation (1) there exists the following discrete approximation by variable x(2) iPSIsub(n, t) = (PSIsub(n+1)-2PSIsub(n)+PSIsub(n-1))/(Δx)sup(2)+-(PSIsub(n))sup(2)(PSIsub(n+1)+PSIsub(n-1)), n=0, +-1, +-2... where PSIsub(n)(+) is the corresponding value of PSI(x, t) function in the node and divisions with the equilibrium step Δx. The main problem is obtaining analytically exact solutions of the equations (2). The analysis of the equation system (2) is performed on the base of the discrete analogue of the periodic variant of the inverse scattering problem method developed with the aid of nonlinear equations of the Korteweg-de Vries type. Obtained in explicit form are analytical solutions of the equations system (2). The solutions are expressed through the Riemann THETA-function [ru

  17. Inferring time‐varying recharge from inverse analysis of long‐term water levels

    Science.gov (United States)

    Dickinson, Jesse; Hanson, R.T.; Ferré, T.P.A.; Leake, S.A.

    2004-01-01

    Water levels in aquifers typically vary in response to time‐varying rates of recharge, suggesting the possibility of inferring time‐varying recharge rates on the basis of long‐term water level records. Presumably, in the southwestern United States (Arizona, Nevada, New Mexico, southern California, and southern Utah), rates of mountain front recharge to alluvial aquifers depend on variations in precipitation rates due to known climate cycles such as the El Niño‐Southern Oscillation index and the Pacific Decadal Oscillation. This investigation examined the inverse application of a one‐dimensional analytical model for periodic flow described by Lloyd R. Townley in 1995 to estimate periodic recharge variations on the basis of variations in long‐term water level records using southwest aquifers as the case study. Time‐varying water level records at various locations along the flow line were obtained by simulation of forward models of synthetic basins with applied sinusoidal recharge of either a single period or composite of multiple periods of length similar to known climate cycles. Periodic water level components, reconstructed using singular spectrum analysis (SSA), were used to calibrate the analytical model to estimate each recharge component. The results demonstrated that periodic recharge estimates were most accurate in basins with nearly uniform transmissivity and the accuracy of the recharge estimates depends on monitoring well location. A case study of the San Pedro Basin, Arizona, is presented as an example of calibrating the analytical model to real data.

  18. The noise of ultrashort pulse mode-locked lasers beyond the slowly varying envelope approximation

    International Nuclear Information System (INIS)

    Takushima, Y; Haus, H A; Kaertner, F X

    2004-01-01

    The zero-point fluctuations in an L-C circuit of finite Q are revisited. The zero-point energy is shown to approach the value of hbarω 0 /2 only in the limit of an infinite Q. A Fabry-Perot resonator, on the other hand, has bounded zero-point energies of its modes that are equal to hbarω n /2 for each resonance. Based on the Fabry-Perot resonator with broadband noise, we analyse the noise of an ultrafast mode-locked laser when the slowly varying envelope approximation (SVEA) is not valid. This is achieved by reinterpreting the quantized form of the master equation of mode locking as an equation of motion for the electric field rather than for the creation operator of a photon. It is found that in this formulation quantum correlations exist that are not present in the SVEA. The correlations become evident in the spectrum of the zero-point fluctuations and therefore in the background noise of the laser. This behaviour can be detected by homodyne detection of the laser output. The linewidth of the frequency comb generated by the mode-locked laser is not affected by these correlations and is given by the Schawlow-Townes linewidth of an equivalent continuous wave taking the additional intracavity loss due to the mode locking process into account

  19. Efficient full decay inversion of MRS data with a stretched-exponential approximation of the ? distribution

    Science.gov (United States)

    Behroozmand, Ahmad A.; Auken, Esben; Fiandaca, Gianluca; Christiansen, Anders Vest; Christensen, Niels B.

    2012-08-01

    We present a new, efficient and accurate forward modelling and inversion scheme for magnetic resonance sounding (MRS) data. MRS, also called surface-nuclear magnetic resonance (surface-NMR), is the only non-invasive geophysical technique that directly detects free water in the subsurface. Based on the physical principle of NMR, protons of the water molecules in the subsurface are excited at a specific frequency, and the superposition of signals from all protons within the excited earth volume is measured to estimate the subsurface water content and other hydrological parameters. In this paper, a new inversion scheme is presented in which the entire data set is used, and multi-exponential behaviour of the NMR signal is approximated by the simple stretched-exponential approach. Compared to the mono-exponential interpretation of the decaying NMR signal, we introduce a single extra parameter, the stretching exponent, which helps describe the porosity in terms of a single relaxation time parameter, and helps to determine correct initial amplitude and relaxation time of the signal. Moreover, compared to a multi-exponential interpretation of the MRS data, the decay behaviour is approximated with considerably fewer parameters. The forward response is calculated in an efficient numerical manner in terms of magnetic field calculation, discretization and integration schemes, which allows fast computation while maintaining accuracy. A piecewise linear transmitter loop is considered for electromagnetic modelling of conductivities in the layered half-space providing electromagnetic modelling of arbitrary loop shapes. The decaying signal is integrated over time windows, called gates, which increases the signal-to-noise ratio, particularly at late times, and the data vector is described with a minimum number of samples, that is, gates. The accuracy of the forward response is investigated by comparing a MRS forward response with responses from three other approaches outlining

  20. Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

    Science.gov (United States)

    Kaporin, I. E.

    2012-02-01

    In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

  1. Determination of the aerosol size distribution by analytic inversion of the extinction spectrum in the complex anomalous diffraction approximation.

    Science.gov (United States)

    Franssens, G; De Maziére, M; Fonteyn, D

    2000-08-20

    A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz's model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.

  2. Nodal approximations of varying order by energy group for solving the diffusion equation

    International Nuclear Information System (INIS)

    Broda, J.T.

    1992-02-01

    The neutron flux across the nuclear reactor core is of interest to reactor designers and others. The diffusion equation, an integro-differential equation in space and energy, is commonly used to determine the flux level. However, the solution of a simplified version of this equation when automated is very time consuming. Since the flux level changes with time, in general, this calculation must be made repeatedly. Therefore solution techniques that speed the calculation while maintaining accuracy are desirable. One factor that contributes to the solution time is the spatial flux shape approximation used. It is common practice to use the same order flux shape approximation in each energy group even though this method may not be the most efficient. The one-dimensional, two-energy group diffusion equation was solved, for the node average flux and core k-effective, using two sets of spatial shape approximations for each of three reactor types. A fourth-order approximation in both energy groups forms the first set of approximations used. The second set used combines a second-order approximation with a fourth-order approximation in energy group two. Comparison of the results from the two approximation sets show that the use of a different order spatial flux shape approximation results in considerable loss in accuracy for the pressurized water reactor modeled. However, the loss in accuracy is small for the heavy water and graphite reactors modeled. The use of different order approximations in each energy group produces mixed results. Further investigation into the accuracy and computing time is required before any quantitative advantage of the use of the second-order approximation in energy group one and the fourth-order approximation in energy group two can be determined

  3. Models of few optical cycle solitons beyond the slowly varying envelope approximation

    International Nuclear Information System (INIS)

    Leblond, H.; Mihalache, D.

    2013-01-01

    In the past years there was a huge interest in experimental and theoretical studies in the area of few-optical-cycle pulses and in the broader fast growing field of the so-called extreme nonlinear optics. This review concentrates on theoretical studies performed in the past decade concerning the description of few optical cycle solitons beyond the slowly varying envelope approximation (SVEA). Here we systematically use the powerful reductive expansion method (alias multiscale analysis) in order to derive simple integrable and nonintegrable evolution models describing both nonlinear wave propagation and interaction of ultrashort (femtosecond) pulses. To this aim we perform the multiple scale analysis on the Maxwell–Bloch equations and the corresponding Schrödinger–von Neumann equation for the density matrix of two-level atoms. We analyze in detail both long-wave and short-wave propagation models. The propagation of ultrashort few-optical-cycle solitons in quadratic and cubic nonlinear media are adequately described by generic integrable and nonintegrable nonlinear evolution equations such as the Korteweg–de Vries equation, the modified Korteweg–de Vries equation, the complex modified Korteweg–de Vries equation, the sine–Gordon equation, the cubic generalized Kadomtsev–Petviashvili equation, and the two-dimensional sine–Gordon equation. Moreover, we consider the propagation of few-cycle optical solitons in both (1+1)- and (2+1)-dimensional physical settings. A generalized modified Korteweg–de Vries equation is introduced in order to describe robust few-optical-cycle dissipative solitons. We investigate in detail the existence and robustness of both linearly polarized and circularly polarized few-cycle solitons, that is, we also take into account the effect of the vectorial nature of the electric field. Some of these results concerning the systematic use of the reductive expansion method beyond the SVEA can be relatively easily extended to few

  4. Iterative algorithms for the input and state recovery from the approximate inverse of strictly proper multivariable systems

    Science.gov (United States)

    Chen, Liwen; Xu, Qiang

    2018-02-01

    This paper proposes new iterative algorithms for the unknown input and state recovery from the system outputs using an approximate inverse of the strictly proper linear time-invariant (LTI) multivariable system. One of the unique advantages from previous system inverse algorithms is that the output differentiation is not required. The approximate system inverse is stable due to the systematic optimal design of a dummy feedthrough D matrix in the state-space model via the feedback stabilization. The optimal design procedure avoids trial and error to identify such a D matrix which saves tremendous amount of efforts. From the derived and proved convergence criteria, such an optimal D matrix also guarantees the convergence of algorithms. Illustrative examples show significant improvement of the reference input signal tracking by the algorithms and optimal D design over non-iterative counterparts on controllable or stabilizable LTI systems, respectively. Case studies of two Boeing-767 aircraft aerodynamic models further demonstrate the capability of the proposed methods.

  5. Frames of exponentials:lower frame bounds for finite subfamilies, and approximation of the inverse frame operator

    DEFF Research Database (Denmark)

    Christensen, Ole; Lindner, Alexander M

    2001-01-01

    We give lower frame bounds for finite subfamilies of a frame of exponentials {e(i lambdak(.))}k is an element ofZ in L-2(-pi,pi). We also present a method for approximation of the inverse frame operator corresponding to {e(i lambdak(.))}k is an element ofZ, where knowledge of the frame bounds for...

  6. Eddy current imaging. Limits of the born approximation and advantages of an exact solution to the inverse problem

    International Nuclear Information System (INIS)

    Hamman, E.; Zorgati, R.

    1995-01-01

    Eddy current non-destructive testing is used by EDF to detect flaws affecting conductive objects such as steam generator tubes. With a view to obtaining ever more accurate information on equipment integrity, thereby facilitating diagnosis, studies aimed at using measurements to reconstruct an image of the flaw have been proceeding now for about ten years. In this context, our approach to eddy current imaging is based on inverse problem formalism. The direct problem, involving a mathematical model linking measurements provided by a probe with variables characterizing the defect, is dealt with elsewhere. Using the model results, we study the possibility of inverting it, i.e. of reconstructing an image of the flaw from the measurements. We first give an overview of the different inversion techniques, representative of the state of the art and all based on linearization of the inverse problem by means of the Born approximation. The model error resulting from an excessive Born approximation nevertheless severely limits the quantity of the images which can be obtained. In order to counteract this often critical error and extend the eddy current imaging application field, we have to del with the non-linear inverse problem. A method derived from recent research is proposed and implemented to ensure consistency with the exact model. Based on an 'optimization' type approach and provided with a convergence theorem, the method is highly efficient. (authors). 17 refs., 7 figs., 1 append

  7. The varying cosmological constant: a new approximation to the Friedmann equations and universe model

    Science.gov (United States)

    Öztaş, Ahmet M.; Dil, Emre; Smith, Michael L.

    2018-05-01

    We investigate the time-dependent nature of the cosmological constant, Λ, of the Einstein Field Equation (EFE). Beginning with the Einstein-Hilbert action as our fundamental principle we develop a modified version of the EFE allowing the value of Λ to vary as a function of time, Λ(t), indirectly, for an expanding universe. We follow the evolving Λ presuming four-dimensional space-time and a flat universe geometry and present derivations of Λ(t) as functions of the Hubble constant, matter density, and volume changes which can be traced back to the radiation epoch. The models are more detailed descriptions of the Λ dependence on cosmological factors than previous, allowing calculations of the important parameters, Ωm and Ωr, to deep lookback times. Since we derive these without the need for extra dimensions or other special conditions our derivations are useful for model evaluation with astronomical data. This should aid resolution of several difficult problems of astronomy such as the best value for the Hubble constant at present and at recombination.

  8. Time-varying effect moderation using the structural nested mean model: estimation using inverse-weighted regression with residuals

    Science.gov (United States)

    Almirall, Daniel; Griffin, Beth Ann; McCaffrey, Daniel F.; Ramchand, Rajeev; Yuen, Robert A.; Murphy, Susan A.

    2014-01-01

    This article considers the problem of examining time-varying causal effect moderation using observational, longitudinal data in which treatment, candidate moderators, and possible confounders are time varying. The structural nested mean model (SNMM) is used to specify the moderated time-varying causal effects of interest in a conditional mean model for a continuous response given time-varying treatments and moderators. We present an easy-to-use estimator of the SNMM that combines an existing regression-with-residuals (RR) approach with an inverse-probability-of-treatment weighting (IPTW) strategy. The RR approach has been shown to identify the moderated time-varying causal effects if the time-varying moderators are also the sole time-varying confounders. The proposed IPTW+RR approach provides estimators of the moderated time-varying causal effects in the SNMM in the presence of an additional, auxiliary set of known and measured time-varying confounders. We use a small simulation experiment to compare IPTW+RR versus the traditional regression approach and to compare small and large sample properties of asymptotic versus bootstrap estimators of the standard errors for the IPTW+RR approach. This article clarifies the distinction between time-varying moderators and time-varying confounders. We illustrate the methodology in a case study to assess if time-varying substance use moderates treatment effects on future substance use. PMID:23873437

  9. Approximate P-wave ray tracing and dynamic ray tracing in weakly orthorhombic media of varying symmetry orientation

    KAUST Repository

    Masmoudi, Nabil; Pšenčí k, Ivan

    2014-01-01

    We present an approximate, but efficient and sufficiently accurate P-wave ray tracing and dynamic ray tracing procedure for 3D inhomogeneous, weakly orthorhombic media with varying orientation of symmetry planes. In contrast to commonly used approaches, the orthorhombic symmetry is preserved at any point of the model. The model is described by six weak-anisotropy parameters and three Euler angles, which may vary arbitrarily, but smoothly, throughout the model. We use the procedure for the calculation of rays and corresponding two-point traveltimes in a VSP experiment in a part of the BP benchmark model generalized to orthorhombic symmetry.

  10. Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

    Science.gov (United States)

    Cui, Tiangang; Marzouk, Youssef; Willcox, Karen

    2016-06-01

    Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.

  11. Approximate Global Convergence and Quasi-Reversibility for a Coefficient Inverse Problem with Backscattering Data

    Science.gov (United States)

    2011-04-01

    L1u. Assume that geodesic lines, generated by the eikonal equation corresponding to the function c (x) are regular, i.e. any two points in R3 can be...source x0 is located far from Ω, then similarly with (107) ∆l (x, x0) ≈ 0 in Ω. The function l (x, x0) satisfies the eikonal equation [38] |∇xl (x, x0...called “inverse kinematic problem” which aims to recover the function c (x) from the eikonal equation assuming that the function l (x, x0) is known for

  12. General factorization relations and consistency conditions in the sudden approximation via infinite matrix inversion

    International Nuclear Information System (INIS)

    Chan, C.K.; Hoffman, D.K.; Evans, J.W.

    1985-01-01

    Local, i.e., multiplicative, operators satisfy well-known linear factorization relations wherein matrix elements (between states associated with a complete set of wave functions) can be obtained as a linear combination of those out of the ground state (the input data). Analytic derivation of factorization relations for general state input data results in singular integral expressions for the coefficients, which can, however, be regularized using consistency conditions between matrix elements out of a single (nonground) state. Similar results hold for suitable ''symmetry class'' averaged matrix elements where the symmetry class projection operators are ''complete.'' In several cases where the wave functions or projection operators incorporate orthogonal polynomial dependence, we show that the ground state factorization relations have a simplified structure allowing an alternative derivation of the general factorization relations via an infinite matrix inversion procedure. This form is shown to have some advantages over previous versions. In addition, this matrix inversion procedure obtains all consistency conditions (which is not always the case from regularization of singular integrals)

  13. ISO learning approximates a solution to the inverse-controller problem in an unsupervised behavioral paradigm.

    Science.gov (United States)

    Porr, Bernd; von Ferber, Christian; Wörgötter, Florentin

    2003-04-01

    In "Isotropic Sequence Order Learning" (pp. 831-864 in this issue), we introduced a novel algorithm for temporal sequence learning (ISO learning). Here, we embed this algorithm into a formal nonevaluating (teacher free) environment, which establishes a sensor-motor feedback. The system is initially guided by a fixed reflex reaction, which has the objective disadvantage that it can react only after a disturbance has occurred. ISO learning eliminates this disadvantage by replacing the reflex-loop reactions with earlier anticipatory actions. In this article, we analytically demonstrate that this process can be understood in terms of control theory, showing that the system learns the inverse controller of its own reflex. Thereby, this system is able to learn a simple form of feedforward motor control.

  14. Inversions

    Science.gov (United States)

    Brown, Malcolm

    2009-01-01

    Inversions are fascinating phenomena. They are reversals of the normal or expected order. They occur across a wide variety of contexts. What do inversions have to do with learning spaces? The author suggests that they are a useful metaphor for the process that is unfolding in higher education with respect to education. On the basis of…

  15. Inversion of Solid Earth's Varying Shape 2: Using Self-Consistency to Infer Static Ocean Topography

    Science.gov (United States)

    Blewitt, G.; Clarke, P. J.

    2002-12-01

    We have developed a spectral approach to invert for the redistribution of mass on the Earth's surface given precise global geodetic measurements of the solid Earth's geometrical shape. We used the elastic load Love number formalism to characterize the redistributed mass as a spherical harmonic expansion, truncated at some degree and order n. [Clarke and Blewitt, this meeting]. Here we incorporate the additional physical constraint that the sea surface in hydrostatic equilibrium corresponds to an equipotential surface, to infer the non-steric component of static ocean topography. Our model rigorously accounts for self-gravitation of the ocean, continental surface mass, and the deformed solid Earth, such that the sea surface adopts a new equipotential surface consistent with ocean-land mass exchange, deformation of the geoid, deformation of the sea floor, and the geographical configuration of the oceans and continents. We develop a self-consistent spectral inversion method to solve for the distribution of continental surface mass that would generate geographic variations in relative mean sea level such that the total (ocean plus continental) mass distribution agrees with the original geodetic estimates to degree and order n. We apply this theory to study the contribution of seasonal inter-hemispheric (degree-1) mass transfer to seasonal variation in static ocean topography, using a published empirical seasonal model for degree-1 surface loading derived using GPS coordinate time series from the global IGS network [Blewitt et al., Science 294, 2,342-2,345, 2001]. The resulting predictions of seasonal variations of relative sea level strongly depend on location, with peak variations ranging from 3 mm to 19 mm. The largest peak variations are predicted in mid-August around Antarctica and the southern hemisphere in general; the lowest variations are predicted in the northern hemisphere. Corresponding maximum continental loading occurs in Canada and Siberia at the water

  16. Study on the generalized WKB approximation for the inverse scattering problem at fixed energy for complex potentials

    International Nuclear Information System (INIS)

    Pozdnyakov, Yu.A.; Terenetskij, K.O.

    1981-01-01

    The approximate method for solution of the inverse scattering problem (ISP) at fixed energy for complex spherically symmetric potentials decreasing faster 1/r is considered. The method is based on using a generalized WKB approximation. For the designed potential V(r) a sufficiently ''close'' reference potential V(r) has been chosen. For both potentials S-matrix elements (ME) have been calculated and inversion procedure has been carried out. S-ME have been calculated for integral-valued and intermediate angular moment values. S-ME are presented in a graphical form for being restored reference, and restored potentials for proton scattering with Esub(p)=49.48 MeV energy on 12 C nuclei. The restoration is the better the ''closer'' the sought-for potential to the reference one. This allows to specify the potential by means of iterations: the restored potential can be used as a reference one, etc. The operation of a restored potential smoothing before the following iteration is introduced. Drawbacks and advantages of the ISP solution method under consideration are pointed out. The method application is strongly limited by the requirement that the energy should be higher than a certain ''critical'' one. The method is applicable in a wider region of particle energies (in the low-energies direction) than the ordinary WKB method. The method is more simple in realization conformably to complex potentials. The investigations carried out of the proposed ISP solution method at fixed energy for complex spherically-symmetric potentials allow to conclude that the method can be successFully applied to specify the central part of interaction of nucleons, α-particles and heavy ions of average and high energies with atomic nuclei [ru

  17. Fluid approximation analysis of a call center model with time-varying arrivals and after-call work

    Directory of Open Access Journals (Sweden)

    Yosuke Kawai

    2015-12-01

    Full Text Available Important features to be included in queueing-theoretic models of the call center operation are multiple servers, impatient customers, time-varying arrival process, and operator’s after-call work (ACW. We propose a fluid approximation technique for the queueing model with these features by extending the analysis of a similar model without ACW recently developed by Liu and Whitt (2012. Our model assumes that the service for each quantum of fluid consists of a sequence of two stages, the first stage for the conversation with a customer and the second stage for the ACW. When the duration of each stage has exponential, hyperexponential or hypo-exponential distribution, we derive the time-dependent behavior of the content of fluid in each stage of service as well as that in the waiting room. Numerical examples are shown to illustrate the system performance for the cases in which the input rate and/or the number of servers vary in sinusoidal fashion as well as in adaptive ways and in stationary cases.

  18. An approximate inversion method of geoelectrical sounding data using linear and bayesian statistical approaches. Examples of Tritrivakely volcanic lake and Mahitsy area (central part of Madagascar)

    International Nuclear Information System (INIS)

    Ranaivo Nomenjanahary, F.; Rakoto, H.; Ratsimbazafy, J.B.

    1994-08-01

    This paper is concerned with resistivity sounding measurements performed from single site (vertical sounding) or from several sites (profiles) within a bounded area. The objective is to present an accurate information about the study area and to estimate the likelihood of the produced quantitative models. The achievement of this objective obviously requires quite relevant data and processing methods. It also requires interpretation methods which should take into account the probable effect of an heterogeneous structure. In front of such difficulties, the interpretation of resistivity sounding data inevitably involves the use of inversion methods. We suggest starting the interpretation in simple situation (1-D approximation), and using the rough but correct model obtained as an a-priori model for any more refined interpretation. Related to this point of view, special attention should be paid for the inverse problem applied to the resistivity sounding data. This inverse problem is nonlinear, while linearity inherent in the functional response used to describe the physical experiment. Two different approaches are used to build an approximate but higher dimensional inversion of geoelectrical data: the linear approach and the bayesian statistical approach. Some illustrations of their application in resistivity sounding data acquired at Tritrivakely volcanic lake (single site) and at Mahitsy area (several sites) will be given. (author). 28 refs, 7 figs

  19. Physical models for the hypothesized F(nu) varies as the inverse of nu infrared to X-ray continuum of quasi-stellar objects

    International Nuclear Information System (INIS)

    Stein, W.A.

    1991-01-01

    Models for producing the large ultraviolet bump, low-energy X-rays and the hypothesized F(nu) varies as the inverse of nu IR to X-ray continua of QSOs are investigated. Thermal Comptonization in a hot corona of an accretion disk appears to offer the best potential. However, under the energy input conditions in QSOs a corona will reach T above 100 million K. It must be optically thin, so as to not Comptonize the accretion disk ultraviolet emission to an unacceptable extent. However, it then cannot Comptonize a low-frequency source to an F(nu) varies as the inverse of nu continuum extending from the infrared to X-rays. An inner corona, possibly optically thick because of n varies as the sq rt of r density increase, is required for the F(nu) varies as the inverse of nu continuum, but it cannot therefore cover the UV-emitting accretion disk. However, then a Wien peak associated with this inner volume may be implied at 10 keV, contrary to observations. 42 refs

  20. The use of Trefftz functions for approximation of measurement data in an inverse problem of flow boiling in a minichannel

    Directory of Open Access Journals (Sweden)

    Hozejowski Leszek

    2012-04-01

    Full Text Available The paper is devoted to a computational problem of predicting a local heat transfer coefficient from experimental temperature data. The experimental part refers to boiling flow of a refrigerant in a minichannel. Heat is dissipated from heating alloy to the flowing liquid due to forced convection. The mathematical model of the problem consists of the governing Poisson equation and the proper boundary conditions. For accurate results it is required to smooth the measurements which was obtained by using Trefftz functions. The measurements were approximated with a linear combination of Trefftz functions. Due to the computational procedure in which the measurement errors are known, it was possible to smooth the data and also to reduce the residuals of approximation on the boundaries.

  1. Analytical inversions in remote sensing of particle size distributions. IV - Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation

    Science.gov (United States)

    Fymat, A. L.; Smith, C. B.

    1979-01-01

    It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.

  2. Estimation of time-varying pollutant emission rates in a ventilated enclosure: inversion of a reduced model obtained by experimental application of the modal identification method

    International Nuclear Information System (INIS)

    Girault, M; Maillet, D; Bonthoux, F; Galland, B; Martin, P; Braconnier, R; Fontaine, J R

    2008-01-01

    A method is proposed for the estimation of time-varying emission rates of pollutant sources in a ventilated enclosure, through the resolution of an inverse forced convection problem. Unsteady transport–diffusion of the pollutant is considered, with the assumption of a stationary velocity field remaining unchanged during emission (passive contaminant). The pollutant transport equation is therefore linear with respect to concentration. The source's location is also supposed to be known. As the first step, a reduced model (RM) linking concentrations at a set of control points to emission rates of sources is identified from experimental data by using the modal identification method (MIM). This parameter estimation problem uses transient contaminant concentration measurements made at control points inside the ventilated enclosure, corresponding to increasing and decreasing steps of emission rates. Such experimental modelling allows us to avoid dealing with a CFD code involving turbulence modelling and to get rid of uncertainties about sensors position. In a second step, the identified RM is used to solve an inverse forced convection problem: from contaminant concentration measured at the same control points, rates of sources emitting simultaneously are estimated with a sequential in time algorithm using future time steps

  3. Rational Approximations of the Inverse Gaussian Function.

    Science.gov (United States)

    Byars, Jackson A.; Roscoe, John T.

    There are at least two situations in which the behavioral scientist wishes to transform uniformly distributed data into normally distributed data: (1) In studies of sampling distributions where uniformly distributed pseudo-random numbers are generated by a computer but normally distributed numbers are desired; and (2) In measurement applications…

  4. Displacement Parameter Inversion for a Novel Electromagnetic Underground Displacement Sensor

    Directory of Open Access Journals (Sweden)

    Nanying Shentu

    2014-05-01

    Full Text Available Underground displacement monitoring is an effective method to explore deep into rock and soil masses for execution of subsurface displacement measurements. It is not only an important means of geological hazards prediction and forecasting, but also a forefront, hot and sophisticated subject in current geological disaster monitoring. In previous research, the authors had designed a novel electromagnetic underground horizontal displacement sensor (called the H-type sensor by combining basic electromagnetic induction principles with modern sensing techniques and established a mutual voltage measurement theoretical model called the Equation-based Equivalent Loop Approach (EELA. Based on that work, this paper presents an underground displacement inversion approach named “EELA forward modeling-approximate inversion method”. Combining the EELA forward simulation approach with the approximate optimization inversion theory, it can deduce the underground horizontal displacement through parameter inversion of the H-type sensor. Comprehensive and comparative studies have been conducted between the experimentally measured and theoretically inversed values of horizontal displacement under counterpart conditions. The results show when the measured horizontal displacements are in the 0–100 mm range, the horizontal displacement inversion discrepancy is generally tested to be less than 3 mm under varied tilt angles and initial axial distances conditions, which indicates that our proposed parameter inversion method can predict underground horizontal displacement measurements effectively and robustly for the H-type sensor and the technique is applicable for practical geo-engineering applications.

  5. Approximate Likelihood

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...

  6. Diophantine approximation

    CERN Document Server

    Schmidt, Wolfgang M

    1980-01-01

    "In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)

  7. Inverse photoemission

    International Nuclear Information System (INIS)

    Namatame, Hirofumi; Taniguchi, Masaki

    1994-01-01

    Photoelectron spectroscopy is regarded as the most powerful means since it can measure almost perfectly the occupied electron state. On the other hand, inverse photoelectron spectroscopy is the technique for measuring unoccupied electron state by using the inverse process of photoelectron spectroscopy, and in principle, the similar experiment to photoelectron spectroscopy becomes feasible. The development of the experimental technology for inverse photoelectron spectroscopy has been carried out energetically by many research groups so far. At present, the heightening of resolution of inverse photoelectron spectroscopy, the development of inverse photoelectron spectroscope in which light energy is variable and so on are carried out. But the inverse photoelectron spectroscope for vacuum ultraviolet region is not on the market. In this report, the principle of inverse photoelectron spectroscopy and the present state of the spectroscope are described, and the direction of the development hereafter is groped. As the experimental equipment, electron guns, light detectors and so on are explained. As the examples of the experiment, the inverse photoelectron spectroscopy of semimagnetic semiconductors and resonance inverse photoelectron spectroscopy are reported. (K.I.)

  8. An improved saddlepoint approximation.

    Science.gov (United States)

    Gillespie, Colin S; Renshaw, Eric

    2007-08-01

    Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm.

  9. Sharp spatially constrained inversion

    DEFF Research Database (Denmark)

    Vignoli, Giulio G.; Fiandaca, Gianluca G.; Christiansen, Anders Vest C A.V.C.

    2013-01-01

    We present sharp reconstruction of multi-layer models using a spatially constrained inversion with minimum gradient support regularization. In particular, its application to airborne electromagnetic data is discussed. Airborne surveys produce extremely large datasets, traditionally inverted...... by using smoothly varying 1D models. Smoothness is a result of the regularization constraints applied to address the inversion ill-posedness. The standard Occam-type regularized multi-layer inversion produces results where boundaries between layers are smeared. The sharp regularization overcomes...... inversions are compared against classical smooth results and available boreholes. With the focusing approach, the obtained blocky results agree with the underlying geology and allow for easier interpretation by the end-user....

  10. Inverse Limits

    CERN Document Server

    Ingram, WT

    2012-01-01

    Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influen

  11. Approximate systems with confluent bonding mappings

    OpenAIRE

    Lončar, Ivan

    2001-01-01

    If X = {Xn, pnm, N} is a usual inverse system with confluent (monotone) bonding mappings, then the projections are confluent (monotone). This is not true for approximate inverse system. The main purpose of this paper is to show that the property of Kelley (smoothness) of the space Xn is a sufficient condition for the confluence (monotonicity) of the projections.

  12. Mapping moveout approximations in TI media

    KAUST Repository

    Stovas, Alexey; Alkhalifah, Tariq Ali

    2013-01-01

    Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

  13. Mapping moveout approximations in TI media

    KAUST Repository

    Stovas, Alexey

    2013-11-21

    Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

  14. Inverse Kinematics

    Directory of Open Access Journals (Sweden)

    Joel Sereno

    2010-01-01

    Full Text Available Inverse kinematics is the process of converting a Cartesian point in space into a set of joint angles to more efficiently move the end effector of a robot to a desired orientation. This project investigates the inverse kinematics of a robotic hand with fingers under various scenarios. Assuming the parameters of a provided robot, a general equation for the end effector point was calculated and used to plot the region of space that it can reach. Further, the benefits obtained from the addition of a prismatic joint versus an extra variable angle joint were considered. The results confirmed that having more movable parts, such as prismatic points and changing angles, increases the effective reach of a robotic hand.

  15. Multidimensional inversion

    International Nuclear Information System (INIS)

    Desesquelles, P.

    1997-01-01

    Computer Monte Carlo simulations occupy an increasingly important place between theory and experiment. This paper introduces a global protocol for the comparison of model simulations with experimental results. The correlated distributions of the model parameters are determined using an original recursive inversion procedure. Multivariate analysis techniques are used in order to optimally synthesize the experimental information with a minimum number of variables. This protocol is relevant in all fields if physics dealing with event generators and multi-parametric experiments. (authors)

  16. Diophantine approximation and badly approximable sets

    DEFF Research Database (Denmark)

    Kristensen, S.; Thorn, R.; Velani, S.

    2006-01-01

    . The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

  17. Approximation methods in probability theory

    CERN Document Server

    Čekanavičius, Vydas

    2016-01-01

    This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

  18. Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method

    Czech Academy of Sciences Publication Activity Database

    Benzi, M.; Cullum, J. K.; Tůma, Miroslav

    2000-01-01

    Roč. 22, č. 4 (2000), s. 1318-1332 ISSN 1064-8275 R&D Projects: GA AV ČR IAA2030706; GA AV ČR IAA2030801 Institutional research plan: AV0Z1030915 Subject RIV: BA - General Mathematics Impact factor: 1.421, year: 2000

  19. Bayesian seismic AVO inversion

    Energy Technology Data Exchange (ETDEWEB)

    Buland, Arild

    2002-07-01

    A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P-wave velocity, S-wave velocity and density. Distributions for other elastic parameters can also be assessed, for example acoustic impedance, shear impedance and P-wave to S-wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance, hence exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3-D dataset from the Sleipner Field. The results show good agreement with well logs but the uncertainty is high. The stochastic model includes uncertainties of both the elastic parameters, the wavelet and the seismic and well log data. The posterior distribution is explored by Markov chain Monte Carlo simulation using the Gibbs sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The uncertainty of the estimated wavelet is low. In the Heidrun examples the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results. We have developed a 3-D linearized AVO inversion method with spatially coupled model parameters where the objective is to obtain posterior distributions for P-wave velocity, S

  20. Stability study of pre-stack seismic inversion based on the full Zoeppritz equation

    Science.gov (United States)

    Liang, Lifeng; Zhang, Hongbing; Guo, Qiang; Saeed, Wasif; Shang, Zuoping; Huang, Guojiao

    2017-10-01

    Pre-stack seismic inversion is highly important and complicated. Its result is non-unique, and the process is unstable because pre-stack seismic inversion is an ill-posed problem that simultaneously obtains the results of multiple parameters. Combining the full Zoeppritz equation and additional assumptions with edge-preserving regularization (EPR) can help mitigate the problem. To achieve this combination, we developed an inversion method by constructing a new objective function, which includes the EPR and the Markov random field. The method directly gains reflectivity R PP by the full Zoeppritz equation instead of its approximations and effectively controls the stability of simultaneous inversion by two additional assumptions: the sectional constant V S/V P and the generalized Gardner equation. Thus, the simultaneous inversion of multiple parameters is directed toward to V P, ΔL S (the fitting deviation of V S) and density, and the generalized Gardner equation is regarded as a constraint from which the fitting relationship is derived. We applied the fast simulated annealing algorithm to solve the nonlinear optimization problem. The test results on 2D synthetic data indicated that the stability of simultaneous inversion for V P, ΔL S and density is better than these for V P, V S, and density. The inverted result of density gradually worsens as the deviation ΔL D (the fitting deviation of the density) increases. Moreover, the inverted results were acceptable when using the fitting relationships with error, although they showed varying degrees of influence. We constructed time-varying and space-varying fitting relationships using the logging data in pre-stack inversion of the field seismic data. This improved the inverted results of the simultaneous inversion for complex geological models. Finally, the inverted results of the field data distinctly revealed more detailed information about the layers and matched well with the logging data along the wells over most

  1. The Inverse of Banded Matrices

    Science.gov (United States)

    2013-01-01

    indexed entries all zeros. In this paper, generalizing a method of Mallik (1999) [5], we give the LU factorization and the inverse of the matrix Br,n (if it...r ≤ i ≤ r, 1 ≤ j ≤ r, with the remaining un-indexed entries all zeros. In this paper generalizing a method of Mallik (1999) [5...matrices and applications to piecewise cubic approximation, J. Comput. Appl. Math. 8 (4) (1982) 285–288. [5] R.K. Mallik , The inverse of a lower

  2. Research on Joint Parameter Inversion for an Integrated Underground Displacement 3D Measuring Sensor

    Directory of Open Access Journals (Sweden)

    Nanying Shentu

    2015-04-01

    Full Text Available Underground displacement monitoring is a key means to monitor and evaluate geological disasters and geotechnical projects. There exist few practical instruments able to monitor subsurface horizontal and vertical displacements simultaneously due to monitoring invisibility and complexity. A novel underground displacement 3D measuring sensor had been proposed in our previous studies, and great efforts have been taken in the basic theoretical research of underground displacement sensing and measuring characteristics by virtue of modeling, simulation and experiments. This paper presents an innovative underground displacement joint inversion method by mixing a specific forward modeling approach with an approximate optimization inversion procedure. It can realize a joint inversion of underground horizontal displacement and vertical displacement for the proposed 3D sensor. Comparative studies have been conducted between the measured and inversed parameters of underground horizontal and vertical displacements under a variety of experimental and inverse conditions. The results showed that when experimentally measured horizontal displacements and vertical displacements are both varied within 0 ~ 30 mm, horizontal displacement and vertical displacement inversion discrepancies are generally less than 3 mm and 1 mm, respectively, under three kinds of simulated underground displacement monitoring circumstances. This implies that our proposed underground displacement joint inversion method is robust and efficient to predict the measuring values of underground horizontal and vertical displacements for the proposed sensor.

  3. Bayesian approach to inverse statistical mechanics

    Science.gov (United States)

    Habeck, Michael

    2014-05-01

    Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

  4. Modulated Pade approximant

    International Nuclear Information System (INIS)

    Ginsburg, C.A.

    1980-01-01

    In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)

  5. Approximation Properties of Certain Summation Integral Type Operators

    Directory of Open Access Journals (Sweden)

    Patel P.

    2015-03-01

    Full Text Available In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

  6. Inverse problems of geophysics

    International Nuclear Information System (INIS)

    Yanovskaya, T.B.

    2003-07-01

    This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given

  7. Sparse approximation with bases

    CERN Document Server

    2015-01-01

    This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

  8. Approximate symmetries of Hamiltonians

    Science.gov (United States)

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

    We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

  9. Inverse problem in nuclear physics

    International Nuclear Information System (INIS)

    Zakhariev, B.N.

    1976-01-01

    The method of reconstruction of interaction from the scattering data is formulated in the frame of the R-matrix theory in which the potential is determined by position of resonance Esub(lambda) and their reduced widths γ 2 lambda. In finite difference approximation for the Schroedinger equation this new approach allows to make the logics of the inverse problem IP more clear. A possibility of applications of IP formalism to various nuclear systems is discussed. (author)

  10. A novel anisotropic inversion approach for magnetotelluric data from subsurfaces with orthogonal geoelectric strike directions

    Science.gov (United States)

    Schmoldt, Jan-Philipp; Jones, Alan G.

    2013-12-01

    The key result of this study is the development of a novel inversion approach for cases of orthogonal, or close to orthogonal, geoelectric strike directions at different depth ranges, for example, crustal and mantle depths. Oblique geoelectric strike directions are a well-known issue in commonly employed isotropic 2-D inversion of MT data. Whereas recovery of upper (crustal) structures can, in most cases, be achieved in a straightforward manner, deriving lower (mantle) structures is more challenging with isotropic 2-D inversion in the case of an overlying region (crust) with different geoelectric strike direction. Thus, investigators may resort to computationally expensive and more limited 3-D inversion in order to derive the electric resistivity distribution at mantle depths. In the novel approaches presented in this paper, electric anisotropy is used to image 2-D structures in one depth range, whereas the other region is modelled with an isotropic 1-D or 2-D approach, as a result significantly reducing computational costs of the inversion in comparison with 3-D inversion. The 1- and 2-D versions of the novel approach were tested using a synthetic 3-D subsurface model with orthogonal strike directions at crust and mantle depths and their performance was compared to results of isotropic 2-D inversion. Structures at crustal depths were reasonably well recovered by all inversion approaches, whereas recovery of mantle structures varied significantly between the different approaches. Isotropic 2-D inversion models, despite decomposition of the electric impedance tensor and using a wide range of inversion parameters, exhibited severe artefacts thereby confirming the requirement of either an enhanced or a higher dimensionality inversion approach. With the anisotropic 1-D inversion approach, mantle structures of the synthetic model were recovered reasonably well with anisotropy values parallel to the mantle strike direction (in this study anisotropy was assigned to the

  11. Approximating distributions from moments

    Science.gov (United States)

    Pawula, R. F.

    1987-11-01

    A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.

  12. CONTRIBUTIONS TO RATIONAL APPROXIMATION,

    Science.gov (United States)

    Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

  13. Approximation techniques for engineers

    CERN Document Server

    Komzsik, Louis

    2006-01-01

    Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.

  14. Experimental characterization of methane inverse diffusion flame

    KAUST Repository

    Elbaz, Ayman M.; Roberts, William L.

    2014-01-01

    This article presents 10-kHz images of OH-PLIF simultaneously with 2-D PIV measurements in an inverse methane diffusion flame. Under a constant fuel flow rate, the central air jet Re was varied, leading to air to fuel velocity ratio, Vr, to vary

  15. Expectation Consistent Approximate Inference

    DEFF Research Database (Denmark)

    Opper, Manfred; Winther, Ole

    2005-01-01

    We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...

  16. Ordered cones and approximation

    CERN Document Server

    Keimel, Klaus

    1992-01-01

    This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

  17. Effect of coupling asymmetry on mean-field solutions of the direct and inverse Sherrington-Kirkpatrick model

    DEFF Research Database (Denmark)

    Sakellariou, Jason; Roudi, Yasser; Mezard, Marc

    2012-01-01

    We study how the degree of symmetry in the couplings influences the performance of three mean field methods used for solving the direct and inverse problems for generalized Sherrington-Kirkpatrick models. In this context, the direct problem is predicting the potentially time-varying magnetizations...... than the other two approximations, TAP outperforms MF when the coupling matrix is nearly symmetric, while MF works better when it is strongly asymmetric. For the inverse problem, MF performs better than both TAP and nMF, although an ad hoc adjustment of TAP can make it comparable to MF. For high...

  18. A Joint Method of Envelope Inversion Combined with Hybrid-domain Full Waveform Inversion

    Science.gov (United States)

    CUI, C.; Hou, W.

    2017-12-01

    Full waveform inversion (FWI) aims to construct high-precision subsurface models by fully using the information in seismic records, including amplitude, travel time, phase and so on. However, high non-linearity and the absence of low frequency information in seismic data lead to the well-known cycle skipping problem and make inversion easily fall into local minima. In addition, those 3D inversion methods that are based on acoustic approximation ignore the elastic effects in real seismic field, and make inversion harder. As a result, the accuracy of final inversion results highly relies on the quality of initial model. In order to improve stability and quality of inversion results, multi-scale inversion that reconstructs subsurface model from low to high frequency are applied. But, the absence of very low frequencies (time domain and inversion in the frequency domain. To accelerate the inversion, we adopt CPU/GPU heterogeneous computing techniques. There were two levels of parallelism. In the first level, the inversion tasks are decomposed and assigned to each computation node by shot number. In the second level, GPU multithreaded programming is used for the computation tasks in each node, including forward modeling, envelope extraction, DFT (discrete Fourier transform) calculation and gradients calculation. Numerical tests demonstrated that the combined envelope inversion + hybrid-domain FWI could obtain much faithful and accurate result than conventional hybrid-domain FWI. The CPU/GPU heterogeneous parallel computation could improve the performance speed.

  19. Approximate and renormgroup symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling

    2009-07-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  20. Approximate and renormgroup symmetries

    International Nuclear Information System (INIS)

    Ibragimov, Nail H.; Kovalev, Vladimir F.

    2009-01-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  1. Approximations of Fuzzy Systems

    Directory of Open Access Journals (Sweden)

    Vinai K. Singh

    2013-03-01

    Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions

  2. General Rytov approximation.

    Science.gov (United States)

    Potvin, Guy

    2015-10-01

    We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.

  3. Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

    Science.gov (United States)

    Irving, J.; Koepke, C.; Elsheikh, A. H.

    2017-12-01

    Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward process model linking subsurface parameters to measured data, which is typically assumed to be known perfectly in the inversion procedure. However, in order to make the stochastic solution of the inverse problem computationally tractable using, for example, Markov-chain-Monte-Carlo (MCMC) methods, fast approximations of the forward model are commonly employed. This introduces model error into the problem, which has the potential to significantly bias posterior statistics and hamper data integration efforts if not properly accounted for. Here, we present a new methodology for addressing the issue of model error in Bayesian solutions to hydrogeophysical inverse problems that is geared towards the common case where these errors cannot be effectively characterized globally through some parametric statistical distribution or locally based on interpolation between a small number of computed realizations. Rather than focusing on the construction of a global or local error model, we instead work towards identification of the model-error component of the residual through a projection-based approach. In this regard, pairs of approximate and detailed model runs are stored in a dictionary that grows at a specified rate during the MCMC inversion procedure. At each iteration, a local model-error basis is constructed for the current test set of model parameters using the K-nearest neighbour entries in the dictionary, which is then used to separate the model error from the other error sources before computing the likelihood of the proposed set of model parameters. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar traveltime data for three different subsurface parameterizations of varying complexity. The synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed in the inversion

  4. Geometric approximation algorithms

    CERN Document Server

    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.

  5. INTOR cost approximation

    International Nuclear Information System (INIS)

    Knobloch, A.F.

    1980-01-01

    A simplified cost approximation for INTOR parameter sets in a narrow parameter range is shown. Plausible constraints permit the evaluation of the consequences of parameter variations on overall cost. (orig.) [de

  6. Hierarchical matrix approximation of large covariance matrices

    KAUST Repository

    Litvinenko, Alexander

    2015-01-07

    We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design

  7. Hierarchical matrix approximation of large covariance matrices

    KAUST Repository

    Litvinenko, Alexander

    2015-01-05

    We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.

  8. Hierarchical matrix approximation of large covariance matrices

    KAUST Repository

    Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul

    2015-01-01

    We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design

  9. Hierarchical matrix approximation of large covariance matrices

    KAUST Repository

    Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul

    2015-01-01

    We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.

  10. Approximation and Computation

    CERN Document Server

    Gautschi, Walter; Rassias, Themistocles M

    2011-01-01

    Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg

  11. Approximate kernel competitive learning.

    Science.gov (United States)

    Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang

    2015-03-01

    Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.

  12. Wave-equation dispersion inversion

    KAUST Repository

    Li, Jing

    2016-12-08

    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

  13. Perturbation expansions generated by an approximate propagator

    International Nuclear Information System (INIS)

    Znojil, M.

    1987-01-01

    Starting from a knowledge of an approximate propagator R at some trial energy guess E 0 , a new perturbative prescription for p-plet of bound states and of their energies is proposed. It generalizes the Rayleigh-Schroedinger (RS) degenerate perturbation theory to the nondiagonal operators R (eliminates a RS need of their diagnolisation) and defines an approximate Hamiltonian T by mere inversion. The deviation V of T from the exact Hamiltonian H is assumed small only after a substraction of a further auxiliary Hartree-Fock-like separable ''selfconsistent'' potential U of rank p. The convergence is illustrated numerically on the anharmonic oscillator example

  14. On Covering Approximation Subspaces

    Directory of Open Access Journals (Sweden)

    Xun Ge

    2009-06-01

    Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

  15. Efeitos da transformação de uma variável com distribuição normal em sua inversa sobre os parâmetros de sua distribuição usando técnicas de Monte Carlo Effects of transforming a normally distributed variable into its inverse on parameters of the distribution using Monte Carlo techniques

    Directory of Open Access Journals (Sweden)

    Mirella Leme Franco Geraldini Sirol

    2006-06-01

    Full Text Available Foram realizados quatro estudos de simulação para verificar a distribuição de inversas de variáveis com distribuição normal, em função de diferentes variâncias, médias, pontos de truncamentos e tamanhos amostrais. As variáveis simuladas foram GMD, com distribuição normal, representando o ganho médio diário e DIAS, obtido a partir da inversa de GMD, representando dias para se obter determinado peso. Em todos os estudos, foi utilizado o sistema SAS® (1990 para simulação dos dados e para posterior análise dos resultados. As médias amostrais de DIAS foram dependentes dos desvios-padrão utilizados na simulação. As análises de regressão mostraram redução da média e do desvio-padrão de DIAS em função do aumento na média de GMD. A inclusão de um ponto de truncamento entre 10 e 25% do valor da média de GMD reduziu a média de GMD e aumentou a de DIAS, quando o coeficiente de variação de GMD foi superior a 25%. O efeito do tamanho dos grupos nas médias de GMD e DIAS não foi significativo, mas o desvio-padrão e CV amostrais médios de GMD aumentaram com o tamanho do grupo. Em virtude da dependência entre a média e o desvio-padrão e da variação observada nos desvios-padrão de DIAS em função do tamanho do grupo, a utilização de DIAS como critério de seleção pode diminuir a acurácia da variação. Portanto, para a substituição de GMD por DIAS, é necessária a utilização de um método de análise robusto o suficiente para a eliminação da heterogeneidade de variância.Four simulation studies were conducted to verify the distribution of the inverse of variables with normal distribution, relatively to variances, averages, truncation points and sample sizes. The variables simulated were GMD, with normal distribution and representing average daily gain, and DIAS defined as a multiple of the inverse of GMD and representing days to reach a fixed body weight. The SAS® (1990 system was used, for simulation

  16. On Convex Quadratic Approximation

    NARCIS (Netherlands)

    den Hertog, D.; de Klerk, E.; Roos, J.

    2000-01-01

    In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

  17. Prestack wavefield approximations

    KAUST Repository

    Alkhalifah, Tariq

    2013-01-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

  18. Approximating The DCM

    DEFF Research Database (Denmark)

    Madsen, Rasmus Elsborg

    2005-01-01

    The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM...

  19. Approximation by Cylinder Surfaces

    DEFF Research Database (Denmark)

    Randrup, Thomas

    1997-01-01

    We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...

  20. Prestack wavefield approximations

    KAUST Repository

    Alkhalifah, Tariq

    2013-09-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

  1. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2011-01-01

    Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.

  2. Topology, calculus and approximation

    CERN Document Server

    Komornik, Vilmos

    2017-01-01

    Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

  3. Acute puerperal uterine inversion

    International Nuclear Information System (INIS)

    Hussain, M.; Liaquat, N.; Noorani, K.; Bhutta, S.Z; Jabeen, T.

    2004-01-01

    Objective: To determine the frequency, causes, clinical presentations, management and maternal mortality associated with acute puerperal inversion of the uterus. Materials and Methods: All the patients who developed acute puerperal inversion of the uterus either in or outside the JPMC were included in the study. Patients of chronic uterine inversion were not included in the present study. Abdominal and vaginal examination was done to confirm and classify inversion into first, second or third degrees. Results: 57036 deliveries and 36 acute uterine inversions occurred during the study period, so the frequency of uterine inversion was 1 in 1584 deliveries. Mismanagement of third stage of labour was responsible for uterine inversion in 75% of patients. Majority of the patients presented with shock, either hypovolemic (69%) or neurogenic (13%) in origin. Manual replacement of the uterus under general anaesthesia with 2% halothane was successfully done in 35 patients (97.5%). Abdominal hysterectomy was done in only one patient. There were three maternal deaths due to inversion. Conclusion: Proper education and training regarding placental delivery, diagnosis and management of uterine inversion must be imparted to the maternity care providers especially to traditional birth attendants and family physicians to prevent this potentially life-threatening condition. (author)

  4. Approximate Bayesian recursive estimation

    Czech Academy of Sciences Publication Activity Database

    Kárný, Miroslav

    2014-01-01

    Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf

  5. Approximating Preemptive Stochastic Scheduling

    OpenAIRE

    Megow Nicole; Vredeveld Tjark

    2009-01-01

    We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...

  6. Optimization and approximation

    CERN Document Server

    Pedregal, Pablo

    2017-01-01

    This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

  7. On transparent potentials: a Born approximation study

    International Nuclear Information System (INIS)

    Coudray, C.

    1980-01-01

    In the frame of the scattering inverse problem at fixed energy, a class of potentials transparent in Born approximation is obtained. All these potentials are spherically symmetric and are oscillating functions of the reduced radial variable. Amongst them, the Born approximation of the transparent potential of the Newton-Sabatier method is found. In the same class, quasi-transparent potentials are exhibited. Very general features of potentials transparent in Born approximation are then stated. And bounds are given for the exact scattering amplitudes corresponding to most of the potentials previously exhibited. These bounds, obtained at fixed energy, and for large values of the angular momentum, are found to be independent on the energy

  8. Cyclic approximation to stasis

    Directory of Open Access Journals (Sweden)

    Stewart D. Johnson

    2009-06-01

    Full Text Available Neighborhoods of points in $mathbb{R}^n$ where a positive linear combination of $C^1$ vector fields sum to zero contain, generically, cyclic trajectories that switch between the vector fields. Such points are called stasis points, and the approximating switching cycle can be chosen so that the timing of the switches exactly matches the positive linear weighting. In the case of two vector fields, the stasis points form one-dimensional $C^1$ manifolds containing nearby families of two-cycles. The generic case of two flows in $mathbb{R}^3$ can be diffeomorphed to a standard form with cubic curves as trajectories.

  9. On the WKBJ approximation

    International Nuclear Information System (INIS)

    El Sawi, M.

    1983-07-01

    A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)

  10. The relaxation time approximation

    International Nuclear Information System (INIS)

    Gairola, R.P.; Indu, B.D.

    1991-01-01

    A plausible approximation has been made to estimate the relaxation time from a knowledge of the transition probability of phonons from one state (r vector, q vector) to other state (r' vector, q' vector), as a result of collision. The relaxation time, thus obtained, shows a strong dependence on temperature and weak dependence on the wave vector. In view of this dependence, relaxation time has been expressed in terms of a temperature Taylor's series in the first Brillouin zone. Consequently, a simple model for estimating the thermal conductivity is suggested. the calculations become much easier than the Callaway model. (author). 14 refs

  11. Polynomial approximation on polytopes

    CERN Document Server

    Totik, Vilmos

    2014-01-01

    Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.

  12. Finite elements and approximation

    CERN Document Server

    Zienkiewicz, O C

    2006-01-01

    A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

  13. Inverse logarithmic potential problem

    CERN Document Server

    Cherednichenko, V G

    1996-01-01

    The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

  14. Inverse Kinematics using Quaternions

    DEFF Research Database (Denmark)

    Henriksen, Knud; Erleben, Kenny; Engell-Nørregård, Morten

    In this project I describe the status of inverse kinematics research, with the focus firmly on the methods that solve the core problem. An overview of the different methods are presented Three common methods used in inverse kinematics computation have been chosen as subject for closer inspection....

  15. Time-lapse three-dimensional inversion of complex conductivity data using an active time constrained (ATC) approach

    Science.gov (United States)

    Karaoulis, M.; Revil, A.; Werkema, D.D.; Minsley, B.J.; Woodruff, W.F.; Kemna, A.

    2011-01-01

    Induced polarization (more precisely the magnitude and phase of impedance of the subsurface) is measured using a network of electrodes located at the ground surface or in boreholes. This method yields important information related to the distribution of permeability and contaminants in the shallow subsurface. We propose a new time-lapse 3-D modelling and inversion algorithm to image the evolution of complex conductivity over time. We discretize the subsurface using hexahedron cells. Each cell is assigned a complex resistivity or conductivity value. Using the finite-element approach, we model the in-phase and out-of-phase (quadrature) electrical potentials on the 3-D grid, which are then transformed into apparent complex resistivity. Inhomogeneous Dirichlet boundary conditions are used at the boundary of the domain. The calculation of the Jacobian matrix is based on the principles of reciprocity. The goal of time-lapse inversion is to determine the change in the complex resistivity of each cell of the spatial grid as a function of time. Each model along the time axis is called a 'reference space model'. This approach can be simplified into an inverse problem looking for the optimum of several reference space models using the approximation that the material properties vary linearly in time between two subsequent reference models. Regularizations in both space domain and time domain reduce inversion artefacts and improve the stability of the inversion problem. In addition, the use of the time-lapse equations allows the simultaneous inversion of data obtained at different times in just one inversion step (4-D inversion). The advantages of this new inversion algorithm are demonstrated on synthetic time-lapse data resulting from the simulation of a salt tracer test in a heterogeneous random material described by an anisotropic semi-variogram. ?? 2011 The Authors Geophysical Journal International ?? 2011 RAS.

  16. Plasma Physics Approximations in Ares

    International Nuclear Information System (INIS)

    Managan, R. A.

    2015-01-01

    Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, Fn( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A α (ζ ),A β (ζ ), ζ, f(ζ ) = (1 + e -μ/θ )F 1/2 (μ/θ), F 1/2 '/F 1/2 , F c α , and F c β . In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.

  17. Approximate Bayesian computation.

    Directory of Open Access Journals (Sweden)

    Mikael Sunnåker

    Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.

  18. The random phase approximation

    International Nuclear Information System (INIS)

    Schuck, P.

    1985-01-01

    RPA is the adequate theory to describe vibrations of the nucleus of very small amplitudes. These vibrations can either be forced by an external electromagnetic field or can be eigenmodes of the nucleus. In a one dimensional analogue the potential corresponding to such eigenmodes of very small amplitude should be rather stiff otherwise the motion risks to be a large amplitude one and to enter a region where the approximation is not valid. This means that nuclei which are supposedly well described by RPA must have a very stable groundstate configuration (must e.g. be very stiff against deformation). This is usually the case for doubly magic nuclei or close to magic nuclei which are in the middle of proton and neutron shells which develop a very stable groundstate deformation; we take the deformation as an example but there are many other possible degrees of freedom as, for example, compression modes, isovector degrees of freedom, spin degrees of freedom, and many more

  19. The quasilocalized charge approximation

    International Nuclear Information System (INIS)

    Kalman, G J; Golden, K I; Donko, Z; Hartmann, P

    2005-01-01

    The quasilocalized charge approximation (QLCA) has been used for some time as a formalism for the calculation of the dielectric response and for determining the collective mode dispersion in strongly coupled Coulomb and Yukawa liquids. The approach is based on a microscopic model in which the charges are quasilocalized on a short-time scale in local potential fluctuations. We review the conceptual basis and theoretical structure of the QLC approach and together with recent results from molecular dynamics simulations that corroborate and quantify the theoretical concepts. We also summarize the major applications of the QLCA to various physical systems, combined with the corresponding results of the molecular dynamics simulations and point out the general agreement and instances of disagreement between the two

  20. An inverse heat transfer problem for optimization of the thermal ...

    Indian Academy of Sciences (India)

    This paper takes a different approach towards identification of the thermal process in machining, using inverse heat transfer problem. Inverse heat transfer method allows the closest possible experimental and analytical approximation of thermal state for a machining process. Based on a temperature measured at any point ...

  1. Discrete inverse scattering theory and the continuum limit

    International Nuclear Information System (INIS)

    Berryman, J.G.; Greene, R.R.

    1978-01-01

    The class of satisfactory difference approximations for the Schroedinger equation in discrete inverse scattering theory is shown smaller than previously supposed. A fast algorithm (analogous to the Levinson algorithm for Toeplitz matrices) is found for solving the discrete inverse problem. (Auth.)

  2. Seismic inverse scattering in the downward continuation approach

    NARCIS (Netherlands)

    Stolk, C.C.; de Hoop, M.V.

    Seismic data are commonly modeled by a linearization around a smooth background medium in combination with a high frequency approximation. The perturbation of the medium coefficient is assumed to contain the discontinuities. This leads to two inverse problems, first the linearized inverse problem

  3. Modeling of uncertainties in statistical inverse problems

    International Nuclear Information System (INIS)

    Kaipio, Jari

    2008-01-01

    In all real world problems, the models that tie the measurements to the unknowns of interest, are at best only approximations for reality. While moderate modeling and approximation errors can be tolerated with stable problems, inverse problems are a notorious exception. Typical modeling errors include inaccurate geometry, unknown boundary and initial data, properties of noise and other disturbances, and simply the numerical approximations of the physical models. In principle, the Bayesian approach to inverse problems, in which all uncertainties are modeled as random variables, is capable of handling these uncertainties. Depending on the type of uncertainties, however, different strategies may be adopted. In this paper we give an overview of typical modeling errors and related strategies within the Bayesian framework.

  4. Gravity inversion code

    International Nuclear Information System (INIS)

    Burkhard, N.R.

    1979-01-01

    The gravity inversion code applies stabilized linear inverse theory to determine the topography of a subsurface density anomaly from Bouguer gravity data. The gravity inversion program consists of four source codes: SEARCH, TREND, INVERT, and AVERAGE. TREND and INVERT are used iteratively to converge on a solution. SEARCH forms the input gravity data files for Nevada Test Site data. AVERAGE performs a covariance analysis on the solution. This document describes the necessary input files and the proper operation of the code. 2 figures, 2 tables

  5. Interplay of Nitrogen-Atom Inversion and Conformational Inversion in Enantiomerization of 1H-1-Benzazepines.

    Science.gov (United States)

    Ramig, Keith; Subramaniam, Gopal; Karimi, Sasan; Szalda, David J; Ko, Allen; Lam, Aaron; Li, Jeffrey; Coaderaj, Ani; Cavdar, Leyla; Bogdan, Lukasz; Kwon, Kitae; Greer, Edyta M

    2016-04-15

    A series of 2,4-disubstituted 1H-1-benzazepines, 2a-d, 4, and 6, were studied, varying both the substituents at C2 and C4 and at the nitrogen atom. The conformational inversion (ring-flip) and nitrogen-atom inversion (N-inversion) energetics were studied by variable-temperature NMR spectroscopy and computations. The steric bulk of the nitrogen-atom substituent was found to affect both the conformation of the azepine ring and the geometry around the nitrogen atom. Also affected were the Gibbs free energy barriers for the ring-flip and the N-inversion. When the nitrogen-atom substituent was alkyl, as in 2a-c, the geometry of the nitrogen atom was nearly planar and the azepine ring was highly puckered; the result was a relatively high-energy barrier to ring-flip and a low barrier to N-inversion. Conversely, when the nitrogen-atom substituent was a hydrogen atom, as in 2d, 4, and 6, the nitrogen atom was significantly pyramidalized and the azepine ring was less puckered; the result here was a relatively high energy barrier to N-inversion and a low barrier to ring-flip. In these N-unsubstituted compounds, it was found computationally that the lowest-energy stereodynamic process was ring-flip coupled with N-inversion, as N-inversion alone had a much higher energy barrier.

  6. Ensemble Kalman methods for inverse problems

    International Nuclear Information System (INIS)

    Iglesias, Marco A; Law, Kody J H; Stuart, Andrew M

    2013-01-01

    The ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 (Evensen 1994 J. Geophys. Res. 99 10143–62) as a novel method for data assimilation: state estimation for noisily observed time-dependent problems. Since that time it has had enormous impact in many application domains because of its robustness and ease of implementation, and numerical evidence of its accuracy. In this paper we propose the application of an iterative ensemble Kalman method for the solution of a wide class of inverse problems. In this context we show that the estimate of the unknown function that we obtain with the ensemble Kalman method lies in a subspace A spanned by the initial ensemble. Hence the resulting error may be bounded above by the error found from the best approximation in this subspace. We provide numerical experiments which compare the error incurred by the ensemble Kalman method for inverse problems with the error of the best approximation in A, and with variants on traditional least-squares approaches, restricted to the subspace A. In so doing we demonstrate that the ensemble Kalman method for inverse problems provides a derivative-free optimization method with comparable accuracy to that achieved by traditional least-squares approaches. Furthermore, we also demonstrate that the accuracy is of the same order of magnitude as that achieved by the best approximation. Three examples are used to demonstrate these assertions: inversion of a compact linear operator; inversion of piezometric head to determine hydraulic conductivity in a Darcy model of groundwater flow; and inversion of Eulerian velocity measurements at positive times to determine the initial condition in an incompressible fluid. (paper)

  7. Approximate quantum Markov chains

    CERN Document Server

    Sutter, David

    2018-01-01

    This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...

  8. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2012-05-01

    Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.

  9. Inverse planning IMRT

    International Nuclear Information System (INIS)

    Rosenwald, J.-C.

    2008-01-01

    The lecture addressed the following topics: Optimizing radiotherapy dose distribution; IMRT contributes to optimization of energy deposition; Inverse vs direct planning; Main steps of IMRT; Background of inverse planning; General principle of inverse planning; The 3 main components of IMRT inverse planning; The simplest cost function (deviation from prescribed dose); The driving variable : the beamlet intensity; Minimizing a 'cost function' (or 'objective function') - the walker (or skier) analogy; Application to IMRT optimization (the gradient method); The gradient method - discussion; The simulated annealing method; The optimization criteria - discussion; Hard and soft constraints; Dose volume constraints; Typical user interface for definition of optimization criteria; Biological constraints (Equivalent Uniform Dose); The result of the optimization process; Semi-automatic solutions for IMRT; Generalisation of the optimization problem; Driving and driven variables used in RT optimization; Towards multi-criteria optimization; and Conclusions for the optimization phase. (P.A.)

  10. Fast space-varying convolution using matrix source coding with applications to camera stray light reduction.

    Science.gov (United States)

    Wei, Jianing; Bouman, Charles A; Allebach, Jan P

    2014-05-01

    Many imaging applications require the implementation of space-varying convolution for accurate restoration and reconstruction of images. Here, we use the term space-varying convolution to refer to linear operators whose impulse response has slow spatial variation. In addition, these space-varying convolution operators are often dense, so direct implementation of the convolution operator is typically computationally impractical. One such example is the problem of stray light reduction in digital cameras, which requires the implementation of a dense space-varying deconvolution operator. However, other inverse problems, such as iterative tomographic reconstruction, can also depend on the implementation of dense space-varying convolution. While space-invariant convolution can be efficiently implemented with the fast Fourier transform, this approach does not work for space-varying operators. So direct convolution is often the only option for implementing space-varying convolution. In this paper, we develop a general approach to the efficient implementation of space-varying convolution, and demonstrate its use in the application of stray light reduction. Our approach, which we call matrix source coding, is based on lossy source coding of the dense space-varying convolution matrix. Importantly, by coding the transformation matrix, we not only reduce the memory required to store it; we also dramatically reduce the computation required to implement matrix-vector products. Our algorithm is able to reduce computation by approximately factoring the dense space-varying convolution operator into a product of sparse transforms. Experimental results show that our method can dramatically reduce the computation required for stray light reduction while maintaining high accuracy.

  11. Inverse source problems for eddy current equations

    International Nuclear Information System (INIS)

    Rodríguez, Ana Alonso; Valli, Alberto; Camaño, Jessika

    2012-01-01

    We study the inverse source problem for the eddy current approximation of Maxwell equations. As for the full system of Maxwell equations, we show that a volume current source cannot be uniquely identified by knowledge of the tangential components of the electromagnetic fields on the boundary, and we characterize the space of non-radiating sources. On the other hand, we prove that the inverse source problem has a unique solution if the source is supported on the boundary of a subdomain or if it is the sum of a finite number of dipoles. We address the applicability of this result for the localization of brain activity from electroencephalography and magnetoencephalography measurements. (paper)

  12. Saddlepoint Approximations in Conditional Inference

    Science.gov (United States)

    1990-06-11

    Then the inverse transform can be written as (%, Y) = (T, q(T, Z)) for some function q. When the transform is not one to one, the domain should be...general regularity conditions described at the beginning of this section hold and that the solution t1 in (9) exists. Denote the inverse transform by (X, Y...density hn(t 0 l z) are desired. Then the inverse transform (Y, ) = (T, q(T, Z)) exists and the variable v in the cumulant generating function K(u, v

  13. Nonlinear adaptive inverse control via the unified model neural network

    Science.gov (United States)

    Jeng, Jin-Tsong; Lee, Tsu-Tian

    1999-03-01

    In this paper, we propose a new nonlinear adaptive inverse control via a unified model neural network. In order to overcome nonsystematic design and long training time in nonlinear adaptive inverse control, we propose the approximate transformable technique to obtain a Chebyshev Polynomials Based Unified Model (CPBUM) neural network for the feedforward/recurrent neural networks. It turns out that the proposed method can use less training time to get an inverse model. Finally, we apply this proposed method to control magnetic bearing system. The experimental results show that the proposed nonlinear adaptive inverse control architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.

  14. ipw: An R Package for Inverse Probability Weighting

    Directory of Open Access Journals (Sweden)

    Ronald B. Geskus

    2011-10-01

    Full Text Available We describe the R package ipw for estimating inverse probability weights. We show how to use the package to fit marginal structural models through inverse probability weighting, to estimate causal effects. Our package can be used with data from a point treatment situation as well as with a time-varying exposure and time-varying confounders. It can be used with binomial, categorical, ordinal and continuous exposure variables.

  15. Self-similar factor approximants

    International Nuclear Information System (INIS)

    Gluzman, S.; Yukalov, V.I.; Sornette, D.

    2003-01-01

    The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties

  16. Time-varying BRDFs.

    Science.gov (United States)

    Sun, Bo; Sunkavalli, Kalyan; Ramamoorthi, Ravi; Belhumeur, Peter N; Nayar, Shree K

    2007-01-01

    The properties of virtually all real-world materials change with time, causing their bidirectional reflectance distribution functions (BRDFs) to be time varying. However, none of the existing BRDF models and databases take time variation into consideration; they represent the appearance of a material at a single time instance. In this paper, we address the acquisition, analysis, modeling, and rendering of a wide range of time-varying BRDFs (TVBRDFs). We have developed an acquisition system that is capable of sampling a material's BRDF at multiple time instances, with each time sample acquired within 36 sec. We have used this acquisition system to measure the BRDFs of a wide range of time-varying phenomena, which include the drying of various types of paints (watercolor, spray, and oil), the drying of wet rough surfaces (cement, plaster, and fabrics), the accumulation of dusts (household and joint compound) on surfaces, and the melting of materials (chocolate). Analytic BRDF functions are fit to these measurements and the model parameters' variations with time are analyzed. Each category exhibits interesting and sometimes nonintuitive parameter trends. These parameter trends are then used to develop analytic TVBRDF models. The analytic TVBRDF models enable us to apply effects such as paint drying and dust accumulation to arbitrary surfaces and novel materials.

  17. Inverse design of multicomponent assemblies

    Science.gov (United States)

    Piñeros, William D.; Lindquist, Beth A.; Jadrich, Ryan B.; Truskett, Thomas M.

    2018-03-01

    Inverse design can be a useful strategy for discovering interactions that drive particles to spontaneously self-assemble into a desired structure. Here, we extend an inverse design methodology—relative entropy optimization—to determine isotropic interactions that promote assembly of targeted multicomponent phases, and we apply this extension to design interactions for a variety of binary crystals ranging from compact triangular and square architectures to highly open structures with dodecagonal and octadecagonal motifs. We compare the resulting optimized (self- and cross) interactions for the binary assemblies to those obtained from optimization of analogous single-component systems. This comparison reveals that self-interactions act as a "primer" to position particles at approximately correct coordination shell distances, while cross interactions act as the "binder" that refines and locks the system into the desired configuration. For simpler binary targets, it is possible to successfully design self-assembling systems while restricting one of these interaction types to be a hard-core-like potential. However, optimization of both self- and cross interaction types appears necessary to design for assembly of more complex or open structures.

  18. Action understanding as inverse planning.

    Science.gov (United States)

    Baker, Chris L; Saxe, Rebecca; Tenenbaum, Joshua B

    2009-12-01

    Humans are adept at inferring the mental states underlying other agents' actions, such as goals, beliefs, desires, emotions and other thoughts. We propose a computational framework based on Bayesian inverse planning for modeling human action understanding. The framework represents an intuitive theory of intentional agents' behavior based on the principle of rationality: the expectation that agents will plan approximately rationally to achieve their goals, given their beliefs about the world. The mental states that caused an agent's behavior are inferred by inverting this model of rational planning using Bayesian inference, integrating the likelihood of the observed actions with the prior over mental states. This approach formalizes in precise probabilistic terms the essence of previous qualitative approaches to action understanding based on an "intentional stance" [Dennett, D. C. (1987). The intentional stance. Cambridge, MA: MIT Press] or a "teleological stance" [Gergely, G., Nádasdy, Z., Csibra, G., & Biró, S. (1995). Taking the intentional stance at 12 months of age. Cognition, 56, 165-193]. In three psychophysical experiments using animated stimuli of agents moving in simple mazes, we assess how well different inverse planning models based on different goal priors can predict human goal inferences. The results provide quantitative evidence for an approximately rational inference mechanism in human goal inference within our simplified stimulus paradigm, and for the flexible nature of goal representations that human observers can adopt. We discuss the implications of our experimental results for human action understanding in real-world contexts, and suggest how our framework might be extended to capture other kinds of mental state inferences, such as inferences about beliefs, or inferring whether an entity is an intentional agent.

  19. Impurity levels: corrections to the effective mass approximation

    International Nuclear Information System (INIS)

    Bentosela, F.

    1977-07-01

    Some rigorous results concerning the effective mass approximation used for the calculation of the impurity levels in semiconductors are presented. Each energy level is expressed as an asymptotic series in the inverse of the dielectric constant K, in the case where the impurity potential is 1/μ

  20. Approximation of reliability of direct genomic breeding values

    Science.gov (United States)

    Two methods to efficiently approximate theoretical genomic reliabilities are presented. The first method is based on the direct inverse of the left hand side (LHS) of mixed model equations. It uses the genomic relationship matrix for a small subset of individuals with the highest genomic relationshi...

  1. Sinc-Approximations of Fractional Operators: A Computing Approach

    Directory of Open Access Journals (Sweden)

    Gerd Baumann

    2015-06-01

    Full Text Available We discuss a new approach to represent fractional operators by Sinc approximation using convolution integrals. A spin off of the convolution representation is an effective inverse Laplace transform. Several examples demonstrate the application of the method to different practical problems.

  2. International Conference Approximation Theory XV

    CERN Document Server

    Schumaker, Larry

    2017-01-01

    These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...

  3. Flame structure of methane inverse diffusion flame

    KAUST Repository

    Elbaz, Ayman M.

    2014-07-01

    This paper presents high speed images of OH-PLIF at 10. kHz simultaneously with 2D PIV (particle image velocimetry) measurements collected along the entire length of an inverse diffusion flame with circumferentially arranged methane fuel jets. For a fixed fuel flow rate, the central air jet Re was varied, leading to four air to fuel velocity ratios, namely Vr = 20.7, 29, 37.4 and 49.8. A double flame structure could be observed composed of a lower fuel entrainment region and an upper mixing and intense combustion region. The entrainment region was enveloped by an early OH layer, and then merged through a very thin OH neck to an annular OH layer located at the shear layer of the air jet. The two branches of this annular OH layer broaden as they moved downstream and eventfully merged together. Three types of events were observed common to all flames: breaks, closures and growing kernels. In upstream regions of the flames, the breaks were counterbalanced by flame closures. These breaks in OH signal were found to occur at locations where locally high velocity flows were impinging on the flame. As the Vr increased to 37.4, the OH layers became discontinuous over the downstream region of the flame, and these regions of low or no OH moved upstream. With further increases in Vr, these OH pockets act as flame kernels, growing as they moved downstream, and became the main mechanism for flame re-ignition. Along the flame length, the direction of the two dimensional principle compressive strain rate axis exhibited a preferred orientation of approximately 45° with respect to the flow direction. Moreover, the OH zones were associated with elongated regions of high vorticity. © 2013 Elsevier Inc.

  4. Limits to Nonlinear Inversion

    DEFF Research Database (Denmark)

    Mosegaard, Klaus

    2012-01-01

    For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...... pure meta-heuristics. We study problem-adapted inversion algorithms that exploit the knowledge of the smoothness of the misfit function of the problem. Optimal sampling strategies exist for such problems, but many of these problems remain hard. © 2012 Springer-Verlag....

  5. Inverse scale space decomposition

    DEFF Research Database (Denmark)

    Schmidt, Marie Foged; Benning, Martin; Schönlieb, Carola-Bibiane

    2018-01-01

    We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and even and positively one-homogeneous regularisation functionals, can decompose data represented...... by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums...... of the subgradients of the singular vectors in the subdifferential of the regularisation functional at zero. We also address the converse question of when the inverse scale space flow returns a generalised singular vector given that the initial data is arbitrary (and therefore not necessarily in the range...

  6. Generalized inverses theory and computations

    CERN Document Server

    Wang, Guorong; Qiao, Sanzheng

    2018-01-01

    This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.

  7. Some results on inverse scattering

    International Nuclear Information System (INIS)

    Ramm, A.G.

    2008-01-01

    A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: (1) Property C and applications, (2) Stable inversion of fixed-energy 3D scattering data and its error estimate, (3) Inverse scattering with 'incomplete' data, (4) Inverse scattering for inhomogeneous Schroedinger equation, (5) Krein's inverse scattering method, (6) Invertibility of the steps in Gel'fand-Levitan, Marchenko, and Krein inversion methods, (7) The Newton-Sabatier and Cox-Thompson procedures are not inversion methods, (8) Resonances: existence, location, perturbation theory, (9) Born inversion as an ill-posed problem, (10) Inverse obstacle scattering with fixed-frequency data, (11) Inverse scattering with data at a fixed energy and a fixed incident direction, (12) Creating materials with a desired refraction coefficient and wave-focusing properties. (author)

  8. Inverse problemfor an inhomogeneous elastic beam at a combined strength

    Directory of Open Access Journals (Sweden)

    Andreev Vladimir Igorevich

    2014-01-01

    Full Text Available In the article the authors describe a method of optimizing the stress state of an elastic beam, subject to the simultaneous action of the central concentrated force and bending moment. The optimization method is based on solving the inverse problem of the strength of materials, consisting in defining the law of changing in elasticity modulus with beam cross-section altitude. With this changing the stress state will be preset. Most problems of the elasticity theory of inhomogeneous bodies are solved in direct formulation, the essence of which is to determine the stress-strain state of a body at the known dependences of the material elastic characteristics from the coordinates. There are also some solutions of the inverse problems of the elasticity theory, in which the dependences of the mechanical characteristics from the coordinates, at which the stress state of a body is preset, are determined. In the paper the authors solve the problem of finding a dependence modulus of elasticity, where the stresses will be constant over the beam’s cross section. We will solve the problem of combined strength (in the case of the central stretching and bending. We will use an iterative method. As the initial solution, we take the solution for a homogeneous material. As the first approximation, we consider the stress state of a beam, when the modulus of elasticity varies linearly. According to the results, it can be stated that three approximations are sufficient in the considered problem. The obtained results allow us to use them in assessing the strength of a beam and its optimization.

  9. A 2.5-D Diffraction Tomography Inversion Scheme for Ground Penetrating Radar

    DEFF Research Database (Denmark)

    Meincke, Peter

    1999-01-01

    A new 2.5-D inversion scheme is derived for ground penetrating radar (GPR) that applies to a monostatic fixed-offset measurement configuration. The inversion scheme, which is based upon the first Born approximation and the pseudo-inverse operator, takes rigorously into account the planar air...

  10. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-01

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  11. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-07

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  12. Three-dimensional inversion of multisource array electromagnetic data

    Science.gov (United States)

    Tartaras, Efthimios

    Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM

  13. Angle-domain inverse scattering migration/inversion in isotropic media

    Science.gov (United States)

    Li, Wuqun; Mao, Weijian; Li, Xuelei; Ouyang, Wei; Liang, Quan

    2018-07-01

    The classical seismic asymptotic inversion can be transformed into a problem of inversion of generalized Radon transform (GRT). In such methods, the combined parameters are linearly attached to the scattered wave-field by Born approximation and recovered by applying an inverse GRT operator to the scattered wave-field data. Typical GRT-style true-amplitude inversion procedure contains an amplitude compensation process after the weighted migration via dividing an illumination associated matrix whose elements are integrals of scattering angles. It is intuitional to some extent that performs the generalized linear inversion and the inversion of GRT together by this process for direct inversion. However, it is imprecise to carry out such operation when the illumination at the image point is limited, which easily leads to the inaccuracy and instability of the matrix. This paper formulates the GRT true-amplitude inversion framework in an angle-domain version, which naturally degrades the external integral term related to the illumination in the conventional case. We solve the linearized integral equation for combined parameters of different fixed scattering angle values. With this step, we obtain high-quality angle-domain common-image gathers (CIGs) in the migration loop which provide correct amplitude-versus-angle (AVA) behavior and reasonable illumination range for subsurface image points. Then we deal with the over-determined problem to solve each parameter in the combination by a standard optimization operation. The angle-domain GRT inversion method keeps away from calculating the inaccurate and unstable illumination matrix. Compared with the conventional method, the angle-domain method can obtain more accurate amplitude information and wider amplitude-preserved range. Several model tests demonstrate the effectiveness and practicability.

  14. Bayesian probability theory and inverse problems

    International Nuclear Information System (INIS)

    Kopec, S.

    1994-01-01

    Bayesian probability theory is applied to approximate solving of the inverse problems. In order to solve the moment problem with the noisy data, the entropic prior is used. The expressions for the solution and its error bounds are presented. When the noise level tends to zero, the Bayesian solution tends to the classic maximum entropy solution in the L 2 norm. The way of using spline prior is also shown. (author)

  15. An inverse problem in a parabolic equation

    Directory of Open Access Journals (Sweden)

    Zhilin Li

    1998-11-01

    Full Text Available In this paper, an inverse problem in a parabolic equation is studied. An unknown function in the equation is related to two integral equations in terms of heat kernel. One of the integral equations is well-posed while another is ill-posed. A regularization approach for constructing an approximate solution to the ill-posed integral equation is proposed. Theoretical analysis and numerical experiment are provided to support the method.

  16. Forms of Approximate Radiation Transport

    CERN Document Server

    Brunner, G

    2002-01-01

    Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.

  17. Approximation by planar elastic curves

    DEFF Research Database (Denmark)

    Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge

    2016-01-01

    We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....

  18. Inversion assuming weak scattering

    DEFF Research Database (Denmark)

    Xenaki, Angeliki; Gerstoft, Peter; Mosegaard, Klaus

    2013-01-01

    due to the complex nature of the field. A method based on linear inversion is employed to infer information about the statistical properties of the scattering field from the obtained cross-spectral matrix. A synthetic example based on an active high-frequency sonar demonstrates that the proposed...

  19. Calculation of the inverse data space via sparse inversion

    KAUST Repository

    Saragiotis, Christos

    2011-01-01

    The inverse data space provides a natural separation of primaries and surface-related multiples, as the surface multiples map onto the area around the origin while the primaries map elsewhere. However, the calculation of the inverse data is far from trivial as theory requires infinite time and offset recording. Furthermore regularization issues arise during inversion. We perform the inversion by minimizing the least-squares norm of the misfit function by constraining the $ell_1$ norm of the solution, being the inverse data space. In this way a sparse inversion approach is obtained. We show results on field data with an application to surface multiple removal.

  20. Inverse Problems and Uncertainty Quantification

    KAUST Repository

    Litvinenko, Alexander

    2014-01-06

    In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) modelare strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time- consuming and slowly convergent Monte Carlo sampling. The developed sampling- free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.

  1. Inverse Problems and Uncertainty Quantification

    KAUST Repository

    Litvinenko, Alexander; Matthies, Hermann G.

    2014-01-01

    In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) modelare strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time- consuming and slowly convergent Monte Carlo sampling. The developed sampling- free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.

  2. Inverse problems and uncertainty quantification

    KAUST Repository

    Litvinenko, Alexander

    2013-12-18

    In a Bayesian setting, inverse problems and uncertainty quantification (UQ)— the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time- consuming and slowly convergent Monte Carlo sampling. The developed sampling- free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.

  3. Exact constants in approximation theory

    CERN Document Server

    Korneichuk, N

    1991-01-01

    This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base

  4. International Conference Approximation Theory XIV

    CERN Document Server

    Schumaker, Larry

    2014-01-01

    This volume developed from papers presented at the international conference Approximation Theory XIV,  held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.

  5. Bispectral Inversion: The Construction of a Time Series from Its Bispectrum

    Science.gov (United States)

    1988-04-13

    take the inverse transform . Since the goal is to compute a time series given its bispectrum, it would also be nice to stay entirely in the frequency...domain and be able to go directly from the bispectrum to the Fourier transform of the time series without the need to inverse transform continuous...the picture. The approximations arise from representing the bicovariance, which is the inverse transform of a continuous function, by the inverse disrte

  6. The impact of approximations and arbitrary choices on geophysical images

    Science.gov (United States)

    Valentine, Andrew P.; Trampert, Jeannot

    2016-01-01

    Whenever a geophysical image is to be constructed, a variety of choices must be made. Some, such as those governing data selection and processing, or model parametrization, are somewhat arbitrary: there may be little reason to prefer one choice over another. Others, such as defining the theoretical framework within which the data are to be explained, may be more straightforward: typically, an `exact' theory exists, but various approximations may need to be adopted in order to make the imaging problem computationally tractable. Differences between any two images of the same system can be explained in terms of differences between these choices. Understanding the impact of each particular decision is essential if images are to be interpreted properly-but little progress has been made towards a quantitative treatment of this effect. In this paper, we consider a general linearized inverse problem, applicable to a wide range of imaging situations. We write down an expression for the difference between two images produced using similar inversion strategies, but where different choices have been made. This provides a framework within which inversion algorithms may be analysed, and allows us to consider how image effects may arise. In this paper, we take a general view, and do not specialize our discussion to any specific imaging problem or setup (beyond the restrictions implied by the use of linearized inversion techniques). In particular, we look at the concept of `hybrid inversion', in which highly accurate synthetic data (typically the result of an expensive numerical simulation) is combined with an inverse operator constructed based on theoretical approximations. It is generally supposed that this offers the benefits of using the more complete theory, without the full computational costs. We argue that the inverse operator is as important as the forward calculation in determining the accuracy of results. We illustrate this using a simple example, based on imaging the

  7. Linearized inversion of two components seismic data; Inversion linearisee de donnees sismiques a deux composantes

    Energy Technology Data Exchange (ETDEWEB)

    Lebrun, D.

    1997-05-22

    The aim of the dissertation is the linearized inversion of multicomponent seismic data for 3D elastic horizontally stratified media, using Born approximation. A Jacobian matrix is constructed; it will be used to model seismic data from elastic parameters. The inversion technique, relying on single value decomposition (SVD) of the Jacobian matrix, is described. Next, the resolution of inverted elastic parameters is quantitatively studies. A first use of the technique is shown in the frame of an evaluation of a sea bottom acquisition (synthetic data). Finally, a real data set acquired with conventional marine technique is inverted. (author) 70 refs.

  8. Approximate truncation robust computed tomography—ATRACT

    International Nuclear Information System (INIS)

    Dennerlein, Frank; Maier, Andreas

    2013-01-01

    We present an approximate truncation robust algorithm to compute tomographic images (ATRACT). This algorithm targets at reconstructing volumetric images from cone-beam projections in scenarios where these projections are highly truncated in each dimension. It thus facilitates reconstructions of small subvolumes of interest, without involving prior knowledge about the object. Our method is readily applicable to medical C-arm imaging, where it may contribute to new clinical workflows together with a considerable reduction of x-ray dose. We give a detailed derivation of ATRACT that starts from the conventional Feldkamp filtered-backprojection algorithm and that involves, as one component, a novel original formula for the inversion of the two-dimensional Radon transform. Discretization and numerical implementation are discussed and reconstruction results from both, simulated projections and first clinical data sets are presented. (paper)

  9. Application of tomographic inversion in studying airglow in the mesopause region

    Directory of Open Access Journals (Sweden)

    T. Nygrén

    Full Text Available It is pointed out that observations of periodic nightglow structures give excellent information on atmospheric gravity waves in the mesosphere and lower thermosphere. The periods, the horizontal wavelengths and the phase speeds of the waves can be determined from airglow images and, using several cameras, the approximate altitude of the luminous layer can also be determined by triangulation. In this paper the possibility of applying tomographic methods for reconstructing the airglow structures is investigated using numerical simulations. A ground-based chain of cameras is assumed, two-dimensional airglow models in the vertical plane above the chain are constructed, and simulated data are calculated by integrating the models along a great number of rays with different elevation angles for each camera. After addition of random noise, these data are then inverted to obtain reconstructions of the models. A tomographic analysis package originally designed for satellite radiotomography is used in the inversion. The package is based on a formulation of stochastic inversion which allows the input of a priori information to the solver in terms of regularization variances. The reconstruction is carried out in two stages. In the first inversion, constant regularization variances are used within a wide altitude range. The results are used in determining the approximate altitude range of the airglow structures. Then, in the second inversion, constant non-zero regularization variances are used inside this region and zero variances outside it. With this method reliable reconstructions of the models are obtained. The number of cameras as well as their separations are varied in order to find out the limitations of the method.

    Key words. Tomography · Airglow · Mesopause · Gravity waves

  10. Electrochemically driven emulsion inversion

    Science.gov (United States)

    Johans, Christoffer; Kontturi, Kyösti

    2007-09-01

    It is shown that emulsions stabilized by ionic surfactants can be inverted by controlling the electrical potential across the oil-water interface. The potential dependent partitioning of sodium dodecyl sulfate (SDS) was studied by cyclic voltammetry at the 1,2-dichlorobenzene|water interface. In the emulsion the potential control was achieved by using a potential-determining salt. The inversion of a 1,2-dichlorobenzene-in-water (O/W) emulsion stabilized by SDS was followed by conductometry as a function of added tetrapropylammonium chloride. A sudden drop in conductivity was observed, indicating the change of the continuous phase from water to 1,2-dichlorobenzene, i.e. a water-in-1,2-dichlorobenzene emulsion was formed. The inversion potential is well in accordance with that predicted by the hydrophilic-lipophilic deviation if the interfacial potential is appropriately accounted for.

  11. varying elastic parameters distributions

    KAUST Repository

    Moussawi, Ali

    2014-12-01

    The experimental identication of mechanical properties is crucial in mechanics for understanding material behavior and for the development of numerical models. Classical identi cation procedures employ standard shaped specimens, assume that the mechanical elds in the object are homogeneous, and recover global properties. Thus, multiple tests are required for full characterization of a heterogeneous object, leading to a time consuming and costly process. The development of non-contact, full- eld measurement techniques from which complex kinematic elds can be recorded has opened the door to a new way of thinking. From the identi cation point of view, suitable methods can be used to process these complex kinematic elds in order to recover multiple spatially varying parameters through one test or a few tests. The requirement is the development of identi cation techniques that can process these complex experimental data. This thesis introduces a novel identi cation technique called the constitutive compatibility method. The key idea is to de ne stresses as compatible with the observed kinematic eld through the chosen class of constitutive equation, making possible the uncoupling of the identi cation of stress from the identi cation of the material parameters. This uncoupling leads to parametrized solutions in cases where 5 the solution is non-unique (due to unknown traction boundary conditions) as demonstrated on 2D numerical examples. First the theory is outlined and the method is demonstrated in 2D applications. Second, the method is implemented within a domain decomposition framework in order to reduce the cost for processing very large problems. Finally, it is extended to 3D numerical examples. Promising results are shown for 2D and 3D problems.

  12. Electron dose map inversion based on several algorithms

    International Nuclear Information System (INIS)

    Li Gui; Zheng Huaqing; Wu Yican; Fds Team

    2010-01-01

    The reconstruction to the electron dose map in radiation therapy was investigated by constructing the inversion model of electron dose map with different algorithms. The inversion model of electron dose map based on nonlinear programming was used, and this model was applied the penetration dose map to invert the total space one. The realization of this inversion model was by several inversion algorithms. The test results with seven samples show that except the NMinimize algorithm, which worked for just one sample, with great error,though,all the inversion algorithms could be realized to our inversion model rapidly and accurately. The Levenberg-Marquardt algorithm, having the greatest accuracy and speed, could be considered as the first choice in electron dose map inversion.Further tests show that more error would be created when the data close to the electron range was used (tail error). The tail error might be caused by the approximation of mean energy spectra, and this should be considered to improve the method. The time-saving and accurate algorithms could be used to achieve real-time dose map inversion. By selecting the best inversion algorithm, the clinical need in real-time dose verification can be satisfied. (authors)

  13. Channelling versus inversion

    DEFF Research Database (Denmark)

    Gale, A.S.; Surlyk, Finn; Anderskouv, Kresten

    2013-01-01

    Evidence from regional stratigraphical patterns in Santonian−Campanian chalk is used to infer the presence of a very broad channel system (5 km across) with a depth of at least 50 m, running NNW−SSE across the eastern Isle of Wight; only the western part of the channel wall and fill is exposed. W......−Campanian chalks in the eastern Isle of Wight, involving penecontemporaneous tectonic inversion of the underlying basement structure, are rejected....

  14. Reactivity in inverse micelles

    International Nuclear Information System (INIS)

    Brochette, Pascal

    1987-01-01

    This research thesis reports the study of the use of micro-emulsions of water in oil as reaction support. Only the 'inverse micelles' domain of the ternary mixing (water/AOT/isooctane) has been studied. The main addressed issues have been: the micro-emulsion disturbance in presence of reactants, the determination of reactant distribution and the resulting kinetic theory, the effect of the interface on electron transfer reactions, and finally protein solubilization [fr

  15. Inverse transition radiation

    International Nuclear Information System (INIS)

    Steinhauer, L.C.; Romea, R.D.; Kimura, W.D.

    1997-01-01

    A new method for laser acceleration is proposed based upon the inverse process of transition radiation. The laser beam intersects an electron-beam traveling between two thin foils. The principle of this acceleration method is explored in terms of its classical and quantum bases and its inverse process. A closely related concept based on the inverse of diffraction radiation is also presented: this concept has the significant advantage that apertures are used to allow free passage of the electron beam. These concepts can produce net acceleration because they do not satisfy the conditions in which the Lawson-Woodward theorem applies (no net acceleration in an unbounded vacuum). Finally, practical aspects such as damage limits at optics are employed to find an optimized set of parameters. For reasonable assumptions an acceleration gradient of 200 MeV/m requiring a laser power of less than 1 GW is projected. An interesting approach to multi-staging the acceleration sections is also presented. copyright 1997 American Institute of Physics

  16. Intersections, ideals, and inversion

    International Nuclear Information System (INIS)

    Vasco, D.W.

    1998-01-01

    Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly one dimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons

  17. Intersections, ideals, and inversion

    Energy Technology Data Exchange (ETDEWEB)

    Vasco, D.W.

    1998-10-01

    Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly onedimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons.

  18. Trimming and procrastination as inversion techniques

    Science.gov (United States)

    Backus, George E.

    1996-12-01

    By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.

  19. Some results in Diophantine approximation

    DEFF Research Database (Denmark)

    Pedersen, Steffen Højris

    the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered......This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...

  20. Limitations of shallow nets approximation.

    Science.gov (United States)

    Lin, Shao-Bo

    2017-10-01

    In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

  1. Testing earthquake source inversion methodologies

    KAUST Repository

    Page, Morgan T.; Mai, Paul Martin; Schorlemmer, Danijel

    2011-01-01

    Source Inversion Validation Workshop; Palm Springs, California, 11-12 September 2010; Nowadays earthquake source inversions are routinely performed after large earthquakes and represent a key connection between recorded seismic and geodetic data

  2. Chromosomal inversion differences correlate with range overlap in passerine birds.

    Science.gov (United States)

    Hooper, Daniel M; Price, Trevor D

    2017-10-01

    Chromosomal inversions evolve frequently but the reasons for this remain unclear. We used cytological descriptions of 411 species of passerine birds to identify large pericentric inversion differences between species, based on the position of the centromere. Within 81 small clades comprising 284 of the species, we found 319 differences on the 9 largest autosomes combined, 56 on the Z chromosome, and 55 on the W chromosome. We also identified inversions present within 32 species. Using a new fossil-calibrated phylogeny, we examined the phylogenetic, demographic and genomic context in which these inversions have evolved. The number of inversion differences between closely related species is consistently predicted by whether the ranges of species overlap, even when time is controlled for as far as is possible. Fixation rates vary across the autosomes, but inversions are more likely to be fixed on the Z chromosome than the average autosome. Variable mutagenic input alone (estimated by chromosome size, map length, GC content or repeat density) cannot explain the differences between chromosomes in the number of inversions fixed. Together, these results support a model in which inversions increase because of their effects on recombination suppression in the face of hybridization. Other factors associated with hybridization may also contribute, including the possibility that inversions contain incompatibility alleles, making taxa less likely to collapse following secondary contact.

  3. Spherical Approximation on Unit Sphere

    Directory of Open Access Journals (Sweden)

    Eman Samir Bhaya

    2018-01-01

    Full Text Available In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of  functions in  spaces defined on unit sphere. our central problem is to describe the approximation behavior of functions in    spaces for  by modulus of smoothness of functions.

  4. Inverse scattering with supersymmetric quantum mechanics

    International Nuclear Information System (INIS)

    Baye, Daniel; Sparenberg, Jean-Marc

    2004-01-01

    The application of supersymmetric quantum mechanics to the inverse scattering problem is reviewed. The main difference with standard treatments of the inverse problem lies in the simple and natural extension to potentials with singularities at the origin and with a Coulomb behaviour at infinity. The most general form of potentials which are phase-equivalent to a given potential is discussed. The use of singular potentials allows adding or removing states from the bound spectrum without contradicting the Levinson theorem. Physical applications of phase-equivalent potentials in nuclear reactions and in three-body systems are described. Derivation of a potential from the phase shift at fixed orbital momentum can also be performed with the supersymmetric inversion by using a Bargmann-type approximation of the scattering matrix or phase shift. A unique singular potential without bound states can be obtained from any phase shift. A limited number of bound states depending on the singularity can then be added. This inversion procedure is illustrated with nucleon-nucleon scattering

  5. Multiscale Phase Inversion of Seismic Data

    KAUST Repository

    Fu, Lei

    2017-12-02

    We present a scheme for multiscale phase inversion (MPI) of seismic data that is less sensitive to the unmodeled physics of wave propagation and a poor starting model than standard full waveform inversion (FWI). To avoid cycle-skipping, the multiscale strategy temporally integrates the traces several times, i.e. high-order integration, to produce low-boost seismograms that are used as input data for the initial iterations of MPI. As the iterations proceed, higher frequencies in the data are boosted by using integrated traces of lower order as the input data. The input data are also filtered into different narrow frequency bands for the MPI implementation. At low frequencies, we show that MPI with windowed reflections approximates wave equation inversion of the reflection traveltimes, except no traveltime picking is needed. Numerical results with synthetic acoustic data show that MPI is more robust than conventional multiscale FWI when the initial model is far from the true model. Results from synthetic viscoacoustic and elastic data show that MPI is less sensitive than FWI to some of the unmodeled physics. Inversion of marine data shows that MPI is more robust and produces modestly more accurate results than FWI for this data set.

  6. Approximate circuits for increased reliability

    Science.gov (United States)

    Hamlet, Jason R.; Mayo, Jackson R.

    2015-08-18

    Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.

  7. Inverse planning and optimization: a comparison of solutions

    Energy Technology Data Exchange (ETDEWEB)

    Ringor, Michael [School of Health Sciences, Purdue University, West Lafayette, IN (United States); Papiez, Lech [Department of Radiation Oncology, Indiana University, Indianapolis, IN (United States)

    1998-09-01

    The basic problem in radiation therapy treatment planning is to determine an appropriate set of treatment parameters that would induce an effective dose distribution inside a patient. One can approach this task as an inverse problem, or as an optimization problem. In this presentation, we compare both approaches. The inverse problem is presented as a dose reconstruction problem similar to tomography reconstruction. We formulate the optimization problem as linear and quadratic programs. Explicit comparisons are made between the solutions obtained by inversion and those obtained by optimization for the case in which scatter and attenuation are ignored (the NS-NA approximation)

  8. Theory of the inverse Faraday effect in metals

    International Nuclear Information System (INIS)

    Hertel, Riccardo

    2006-01-01

    An analytic expression is given for the inverse Faraday effect, i.e., for the magnetization occurring in a transparent medium exposed to a circularly polarized high-frequency electromagnetic wave. Using a microscopic approach based on the Drude approximation of a free-electron gas, the magnetization of the medium due to the inverse Faraday effect is identified as the result of microscopic solenoidal currents generated by the electromagnetic wave. In contrast to the better known phenomenological derivation, this microscopic treatment provides important information on the frequency dependence of the inverse Faraday effect

  9. Children's strategies to solving additive inverse problems: a preliminary analysis

    Science.gov (United States)

    Ding, Meixia; Auxter, Abbey E.

    2017-03-01

    Prior studies show that elementary school children generally "lack" formal understanding of inverse relations. This study goes beyond lack to explore what children might "have" in their existing conception. A total of 281 students, kindergarten to third grade, were recruited to respond to a questionnaire that involved both contextual and non-contextual tasks on inverse relations, requiring both computational and explanatory skills. Results showed that children demonstrated better performance in computation than explanation. However, many students' explanations indicated that they did not necessarily utilize inverse relations for computation. Rather, they appeared to possess partial understanding, as evidenced by their use of part-whole structure, which is a key to understanding inverse relations. A close inspection of children's solution strategies further revealed that the sophistication of children's conception of part-whole structure varied in representation use and unknown quantity recognition, which suggests rich opportunities to develop students' understanding of inverse relations in lower elementary classrooms.

  10. Fitting Social Network Models Using Varying Truncation Stochastic Approximation MCMC Algorithm

    KAUST Repository

    Jin, Ick Hoon; Liang, Faming

    2013-01-01

    The exponential random graph model (ERGM) plays a major role in social network analysis. However, parameter estimation for the ERGM is a hard problem due to the intractability of its normalizing constant and the model degeneracy. The existing

  11. Electrical resistance imaging of a time-varying interface in stratified flows using an unscented Kalman filter

    International Nuclear Information System (INIS)

    Ijaz, Umer Zeeshan; Khambampati, Anil Kumar; Kim, Kyung Youn; Chung, Soon Il; Kim, Sin

    2008-01-01

    In this paper, we estimate a time-varying interfacial boundary in stratified flows of two immiscible liquids using electrical resistance tomography. The interfacial boundary is approximated with front points spaced discretely along the interface. The design variables to be estimated are the locations of the front points, which are varying with the moving interface. The inverse problem is treated as a stochastic nonlinear state estimation problem with the nonstationary phase boundary (state) being estimated with the aid of an unscented Kalman filter. Numerical experiments are performed to evaluate the performance of an unscented Kalman filter. Specifically, a detailed analysis has been done on the effect of the number of front points and contrast ratio on the reconstruction performance. The reconstruction results show that an unscented Kalman filter is better suited for estimation in comparison to the conventional extended Kalman filter

  12. Construction and Experimental Implementation of a Model-Based Inverse Filter to Attenuate Hysteresis in Ferroelectric Transducers

    National Research Council Canada - National Science Library

    Hatch, Andrew G; Smith, Ralph C; De, Tathagata; Salapaka, Murti V

    2005-01-01

    .... In this paper, we illustrate the construction of inverse filters, based on homogenized energy models, which can be used to approximately linearize the piezoceramic transducer behavior for linear...

  13. Introduction to Schroedinger inverse scattering

    International Nuclear Information System (INIS)

    Roberts, T.M.

    1991-01-01

    Schroedinger inverse scattering uses scattering coefficients and bound state data to compute underlying potentials. Inverse scattering has been studied extensively for isolated potentials q(x), which tend to zero as vertical strokexvertical stroke→∞. Inverse scattering for isolated impurities in backgrounds p(x) that are periodic, are Heaviside steps, are constant for x>0 and periodic for x<0, or that tend to zero as x→∞ and tend to ∞ as x→-∞, have also been studied. This paper identifies literature for the five inverse problems just mentioned, and for four other inverse problems. Heaviside-step backgrounds are discussed at length. (orig.)

  14. Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

    Science.gov (United States)

    Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

    2018-06-01

    An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.

  15. Traveltime approximations for inhomogeneous HTI media

    KAUST Repository

    Alkhalifah, Tariq Ali

    2011-01-01

    Traveltimes information is convenient for parameter estimation especially if the medium is described by an anisotropic set of parameters. This is especially true if we could relate traveltimes analytically to these medium parameters, which is generally hard to do in inhomogeneous media. As a result, I develop traveltimes approximations for horizontaly transversely isotropic (HTI) media as simplified and even linear functions of the anisotropic parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to η and the azimuthal symmetry direction (usually used to describe the fracture direction) from a generally inhomogeneous elliptically anisotropic background medium. The resulting approximations can provide accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations out there. These equations will allow us to readily extend the inhomogenous background elliptical anisotropic model to an HTI with a variable, but smoothly varying, η and horizontal symmetry direction values. © 2011 Society of Exploration Geophysicists.

  16. The efficiency of Flory approximation

    International Nuclear Information System (INIS)

    Obukhov, S.P.

    1984-01-01

    The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)

  17. Ionogram inversion for a tilted ionosphere

    International Nuclear Information System (INIS)

    Wright, J.W.

    1990-01-01

    Digital ionosondes such as the Dynasonde disclose that the ionosphere is seldom horizontal even when it is plane stratified to a good approximation. The local magnetic dip does not then determine correctly the radiowave propagation angle for inversion of the ionogram to a plasma density profile. The measured echo direction of arrival can be used together with the known dip for an improved propagation angle. The effects are small for simple one-parameter laminae but become important when differential (ordinary, extraordinary) retardations are used to aid correction for valley and starting ambiguities. The resulting profile describes the plasma distribution along the direction of observation, rather than the vertical; it thus conveys information about horizontal gradients. Observations suggest that advantages in inversion methods may be practicable for application to modern ionosonde recordings, by which local lateral structure can be described in greater detail. 20 refs

  18. Voxel inversion of airborne electromagnetic data for improved model integration

    Science.gov (United States)

    Fiandaca, Gianluca; Auken, Esben; Kirkegaard, Casper; Vest Christiansen, Anders

    2014-05-01

    Inversion of electromagnetic data has migrated from single site interpretations to inversions including entire surveys using spatial constraints to obtain geologically reasonable results. Though, the model space is usually linked to the actual observation points. For airborne electromagnetic (AEM) surveys the spatial discretization of the model space reflects the flight lines. On the contrary, geological and groundwater models most often refer to a regular voxel grid, not correlated to the geophysical model space, and the geophysical information has to be relocated for integration in (hydro)geological models. We have developed a new geophysical inversion algorithm working directly in a voxel grid disconnected from the actual measuring points, which then allows for informing directly geological/hydrogeological models. The new voxel model space defines the soil properties (like resistivity) on a set of nodes, and the distribution of the soil properties is computed everywhere by means of an interpolation function (e.g. inverse distance or kriging). Given this definition of the voxel model space, the 1D forward responses of the AEM data are computed as follows: 1) a 1D model subdivision, in terms of model thicknesses, is defined for each 1D data set, creating "virtual" layers. 2) the "virtual" 1D models at the sounding positions are finalized by interpolating the soil properties (the resistivity) in the center of the "virtual" layers. 3) the forward response is computed in 1D for each "virtual" model. We tested the new inversion scheme on an AEM survey carried out with the SkyTEM system close to Odder, in Denmark. The survey comprises 106054 dual mode AEM soundings, and covers an area of approximately 13 km X 16 km. The voxel inversion was carried out on a structured grid of 260 X 325 X 29 xyz nodes (50 m xy spacing), for a total of 2450500 inversion parameters. A classical spatially constrained inversion (SCI) was carried out on the same data set, using 106054

  19. Plasma diagnostics by Abel inversion in hyperbolic geometry

    International Nuclear Information System (INIS)

    Alhasi, A.S.; Elliott, J.A.

    1992-01-01

    Plasma confined in the UMIST linear quadrupole adopts a configuration with approximately hyperbolic symmetry. The normal diagnostic is a Langmuir probe, but we have developed an alternative method using optical emission tomography based upon an analytic Abel inversion. Plasma radiance is obtained as a function of a parameter identifying magnetic flux surfaces. The inversion algorithm has been tested using artificial data. Experimentally, the results show that ionizing collisions cause the confined plasma distribution to broaden as the plasma travels through the confining field. This is shown to be a consequence of the approximate incompressibility of the E x B flow. (author)

  20. Inverse Faraday Effect Revisited

    Science.gov (United States)

    Mendonça, J. T.; Ali, S.; Davies, J. R.

    2010-11-01

    The inverse Faraday effect is usually associated with circularly polarized laser beams. However, it was recently shown that it can also occur for linearly polarized radiation [1]. The quasi-static axial magnetic field by a laser beam propagating in plasma can be calculated by considering both the spin and the orbital angular momenta of the laser pulse. A net spin is present when the radiation is circularly polarized and a net orbital angular momentum is present if there is any deviation from perfect rotational symmetry. This orbital angular momentum has recently been discussed in the plasma context [2], and can give an additional contribution to the axial magnetic field, thus enhancing or reducing the inverse Faraday effect. As a result, this effect that is usually attributed to circular polarization can also be excited by linearly polarized radiation, if the incident laser propagates in a Laguerre-Gauss mode carrying a finite amount of orbital angular momentum.[4pt] [1] S. ALi, J.R. Davies and J.T. Mendonca, Phys. Rev. Lett., 105, 035001 (2010).[0pt] [2] J. T. Mendonca, B. Thidé, and H. Then, Phys. Rev. Lett. 102, 185005 (2009).

  1. Approximate Implicitization Using Linear Algebra

    Directory of Open Access Journals (Sweden)

    Oliver J. D. Barrowclough

    2012-01-01

    Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.

  2. Rollout sampling approximate policy iteration

    NARCIS (Netherlands)

    Dimitrakakis, C.; Lagoudakis, M.G.

    2008-01-01

    Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a

  3. Framework for sequential approximate optimization

    NARCIS (Netherlands)

    Jacobs, J.H.; Etman, L.F.P.; Keulen, van F.; Rooda, J.E.

    2004-01-01

    An object-oriented framework for Sequential Approximate Optimization (SAO) isproposed. The framework aims to provide an open environment for thespecification and implementation of SAO strategies. The framework is based onthe Python programming language and contains a toolbox of Python

  4. Approximate deconvolution models of turbulence analysis, phenomenology and numerical analysis

    CERN Document Server

    Layton, William J

    2012-01-01

    This volume presents a mathematical development of a recent approach to the modeling and simulation of turbulent flows based on methods for the approximate solution of inverse problems. The resulting Approximate Deconvolution Models or ADMs have some advantages over more commonly used turbulence models – as well as some disadvantages. Our goal in this book is to provide a clear and complete mathematical development of ADMs, while pointing out the difficulties that remain. In order to do so, we present the analytical theory of ADMs, along with its connections, motivations and complements in the phenomenology of and algorithms for ADMs.

  5. Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem

    International Nuclear Information System (INIS)

    Pan, Yu; James, Matthew R.; Miao, Zibo; Amini, Nina H.; Ugrinovskii, Valery

    2015-01-01

    Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable. (orig.)

  6. Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE

    Directory of Open Access Journals (Sweden)

    Chunlong Sun

    2017-01-01

    Full Text Available The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data give good approximations to the exact order demonstrating the efficiency of the inversion algorithm and numerical stability of the inversion problem.

  7. Inverse fusion PCR cloning.

    Directory of Open Access Journals (Sweden)

    Markus Spiliotis

    Full Text Available Inverse fusion PCR cloning (IFPC is an easy, PCR based three-step cloning method that allows the seamless and directional insertion of PCR products into virtually all plasmids, this with a free choice of the insertion site. The PCR-derived inserts contain a vector-complementary 5'-end that allows a fusion with the vector by an overlap extension PCR, and the resulting amplified insert-vector fusions are then circularized by ligation prior transformation. A minimal amount of starting material is needed and experimental steps are reduced. Untreated circular plasmid, or alternatively bacteria containing the plasmid, can be used as templates for the insertion, and clean-up of the insert fragment is not urgently required. The whole cloning procedure can be performed within a minimal hands-on time and results in the generation of hundreds to ten-thousands of positive colonies, with a minimal background.

  8. Inverse plasma equilibria

    International Nuclear Information System (INIS)

    Hicks, H.R.; Dory, R.A.; Holmes, J.A.

    1983-01-01

    We illustrate in some detail a 2D inverse-equilibrium solver that was constructed to analyze tokamak configurations and stellarators (the latter in the context of the average method). To ensure that the method is suitable not only to determine equilibria, but also to provide appropriately represented data for existing stability codes, it is important to be able to control the Jacobian, tilde J is identical to delta(R,Z)/delta(rho, theta). The form chosen is tilde J = J 0 (rho)R/sup l/rho where rho is a flux surface label, and l is an integer. The initial implementation is for a fixed conducting-wall boundary, but the technique can be extended to a free-boundary model

  9. Legendre-tau approximations for functional differential equations

    Science.gov (United States)

    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.

  10. A 3D domain decomposition approach for the identification of spatially varying elastic material parameters

    KAUST Repository

    Moussawi, Ali; Lubineau, Gilles; Xu, Jiangping; Pan, Bing

    2015-01-01

    Summary: The post-treatment of (3D) displacement fields for the identification of spatially varying elastic material parameters is a large inverse problem that remains out of reach for massive 3D structures. We explore here the potential

  11. Nuclear Hartree-Fock approximation testing and other related approximations

    International Nuclear Information System (INIS)

    Cohenca, J.M.

    1970-01-01

    Hartree-Fock, and Tamm-Dancoff approximations are tested for angular momentum of even-even nuclei. Wave functions, energy levels and momenta are comparatively evaluated. Quadripole interactions are studied following the Elliott model. Results are applied to Ne 20 [pt

  12. Transmuted Generalized Inverse Weibull Distribution

    OpenAIRE

    Merovci, Faton; Elbatal, Ibrahim; Ahmed, Alaa

    2013-01-01

    A generalization of the generalized inverse Weibull distribution so-called transmuted generalized inverse Weibull dis- tribution is proposed and studied. We will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking generalized inverse Weibull distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. Various structural properties including explicit expression...

  13. Solving of L0 norm constrained EEG inverse problem.

    Science.gov (United States)

    Xu, Peng; Lei, Xu; Hu, Xiao; Yao, Dezhong

    2009-01-01

    l(0) norm is an effective constraint used to solve EEG inverse problem for a sparse solution. However, due to the discontinuous and un-differentiable properties, it is an open issue to solve the l(0) norm constrained problem, which is usually instead solved by using some alternative functions like l(1) norm to approximate l(0) norm. In this paper, a continuous and differentiable function having the same form as the transfer function of Butterworth low-pass filter is introduced to approximate l(0) norm constraint involved in EEG inverse problem. The new approximation based approach was compared with l(1) norm and LORETA solutions on a realistic head model using simulated sources. The preliminary results show that this alternative approximation to l(0) norm is promising for the estimation of EEG sources with sparse distribution.

  14. Shearlets and Optimally Sparse Approximations

    DEFF Research Database (Denmark)

    Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q

    2012-01-01

    Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....

  15. Diophantine approximation and Dirichlet series

    CERN Document Server

    Queffélec, Hervé

    2013-01-01

    This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...

  16. Approximations to camera sensor noise

    Science.gov (United States)

    Jin, Xiaodan; Hirakawa, Keigo

    2013-02-01

    Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

  17. Rational approximations for tomographic reconstructions

    International Nuclear Information System (INIS)

    Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas

    2013-01-01

    We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp–Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image. (paper)

  18. Specimen loading list for the varying temperature experiment

    International Nuclear Information System (INIS)

    Qualls, A.L.; Sitterson, R.G.

    1998-01-01

    The varying temperature experiment HFIR-RB-13J has been assembled and inserted in the reactor. Approximately 5300 specimens were cleaned, inspected, matched, and loaded into four specimen holders. A listing of each specimen loaded into the steady temperature holder, its position in the capsule, and the identification of the corresponding specimen loaded into the varying temperature holder is presented in this report

  19. Approximate reasoning in physical systems

    International Nuclear Information System (INIS)

    Mutihac, R.

    1991-01-01

    The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author)

  20. Face Recognition using Approximate Arithmetic

    DEFF Research Database (Denmark)

    Marso, Karol

    Face recognition is image processing technique which aims to identify human faces and found its use in various different fields for example in security. Throughout the years this field evolved and there are many approaches and many different algorithms which aim to make the face recognition as effective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....

  1. Calculation of the inverse data space via sparse inversion

    KAUST Repository

    Saragiotis, Christos; Doulgeris, Panagiotis C.; Verschuur, Dirk Jacob Eric

    2011-01-01

    The inverse data space provides a natural separation of primaries and surface-related multiples, as the surface multiples map onto the area around the origin while the primaries map elsewhere. However, the calculation of the inverse data is far from

  2. Inverse feasibility problems of the inverse maximum flow problems

    Indian Academy of Sciences (India)

    199–209. c Indian Academy of Sciences. Inverse feasibility problems of the inverse maximum flow problems. ADRIAN DEACONU. ∗ and ELEONOR CIUREA. Department of Mathematics and Computer Science, Faculty of Mathematics and Informatics, Transilvania University of Brasov, Brasov, Iuliu Maniu st. 50,. Romania.

  3. Green-Ampt approximations: A comprehensive analysis

    Science.gov (United States)

    Ali, Shakir; Islam, Adlul; Mishra, P. K.; Sikka, Alok K.

    2016-04-01

    Green-Ampt (GA) model and its modifications are widely used for simulating infiltration process. Several explicit approximate solutions to the implicit GA model have been developed with varying degree of accuracy. In this study, performance of nine explicit approximations to the GA model is compared with the implicit GA model using the published data for broad range of soil classes and infiltration time. The explicit GA models considered are Li et al. (1976) (LI), Stone et al. (1994) (ST), Salvucci and Entekhabi (1994) (SE), Parlange et al. (2002) (PA), Barry et al. (2005) (BA), Swamee et al. (2012) (SW), Ali et al. (2013) (AL), Almedeij and Esen (2014) (AE), and Vatankhah (2015) (VA). Six statistical indicators (e.g., percent relative error, maximum absolute percent relative error, average absolute percent relative errors, percent bias, index of agreement, and Nash-Sutcliffe efficiency) and relative computer computation time are used for assessing the model performance. Models are ranked based on the overall performance index (OPI). The BA model is found to be the most accurate followed by the PA and VA models for variety of soil classes and infiltration periods. The AE, SW, SE, and LI model also performed comparatively better. Based on the overall performance index, the explicit models are ranked as BA > PA > VA > LI > AE > SE > SW > ST > AL. Results of this study will be helpful in selection of accurate and simple explicit approximate GA models for solving variety of hydrological problems.

  4. Local approximation of a metapopulation's equilibrium.

    Science.gov (United States)

    Barbour, A D; McVinish, R; Pollett, P K

    2018-04-18

    We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously.

  5. Approximate Reanalysis in Topology Optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole

    2009-01-01

    In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...

  6. Approximate Matching of Hierarchial Data

    DEFF Research Database (Denmark)

    Augsten, Nikolaus

    -grams of a tree are all its subtrees of a particular shape. Intuitively, two trees are similar if they have many pq-grams in common. The pq-gram distance is an efficient and effective approximation of the tree edit distance. We analyze the properties of the pq-gram distance and compare it with the tree edit...

  7. Approximation of Surfaces by Cylinders

    DEFF Research Database (Denmark)

    Randrup, Thomas

    1998-01-01

    We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...

  8. Approximation properties of haplotype tagging

    Directory of Open Access Journals (Sweden)

    Dreiseitl Stephan

    2006-01-01

    Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.

  9. All-Norm Approximation Algorithms

    NARCIS (Netherlands)

    Azar, Yossi; Epstein, Leah; Richter, Yossi; Woeginger, Gerhard J.; Penttonen, Martti; Meineche Schmidt, Erik

    2002-01-01

    A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓ p norms. We address this problem by introducing the concept of an All-norm ρ-approximation

  10. Truthful approximations to range voting

    DEFF Research Database (Denmark)

    Filos-Ratsika, Aris; Miltersen, Peter Bro

    We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...

  11. On badly approximable complex numbers

    DEFF Research Database (Denmark)

    Esdahl-Schou, Rune; Kristensen, S.

    We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...

  12. Approximate reasoning in decision analysis

    Energy Technology Data Exchange (ETDEWEB)

    Gupta, M M; Sanchez, E

    1982-01-01

    The volume aims to incorporate the recent advances in both theory and applications. It contains 44 articles by 74 contributors from 17 different countries. The topics considered include: membership functions; composite fuzzy relations; fuzzy logic and inference; classifications and similarity measures; expert systems and medical diagnosis; psychological measurements and human behaviour; approximate reasoning and decision analysis; and fuzzy clustering algorithms.

  13. Rational approximation of vertical segments

    Science.gov (United States)

    Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte

    2007-08-01

    In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.

  14. Pythagorean Approximations and Continued Fractions

    Science.gov (United States)

    Peralta, Javier

    2008-01-01

    In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…

  15. Ultrafast Approximation for Phylogenetic Bootstrap

    NARCIS (Netherlands)

    Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt

    Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and

  16. Mathematical properties of numerical inversion for jet calibrations

    Energy Technology Data Exchange (ETDEWEB)

    Cukierman, Aviv [Physics Department, Stanford University, Stanford, CA 94305 (United States); SLAC National Accelerator Laboratory, Stanford University, Menlo Park, CA 94025 (United States); Nachman, Benjamin, E-mail: bnachman@cern.ch [Physics Department, Stanford University, Stanford, CA 94305 (United States); SLAC National Accelerator Laboratory, Stanford University, Menlo Park, CA 94025 (United States); Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94704 (United States)

    2017-06-21

    Numerical inversion is a general detector calibration technique that is independent of the underlying spectrum. This procedure is formalized and important statistical properties are presented, using high energy jets at the Large Hadron Collider as an example setting. In particular, numerical inversion is inherently biased and common approximations to the calibrated jet energy tend to over-estimate the resolution. Analytic approximations to the closure and calibrated resolutions are demonstrated to effectively predict the full forms under realistic conditions. Finally, extensions of numerical inversion are presented which can reduce the inherent biases. These methods will be increasingly important to consider with degraded resolution at low jet energies due to a much higher instantaneous luminosity in the near future.

  17. Rayleigh scattering and nonlinear inversion of elastic waves

    Energy Technology Data Exchange (ETDEWEB)

    Gritto, Roland [Univ. of California, Berkeley, CA (United States)

    1995-12-01

    Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of -100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to kpR = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.

  18. Confidence Intervals for Asbestos Fiber Counts: Approximate Negative Binomial Distribution.

    Science.gov (United States)

    Bartley, David; Slaven, James; Harper, Martin

    2017-03-01

    The negative binomial distribution is adopted for analyzing asbestos fiber counts so as to account for both the sampling errors in capturing only a finite number of fibers and the inevitable human variation in identifying and counting sampled fibers. A simple approximation to this distribution is developed for the derivation of quantiles and approximate confidence limits. The success of the approximation depends critically on the use of Stirling's expansion to sufficient order, on exact normalization of the approximating distribution, on reasonable perturbation of quantities from the normal distribution, and on accurately approximating sums by inverse-trapezoidal integration. Accuracy of the approximation developed is checked through simulation and also by comparison to traditional approximate confidence intervals in the specific case that the negative binomial distribution approaches the Poisson distribution. The resulting statistics are shown to relate directly to early research into the accuracy of asbestos sampling and analysis. Uncertainty in estimating mean asbestos fiber concentrations given only a single count is derived. Decision limits (limits of detection) and detection limits are considered for controlling false-positive and false-negative detection assertions and are compared to traditional limits computed assuming normal distributions. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

  19. Multiscale Seismic Inversion in the Data and Image Domains

    KAUST Repository

    Zhang, Sanzong

    2015-12-01

    I present a general methodology for inverting seismic data in either the data or image domains. It partially overcomes one of the most serious problems with current waveform inversion methods, which is the tendency to converge to models far from the actual one. The key idea is to develop a multiscale misfit function that is composed of both a simplified version of the data and one associated with the complex part of the data. Misfit functions based on simple data are characterized by many fewer local minima so that a gradient optimization method can make quick progress in getting to the general vicinity of the actual model. Once we are near the actual model, we then use the gradient based on the more complex data. Below, we describe two implementations of this multiscale strategy: wave equation traveltime inversion in the data domain and generalized differential semblance optimization in the image domain. • Wave Equation Traveltime Inversion in the Data Domain (WT): The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we present a waveequation method that inverts the traveltimes of reflection events, and so is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function is a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag which maximizes the crosscorrelation amplitude represents the reflection-traveltime residual that is back-projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions are introduced to estimate the reflection-traveltime residual by semblance analysis and scanning. In theory, only the traveltime information is inverted and there is no need to precisely fit the amplitudes or assume a high-frequency approximation. Results

  20. Face inversion increases attractiveness.

    Science.gov (United States)

    Leder, Helmut; Goller, Juergen; Forster, Michael; Schlageter, Lena; Paul, Matthew A

    2017-07-01

    Assessing facial attractiveness is a ubiquitous, inherent, and hard-wired phenomenon in everyday interactions. As such, it has highly adapted to the default way that faces are typically processed: viewing faces in upright orientation. By inverting faces, we can disrupt this default mode, and study how facial attractiveness is assessed. Faces, rotated at 90 (tilting to either side) and 180°, were rated on attractiveness and distinctiveness scales. For both orientations, we found that faces were rated more attractive and less distinctive than upright faces. Importantly, these effects were more pronounced for faces rated low in upright orientation, and smaller for highly attractive faces. In other words, the less attractive a face was, the more it gained in attractiveness by inversion or rotation. Based on these findings, we argue that facial attractiveness assessments might not rely on the presence of attractive facial characteristics, but on the absence of distinctive, unattractive characteristics. These unattractive characteristics are potentially weighed against an individual, attractive prototype in assessing facial attractiveness. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.

  1. Inverse problem in hydrogeology

    Science.gov (United States)

    Carrera, Jesús; Alcolea, Andrés; Medina, Agustín; Hidalgo, Juan; Slooten, Luit J.

    2005-03-01

    The state of the groundwater inverse problem is synthesized. Emphasis is placed on aquifer characterization, where modelers have to deal with conceptual model uncertainty (notably spatial and temporal variability), scale dependence, many types of unknown parameters (transmissivity, recharge, boundary conditions, etc.), nonlinearity, and often low sensitivity of state variables (typically heads and concentrations) to aquifer properties. Because of these difficulties, calibration cannot be separated from the modeling process, as it is sometimes done in other fields. Instead, it should be viewed as one step in the process of understanding aquifer behavior. In fact, it is shown that actual parameter estimation methods do not differ from each other in the essence, though they may differ in the computational details. It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data (temperature, occurrence and concentration of isotopes, age, etc.), proper accounting of uncertainty, etc. Despite this, even with existing codes, automatic calibration facilitates enormously the task of modeling. Therefore, it is contended that its use should become standard practice. L'état du problème inverse des eaux souterraines est synthétisé. L'accent est placé sur la caractérisation de l'aquifère, où les modélisateurs doivent jouer avec l'incertitude des modèles conceptuels (notamment la variabilité spatiale et temporelle), les facteurs d'échelle, plusieurs inconnues sur différents paramètres (transmissivité, recharge, conditions aux limites, etc.), la non linéarité, et souvent la sensibilité de plusieurs variables d'état (charges hydrauliques, concentrations) des propriétés de l'aquifère. A cause de ces difficultés, le calibrage ne peut êtreséparé du processus de modélisation, comme c'est le

  2. Multiples waveform inversion

    KAUST Repository

    Zhang, Dongliang

    2013-01-01

    To increase the illumination of the subsurface and to eliminate the dependency of FWI on the source wavelet, we propose multiples waveform inversion (MWI) that transforms each hydrophone into a virtual point source with a time history equal to that of the recorded data. These virtual sources are used to numerically generate downgoing wavefields that are correlated with the backprojected surface-related multiples to give the migration image. Since the recorded data are treated as the virtual sources, knowledge of the source wavelet is not required, and the subsurface illumination is greatly enhanced because the entire free surface acts as an extended source compared to the radiation pattern of a traditional point source. Numerical tests on the Marmousi2 model show that the convergence rate and the spatial resolution of MWI is, respectively, faster and more accurate then FWI. The potential pitfall with this method is that the multiples undergo more than one roundtrip to the surface, which increases attenuation and reduces spatial resolution. This can lead to less resolved tomograms compared to conventional FWI. The possible solution is to combine both FWI and MWI in inverting for the subsurface velocity distribution.

  3. An interpretation of signature inversion

    International Nuclear Information System (INIS)

    Onishi, Naoki; Tajima, Naoki

    1988-01-01

    An interpretation in terms of the cranking model is presented to explain why signature inversion occurs for positive γ of the axially asymmetric deformation parameter and emerges into specific orbitals. By introducing a continuous variable, the eigenvalue equation can be reduced to a one dimensional Schroedinger equation by means of which one can easily understand the cause of signature inversion. (author)

  4. Inverse problems for Maxwell's equations

    CERN Document Server

    Romanov, V G

    1994-01-01

    The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

  5. Inverse modeling of FIB milling by dose profile optimization

    International Nuclear Information System (INIS)

    Lindsey, S.; Waid, S.; Hobler, G.; Wanzenböck, H.D.; Bertagnolli, E.

    2014-01-01

    FIB technologies possess a unique ability to form topographies that are difficult or impossible to generate with binary etching through typical photo-lithography. The ability to arbitrarily vary the spatial dose distribution and therefore the amount of milling opens possibilities for the production of a wide range of functional structures with applications in biology, chemistry, and optics. However in practice, the realization of these goals is made difficult by the angular dependence of the sputtering yield and redeposition effects that vary as the topography evolves. An inverse modeling algorithm that optimizes dose profiles, defined as the superposition of time invariant pixel dose profiles (determined from the beam parameters and pixel dwell times), is presented. The response of the target to a set of pixel dwell times in modeled by numerical continuum simulations utilizing 1st and 2nd order sputtering and redeposition, the resulting surfaces are evaluated with respect to a target topography in an error minimization routine. Two algorithms for the parameterization of pixel dwell times are presented, a direct pixel dwell time method, and an abstracted method that uses a refineable piecewise linear cage function to generate pixel dwell times from a minimal number of parameters. The cage function method demonstrates great flexibility and efficiency as compared to the direct fitting method with performance enhancements exceeding ∼10× as compared to direct fitting for medium to large simulation sets. Furthermore, the refineable nature of the cage function enables solutions to adapt to the desired target function. The optimization algorithm, although working with stationary dose profiles, is demonstrated to be applicable also outside the quasi-static approximation. Experimental data confirms the viability of the solutions for 5 × 7 μm deep lens like structures defined by 90 pixel dwell times

  6. Carleman estimates and applications to inverse problems for hyperbolic systems

    CERN Document Server

    Bellassoued, Mourad

    2017-01-01

    This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of wh...

  7. Algebraic properties of generalized inverses

    CERN Document Server

    Cvetković‐Ilić, Dragana S

    2017-01-01

    This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, Ph...

  8. Parameterization analysis and inversion for orthorhombic media

    KAUST Repository

    Masmoudi, Nabil

    2018-05-01

    Accounting for azimuthal anisotropy is necessary for the processing and inversion of wide-azimuth and wide-aperture seismic data because wave speeds naturally depend on the wave propagation direction. Orthorhombic anisotropy is considered the most effective anisotropic model that approximates the azimuthal anisotropy we observe in seismic data. In the framework of full wave form inversion (FWI), the large number of parameters describing orthorhombic media exerts a considerable trade-off and increases the non-linearity of the inversion problem. Choosing a suitable parameterization for the model, and identifying which parameters in that parameterization could be well resolved, are essential to a successful inversion. In this thesis, I derive the radiation patterns for different acoustic orthorhombic parameterization. Analyzing the angular dependence of the scattering of the parameters of different parameterizations starting with the conventionally used notation, I assess the potential trade-off between the parameters and the resolution in describing the data and inverting for the parameters. In order to build practical inversion strategies, I suggest new parameters (called deviation parameters) for a new parameterization style in orthorhombic media. The novel parameters denoted ∈d, ƞd and δd are dimensionless and represent a measure of deviation between the vertical planes in orthorhombic anisotropy. The main feature of the deviation parameters consists of keeping the scattering of the vertical transversely isotropic (VTI) parameters stationary with azimuth. Using these scattering features, we can condition FWI to invert for the parameters which the data are sensitive to, at different stages, scales, and locations in the model. With this parameterization, the data are mainly sensitive to the scattering of 3 parameters (out of six that describe an acoustic orthorhombic medium): the horizontal velocity in the x1 direction, ∈1 which provides scattering mainly near

  9. APPROXIMATION AND INVERSION OF A COMPLEX METEOROLOGICAL SYSTEM VIA LOCAL LINEAR FILTERS. (R825381)

    Science.gov (United States)

    The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

  10. Seismic Imaging and Velocity Analysis Using a Pseudo Inverse to the Extended Born Approximation

    KAUST Repository

    Alali, Abdullah A.

    2018-01-01

    the correct model. The most commonly used technique is differential semblance optimization (DSO), which depends on applying an image extension and penalizing the energy in the non-physical extension. However, studies show that the conventional DSO gradient

  11. Beyond the random phase approximation

    DEFF Research Database (Denmark)

    Olsen, Thomas; Thygesen, Kristian S.

    2013-01-01

    We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...... functional theory and the adiabatic connection fluctuation-dissipation theorem and contains no fitted parameters. The new kernel is shown to preserve the accurate description of dispersive interactions from RPA while significantly improving the description of short-range correlation in molecules, insulators......, and metals. For molecular atomization energies, the rALDA is a factor of 7 better than RPA and a factor of 4 better than the Perdew-Burke-Ernzerhof (PBE) functional when compared to experiments, and a factor of 3 (1.5) better than RPA (PBE) for cohesive energies of solids. For transition metals...

  12. Hydrogen: Beyond the Classic Approximation

    International Nuclear Information System (INIS)

    Scivetti, Ivan

    2003-01-01

    The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position

  13. Approximation errors during variance propagation

    International Nuclear Information System (INIS)

    Dinsmore, Stephen

    1986-01-01

    Risk and reliability analyses are often performed by constructing and quantifying large fault trees. The inputs to these models are component failure events whose probability of occuring are best represented as random variables. This paper examines the errors inherent in two approximation techniques used to calculate the top event's variance from the inputs' variance. Two sample fault trees are evaluated and several three dimensional plots illustrating the magnitude of the error over a wide range of input means and variances are given

  14. WKB approximation in atomic physics

    International Nuclear Information System (INIS)

    Karnakov, Boris Mikhailovich

    2013-01-01

    Provides extensive coverage of the Wentzel-Kramers-Brillouin approximation and its applications. Presented as a sequence of problems with highly detailed solutions. Gives a concise introduction for calculating Rydberg states, potential barriers and quasistationary systems. This book has evolved from lectures devoted to applications of the Wentzel-Kramers-Brillouin- (WKB or quasi-classical) approximation and of the method of 1/N -expansion for solving various problems in atomic and nuclear physics. The intent of this book is to help students and investigators in this field to extend their knowledge of these important calculation methods in quantum mechanics. Much material is contained herein that is not to be found elsewhere. WKB approximation, while constituting a fundamental area in atomic physics, has not been the focus of many books. A novel method has been adopted for the presentation of the subject matter, the material is presented as a succession of problems, followed by a detailed way of solving them. The methods introduced are then used to calculate Rydberg states in atomic systems and to evaluate potential barriers and quasistationary states. Finally, adiabatic transition and ionization of quantum systems are covered.

  15. Inverse Cerenkov experiment

    International Nuclear Information System (INIS)

    Kimura, W.D.

    1993-01-01

    The final report describes work performed to investigate inverse Cherenkov acceleration (ICA) as a promising method for laser particle acceleration. In particular, an improved configuration of ICA is being tested in a experiment presently underway on the Accelerator Test Facility (ATF). In the experiment, the high peak power (∼ 10 GW) linearly polarized ATF CO 2 laser beam is converted to a radially polarized beam. This is beam is focused with an axicon at the Cherenkov angle onto the ATF 50-MeV e-beam inside a hydrogen gas cell, where the gas acts as the phase matching medium of the interaction. An energy gain of ∼12 MeV is predicted assuming a delivered laser peak power of 5 GW. The experiment is divided into two phases. The Phase I experiments, which were completed in the spring of 1992, were conducted before the ATF e-beam was available and involved several successful tests of the optical systems. Phase II experiments are with the e-beam and laser beam, and are still in progress. The ATF demonstrated delivery of the e-beam to the experiment in Dec. 1992. A preliminary ''debugging'' run with the e-beam and laser beam occurred in May 1993. This revealed the need for some experimental modifications, which have been implemented. The second run is tentatively scheduled for October or November 1993. In parallel to the experimental efforts has been ongoing theoretical work to support the experiment and investigate improvement and/or offshoots. One exciting offshoot has been theoretical work showing that free-space laser acceleration of electrons is possible using a radially-polarized, axicon-focused laser beam, but without any phase-matching gas. The Monte Carlo code used to model the ICA process has been upgraded and expanded to handle different types of laser beam input profiles

  16. Inverse Problems in a Bayesian Setting

    KAUST Repository

    Matthies, Hermann G.

    2016-02-13

    In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.

  17. Inverse Problems in a Bayesian Setting

    KAUST Repository

    Matthies, Hermann G.; Zander, Elmar; Rosić, Bojana V.; Litvinenko, Alexander; Pajonk, Oliver

    2016-01-01

    In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.

  18. Introduction to the mathematics of inversion in remote sensing and indirect measurements

    CERN Document Server

    Twomey, S

    2013-01-01

    Developments in Geomathematics, 3: Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements focuses on the application of the mathematics of inversion in remote sensing and indirect measurements, including vectors and matrices, eigenvalues and eigenvectors, and integral equations. The publication first examines simple problems involving inversion, theory of large linear systems, and physical and geometric aspects of vectors and matrices. Discussions focus on geometrical view of matrix operations, eigenvalues and eigenvectors, matrix products, inverse of a matrix, transposition and rules for product inversion, and algebraic elimination. The manuscript then tackles the algebraic and geometric aspects of functions and function space and linear inversion methods, as well as the algebraic and geometric nature of constrained linear inversion, least squares solution, approximation by sums of functions, and integral equations. The text examines information content of indirect sensing m...

  19. Support Minimized Inversion of Acoustic and Elastic Wave Scattering

    Science.gov (United States)

    Safaeinili, Ali

    Inversion of limited data is common in many areas of NDE such as X-ray Computed Tomography (CT), Ultrasonic and eddy current flaw characterization and imaging. In many applications, it is common to have a bias toward a solution with minimum (L^2)^2 norm without any physical justification. When it is a priori known that objects are compact as, say, with cracks and voids, by choosing "Minimum Support" functional instead of the minimum (L^2)^2 norm, an image can be obtained that is equally in agreement with the available data, while it is more consistent with what is most probably seen in the real world. We have utilized a minimum support functional to find a solution with the smallest volume. This inversion algorithm is most successful in reconstructing objects that are compact like voids and cracks. To verify this idea, we first performed a variational nonlinear inversion of acoustic backscatter data using minimum support objective function. A full nonlinear forward model was used to accurately study the effectiveness of the minimized support inversion without error due to the linear (Born) approximation. After successful inversions using a full nonlinear forward model, a linearized acoustic inversion was developed to increase speed and efficiency in imaging process. The results indicate that by using minimum support functional, we can accurately size and characterize voids and/or cracks which otherwise might be uncharacterizable. An extremely important feature of support minimized inversion is its ability to compensate for unknown absolute phase (zero-of-time). Zero-of-time ambiguity is a serious problem in the inversion of the pulse-echo data. The minimum support inversion was successfully used for the inversion of acoustic backscatter data due to compact scatterers without the knowledge of the zero-of-time. The main drawback to this type of inversion is its computer intensiveness. In order to make this type of constrained inversion available for common use, work

  20. Linear GPR inversion for lossy soil and a planar air-soil interface

    DEFF Research Database (Denmark)

    Meincke, Peter

    2001-01-01

    A three-dimensional inversion scheme for fixed-offset ground penetrating radar (GPR) is derived that takes into account the loss in the soil and the planar air-soil interface. The forward model of this inversion scheme is based upon the first Born approximation and the dyadic Green function...

  1. Potentials of the inverse scattering problem in the three-nucleon problem

    International Nuclear Information System (INIS)

    Pushkash, A.M.; Simenog, I.V.; Shapoval, D.V.

    1993-01-01

    Possibilities of using the method of the inverse scattering problem for describing simultaneously the two-nucleon and the low-energy three-nucleon data in the S-interaction approximation are examined. 20 refs., 3 figs., 1 tab

  2. Local facet approximation for image stitching

    Science.gov (United States)

    Li, Jing; Lai, Shiming; Liu, Yu; Wang, Zhengming; Zhang, Maojun

    2018-01-01

    Image stitching aims at eliminating multiview parallax and generating a seamless panorama given a set of input images. This paper proposes a local adaptive stitching method, which could achieve both accurate and robust image alignments across the whole panorama. A transformation estimation model is introduced by approximating the scene as a combination of neighboring facets. Then, the local adaptive stitching field is constructed using a series of linear systems of the facet parameters, which enables the parallax handling in three-dimensional space. We also provide a concise but effective global projectivity preserving technique that smoothly varies the transformations from local adaptive to global planar. The proposed model is capable of stitching both normal images and fisheye images. The efficiency of our method is quantitatively demonstrated in the comparative experiments on several challenging cases.

  3. Hydromagnetic turbulence in the direct interaction approximation

    International Nuclear Information System (INIS)

    Nagarajan, S.

    1975-01-01

    The dissertation is concerned with the nature of turbulence in a medium with large electrical conductivity. Three distinct though inter-related questions are asked. Firstly, the evolution of a weak, random initial magnetic field in a highly conducting, isotropically turbulent fluid is discussed. This was first discussed in the paper 'Growth of Turbulent Magnetic Fields' by Kraichnan and Nagargian. The Physics of Fluids, volume 10, number 4, 1967. Secondly, the direct interaction approximation for hydromagnetic turbulence maintained by stationary, isotropic, random stirring forces is formulated in the wave-number-frequency domain. Thirdly, the dynamical evolution of a weak, random, magnetic excitation in a turbulent electrically conducting fluid is examined under varying kinematic conditions. (G.T.H.)

  4. A Generalization of the Spherical Inversion

    Science.gov (United States)

    Ramírez, José L.; Rubiano, Gustavo N.

    2017-01-01

    In the present article, we introduce a generalization of the spherical inversion. In particular, we define an inversion with respect to an ellipsoid, and prove several properties of this new transformation. The inversion in an ellipsoid is the generalization of the elliptic inversion to the three-dimensional space. We also study the inverse images…

  5. Inverse picobarns to you

    International Nuclear Information System (INIS)

    Anon.

    1994-01-01

    The impact of some spectacular colliding beam records this summer has been muted by the cryptic terminology which scientists invariably use when describing their best achievements. Early this century, nuclear physicists calculated the collision rate of a particle beam with a sample of stationary atoms by multiplying the intensity of the beam (particles per unit area per second), the total number of targets, and the area of each target. In searching for a yardstick to measure this effective 'cross-section', they first thought of a unit called a 'barn', equal to 10 -24 square centimetres, the approximate surface area of a nucleus. A beam crossing such an area would be almost certain to produce a nuclear collision - 'as easy as hitting a barn door'

  6. The quasi-diffusive approximation in transport theory: Local solutions

    International Nuclear Information System (INIS)

    Celaschi, M.; Montagnini, B.

    1995-01-01

    The one velocity, plane geometry integral neutron transport equation is transformed into a system of two equations, one of them being the equation of continuity and the other a generalized Fick's law, in which the usual diffusion coefficient is replaced by a self-adjoint integral operator. As the kernel of this operator is very close to the Green function of a diffusion equation, an approximate inversion by means of a second order differential operator allows to transform these equations into a purely differential system which is shown to be equivalent, in the simplest case, to a diffusion-like equation. The method, the principles of which have been exposed in a previous paper, is here extended and applied to a variety of problems. If the inversion is properly performed, the quasi-diffusive solutions turn out to be quite accurate, even in the vicinity of the interface between different material regions, where elementary diffusion theory usually fails. 16 refs., 3 tabs

  7. Approximate solutions to Mathieu's equation

    Science.gov (United States)

    Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

    2018-06-01

    Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

  8. Approximate Inference for Wireless Communications

    DEFF Research Database (Denmark)

    Hansen, Morten

    This thesis investigates signal processing techniques for wireless communication receivers. The aim is to improve the performance or reduce the computationally complexity of these, where the primary focus area is cellular systems such as Global System for Mobile communications (GSM) (and extensions...... to the optimal one, which usually requires an unacceptable high complexity. Some of the treated approximate methods are based on QL-factorization of the channel matrix. In the work presented in this thesis it is proven how the QL-factorization of frequency-selective channels asymptotically provides the minimum...

  9. Quantum tunneling beyond semiclassical approximation

    International Nuclear Information System (INIS)

    Banerjee, Rabin; Majhi, Bibhas Ranjan

    2008-01-01

    Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.

  10. Generalized Gradient Approximation Made Simple

    International Nuclear Information System (INIS)

    Perdew, J.P.; Burke, K.; Ernzerhof, M.

    1996-01-01

    Generalized gradient approximations (GGA close-quote s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. copyright 1996 The American Physical Society

  11. Quantization effects on the inversion mode of a double gate MOS

    Directory of Open Access Journals (Sweden)

    Kalyan Mondol

    Full Text Available We investigate the quantization effects on the gate capacitance and charge distribution of a double gate MOSFET using a self-consistent solution of Poisson and Schrödinger equations of the industry standard simulation package Silvaco. Quantization effects on the gate C–V are simulated by varying the electron and hole effective masses. We notice that the inversion capacitance value decreases as the effective mass goes below 0.1mo and the shape of the C–V curve changes to step like in the inversion. We also notice that the inversion switches from surface inversion to volume inversion for low effective mass, and the quantization effect (step like shape in C–V and volume inversion in charge profile happen at the same effective mass. Keywords: Double gate MOSFETs, Quantum effects, Energy quantization, Channel inversion, Charge density

  12. Decoupled deblurring filter and its application to elastic migration and inversion

    KAUST Repository

    Feng, Zongcai

    2017-08-17

    We present a decoupled deblurring filter that approximates the multiparameter Hessian inverse by using local filters to approximate its submatrices for the same and different parameter classes. Numerical tests show that the filter not only reduces the footprint noise, balances the amplitudes and increases the resolution of the elastic migration images, but also mitigates the crosstalk artifacts. When used as a preconditioner, it accelerates the convergence rate for elastic inversion.

  13. Impulse approximation in solid helium

    International Nuclear Information System (INIS)

    Glyde, H.R.

    1985-01-01

    The incoherent dynamic form factor S/sub i/(Q, ω) is evaluated in solid helium for comparison with the impulse approximation (IA). The purpose is to determine the Q values for which the IA is valid for systems such a helium where the atoms interact via a potential having a steeply repulsive but not infinite hard core. For 3 He, S/sub i/(Q, ω) is evaluated from first principles, beginning with the pair potential. The density of states g(ω) is evaluated using the self-consistent phonon theory and S/sub i/(Q,ω) is expressed in terms of g(ω). For solid 4 He resonable models of g(ω) using observed input parameters are used to evaluate S/sub i/(Q,ω). In both cases S/sub i/(Q, ω) is found to approach the impulse approximation S/sub IA/(Q, ω) closely for wave vector transfers Q> or approx. =20 A -1 . The difference between S/sub i/ and S/sub IA/, which is due to final state interactions of the scattering atom with the remainder of the atoms in the solid, is also predominantly antisymmetric in (ω-ω/sub R/), where ω/sub R/ is the recoil frequency. This suggests that the symmetrization procedure proposed by Sears to eliminate final state contributions should work well in solid helium

  14. Finite approximations in fluid mechanics

    International Nuclear Information System (INIS)

    Hirschel, E.H.

    1986-01-01

    This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems

  15. Magnus approximation in neutrino oscillations

    International Nuclear Information System (INIS)

    Acero, Mario A; Aguilar-Arevalo, Alexis A; D'Olivo, J C

    2011-01-01

    Oscillations between active and sterile neutrinos remain as an open possibility to explain some anomalous experimental observations. In a four-neutrino (three active plus one sterile) mixing scheme, we use the Magnus expansion of the evolution operator to study the evolution of neutrino flavor amplitudes within the Earth. We apply this formalism to calculate the transition probabilities from active to sterile neutrinos with energies of the order of a few GeV, taking into account the matter effect for a varying terrestrial density.

  16. Limitations of the acoustic approximation for seismic crosshole tomography

    Science.gov (United States)

    Marelli, Stefano; Maurer, Hansruedi

    2010-05-01

    Modelling and inversion of seismic crosshole data is a challenging task in terms of computational resources. Even with the significant increase in power of modern supercomputers, full three-dimensional elastic modelling of high-frequency waveforms generated from hundreds of source positions in several boreholes is still an intractable task. However, it has been recognised that full waveform inversion offers substantially more information compared with traditional travel time tomography. A common strategy to reduce the computational burden for tomographic inversion is to approximate the true elastic wave propagation by acoustic modelling. This approximation assumes that the solid rock units can be treated like fluids (with no shear wave propagation) and is generally considered to be satisfactory so long as only the earliest portions of the recorded seismograms are considered. The main assumption is that most of the energy in the early parts of the recorded seismograms is carried by the faster compressional (P-) waves. Although a limited number of studies exist on the effects of this approximation for surface/marine synthetic reflection seismic data, and show it to be generally acceptable for models with low to moderate impedance contrasts, to our knowledge no comparable studies have been published on the effects for cross-borehole transmission data. An obvious question is whether transmission tomography should be less affected by elastic effects than surface reflection data when only short time windows are applied to primarily capture the first arriving wavetrains. To answer this question we have performed 2D and 3D investigations on the validity of the acoustic approximation for an elastic medium and using crosshole source-receiver configurations. In order to generate consistent acoustic and elastic data sets, we ran the synthetic tests using the same finite-differences time-domain elastic modelling code for both types of simulations. The acoustic approximation was

  17. Statistical perspectives on inverse problems

    DEFF Research Database (Denmark)

    Andersen, Kim Emil

    of the interior of an object from electrical boundary measurements. One part of this thesis concerns statistical approaches for solving, possibly non-linear, inverse problems. Thus inverse problems are recasted in a form suitable for statistical inference. In particular, a Bayesian approach for regularisation...... problem is given in terms of probability distributions. Posterior inference is obtained by Markov chain Monte Carlo methods and new, powerful simulation techniques based on e.g. coupled Markov chains and simulated tempering is developed to improve the computational efficiency of the overall simulation......Inverse problems arise in many scientific disciplines and pertain to situations where inference is to be made about a particular phenomenon from indirect measurements. A typical example, arising in diffusion tomography, is the inverse boundary value problem for non-invasive reconstruction...

  18. Size Estimates in Inverse Problems

    KAUST Repository

    Di Cristo, Michele

    2014-01-01

    Detection of inclusions or obstacles inside a body by boundary measurements is an inverse problems very useful in practical applications. When only finite numbers of measurements are available, we try to detect some information on the embedded

  19. Wave-equation dispersion inversion

    KAUST Repository

    Li, Jing; Feng, Zongcai; Schuster, Gerard T.

    2016-01-01

    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained

  20. Testing earthquake source inversion methodologies

    KAUST Repository

    Page, Morgan T.

    2011-01-01

    Source Inversion Validation Workshop; Palm Springs, California, 11-12 September 2010; Nowadays earthquake source inversions are routinely performed after large earthquakes and represent a key connection between recorded seismic and geodetic data and the complex rupture process at depth. The resulting earthquake source models quantify the spatiotemporal evolution of ruptures. They are also used to provide a rapid assessment of the severity of an earthquake and to estimate losses. However, because of uncertainties in the data, assumed fault geometry and velocity structure, and chosen rupture parameterization, it is not clear which features of these source models are robust. Improved understanding of the uncertainty and reliability of earthquake source inversions will allow the scientific community to use the robust features of kinematic inversions to more thoroughly investigate the complexity of the rupture process and to better constrain other earthquakerelated computations, such as ground motion simulations and static stress change calculations.

  1. Parameter estimation and inverse problems

    CERN Document Server

    Aster, Richard C; Thurber, Clifford H

    2005-01-01

    Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. Class notes have been developed and reside on the World Wide Web for faciliting use and feedback by teaching colleagues. The authors'' treatment promotes an understanding of fundamental and practical issus associated with parameter fitting and inverse problems including basic theory of inverse problems, statistical issues, computational issues, and an understanding of how to analyze the success and limitations of solutions to these probles. The text is also a practical resource for general students and professional researchers, where techniques and concepts can be readily picked up on a chapter-by-chapter basis.Parameter Estimation and Inverse Problems is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who may not have an extensive mathematical background. It is accompanied by a Web site that...

  2. Inversion Therapy: Can It Relieve Back Pain?

    Science.gov (United States)

    Inversion therapy: Can it relieve back pain? Does inversion therapy relieve back pain? Is it safe? Answers from Edward R. Laskowski, M.D. Inversion therapy doesn't provide lasting relief from back ...

  3. Thermal measurements and inverse techniques

    CERN Document Server

    Orlande, Helcio RB; Maillet, Denis; Cotta, Renato M

    2011-01-01

    With its uncommon presentation of instructional material regarding mathematical modeling, measurements, and solution of inverse problems, Thermal Measurements and Inverse Techniques is a one-stop reference for those dealing with various aspects of heat transfer. Progress in mathematical modeling of complex industrial and environmental systems has enabled numerical simulations of most physical phenomena. In addition, recent advances in thermal instrumentation and heat transfer modeling have improved experimental procedures and indirect measurements for heat transfer research of both natural phe

  4. Computation of inverse magnetic cascades

    International Nuclear Information System (INIS)

    Montgomery, D.

    1981-10-01

    Inverse cascades of magnetic quantities for turbulent incompressible magnetohydrodynamics are reviewed, for two and three dimensions. The theory is extended to the Strauss equations, a description intermediate between two and three dimensions appropriate to tokamak magnetofluids. Consideration of the absolute equilibrium Gibbs ensemble for the system leads to a prediction of an inverse cascade of magnetic helicity, which may manifest itself as a major disruption. An agenda for computational investigation of this conjecture is proposed

  5. A method of inversion of satellite magnetic anomaly data

    Science.gov (United States)

    Mayhew, M. A.

    1977-01-01

    A method of finding a first approximation to a crustal magnetization distribution from inversion of satellite magnetic anomaly data is described. Magnetization is expressed as a Fourier Series in a segment of spherical shell. Input to this procedure is an equivalent source representation of the observed anomaly field. Instability of the inversion occurs when high frequency noise is present in the input data, or when the series is carried to an excessively high wave number. Preliminary results are given for the United States and adjacent areas.

  6. Efficient Implementation of GPR Data Inversion in Case of Spatially Varying Antenna Polarizations

    NARCIS (Netherlands)

    Wang, J.; Aubry, P.J.; Yarovyi, O.

    2018-01-01

    Ground penetrating radar imaging from the data acquired with arbitrarily oriented dipole-like antennas is considered. To take into account variations of antenna orientations resulting in spatial rotation of antenna radiation patterns and polarizations of transmitted fields, the full-wave method

  7. EDITORIAL: Inverse Problems in Engineering

    Science.gov (United States)

    West, Robert M.; Lesnic, Daniel

    2007-01-01

    Presented here are 11 noteworthy papers selected from the Fifth International Conference on Inverse Problems in Engineering: Theory and Practice held in Cambridge, UK during 11-15 July 2005. The papers have been peer-reviewed to the usual high standards of this journal and the contributions of reviewers are much appreciated. The conference featured a good balance of the fundamental mathematical concepts of inverse problems with a diverse range of important and interesting applications, which are represented here by the selected papers. Aspects of finite-element modelling and the performance of inverse algorithms are investigated by Autrique et al and Leduc et al. Statistical aspects are considered by Emery et al and Watzenig et al with regard to Bayesian parameter estimation and inversion using particle filters. Electrostatic applications are demonstrated by van Berkel and Lionheart and also Nakatani et al. Contributions to the applications of electrical techniques and specifically electrical tomographies are provided by Wakatsuki and Kagawa, Kim et al and Kortschak et al. Aspects of inversion in optical tomography are investigated by Wright et al and Douiri et al. The authors are representative of the worldwide interest in inverse problems relating to engineering applications and their efforts in producing these excellent papers will be appreciated by many readers of this journal.

  8. Approximating the minimum cycle mean

    Directory of Open Access Journals (Sweden)

    Krishnendu Chatterjee

    2013-07-01

    Full Text Available We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1 First we show that the algorithmic question is reducible in O(n^2 time to the problem of a logarithmic number of min-plus matrix multiplications of n-by-n matrices, where n is the number of vertices of the graph. (2 Second, when the weights are nonnegative, we present the first (1 + ε-approximation algorithm for the problem and the running time of our algorithm is ilde(O(n^ω log^3(nW/ε / ε, where O(n^ω is the time required for the classic n-by-n matrix multiplication and W is the maximum value of the weights.

  9. Spatially varying dispersion to model breakthrough curves.

    Science.gov (United States)

    Li, Guangquan

    2011-01-01

    Often the water flowing in a karst conduit is a combination of contaminated water entering at a sinkhole and cleaner water released from the limestone matrix. Transport processes in the conduit are controlled by advection, mixing (dilution and dispersion), and retention-release. In this article, a karst transport model considering advection, spatially varying dispersion, and dilution (from matrix seepage) is developed. Two approximate Green's functions are obtained using transformation of variables, respectively, for the initial-value problem and for the boundary-value problem. A numerical example illustrates that mixing associated with strong spatially varying conduit dispersion can cause strong skewness and long tailing in spring breakthrough curves. Comparison of the predicted breakthrough curve against that measured from a dye-tracing experiment between Ames Sink and Indian Spring, Northwest Florida, shows that the conduit dispersivity can be as large as 400 m. Such a large number is believed to imply strong solute interaction between the conduit and the matrix and/or multiple flow paths in a conduit network. It is concluded that Taylor dispersion is not dominant in transport in a karst conduit, and the complicated retention-release process between mobile- and immobile waters may be described by strong spatially varying conduit dispersion. Copyright © 2010 The Author(s). Journal compilation © 2010 National Ground Water Association.

  10. Approximation by modified Szasz–Mirakjan operators on weighted ...

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    English translation in Math. Notes 20(5–6) (1976) 996–998. [3] Gadzhiev A D, Positive linear operators in weighted spaces of functions of several vari- ables, Izv. Akad. Nauk. SSR Ser. Fiz-Tekhn. Math. Nauk 4 (1980) 32–37. [4] Gadzhiev A D, Weighted approximation of continuous functions by linear operators on the whole ...

  11. Nonlinear approximation with dictionaries I. Direct estimates

    DEFF Research Database (Denmark)

    Gribonval, Rémi; Nielsen, Morten

    2004-01-01

    We study various approximation classes associated with m-term approximation by elements from a (possibly) redundant dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation w...

  12. Approximate cohomology in Banach algebras | Pourabbas ...

    African Journals Online (AJOL)

    We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As a special case, approximate Hochschild cohomology is ...

  13. Homogeneous approximation property for continuous shearlet transforms in higher dimensions

    Directory of Open Access Journals (Sweden)

    Yu Su

    2016-07-01

    Full Text Available Abstract This paper is concerned with the generalization of the homogeneous approximation property (HAP for a continuous shearlet transform to higher dimensions. First, we give a pointwise convergence result on the inverse shearlet transform in higher dimensions. Second, we show that every pair of admissible shearlets possess the HAP in the sense of L 2 ( R d $L^{2}(R^{d}$ . Third, we give a sufficient condition for the pointwise HAP to hold, which depends on both shearlets and functions to be reconstructed.

  14. On Nash-Equilibria of Approximation-Stable Games

    Science.gov (United States)

    Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh

    One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.

  15. Mantle conductivity obtained by 3-D inversion of magnetic satellite data

    DEFF Research Database (Denmark)

    Kuvshinov, A.; Olsen, Nils

    distributed geomagnetic observatories. Due to the high computational load of a 3-D inversion (requiring thousands of forward calculations), a comprehensive numerical framework is developed to increase the efficiency of the inversion.In particular, we take an advantage of specific features of the IE approach...... and perform the most consuming-time part of the IE forward simulations (the calculation of electric and magnetic tensor Green’s functions) only once. Approximate calculation of the data sensitivities also gives essential speed up of the inversion. We validate our inversion scheme using synthetic induction...

  16. Inversion of the total cross sections for electron-molecule and electron-atom scattering

    International Nuclear Information System (INIS)

    Lun, D.R.; Amos, K.; Allen, L.J.

    1994-01-01

    Inverse scattering theory has been applied to construct the interaction potentials from total cross sections as a function of energy for electrons scattered off of atoms and molecules. The underlying potentials are assumed to be real and energy independent and are evaluated using the Eikonal approximation and with real phase shifts determined from the total cross sections. The inversion potentials have been determined using either a high energy limit approximation or by using a fixed energy inversion method at select energies. These procedures have been used to analyse e - - CH 4 , e - - SiH 4 , e - -Kr and e - -Xe scattering data in particular. 14 refs., 1 tabs., 3 figs

  17. A local adaptive method for the numerical approximation in seismic wave modelling

    Directory of Open Access Journals (Sweden)

    Galuzzi Bruno G.

    2017-12-01

    Full Text Available We propose a new numerical approach for the solution of the 2D acoustic wave equation to model the predicted data in the field of active-source seismic inverse problems. This method consists in using an explicit finite difference technique with an adaptive order of approximation of the spatial derivatives that takes into account the local velocity at the grid nodes. Testing our method to simulate the recorded seismograms in a marine seismic acquisition, we found that the low computational time and the low approximation error of the proposed approach make it suitable in the context of seismic inversion problems.

  18. Asymptotic inverse periods of reflected reactors above prompt critical

    International Nuclear Information System (INIS)

    Spriggs, G.D.; Busch, R.D.

    1995-01-01

    It is commonly assumed that the kinetic behavior of reflected and unreflected reactors is identical. In particular, it is often accepted that a given reactivity change in either type of system will result in an identical asymptotic inverse period. This is generally true for reactivities below prompt critical. For reactivities above prompt critical, however, the asymptotic inverse period can vary in a highly nonlinear fashion with system reactivity depending on the reflector return fraction, the neutron lifetime in the core, and the neutron lifetime in the reflector

  19. An inversion formula for the exponential Radon transform in spatial domain with variable focal-length fan-beam collimation geometry

    International Nuclear Information System (INIS)

    Wen Junhai; Liang Zhengrong

    2006-01-01

    Inverting the exponential Radon transform has a potential use for SPECT (single photon emission computed tomography) imaging in cases where a uniform attenuation can be approximated, such as in brain and abdominal imaging. Tretiak and Metz derived in the frequency domain an explicit inversion formula for the exponential Radon transform in two dimensions for parallel-beam collimator geometry. Progress has been made to extend the inversion formula for fan-beam and varying focal-length fan-beam (VFF) collimator geometries. These previous fan-beam and VFF inversion formulas require a spatially variant filtering operation, which complicates the implementation and imposes a heavy computing burden. In this paper, we present an explicit inversion formula, in which a spatially invariant filter is involved. The formula is derived and implemented in the spatial domain for VFF geometry (where parallel-beam and fan-beam geometries are two special cases). Phantom simulations mimicking SPECT studies demonstrate its accuracy in reconstructing the phantom images and efficiency in computation for the considered collimator geometries

  20. Experimental characterization of methane inverse diffusion flame

    KAUST Repository

    Elbaz, Ayman M.

    2014-06-26

    This article presents 10-kHz images of OH-PLIF simultaneously with 2-D PIV measurements in an inverse methane diffusion flame. Under a constant fuel flow rate, the central air jet Re was varied, leading to air to fuel velocity ratio, Vr, to vary from 8.3 to 66.5. Starting from Vr = 20.7, the flame is commonly characterized by three distinct zones. The length of the lower fuel entrainment region is inversely proportional to Vr. The flames investigated resemble a string shear layer confining this zone, and converging into the second distinct region, the flame neck zone. The third region is the rest of the flame, which spreads in a jet-like manner. The inverse diffusion flames exhibit varying degrees of partial premixing, depending upon on the velocity ratio Vr, and this region of partial premixing evolves into a well-mixed reaction zone along the flame centerline. The OH distribution correlated with the changes in the mean characteristics of the flow through reduction in the local Reynolds number due to heat release. The existence of a flame suppresses or laminarizes the turbulence at early axial locations and promotes fluctuations at the flame tip for flames with Vr < 49.8. In addition, the flame jet width can be correlated to the OH distribution. In upstream regions of the flames, the breaks in OH are counterbalanced by flame closures and are governed by edge flame propagation. These local extinctions were found to occur at locations where large flow structures were impinging on the flame and are associated with a locally higher strain rate or correlated to the local high strain rates at the flame hole edges without this flow impinging. Another contributor to re-ignition was found to be growing flame kernels. As the flames approach global blow-off, these kernels become the main mechanism for re-ignition further downstream of the flames. At low Vr, laminarization within the early regions of the flame provides an effective shield, preventing the jet flow from

  1. Time-varying Crash Risk

    DEFF Research Database (Denmark)

    Christoffersen, Peter; Feunoua, Bruno; Jeon, Yoontae

    We estimate a continuous-time model with stochastic volatility and dynamic crash probability for the S&P 500 index and find that market illiquidity dominates other factors in explaining the stock market crash risk. While the crash probability is time-varying, its dynamic depends only weakly on re...

  2. Eestlased Karlovy Varys / J. R.

    Index Scriptorium Estoniae

    J. R.

    2007-01-01

    Ilmar Raagi mängufilm "Klass" osaleb 42. Karlovy Vary rahvusvahelise filmifestivali võistlusprogrammis "East of the West" ja Asko Kase lühimängufilm "Zen läbi prügi" on valitud festivali kõrvalprogrammi "Forum of Independents"

  3. Esmaklassiline Karlovy Vary / Jaanus Noormets

    Index Scriptorium Estoniae

    Noormets, Jaanus

    2007-01-01

    Ilmar Raagi mängufilm "Klass" võitis 42. Karlovy Vary rahvusvahelise filmifestivalil kaks auhinda - ametliku kõrvalvõistlusprogrammi "East of the West" eripreemia "Special mention" ja Euroopa väärtfilmikinode keti Europa Cinemas preemia. Ka Asko Kase lühifilmi "Zen läbi prügi linastumisest ning teistest auhinnasaajatest ning osalejatest

  4. Optimistlik Karlovy Vary / Jaan Ruus

    Index Scriptorium Estoniae

    Ruus, Jaan, 1938-2017

    2007-01-01

    42. Karlovy Vary rahvusvahelise filmifestivali auhinnatud filmidest (žürii esimees Peter Bart). Kristallgloobuse sai Islandi-Saksamaa "Katseklaasilinn" (režii Baltasar Kormakur), parimaks režissööriks tunnistati norralane Bard Breien ("Negatiivse mõtlemise kunst"). Austraallase Michael James Rowlandi "Hea õnne teekond" sai žürii eripreemia

  5. Perturbation methods and the Melnikov functions for slowly varying oscillators

    International Nuclear Information System (INIS)

    Lakrad, Faouzi; Charafi, Moulay Mustapha

    2005-01-01

    A new approach to obtaining the Melnikov function for homoclinic orbits in slowly varying oscillators is proposed. The present method applies the Lindstedt-Poincare method to determine an approximation of homoclinic solutions. It is shown that the resultant Melnikov condition is the same as that obtained in the usual way involving distance functions in three dimensions by Wiggins and Holmes [Homoclinic orbits in slowly varying oscillators. SIAM J Math Anal 1987;18(3):612

  6. Bounds and asymptotics for orthogonal polynomials for varying weights

    CERN Document Server

    Levin, Eli

    2018-01-01

    This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals.  Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics.  This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices. .

  7. Neutron inverse kinetics via Gaussian Processes

    International Nuclear Information System (INIS)

    Picca, Paolo; Furfaro, Roberto

    2012-01-01

    Highlights: ► A novel technique for the interpretation of experiments in ADS is presented. ► The technique is based on Bayesian regression, implemented via Gaussian Processes. ► GPs overcome the limits of classical methods, based on PK approximation. ► Results compares GPs and ANN performance, underlining similarities and differences. - Abstract: The paper introduces the application of Gaussian Processes (GPs) to determine the subcriticality level in accelerator-driven systems (ADSs) through the interpretation of pulsed experiment data. ADSs have peculiar kinetic properties due to their special core design. For this reason, classical – inversion techniques based on point kinetic (PK) generally fail to generate an accurate estimate of reactor subcriticality. Similarly to Artificial Neural Networks (ANNs), Gaussian Processes can be successfully trained to learn the underlying inverse neutron kinetic model and, as such, they are not limited to the model choice. Importantly, GPs are strongly rooted into the Bayes’ theorem which makes them a powerful tool for statistical inference. Here, GPs have been designed and trained on a set of kinetics models (e.g. point kinetics and multi-point kinetics) for homogeneous and heterogeneous settings. The results presented in the paper show that GPs are very efficient and accurate in predicting the reactivity for ADS-like systems. The variance computed via GPs may provide an indication on how to generate additional data as function of the desired accuracy.

  8. An Entropic Estimator for Linear Inverse Problems

    Directory of Open Access Journals (Sweden)

    Amos Golan

    2012-05-01

    Full Text Available In this paper we examine an Information-Theoretic method for solving noisy linear inverse estimation problems which encompasses under a single framework a whole class of estimation methods. Under this framework, the prior information about the unknown parameters (when such information exists, and constraints on the parameters can be incorporated in the statement of the problem. The method builds on the basics of the maximum entropy principle and consists of transforming the original problem into an estimation of a probability density on an appropriate space naturally associated with the statement of the problem. This estimation method is generic in the sense that it provides a framework for analyzing non-normal models, it is easy to implement and is suitable for all types of inverse problems such as small and or ill-conditioned, noisy data. First order approximation, large sample properties and convergence in distribution are developed as well. Analytical examples, statistics for model comparisons and evaluations, that are inherent to this method, are discussed and complemented with explicit examples.

  9. Wave-equation reflection traveltime inversion

    KAUST Repository

    Zhang, Sanzong

    2011-01-01

    The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. No travel-time picking is needed and no high-frequency approximation is assumed. The mathematical derivation and the numerical examples are presented to partly demonstrate its efficiency and robustness. © 2011 Society of Exploration Geophysicists.

  10. Producing a steady-state population inversion

    International Nuclear Information System (INIS)

    Richards, R.K.; Griffin, D.C.

    1986-03-01

    An observed steady-state transition at 17.5 nm is identified as the 2p 5 3s3p 4 S/sub 3/2/ → 2p 6 3p 2 P/sub 3/2/ transition in Na-like aluminum. The upper level is populated by electron inner shell ionization of metastable Mg-like aluminum. From the emission intensity, the rate coefficient for populating the upper level is calculated to be approximately 5 x 10 -10 ) cm 3 /sec. Since the upper level is quasimetastable with a lifetime 22 times longer than the lower level, it may be possible to produce a population inversion, if a competing process to populate the lower level can be reduced

  11. The inverse problem for Schwinger pair production

    Directory of Open Access Journals (Sweden)

    F. Hebenstreit

    2016-02-01

    Full Text Available The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.

  12. Inverse Diffusion Curves Using Shape Optimization.

    Science.gov (United States)

    Zhao, Shuang; Durand, Fredo; Zheng, Changxi

    2018-07-01

    The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.

  13. Confidence bands for inverse regression models

    International Nuclear Information System (INIS)

    Birke, Melanie; Bissantz, Nicolai; Holzmann, Hajo

    2010-01-01

    We construct uniform confidence bands for the regression function in inverse, homoscedastic regression models with convolution-type operators. Here, the convolution is between two non-periodic functions on the whole real line rather than between two periodic functions on a compact interval, since the former situation arguably arises more often in applications. First, following Bickel and Rosenblatt (1973 Ann. Stat. 1 1071–95) we construct asymptotic confidence bands which are based on strong approximations and on a limit theorem for the supremum of a stationary Gaussian process. Further, we propose bootstrap confidence bands based on the residual bootstrap and prove consistency of the bootstrap procedure. A simulation study shows that the bootstrap confidence bands perform reasonably well for moderate sample sizes. Finally, we apply our method to data from a gel electrophoresis experiment with genetically engineered neuronal receptor subunits incubated with rat brain extract

  14. Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets

    KAUST Repository

    Litvinenko, Alexander

    2017-09-03

    We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the linear algebra, we approximate the discretized covariance function in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations. The H-matrix technique allows us to work with general covariance matrices in an efficient way, since H-matrices can approximate inhomogeneous covariance functions, with a fairly general mesh that is not necessarily axes-parallel, and neither the covariance matrix itself nor its inverse have to be sparse. We demonstrate our method with Monte Carlo simulations and an application to soil moisture data. The C, C++ codes and data are freely available.

  15. Frozen Gaussian approximation for 3D seismic tomography

    Science.gov (United States)

    Chai, Lihui; Tong, Ping; Yang, Xu

    2018-05-01

    Three-dimensional (3D) wave-equation-based seismic tomography is computationally challenging in large scales and high-frequency regime. In this paper, we apply the frozen Gaussian approximation (FGA) method to compute 3D sensitivity kernels and seismic tomography of high-frequency. Rather than standard ray theory used in seismic inversion (e.g. Kirchhoff migration and Gaussian beam migration), FGA is used to compute the 3D high-frequency sensitivity kernels for travel-time or full waveform inversions. Specifically, we reformulate the equations of the forward and adjoint wavefields for the purpose of convenience to apply FGA, and with this reformulation, one can efficiently compute the Green’s functions whose convolutions with source time function produce wavefields needed for the construction of 3D kernels. Moreover, a fast summation method is proposed based on local fast Fourier transform which greatly improves the speed of reconstruction as the last step of FGA algorithm. We apply FGA to both the travel-time adjoint tomography and full waveform inversion (FWI) on synthetic crosswell seismic data with dominant frequencies as high as those of real crosswell data, and confirm again that FWI requires a more sophisticated initial velocity model for the convergence than travel-time adjoint tomography. We also numerically test the accuracy of applying FGA to local earthquake tomography. This study paves the way to directly apply wave-equation-based seismic tomography methods into real data around their dominant frequencies.

  16. ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

    Science.gov (United States)

    Růžek, B.; Kolář, P.

    2009-04-01

    Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good

  17. Newtonian cosmology with a time-varying constant of gravitation

    International Nuclear Information System (INIS)

    McVittie, G.C.

    1978-01-01

    Newtonian cosmology is based on the Eulerian equations of fluid mechanics combined with Poisson's equation modified by the introduction of a time-varying G. Spherically symmetric model universes are worked out with instantaneously uniform densities. They are indeterminate unless instantaneous uniformity of the pressure is imposed. When G varies as an inverse power of the time, the models can in some cases be shown to depend on the solution of a second-order differential equation which also occurs in the Friedmann models of general relativity. In Section 3, a method for 'passing through' a singularity of this equation is proposed which entails making four arbitrary mathematical assumptions. When G varies as (time) -1 , models with initially cycloidal motion are possible, each cycle becoming longer as time progresses. Finally, gravitation becomes so weak that the model expands to infinity. Kinetic and potential energies for the whole model are derived from the basic equations; their sum is not constant. (author)

  18. Inverse source problems in elastodynamics

    Science.gov (United States)

    Bao, Gang; Hu, Guanghui; Kian, Yavar; Yin, Tao

    2018-04-01

    We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain approaches to show uniqueness in determining the spatial function from wave fields on a large sphere over a finite time interval. The stability estimate of the temporal function from the data of one receiver and the uniqueness result using partial boundary data are proved. Our arguments rely heavily on the use of the Fourier transform, which motivates inversion schemes that can be easily implemented. A Landweber iterative algorithm for recovering the spatial function and a non-iterative inversion scheme based on the uniqueness proof for recovering the temporal function are proposed. Numerical examples are demonstrated in both two and three dimensions.

  19. 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)

  20. Inverse comptonization vs. thermal synchrotron

    International Nuclear Information System (INIS)

    Fenimore, E.E.; Klebesadel, R.W.; Laros, J.G.

    1983-01-01

    There are currently two radiation mechanisms being considered for gamma-ray bursts: thermal synchrotron and inverse comptonization. They are mutually exclusive since thermal synchrotron requires a magnetic field of approx. 10 12 Gauss whereas inverse comptonization cannot produce a monotonic spectrum if the field is larger than 10 11 and is too inefficient relative to thermal synchrotron unless the field is less than 10 9 Gauss. Neither mechanism can explain completely the observed characteristics of gamma-ray bursts. However, we conclude that thermal synchrotron is more consistent with the observations if the sources are approx. 40 kpc away whereas inverse comptonization is more consistent if they are approx. 300 pc away. Unfortunately, the source distance is still not known and, thus, the radiation mechanism is still uncertain

  1. Inverse photoemission of uranium oxides

    International Nuclear Information System (INIS)

    Roussel, P.; Morrall, P.; Tull, S.J.

    2009-01-01

    Understanding the itinerant-localised bonding role of the 5f electrons in the light actinides will afford an insight into their unusual physical and chemical properties. In recent years, the combination of core and valance band electron spectroscopies with theoretic modelling have already made significant progress in this area. However, information of the unoccupied density of states is still scarce. When compared to the forward photoemission techniques, measurements of the unoccupied states suffer from significantly less sensitivity and lower resolution. In this paper, we report on our experimental apparatus, which is designed to measure the inverse photoemission spectra of the light actinides. Inverse photoemission spectra of UO 2 and UO 2.2 along with the corresponding core and valance electron spectra are presented in this paper. UO 2 has been reported previously, although through its inclusion here it allows us to compare and contrast results from our experimental apparatus to the previous Bremsstrahlung Isochromat Spectroscopy and Inverse Photoemission Spectroscopy investigations

  2. Optimization for nonlinear inverse problem

    International Nuclear Information System (INIS)

    Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.

    2007-06-01

    The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)

  3. Some Phenomena on Negative Inversion Constructions

    Science.gov (United States)

    Sung, Tae-Soo

    2013-01-01

    We examine the characteristics of NDI (negative degree inversion) and its relation with other inversion phenomena such as SVI (subject-verb inversion) and SAI (subject-auxiliary inversion). The negative element in the NDI construction may be" not," a negative adverbial, or a negative verb. In this respect, NDI has similar licensing…

  4. Flexible time-varying filter banks

    Science.gov (United States)

    Tuncer, Temel E.; Nguyen, Truong Q.

    1993-09-01

    Linear phase maximally flat FIR Butterworth filter approximations are discussed and a new filter design method is introduced. This variable cutoff filter design method uses the cosine modulated versions of a prototype filter. The design procedure is simple and different variants of this procedure can be used to obtain close to optimum linear phase filters. Using this method, flexible time-varying filter banks with good reconstruction error are introduced. These types of oversampled filter banks have small magnitude error which can be easily controlled by the appropriate choice of modulation frequency. This error can be further decreased by magnitude equalization without increasing the computational complexity considerably. Two dimensional design examples are also given.

  5. Computer-Aided Numerical Inversion of Laplace Transform

    Directory of Open Access Journals (Sweden)

    Umesh Kumar

    2000-01-01

    Full Text Available This paper explores the technique for the computer aided numerical inversion of Laplace transform. The inversion technique is based on the properties of a family of three parameter exponential probability density functions. The only limitation in the technique is the word length of the computer being used. The Laplace transform has been used extensively in the frequency domain solution of linear, lumped time invariant networks but its application to the time domain has been limited, mainly because of the difficulty in finding the necessary poles and residues. The numerical inversion technique mentioned above does away with the poles and residues but uses precomputed numbers to find the time response. This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.

  6. Genetic polymorphisms in varied environments.

    Science.gov (United States)

    Powell, J R

    1971-12-03

    Thirteen experimenital populationis of Drosophila willistoni were maintained in cages, in some of which the environments were relatively constant and in others varied. After 45 weeks, the populations were assayed by gel electrophoresis for polymorphisms at 22 protein loci. The average heterozygosity per individual and the average unmber of alleles per locus were higher in populations maintained in heterogeneous environments than in populations in more constant enviroments.

  7. Size Estimates in Inverse Problems

    KAUST Repository

    Di Cristo, Michele

    2014-01-06

    Detection of inclusions or obstacles inside a body by boundary measurements is an inverse problems very useful in practical applications. When only finite numbers of measurements are available, we try to detect some information on the embedded object such as its size. In this talk we review some recent results on several inverse problems. The idea is to provide constructive upper and lower estimates of the area/volume of the unknown defect in terms of a quantity related to the work that can be expressed with the available boundary data.

  8. -Dimensional Fractional Lagrange's Inversion Theorem

    Directory of Open Access Journals (Sweden)

    F. A. Abd El-Salam

    2013-01-01

    Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.

  9. Darwin's "strange inversion of reasoning".

    Science.gov (United States)

    Dennett, Daniel

    2009-06-16

    Darwin's theory of evolution by natural selection unifies the world of physics with the world of meaning and purpose by proposing a deeply counterintuitive "inversion of reasoning" (according to a 19th century critic): "to make a perfect and beautiful machine, it is not requisite to know how to make it" [MacKenzie RB (1868) (Nisbet & Co., London)]. Turing proposed a similar inversion: to be a perfect and beautiful computing machine, it is not requisite to know what arithmetic is. Together, these ideas help to explain how we human intelligences came to be able to discern the reasons for all of the adaptations of life, including our own.

  10. Inverse transport theory and applications

    International Nuclear Information System (INIS)

    Bal, Guillaume

    2009-01-01

    Inverse transport consists of reconstructing the optical properties of a domain from measurements performed at the domain's boundary. This review concerns several types of measurements: time-dependent, time-independent, angularly resolved and angularly averaged measurements. We review recent results on the reconstruction of the optical parameters from such measurements and the stability of such reconstructions. Inverse transport finds applications e.g. in medical imaging (optical tomography, optical molecular imaging) and in geophysical imaging (remote sensing in the Earth's atmosphere). (topical review)

  11. Inverse Interval Matrix: A Survey

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří; Farhadsefat, R.

    2011-01-01

    Roč. 22, - (2011), s. 704-719 E-ISSN 1081-3810 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval matrix * inverse interval matrix * NP-hardness * enclosure * unit midpoint * inverse sign stability * nonnegative invertibility * absolute value equation * algorithm Subject RIV: BA - General Mathematics Impact factor: 0.808, year: 2010 http://www.math.technion.ac.il/iic/ ela / ela -articles/articles/vol22_pp704-719.pdf

  12. Genomic Evidence for Adaptive Inversion Clines in Drosophila melanogaster.

    Science.gov (United States)

    Kapun, Martin; Fabian, Daniel K; Goudet, Jérôme; Flatt, Thomas

    2016-05-01

    Clines in chromosomal inversion polymorphisms-presumably driven by climatic gradients-are common but there is surprisingly little evidence for selection acting on them. Here we address this long-standing issue in Drosophila melanogaster by using diagnostic single nucleotide polymorphism (SNP) markers to estimate inversion frequencies from 28 whole-genome Pool-seq samples collected from 10 populations along the North American east coast. Inversions In(3L)P, In(3R)Mo, and In(3R)Payne showed clear latitudinal clines, and for In(2L)t, In(2R)NS, and In(3R)Payne the steepness of the clinal slopes changed between summer and fall. Consistent with an effect of seasonality on inversion frequencies, we detected small but stable seasonal fluctuations of In(2R)NS and In(3R)Payne in a temperate Pennsylvanian population over 4 years. In support of spatially varying selection, we observed that the cline in In(3R)Payne has remained stable for >40 years and that the frequencies of In(2L)t and In(3R)Payne are strongly correlated with climatic factors that vary latitudinally, independent of population structure. To test whether these patterns are adaptive, we compared the amount of genetic differentiation of inversions versus neutral SNPs and found that the clines in In(2L)t and In(3R)Payne are maintained nonneutrally and independent of admixture. We also identified numerous clinal inversion-associated SNPs, many of which exhibit parallel differentiation along the Australian cline and reside in genes known to affect fitness-related traits. Together, our results provide strong evidence that inversion clines are maintained by spatially-and perhaps also temporally-varying selection. We interpret our data in light of current hypotheses about how inversions are established and maintained. © The Author 2016. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

  13. Quantization effects on the inversion mode of a double gate MOS

    Science.gov (United States)

    Mondol, Kalyan; Hasan, Md. Manzurul; Arafath, Yeasir; Alam, Khairul

    We investigate the quantization effects on the gate capacitance and charge distribution of a double gate MOSFET using a self-consistent solution of Poisson and Schrödinger equations of the industry standard simulation package Silvaco. Quantization effects on the gate C-V are simulated by varying the electron and hole effective masses. We notice that the inversion capacitance value decreases as the effective mass goes below 0.1mo and the shape of the C-V curve changes to step like in the inversion. We also notice that the inversion switches from surface inversion to volume inversion for low effective mass, and the quantization effect (step like shape) in C-V and volume inversion in charge profile happen at the same effective mass.

  14. Particulate inverse opal carbon electrodes for lithium-ion batteries.

    Science.gov (United States)

    Kang, Da-Young; Kim, Sang-Ok; Chae, Yu Jin; Lee, Joong Kee; Moon, Jun Hyuk

    2013-01-29

    Inverse opal carbon materials were used as anodes for lithium ion batteries. We applied particulate inverse opal structures and their dispersion in the formation of anode electrodes via solution casting. We prepared aminophenyl-grafted inverse opal carbons (a-IOC), inverse opal carbons with mesopores (mIOC), and bare inverse opal carbons (IOC) and investigated the electrochemical behavior of these samples as anode materials. Surface modification by aminophenyl groups was confirmed by XPS measurements. TEM images showed mesopores, and the specific area of mIOC was compared with that of IOC using BET analysis. A half-cell test was performed to compare a-IOC with IOC and mIOC with IOC. In the case of the a-IOC structure, the cell test revealed no improvement in the reversible specific capacity or the cycle performance. The mIOC cell showed a reversible specific capacity of 432 mAh/g, and the capacity was maintained at 88%-approximately 380 mAh/g-over 20 cycles.

  15. Anistropically varying conductivity in irreversible electroporation simulations.

    Science.gov (United States)

    Labarbera, Nicholas; Drapaca, Corina

    2017-11-01

    One recent area of cancer research is irreversible electroporation (IRE). Irreversible electroporation is a minimally invasive procedure where needle electrodes are inserted into the body to ablate tumor cells with electricity. The aim of this paper is to propose a mathematical model that incorporates a tissue's conductivity increasing more in the direction of the electrical field as this has been shown to occur in experiments. It was necessary to mathematically derive a valid form of the conductivity tensor such that it is dependent on the electrical field direction and can be easily implemented into numerical software. The derivation of a conductivity tensor that can take arbitrary functions for the conductivity in the directions tangent and normal to the electrical field is the main contribution of this paper. Numerical simulations were performed for isotropic-varying and anisotropic-varying conductivities to evaluate the importance of including the electrical field's direction in the formulation for conductivity. By starting from previously published experimental results, this paper derived a general formulation for an anistropic-varying tensor for implementation into irreversible electroporation modeling software. The anistropic-varying tensor formulation allows the conductivity to take into consideration both electrical field direction and magnitude, as opposed to previous published works that only took into account electrical field magnitude. The anisotropic formulation predicts roughly a five percent decrease in ablation size for the monopolar simulation and approximately a ten percent decrease in ablation size for the bipolar simulations. This is a positive result as previously reported results found the isotropic formulation to overpredict ablation size for both monopolar and bipolar simulations. Furthermore, it was also reported that the isotropic formulation overpredicts the ablation size more for the bipolar case than the monopolar case. Thus, our

  16. Sparse inverse covariance estimation with the graphical lasso.

    Science.gov (United States)

    Friedman, Jerome; Hastie, Trevor; Tibshirani, Robert

    2008-07-01

    We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm--the graphical lasso--that is remarkably fast: It solves a 1000-node problem ( approximately 500,000 parameters) in at most a minute and is 30-4000 times faster than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinshausen and Bühlmann (2006). We illustrate the method on some cell-signaling data from proteomics.

  17. Superconductivity in Pb inverse opal

    International Nuclear Information System (INIS)

    Aliev, Ali E.; Lee, Sergey B.; Zakhidov, Anvar A.; Baughman, Ray H.

    2007-01-01

    Type-II superconducting behavior was observed in highly periodic three-dimensional lead inverse opal prepared by infiltration of melted Pb in blue (D = 160 nm), green (D = 220 nm) and red (D = 300 nm) opals and followed by the extraction of the SiO 2 spheres by chemical etching. The onset of a broad phase transition (ΔT = 0.3 K) was shifted from T c = 7.196 K for bulk Pb to T c = 7.325 K. The upper critical field H c2 (3150 Oe) measured from high-field hysteresis loops exceeds the critical field for bulk lead (803 Oe) fourfold. Two well resolved peaks observed in the hysteresis loops were ascribed to flux penetration into the cylindrical void space that can be found in inverse opal structure and into the periodic structure of Pb nanoparticles. The red inverse opal shows pronounced oscillations of magnetic moment in the mixed state at low temperatures, T 0.9T c has been observed for all of the samples studied. The magnetic field periodicity of resistivity modulation is in good agreement with the lattice parameter of the inverse opal structure. We attribute the failure to observe pronounced modulation in magneto-resistive measurement to difficulties in the precision orientation of the sample along the magnetic field

  18. Inverse problem of solar oscillations

    International Nuclear Information System (INIS)

    Sekii, T.; Shibahashi, H.

    1987-01-01

    The authors present some preliminary results of numerical simulation to infer the sound velocity distribution in the solar interior from the oscillation data of the Sun as the inverse problem. They analyze the acoustic potential itself by taking account of some factors other than the sound velocity, and infer the sound velocity distribution in the deep interior of the Sun

  19. Implementation and testing of a multivariate inverse radiation transport solver

    International Nuclear Information System (INIS)

    Mattingly, John; Mitchell, Dean J.

    2012-01-01

    Detection, identification, and characterization of special nuclear materials (SNM) all face the same basic challenge: to varying degrees, each must infer the presence, composition, and configuration of the SNM by analyzing a set of measured radiation signatures. Solutions to this problem implement inverse radiation transport methods. Given a set of measured radiation signatures, inverse radiation transport estimates properties of the source terms and transport media that are consistent with those signatures. This paper describes one implementation of a multivariate inverse radiation transport solver. The solver simultaneously analyzes gamma spectrometry and neutron multiplicity measurements to fit a one-dimensional radiation transport model with variable layer thicknesses using nonlinear regression. The solver's essential components are described, and its performance is illustrated by application to benchmark experiments conducted with plutonium metal. - Highlights: ► Inverse problems, specifically applied to identifying and characterizing radiation sources . ► Radiation transport. ► Analysis of gamma spectroscopy and neutron multiplicity counting measurements. ► Experimental testing of the inverse solver against measurements of plutonium.

  20. A thermodynamic approximation of the groundstate of antiferromagnetic Heisenberg spin-1/2 lattices

    NARCIS (Netherlands)

    Tielen, G.I.; Iske, P.L.; Caspers, W.J.; Caspers, W.J.

    1991-01-01

    The exact ground state of finite Heisenberg spin−1/2 lattices isstudied. The coefficients of the so-called Ising configurations contributing to the ground state are approximated by Boltzmann-like expressions. These expressions contain a parameter that may be related to an inverse temperature.

  1. A material optimization model to approximate energy bounds for cellular materials under multiload conditions

    DEFF Research Database (Denmark)

    Guedes, J.M.; Rodrigues, H.C.; Bendsøe, Martin P.

    2003-01-01

    This paper describes a computational model, based on inverse homogenization and topology design, for approximating energy bounds for two-phase composites under multiple load cases. The approach allows for the identification of possible single-scale cellular materials that give rise to the optimal...

  2. Workflows for Full Waveform Inversions

    Science.gov (United States)

    Boehm, Christian; Krischer, Lion; Afanasiev, Michael; van Driel, Martin; May, Dave A.; Rietmann, Max; Fichtner, Andreas

    2017-04-01

    Despite many theoretical advances and the increasing availability of high-performance computing clusters, full seismic waveform inversions still face considerable challenges regarding data and workflow management. While the community has access to solvers which can harness modern heterogeneous computing architectures, the computational bottleneck has fallen to these often manpower-bounded issues that need to be overcome to facilitate further progress. Modern inversions involve huge amounts of data and require a tight integration between numerical PDE solvers, data acquisition and processing systems, nonlinear optimization libraries, and job orchestration frameworks. To this end we created a set of libraries and applications revolving around Salvus (http://salvus.io), a novel software package designed to solve large-scale full waveform inverse problems. This presentation focuses on solving passive source seismic full waveform inversions from local to global scales with Salvus. We discuss (i) design choices for the aforementioned components required for full waveform modeling and inversion, (ii) their implementation in the Salvus framework, and (iii) how it is all tied together by a usable workflow system. We combine state-of-the-art algorithms ranging from high-order finite-element solutions of the wave equation to quasi-Newton optimization algorithms using trust-region methods that can handle inexact derivatives. All is steered by an automated interactive graph-based workflow framework capable of orchestrating all necessary pieces. This naturally facilitates the creation of new Earth models and hopefully sparks new scientific insights. Additionally, and even more importantly, it enhances reproducibility and reliability of the final results.

  3. Metamorphic core complex formation by density inversion and lower-crust extrusion.

    Science.gov (United States)

    Martinez, F; Goodliffe, A M; Taylor, B

    2001-06-21

    Metamorphic core complexes are domal uplifts of metamorphic and plutonic rocks bounded by shear zones that separate them from unmetamorphosed cover rocks. Interpretations of how these features form are varied and controversial, and include models involving extension on low-angle normal faults, plutonic intrusions and flexural rotation of initially high-angle normal faults. The D'Entrecasteaux islands of Papua New Guinea are actively forming metamorphic core complexes located within a continental rift that laterally evolves to sea-floor spreading. The continental rifting is recent (since approximately 6 Myr ago), seismogenic and occurring at a rapid rate ( approximately 25 mm yr-1). Here we present evidence-based on isostatic modelling, geological data and heat-flow measurements-that the D'Entrecasteaux core complexes accommodate extension through the vertical extrusion of ductile lower-crust material, driven by a crustal density inversion. Although buoyant extrusion is accentuated in this region by the geological structure present-which consists of dense ophiolite overlaying less-dense continental crust-this mechanism may be generally applicable to regions where thermal expansion lowers crustal density with depth.

  4. Varying Constants, Gravitation and Cosmology

    Directory of Open Access Journals (Sweden)

    Jean-Philippe Uzan

    2011-03-01

    Full Text Available Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. Thus, it is of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We detail the relations between the constants, the tests of the local position invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, solar system observations, meteorite dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of different constants. To finish, we discuss the more speculative possibility of understanding their numerical values and the apparent fine-tuning that they confront us with.

  5. 2.5D far-field diffraction tomography inversion scheme for GPR that takes into account the planar air-soil interface

    DEFF Research Database (Denmark)

    Meincke, Peter

    2001-01-01

    A new 2.5D inversion scheme is derived for fixed-offset ground penetrating radar (GPR) that takes into account the planar air-soil interface. The inversion scheme is based upon the first Born approximation and a far-field approximation of the dyadic Green function for a two-layer medium....

  6. Global WASF-GA: An Evolutionary Algorithm in Multiobjective Optimization to Approximate the Whole Pareto Optimal Front.

    Science.gov (United States)

    Saborido, Rubén; Ruiz, Ana B; Luque, Mariano

    2017-01-01

    In this article, we propose a new evolutionary algorithm for multiobjective optimization called Global WASF-GA ( global weighting achievement scalarizing function genetic algorithm), which falls within the aggregation-based evolutionary algorithms. The main purpose of Global WASF-GA is to approximate the whole Pareto optimal front. Its fitness function is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, in which two reference points are considered (both utopian and nadir objective vectors) and the weight vector used is taken from a set of weight vectors whose inverses are well-distributed. At each iteration, all individuals are classified into different fronts. Each front is formed by the solutions with the lowest values of the ASF for the different weight vectors in the set, using the utopian vector and the nadir vector as reference points simultaneously. Varying the weight vector in the ASF while considering the utopian and the nadir vectors at the same time enables the algorithm to obtain a final set of nondominated solutions that approximate the whole Pareto optimal front. We compared Global WASF-GA to MOEA/D (different versions) and NSGA-II in two-, three-, and five-objective problems. The computational results obtained permit us to conclude that Global WASF-GA gets better performance, regarding the hypervolume metric and the epsilon indicator, than the other two algorithms in many cases, especially in three- and five-objective problems.

  7. Estrelas variáveis

    OpenAIRE

    Viana, Sérgio Manuel de Oliveira

    2001-01-01

    A observação do céu nocturno é uma prática que vem da Antiguidade. Desde então e durante muito tempo pensou-se que as estrelas mantinham o brilho constante. Assim foi até ao século XVI, quando David Fabricius observou uma estrela cujo brilho variava periodicamente. Dois séculos mais tarde, Jonh Goodricke descobriu uma segunda estrela e com o desenvolvimento de instrumentos de observação este conjunto foi muito alargado e hoje inclui o Sol.A variação do brilho das estrelas variáveis permite d...

  8. Trajectory averaging for stochastic approximation MCMC algorithms

    KAUST Repository

    Liang, Faming

    2010-01-01

    to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic

  9. Reduction of Linear Programming to Linear Approximation

    OpenAIRE

    Vaserstein, Leonid N.

    2006-01-01

    It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.

  10. Complexity analysis of accelerated MCMC methods for Bayesian inversion

    International Nuclear Information System (INIS)

    Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M

    2013-01-01

    The Bayesian approach to inverse problems, in which the posterior probability distribution on an unknown field is sampled for the purposes of computing posterior expectations of quantities of interest, is starting to become computationally feasible for partial differential equation (PDE) inverse problems. Balancing the sources of error arising from finite-dimensional approximation of the unknown field, the PDE forward solution map and the sampling of the probability space under the posterior distribution are essential for the design of efficient computational Bayesian methods for PDE inverse problems. We study Bayesian inversion for a model elliptic PDE with an unknown diffusion coefficient. We provide complexity analyses of several Markov chain Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior distribution, given data δ. Particular attention is given to bounds on the overall work required to achieve a prescribed error level ε. Specifically, we first bound the computational complexity of ‘plain’ MCMC, based on combining MCMC sampling with linear complexity multi-level solvers for elliptic PDE. Our (new) work versus accuracy bounds show that the complexity of this approach can be quite prohibitive. Two strategies for reducing the computational complexity are then proposed and analyzed: first, a sparse, parametric and deterministic generalized polynomial chaos (gpc) ‘surrogate’ representation of the forward response map of the PDE over the entire parameter space, and, second, a novel multi-level Markov chain Monte Carlo strategy which utilizes sampling from a multi-level discretization of the posterior and the forward PDE. For both of these strategies, we derive asymptotic bounds on work versus accuracy, and hence asymptotic bounds on the computational complexity of the algorithms. In particular, we provide sufficient conditions on the regularity of the unknown coefficients of the PDE and on the

  11. Some relations between entropy and approximation numbers

    Institute of Scientific and Technical Information of China (English)

    郑志明

    1999-01-01

    A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.

  12. Axiomatic Characterizations of IVF Rough Approximation Operators

    Directory of Open Access Journals (Sweden)

    Guangji Yu

    2014-01-01

    Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.

  13. An approximation for kanban controlled assembly systems

    NARCIS (Netherlands)

    Topan, E.; Avsar, Z.M.

    2011-01-01

    An approximation is proposed to evaluate the steady-state performance of kanban controlled two-stage assembly systems. The development of the approximation is as follows. The considered continuous-time Markov chain is aggregated keeping the model exact, and this aggregate model is approximated

  14. Operator approximant problems arising from quantum theory

    CERN Document Server

    Maher, Philip J

    2017-01-01

    This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.

  15. Inverse photon-photon processes

    International Nuclear Information System (INIS)

    Carimalo, C.; Crozon, M.; Kesler, P.; Parisi, J.

    1981-12-01

    We here consider inverse photon-photon processes, i.e. AB → γγX (where A, B are hadrons, in particular protons or antiprotons), at high energies. As regards the production of a γγ continuum, we show that, under specific conditions the study of such processes might provide some information on the subprocess gg γγ, involving a quark box. It is also suggested to use those processes in order to systematically look for heavy C = + structures (quarkonium states, gluonia, etc.) showing up in the γγ channel. Inverse photon-photon processes might thus become a new and fertile area of investigation in high-energy physics, provided the difficult problem of discriminating between direct photons and indirect ones can be handled in a satisfactory way

  16. Analysis of RAE-1 inversion

    Science.gov (United States)

    Hedland, D. A.; Degonia, P. K.

    1974-01-01

    The RAE-1 spacecraft inversion performed October 31, 1972 is described based upon the in-orbit dynamical data in conjunction with results obtained from previously developed computer simulation models. The computer simulations used are predictive of the satellite dynamics, including boom flexing, and are applicable during boom deployment and retraction, inter-phase coast periods, and post-deployment operations. Attitude data, as well as boom tip data, were analyzed in order to obtain a detailed description of the dynamical behavior of the spacecraft during and after the inversion. Runs were made using the computer model and the results were analyzed and compared with the real time data. Close agreement between the actual recorded spacecraft attitude and the computer simulation results was obtained.

  17. Cophylogeny reconstruction via an approximate Bayesian computation.

    Science.gov (United States)

    Baudet, C; Donati, B; Sinaimeri, B; Crescenzi, P; Gautier, C; Matias, C; Sagot, M-F

    2015-05-01

    Despite an increasingly vast literature on cophylogenetic reconstructions for studying host-parasite associations, understanding the common evolutionary history of such systems remains a problem that is far from being solved. Most algorithms for host-parasite reconciliation use an event-based model, where the events include in general (a subset of) cospeciation, duplication, loss, and host switch. All known parsimonious event-based methods then assign a cost to each type of event in order to find a reconstruction of minimum cost. The main problem with this approach is that the cost of the events strongly influences the reconciliation obtained. Some earlier approaches attempt to avoid this problem by finding a Pareto set of solutions and hence by considering event costs under some minimization constraints. To deal with this problem, we developed an algorithm, called Coala, for estimating the frequency of the events based on an approximate Bayesian computation approach. The benefits of this method are 2-fold: (i) it provides more confidence in the set of costs to be used in a reconciliation, and (ii) it allows estimation of the frequency of the events in cases where the data set consists of trees with a large number of taxa. We evaluate our method on simulated and on biological data sets. We show that in both cases, for the same pair of host and parasite trees, different sets of frequencies for the events lead to equally probable solutions. Moreover, often these solutions differ greatly in terms of the number of inferred events. It appears crucial to take this into account before attempting any further biological interpretation of such reconciliations. More generally, we also show that the set of frequencies can vary widely depending on the input host and parasite trees. Indiscriminately applying a standard vector of costs may thus not be a good strategy. © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.

  18. Parameter Estimation for Partial Differential Equations by Collage-Based Numerical Approximation

    Directory of Open Access Journals (Sweden)

    Xiaoyan Deng

    2009-01-01

    into a minimization problem of a function of several variables after the partial differential equation is approximated by a differential dynamical system. Then numerical schemes for solving this minimization problem are proposed, including grid approximation and ant colony optimization. The proposed schemes are applied to a parameter estimation problem for the Belousov-Zhabotinskii equation, and the results show that the proposed approximation method is efficient for both linear and nonlinear partial differential equations with respect to unknown parameters. At worst, the presented method provides an excellent starting point for traditional inversion methods that must first select a good starting point.

  19. Analysis of corrections to the eikonal approximation

    Science.gov (United States)

    Hebborn, C.; Capel, P.

    2017-11-01

    Various corrections to the eikonal approximations are studied for two- and three-body nuclear collisions with the goal to extend the range of validity of this approximation to beam energies of 10 MeV/nucleon. Wallace's correction does not improve much the elastic-scattering cross sections obtained at the usual eikonal approximation. On the contrary, a semiclassical approximation that substitutes the impact parameter by a complex distance of closest approach computed with the projectile-target optical potential efficiently corrects the eikonal approximation. This opens the possibility to analyze data measured down to 10 MeV/nucleon within eikonal-like reaction models.

  20. Elastic reflection waveform inversion with variable density

    KAUST Repository

    Li, Yuanyuan; Li, Zhenchun; Alkhalifah, Tariq Ali; Guo, Qiang

    2017-01-01

    Elastic full waveform inversion (FWI) provides a better description of the subsurface than those given by the acoustic assumption. However it suffers from a more serious cycle skipping problem compared with the latter. Reflection waveform inversion

  1. Multiple Scattering Model for Optical Coherence Tomography with Rytov Approximation

    KAUST Repository

    Li, Muxingzi

    2017-04-24

    Optical Coherence Tomography (OCT) is a coherence-gated, micrometer-resolution imaging technique that focuses a broadband near-infrared laser beam to penetrate into optical scattering media, e.g. biological tissues. The OCT resolution is split into two parts, with the axial resolution defined by half the coherence length, and the depth-dependent lateral resolution determined by the beam geometry, which is well described by a Gaussian beam model. The depth dependence of lateral resolution directly results in the defocusing effect outside the confocal region and restricts current OCT probes to small numerical aperture (NA) at the expense of lateral resolution near the focus. Another limitation on OCT development is the presence of a mixture of speckles due to multiple scatterers within the coherence length, and other random noise. Motivated by the above two challenges, a multiple scattering model based on Rytov approximation and Gaussian beam optics is proposed for the OCT setup. Some previous papers have adopted the first Born approximation with the assumption of small perturbation of the incident field in inhomogeneous media. The Rytov method of the same order with smooth phase perturbation assumption benefits from a wider spatial range of validity. A deconvolution method for solving the inverse problem associated with the first Rytov approximation is developed, significantly reducing the defocusing effect through depth and therefore extending the feasible range of NA.

  2. Solution accelerators for large scale 3D electromagnetic inverse problems

    International Nuclear Information System (INIS)

    Newman, Gregory A.; Boggs, Paul T.

    2004-01-01

    We provide a framework for preconditioning nonlinear 3D electromagnetic inverse scattering problems using nonlinear conjugate gradient (NLCG) and limited memory (LM) quasi-Newton methods. Key to our approach is the use of an approximate adjoint method that allows for an economical approximation of the Hessian that is updated at each inversion iteration. Using this approximate Hessian as a preconditoner, we show that the preconditioned NLCG iteration converges significantly faster than the non-preconditioned iteration, as well as converging to a data misfit level below that observed for the non-preconditioned method. Similar conclusions are also observed for the LM iteration; preconditioned with the approximate Hessian, the LM iteration converges faster than the non-preconditioned version. At this time, however, we see little difference between the convergence performance of the preconditioned LM scheme and the preconditioned NLCG scheme. A possible reason for this outcome is the behavior of the line search within the LM iteration. It was anticipated that, near convergence, a step size of one would be approached, but what was observed, instead, were step lengths that were nowhere near one. We provide some insights into the reasons for this behavior and suggest further research that may improve the performance of the LM methods

  3. Analytical approximation of neutron physics data

    International Nuclear Information System (INIS)

    Badikov, S.A.; Vinogradov, V.A.; Gaj, E.V.; Rabotnov, N.S.

    1984-01-01

    The method for experimental neutron-physical data analytical approximation by rational functions based on the Pade approximation is suggested. It is shown that the existence of the Pade approximation specific properties in polar zones is an extremely favourable analytical property essentially extending the convergence range and increasing its rate as compared with polynomial approximation. The Pade approximation is the particularly natural instrument for resonance curve processing as the resonances conform to the complex poles of the approximant. But even in a general case analytical representation of the data in this form is convenient and compact. Thus representation of the data on the neutron threshold reaction cross sections (BOSPOR constant library) in the form of rational functions lead to approximately twenty fold reduction of the storaged numerical information as compared with the by-point calculation at the same accWracy

  4. A unified approach to the Darwin approximation

    International Nuclear Information System (INIS)

    Krause, Todd B.; Apte, A.; Morrison, P. J.

    2007-01-01

    There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting

  5. An Approximate Approach to Automatic Kernel Selection.

    Science.gov (United States)

    Ding, Lizhong; Liao, Shizhong

    2016-02-02

    Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

  6. Bounded-Degree Approximations of Stochastic Networks

    Energy Technology Data Exchange (ETDEWEB)

    Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar

    2017-06-01

    We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.

  7. On a complete topological inverse polycyclic monoid

    Directory of Open Access Journals (Sweden)

    S. O. Bardyla

    2016-12-01

    Full Text Available We give sufficient conditions when a topological inverse $\\lambda$-polycyclic monoid $P_{\\lambda}$ is absolutely $H$-closed in the class of topological inverse semigroups. For every infinite cardinal $\\lambda$ we construct the coarsest semigroup inverse topology $\\tau_{mi}$ on $P_\\lambda$ and give an example of a topological inverse monoid $S$ which contains the polycyclic monoid $P_2$ as a dense discrete subsemigroup.

  8. Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem

    Directory of Open Access Journals (Sweden)

    Baiyu Wang

    2014-01-01

    Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.

  9. A smoothing spline that approximates Laplace transform functions only known on measurements on the real axis

    International Nuclear Information System (INIS)

    D’Amore, L; Campagna, R; Murli, A; Galletti, A; Marcellino, L

    2012-01-01

    The scientific and application-oriented interest in the Laplace transform and its inversion is testified by more than 1000 publications in the last century. Most of the inversion algorithms available in the literature assume that the Laplace transform function is available everywhere. Unfortunately, such an assumption is not fulfilled in the applications of the Laplace transform. Very often, one only has a finite set of data and one wants to recover an estimate of the inverse Laplace function from that. We propose a fitting model of data. More precisely, given a finite set of measurements on the real axis, arising from an unknown Laplace transform function, we construct a dth degree generalized polynomial smoothing spline, where d = 2m − 1, such that internally to the data interval it is a dth degree polynomial complete smoothing spline minimizing a regularization functional, and outside the data interval, it mimics the Laplace transform asymptotic behavior, i.e. it is a rational or an exponential function (the end behavior model), and at the boundaries of the data set it joins with regularity up to order m − 1, with the end behavior model. We analyze in detail the generalized polynomial smoothing spline of degree d = 3. This choice was motivated by the (ill)conditioning of the numerical computation which strongly depends on the degree of the complete spline. We prove existence and uniqueness of this spline. We derive the approximation error and give a priori and computable bounds of it on the whole real axis. In such a way, the generalized polynomial smoothing spline may be used in any real inversion algorithm to compute an approximation of the inverse Laplace function. Experimental results concerning Laplace transform approximation, numerical inversion of the generalized polynomial smoothing spline and comparisons with the exponential smoothing spline conclude the work. (paper)

  10. Inversion: A Most Useful Kind of Transformation.

    Science.gov (United States)

    Dubrovsky, Vladimir

    1992-01-01

    The transformation assigning to every point its inverse with respect to a circle with given radius and center is called an inversion. Discusses inversion with respect to points, circles, angles, distances, space, and the parallel postulate. Exercises related to these topics are included. (MDH)

  11. Probabilistic Geoacoustic Inversion in Complex Environments

    Science.gov (United States)

    2015-09-30

    Probabilistic Geoacoustic Inversion in Complex Environments Jan Dettmer School of Earth and Ocean Sciences, University of Victoria, Victoria BC...long-range inversion methods can fail to provide sufficient resolution. For proper quantitative examination of variability, parameter uncertainty must...project aims to advance probabilistic geoacoustic inversion methods for complex ocean environments for a range of geoacoustic data types. The work is

  12. Enhanced approximate cloaking by SH and FSH lining

    International Nuclear Information System (INIS)

    Li, Jingzhi; Liu, Hongyu; Sun, Hongpeng

    2012-01-01

    We consider approximate cloaking from a regularization viewpoint introduced in Kohn et al (2008 Inverse Problems 24 015016) for EIT and further investigated in Kohn et al (2010 Commun. Pure Appl. Math. 63 0973–1016) and Liu (2009 Inverse Problems 25 045006) for the Helmholtz equation. The cloaking schemes given by Kohn et al and Liu are shown to be (optimally) within |ln ρ| −1 in 2D and ρ in 3D of perfect cloaking, where ρ denotes the regularization parameter. In this paper, we show that by employing a sound-hard layer right outside the cloaked region, one could (optimally) achieve ρ N in R N , N ≥ 2, which significantly enhances the near-cloak. We then develop a cloaking scheme by making use of a lossy layer with well-chosen parameters. The lossy-layer cloaking scheme is shown to possess the same cloaking performance as the one with a sound-hard layer. Moreover, it is shown that the lossy layer could be taken as a finite realization of the sound-hard layer. Numerical experiments are also presented to assess the cloaking performances of all the cloaking schemes for comparisons. (paper)

  13. Multiparameter Elastic Full Waveform Inversion with Facies-based Constraints

    Science.gov (United States)

    Zhang, Zhen-dong; Alkhalifah, Tariq; Naeini, Ehsan Zabihi; Sun, Bingbing

    2018-03-01

    Full waveform inversion (FWI) incorporates all the data characteristics to estimate the parameters described by the assumed physics of the subsurface. However, current efforts to utilize full waveform inversion beyond improved acoustic imaging, like in reservoir delineation, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Some anisotropic parameters are insufficiently updated because of their minor contributions to the surface collected data. Adding rock physics constraints to the inversion helps mitigate such limited sensitivity, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a global constraint for the whole area. Since similar rock formations inside the Earth admit consistent elastic properties and relative values of elasticity and anisotropy parameters (this enables us to define them as a seismic facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel approach to use facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such facies using Bayesian theory and update them at each iteration of the inversion using both the inverted models and a prior information. We take the uncertainties of the estimated parameters (approximated by radiation patterns) into consideration and improve the quality of estimated facies maps. Four numerical examples corresponding to different acquisition, physical assumptions and model circumstances are used to verify the effectiveness of the proposed method.

  14. Wave-equation Qs Inversion of Skeletonized Surface Waves

    KAUST Repository

    Li, Jing

    2017-02-08

    We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

  15. Multiparameter Elastic Full Waveform Inversion with Facies-based Constraints

    KAUST Repository

    Zhang, Zhendong

    2018-03-20

    Full waveform inversion (FWI) incorporates all the data characteristics to estimate the parameters described by the assumed physics of the subsurface. However, current efforts to utilize full waveform inversion beyond improved acoustic imaging, like in reservoir delineation, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Some anisotropic parameters are insufficiently updated because of their minor contributions to the surface collected data. Adding rock physics constraints to the inversion helps mitigate such limited sensitivity, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a global constraint for the whole area. Since similar rock formations inside the Earth admit consistent elastic properties and relative values of elasticity and anisotropy parameters (this enables us to define them as a seismic facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel approach to use facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such facies using Bayesian theory and update them at each iteration of the inversion using both the inverted models and a prior information. We take the uncertainties of the estimated parameters (approximated by radiation patterns) into consideration and improve the quality of estimated facies maps. Four numerical examples corresponding to different acquisition, physical assumptions and model circumstances are used to verify the effectiveness of the proposed method.

  16. Wave-equation Qs Inversion of Skeletonized Surface Waves

    KAUST Repository

    Li, Jing; Dutta, Gaurav; Schuster, Gerard T.

    2017-01-01

    We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

  17. Solution of axisymmetric transient inverse heat conduction problems using parameter estimation and multi block methods

    International Nuclear Information System (INIS)

    Azimi, A.; Hannani, S.K.; Farhanieh, B.

    2005-01-01

    In this article, a comparison between two iterative inverse techniques to solve simultaneously two unknown functions of axisymmetric transient inverse heat conduction problems in semi complex geometries is presented. The multi-block structured grid together with blocked-interface nodes is implemented for geometric decomposition of physical domain. Numerical scheme for solution of transient heat conduction equation is the finite element method with frontal technique to solve algebraic system of discrete equations. The inverse heat conduction problem involves simultaneous unknown time varying heat generation and time-space varying boundary condition estimation. Two parameter-estimation techniques are considered, Levenberg-Marquardt scheme and conjugate gradient method with adjoint problem. Numerically computed exact and noisy data are used for the measured transient temperature data needed in the inverse solution. The results of the present study for a configuration including two joined disks with different heights are compared to those of exact heat source and temperature boundary condition, and show good agreement. (author)

  18. Inverse problems and uncertainty quantification

    KAUST Repository

    Litvinenko, Alexander; Matthies, Hermann G.

    2013-01-01

    computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example

  19. Isomorphs in the phase diagram of a model liquid without inverse power law repulsion

    DEFF Research Database (Denmark)

    Veldhorst, Arnold Adriaan; Bøhling, Lasse; Dyre, J. C.

    2012-01-01

    scattering function are calculated. The results are shown to reflect a hidden scale invariance; despite its exponential repulsion the Buckingham potential is well approximated by an inverse power-law plus a linear term in the region of the first peak of the radial distribution function. As a consequence...... the dynamics of the viscous Buckingham liquid is mimicked by a corresponding model with purely repulsive inverse-power-law interactions. The results presented here closely resemble earlier results for Lennard-Jones type liquids, demonstrating that the existence of strong correlations and isomorphs does...... not depend critically on the mathematical form of the repulsion being an inverse power law....

  20. Wenchuan Ms8.0 earthquake coseismic slip distribution inversion

    Directory of Open Access Journals (Sweden)

    Hongbo Tan

    2015-05-01

    Full Text Available By using GPS and gravity data before and after the Wenchuan Ms8.0 earthquake and combining data from geological surveys and geophysical inversion studies, an initial coseismic fault model is constructed. The dip angle changes of the fault slip distribution on the fault plane are inversed, and the inversion results show that the shape of the fault resembles a double-shovel. The Yingxiu–Beichuan Fault is approximately 330 km long, the surface fault dip angle is 65.1°, which gradually reduces with increasing depth to 0° at the detachment layer at a depth of 19.62 km. The Guanxian–Jiangyou Fault is approximately 90 km long, and its dip angle at the surface is 55.3°, which gradually reduces with increasing depth; the fault joins the Yingxiu–Beichuan Fault at 13.75 km. Coseismic slip mainly occurs above a depth of 19 km. There are five concentrated rupture areas, Yingxiu, Wenchuan, Hanwang, Beichuan, and Pingwu, which are consistent with geological survey results and analyses of the aftershock distribution. The rupture mainly has a thrust component with a small dextral strike–slip component. The maximum slip was more than 10 m, which occurred near Beichuan and Hanwang. The seismic moment is 7.84 × 1020 Nm (Mw7.9, which is consistent with the seismological results.

  1. Cosmological applications of Padé approximant

    International Nuclear Information System (INIS)

    Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

    2014-01-01

    As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation

  2. Cosmological applications of Padé approximant

    Science.gov (United States)

    Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

    2014-01-01

    As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.

  3. Inversion of seismic data: how to take the correlated nature of noise into account; Inversion de donnees sismiques: prise en compte de la nature correlee du bruit

    Energy Technology Data Exchange (ETDEWEB)

    Renard, F.

    2003-01-01

    The goal of seismic inversion is to recover an Earth model that best fits some observed data. To reach that goal, we have to minimize an objective function that measures the amplitude of the misfits according to a norm to be chosen in data space. In general, the used norm is the L2 norm. Unfortunately, such a norm is not adapted to data corrupted by correlated noise: the noise is in that case inverted as signal and the inversion results are unacceptable. The goal of this thesis is to obtain satisfactory results to the inverse problem in that situation. For this purpose, we study two inverse problems: reflection tomography and waveform inversion. In reflection tomography, we propose a new formulation of the continuum inverse problem which relies on a H1 norm in data space. This allows us to account for the correlated nature of the noise that corrupts the kinematic information. However, this norm does not give more satisfactory results than the ones obtained with the classical formalism. This is why, for sake of simplicity, we recommend to use this classical formalism. Then we try to understand how to properly sample the kinematic information so as to obtain an accurate approximation of the continuum inverse problem. In waveform inversion, we propose to directly invert data corrupted by some correlated noise. A first idea consists in rejecting the noise in the residues. In that goal, we can use a semi-norm to formulate the inverse problem. This technique gives very good results, except when the data are corrupted by random noise. Thus we propose a second method which consists in retrieving, by solving an inverse problem, the signal and the noise whose sum best fits the data. This technique gives very satisfactory results, even if some random noise pollutes the data, and is moreover solved, thanks to an original algorithm, in a very efficient way. (author)

  4. Modelling tourists arrival using time varying parameter

    Science.gov (United States)

    Suciptawati, P.; Sukarsa, K. G.; Kencana, Eka N.

    2017-06-01

    The importance of tourism and its related sectors to support economic development and poverty reduction in many countries increase researchers’ attentions to study and model tourists’ arrival. This work is aimed to demonstrate time varying parameter (TVP) technique to model the arrival of Korean’s tourists to Bali. The number of Korean tourists whom visiting Bali for period January 2010 to December 2015 were used to model the number of Korean’s tourists to Bali (KOR) as dependent variable. The predictors are the exchange rate of Won to IDR (WON), the inflation rate in Korea (INFKR), and the inflation rate in Indonesia (INFID). Observing tourists visit to Bali tend to fluctuate by their nationality, then the model was built by applying TVP and its parameters were approximated using Kalman Filter algorithm. The results showed all of predictor variables (WON, INFKR, INFID) significantly affect KOR. For in-sample and out-of-sample forecast with ARIMA’s forecasted values for the predictors, TVP model gave mean absolute percentage error (MAPE) as much as 11.24 percent and 12.86 percent, respectively.

  5. Inverse Compton gamma-rays from pulsars

    International Nuclear Information System (INIS)

    Morini, M.

    1983-01-01

    A model is proposed for pulsar optical and gamma-ray emission where relativistic electrons beams: (i) scatter the blackbody photons from the polar cap surface giving inverse Compton gamma-rays and (ii) produce synchrotron optical photons in the light cylinder region which are then inverse Compton scattered giving other gamma-rays. The model is applied to the Vela pulsar, explaining the first gamma-ray pulse by inverse Compton scattering of synchrotron photons near the light cylinder and the second gamma-ray pulse partly by inverse Compton scattering of synchrotron photons and partly by inverse Compton scattering of the thermal blackbody photons near the star surface. (author)

  6. Point-source inversion techniques

    Science.gov (United States)

    Langston, Charles A.; Barker, Jeffrey S.; Pavlin, Gregory B.

    1982-11-01

    A variety of approaches for obtaining source parameters from waveform data using moment-tensor or dislocation point source models have been investigated and applied to long-period body and surface waves from several earthquakes. Generalized inversion techniques have been applied to data for long-period teleseismic body waves to obtain the orientation, time function and depth of the 1978 Thessaloniki, Greece, event, of the 1971 San Fernando event, and of several events associated with the 1963 induced seismicity sequence at Kariba, Africa. The generalized inversion technique and a systematic grid testing technique have also been used to place meaningful constraints on mechanisms determined from very sparse data sets; a single station with high-quality three-component waveform data is often sufficient to discriminate faulting type (e.g., strike-slip, etc.). Sparse data sets for several recent California earthquakes, for a small regional event associated with the Koyna, India, reservoir, and for several events at the Kariba reservoir have been investigated in this way. Although linearized inversion techniques using the moment-tensor model are often robust, even for sparse data sets, there are instances where the simplifying assumption of a single point source is inadequate to model the data successfully. Numerical experiments utilizing synthetic data and actual data for the 1971 San Fernando earthquake graphically demonstrate that severe problems may be encountered if source finiteness effects are ignored. These techniques are generally applicable to on-line processing of high-quality digital data, but source complexity and inadequacy of the assumed Green's functions are major problems which are yet to be fully addressed.

  7. Inversion of GPS meteorology data

    Directory of Open Access Journals (Sweden)

    K. Hocke

    Full Text Available The GPS meteorology (GPS/MET experiment, led by the Universities Corporation for Atmospheric Research (UCAR, consists of a GPS receiver aboard a low earth orbit (LEO satellite which was launched on 3 April 1995. During a radio occultation the LEO satellite rises or sets relative to one of the 24 GPS satellites at the Earth's horizon. Thereby the atmospheric layers are successively sounded by radio waves which propagate from the GPS satellite to the LEO satellite. From the observed phase path increases, which are due to refraction of the radio waves by the ionosphere and the neutral atmosphere, the atmospheric parameter refractivity, density, pressure and temperature are calculated with high accuracy and resolution (0.5–1.5 km. In the present study, practical aspects of the GPS/MET data analysis are discussed. The retrieval is based on the Abelian integral inversion of the atmospheric bending angle profile into the refractivity index profile. The problem of the upper boundary condition of the Abelian integral is described by examples. The statistical optimization approach which is applied to the data above 40 km and the use of topside bending angle profiles from model atmospheres stabilize the inversion. The retrieved temperature profiles are compared with corresponding profiles which have already been calculated by scientists of UCAR and Jet Propulsion Laboratory (JPL, using Abelian integral inversion too. The comparison shows that in some cases large differences occur (5 K and more. This is probably due to different treatment of the upper boundary condition, data runaways and noise. Several temperature profiles with wavelike structures at tropospheric and stratospheric heights are shown. While the periodic structures at upper stratospheric heights could be caused by residual errors of the ionospheric correction method, the periodic temperature fluctuations at heights below 30 km are most likely caused by atmospheric waves (vertically

  8. Bayesian Inversion for Large Scale Antarctic Ice Sheet Flow

    KAUST Repository

    Ghattas, Omar

    2015-01-07

    The flow of ice from the interior of polar ice sheets is the primary contributor to projected sea level rise. One of the main difficulties faced in modeling ice sheet flow is the uncertain spatially-varying Robin boundary condition that describes the resistance to sliding at the base of the ice. Satellite observations of the surface ice flow velocity, along with a model of ice as a creeping incompressible shear-thinning fluid, can be used to infer this uncertain basal boundary condition. We cast this ill-posed inverse problem in the framework of Bayesian inference, which allows us to infer not only the basal sliding parameters, but also the associated uncertainty. To overcome the prohibitive nature of Bayesian methods for large-scale inverse problems, we exploit the fact that, despite the large size of observational data, they typically provide only sparse information on model parameters. We show results for Bayesian inversion of the basal sliding parameter field for the full Antarctic continent, and demonstrate that the work required to solve the inverse problem, measured in number of forward (and adjoint) ice sheet model solves, is independent of the parameter and data dimensions

  9. Bayesian Inversion for Large Scale Antarctic Ice Sheet Flow

    KAUST Repository

    Ghattas, Omar

    2015-01-01

    The flow of ice from the interior of polar ice sheets is the primary contributor to projected sea level rise. One of the main difficulties faced in modeling ice sheet flow is the uncertain spatially-varying Robin boundary condition that describes the resistance to sliding at the base of the ice. Satellite observations of the surface ice flow velocity, along with a model of ice as a creeping incompressible shear-thinning fluid, can be used to infer this uncertain basal boundary condition. We cast this ill-posed inverse problem in the framework of Bayesian inference, which allows us to infer not only the basal sliding parameters, but also the associated uncertainty. To overcome the prohibitive nature of Bayesian methods for large-scale inverse problems, we exploit the fact that, despite the large size of observational data, they typically provide only sparse information on model parameters. We show results for Bayesian inversion of the basal sliding parameter field for the full Antarctic continent, and demonstrate that the work required to solve the inverse problem, measured in number of forward (and adjoint) ice sheet model solves, is independent of the parameter and data dimensions

  10. Multilevel Monte Carlo in Approximate Bayesian Computation

    KAUST Repository

    Jasra, Ajay

    2017-02-13

    In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.

  11. Uniform analytic approximation of Wigner rotation matrices

    Science.gov (United States)

    Hoffmann, Scott E.

    2018-02-01

    We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

  12. Exact and approximate multiple diffraction calculations

    International Nuclear Information System (INIS)

    Alexander, Y.; Wallace, S.J.; Sparrow, D.A.

    1976-08-01

    A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation

  13. Leading-Edge Noise Prediction of General Airfoil Profiles with Spanwise-Varying Inflow Conditions

    NARCIS (Netherlands)

    Miotto, Renato Fuzaro; Wolf, William Roberto; De Santana, Leandro Dantas

    2018-01-01

    This paper presents a study of the leading-edge noise radiated by an airfoil undergoing a turbulent inflow. The noise prediction of generic airfoil profiles subjected to spanwise-varying inflow conditions is performed with the support of Amiet’s theory and the inverse strip technique. In the

  14. Leading-Edge Noise Prediction of General Airfoil Profiles with Spanwise-Varying Inflow Conditions

    NARCIS (Netherlands)

    Miotto, Renato Fuzaro; Wolf, William Roberto; De Santana, Leandro Dantas

    This paper presents a study of the leading-edge noise radiated by an airfoil undergoing a turbulent inflow. The noise prediction of generic airfoil profiles subjected to spanwise-varying inflow conditions is performed with the support of Amiet’s theory and the inverse strip technique. In the

  15. Bent approximations to synchrotron radiation optics

    International Nuclear Information System (INIS)

    Heald, S.

    1981-01-01

    Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors

  16. Local density approximations for relativistic exchange energies

    International Nuclear Information System (INIS)

    MacDonald, A.H.

    1986-01-01

    The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented

  17. Approximate maximum parsimony and ancestral maximum likelihood.

    Science.gov (United States)

    Alon, Noga; Chor, Benny; Pardi, Fabio; Rapoport, Anat

    2010-01-01

    We explore the maximum parsimony (MP) and ancestral maximum likelihood (AML) criteria in phylogenetic tree reconstruction. Both problems are NP-hard, so we seek approximate solutions. We formulate the two problems as Steiner tree problems under appropriate distances. The gist of our approach is the succinct characterization of Steiner trees for a small number of leaves for the two distances. This enables the use of known Steiner tree approximation algorithms. The approach leads to a 16/9 approximation ratio for AML and asymptotically to a 1.55 approximation ratio for MP.

  18. APPROXIMATIONS TO PERFORMANCE MEASURES IN QUEUING SYSTEMS

    Directory of Open Access Journals (Sweden)

    Kambo, N. S.

    2012-11-01

    Full Text Available Approximations to various performance measures in queuing systems have received considerable attention because these measures have wide applicability. In this paper we propose two methods to approximate the queuing characteristics of a GI/M/1 system. The first method is non-parametric in nature, using only the first three moments of the arrival distribution. The second method treads the known path of approximating the arrival distribution by a mixture of two exponential distributions by matching the first three moments. Numerical examples and optimal analysis of performance measures of GI/M/1 queues are provided to illustrate the efficacy of the methods, and are compared with benchmark approximations.

  19. Traveltime approximations for transversely isotropic media with an inhomogeneous background

    KAUST Repository

    Alkhalifah, Tariq

    2011-05-01

    A transversely isotropic (TI) model with a tilted symmetry axis is regarded as one of the most effective approximations to the Earth subsurface, especially for imaging purposes. However, we commonly utilize this model by setting the axis of symmetry normal to the reflector. This assumption may be accurate in many places, but deviations from this assumption will cause errors in the wavefield description. Using perturbation theory and Taylor\\'s series, I expand the solutions of the eikonal equation for 2D TI media with respect to the independent parameter θ, the angle the tilt of the axis of symmetry makes with the vertical, in a generally inhomogeneous TI background with a vertical axis of symmetry. I do an additional expansion in terms of the independent (anellipticity) parameter in a generally inhomogeneous elliptically anisotropic background medium. These new TI traveltime solutions are given by expansions in and θ with coefficients extracted from solving linear first-order partial differential equations. Pade approximations are used to enhance the accuracy of the representation by predicting the behavior of the higher-order terms of the expansion. A simplification of the expansion for homogenous media provides nonhyperbolic moveout descriptions of the traveltime for TI models that are more accurate than other recently derived approximations. In addition, for 3D media, I develop traveltime approximations using Taylor\\'s series type of expansions in the azimuth of the axis of symmetry. The coefficients of all these expansions can also provide us with the medium sensitivity gradients (Jacobian) for nonlinear tomographic-based inversion for the tilt in the symmetry axis. © 2011 Society of Exploration Geophysicists.

  20. Traveltime approximations for transversely isotropic media with an inhomogeneous background

    KAUST Repository

    Alkhalifah, Tariq

    2011-01-01

    A transversely isotropic (TI) model with a tilted symmetry axis is regarded as one of the most effective approximations to the Earth subsurface, especially for imaging purposes. However, we commonly utilize this model by setting the axis of symmetry normal to the reflector. This assumption may be accurate in many places, but deviations from this assumption will cause errors in the wavefield description. Using perturbation theory and Taylor's series, I expand the solutions of the eikonal equation for 2D TI media with respect to the independent parameter θ, the angle the tilt of the axis of symmetry makes with the vertical, in a generally inhomogeneous TI background with a vertical axis of symmetry. I do an additional expansion in terms of the independent (anellipticity) parameter in a generally inhomogeneous elliptically anisotropic background medium. These new TI traveltime solutions are given by expansions in and θ with coefficients extracted from solving linear first-order partial differential equations. Pade approximations are used to enhance the accuracy of the representation by predicting the behavior of the higher-order terms of the expansion. A simplification of the expansion for homogenous media provides nonhyperbolic moveout descriptions of the traveltime for TI models that are more accurate than other recently derived approximations. In addition, for 3D media, I develop traveltime approximations using Taylor's series type of expansions in the azimuth of the axis of symmetry. The coefficients of all these expansions can also provide us with the medium sensitivity gradients (Jacobian) for nonlinear tomographic-based inversion for the tilt in the symmetry axis. © 2011 Society of Exploration Geophysicists.

  1. Approximate Dispersion Relations for Waves on Arbitrary Shear Flows

    Science.gov (United States)

    Ellingsen, S. À.; Li, Y.

    2017-12-01

    An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3-D generalization of the much used approximation by Skop (1987), developed further by Kirby and Chen (1989), but is shown to be more robust, succeeding in situations where the Kirby and Chen model fails. The two approximations incur the same numerical cost and difficulty. While the Kirby and Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability. A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding second-order expression proposed by Kirby and Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our second-order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby and Chen.Plain Language SummaryIn order to answer key questions such as how the ocean surface affects the climate, erodes the coastline and transports nutrients, we must understand how waves move. This is not so easy when depth varying currents are present, as they often are in coastal waters. We have developed a modeling tool for accurately predicting wave properties in such situations, ready for use, for example, in the complex oceanographic computer models. Our

  2. Sub-Millimeter Tests of the Newtonian Inverse Square Law

    International Nuclear Information System (INIS)

    Adelberger, Eric

    2005-01-01

    It is remarkable that small-scale experiments can address important open issues in fundamental science such as: 'why is gravity so weak compared to the other interactions?' and 'why is the cosmological constant so small compared to the predictions of quantum mechanics?' String theory ideas (new scalar particles and extra dimensions) and other notions hint that Newton's Inverse-Square Law could break down at distances less than 1 mm. I will review some motivations for testing the Inverse-Square Law, and discuss recent mechanical experiments with torsion balances, small-scillators, micro-cantilevers, and ultra-cold neutrons. Our torsion-balance experiments have probed for gravitational-strength interactions with length scales down to 70 micrometers, which is approximately the diameter of a human hair.

  3. A variational Bayesian method to inverse problems with impulsive noise

    KAUST Repository

    Jin, Bangti

    2012-01-01

    We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm. © 2011 Elsevier Inc.

  4. Phase Inversion: Inferring Solar Subphotospheric Flow and Other Asphericity from the Distortion of Acoustic Waves

    Science.gov (United States)

    Gough, Douglas; Merryfield, William J.; Toomre, Juri

    1998-01-01

    A method is proposed for analyzing an almost monochromatic train of waves propagating in a single direction in an inhomogeneous medium that is not otherwise changing in time. An effective phase is defined in terms of the Hilbert transform of the wave function, which is related, via the JWKB approximation, to the spatial variation of the background state against which the wave is propagating. The contaminating effect of interference between the truly monochromatic components of the train is eliminated using its propagation properties. Measurement errors, provided they are uncorrelated, are manifest as rapidly varying noise; although that noise can dominate the raw phase-processed signal, it can largely be removed by low-pass filtering. The intended purpose of the analysis is to determine the distortion of solar oscillations induced by horizontal structural variation and material flow. It should be possible to apply the method directly to sectoral modes. The horizontal phase distortion provides a measure of longitudinally averaged properties of the Sun in the vicinity of the equator, averaged also in radius down to the depth to which the modes penetrate. By combining such averages from different modes, the two-dimensional variation can be inferred by standard inversion techniques. After taking due account of horizontal refraction, it should be possible to apply the technique also to locally sectoral modes that propagate obliquely to the equator and thereby build a network of lateral averages at each radius, from which the full three-dimensional structure of the Sun can, in principle, be determined as an inverse Radon transform.

  5. Estimation of Dynamic Friction Process of the Akatani Landslide Based on the Waveform Inversion and Numerical Simulation

    Science.gov (United States)

    Yamada, M.; Mangeney, A.; Moretti, L.; Matsushi, Y.

    2014-12-01

    Understanding physical parameters, such as frictional coefficients, velocity change, and dynamic history, is important issue for assessing and managing the risks posed by deep-seated catastrophic landslides. Previously, landslide motion has been inferred qualitatively from topographic changes caused by the event, and occasionally from eyewitness reports. However, these conventional approaches are unable to evaluate source processes and dynamic parameters. In this study, we use broadband seismic recordings to trace the dynamic process of the deep-seated Akatani landslide that occurred on the Kii Peninsula, Japan, which is one of the best recorded large slope failures. Based on the previous results of waveform inversions and precise topographic surveys done before and after the event, we applied numerical simulations using the SHALTOP numerical model (Mangeney et al., 2007). This model describes homogeneous continuous granular flows on a 3D topography based on a depth averaged thin layer approximation. We assume a Coulomb's friction law with a constant friction coefficient, i. e. the friction is independent of the sliding velocity. We varied the friction coefficients in the simulation so that the resulting force acting on the surface agrees with the single force estimated from the seismic waveform inversion. Figure shows the force history of the east-west components after the band-pass filtering between 10-100 seconds. The force history of the simulation with frictional coefficient 0.27 (thin red line) the best agrees with the result of seismic waveform inversion (thick gray line). Although the amplitude is slightly different, phases are coherent for the main three pulses. This is an evidence that the point-source approximation works reasonably well for this particular event. The friction coefficient during the sliding was estimated to be 0.38 based on the seismic waveform inversion performed by the previous study and on the sliding block model (Yamada et al., 2013

  6. Inverse problems in systems biology

    International Nuclear Information System (INIS)

    Engl, Heinz W; Lu, James; Müller, Stefan; Flamm, Christoph; Schuster, Peter; Kügler, Philipp

    2009-01-01

    Systems biology is a new discipline built upon the premise that an understanding of how cells and organisms carry out their functions cannot be gained by looking at cellular components in isolation. Instead, consideration of the interplay between the parts of systems is indispensable for analyzing, modeling, and predicting systems' behavior. Studying biological processes under this premise, systems biology combines experimental techniques and computational methods in order to construct predictive models. Both in building and utilizing models of biological systems, inverse problems arise at several occasions, for example, (i) when experimental time series and steady state data are used to construct biochemical reaction networks, (ii) when model parameters are identified that capture underlying mechanisms or (iii) when desired qualitative behavior such as bistability or limit cycle oscillations is engineered by proper choices of parameter combinations. In this paper we review principles of the modeling process in systems biology and illustrate the ill-posedness and regularization of parameter identification problems in that context. Furthermore, we discuss the methodology of qualitative inverse problems and demonstrate how sparsity enforcing regularization allows the determination of key reaction mechanisms underlying the qualitative behavior. (topical review)

  7. The seismic reflection inverse problem

    International Nuclear Information System (INIS)

    Symes, W W

    2009-01-01

    The seismic reflection method seeks to extract maps of the Earth's sedimentary crust from transient near-surface recording of echoes, stimulated by explosions or other controlled sound sources positioned near the surface. Reasonably accurate models of seismic energy propagation take the form of hyperbolic systems of partial differential equations, in which the coefficients represent the spatial distribution of various mechanical characteristics of rock (density, stiffness, etc). Thus the fundamental problem of reflection seismology is an inverse problem in partial differential equations: to find the coefficients (or at least some of their properties) of a linear hyperbolic system, given the values of a family of solutions in some part of their domains. The exploration geophysics community has developed various methods for estimating the Earth's structure from seismic data and is also well aware of the inverse point of view. This article reviews mathematical developments in this subject over the last 25 years, to show how the mathematics has both illuminated innovations of practitioners and led to new directions in practice. Two themes naturally emerge: the importance of single scattering dominance and compensation for spectral incompleteness by spatial redundancy. (topical review)

  8. Inversion theory and conformal mapping

    CERN Document Server

    Blair, David E

    2000-01-01

    It is rarely taught in an undergraduate or even graduate curriculum that the only conformal maps in Euclidean space of dimension greater than two are those generated by similarities and inversions in spheres. This is in stark contrast to the wealth of conformal maps in the plane. The principal aim of this text is to give a treatment of this paucity of conformal maps in higher dimensions. The exposition includes both an analytic proof in general dimension and a differential-geometric proof in dimension three. For completeness, enough complex analysis is developed to prove the abundance of conformal maps in the plane. In addition, the book develops inversion theory as a subject, along with the auxiliary theme of circle-preserving maps. A particular feature is the inclusion of a paper by Carath�odory with the remarkable result that any circle-preserving transformation is necessarily a M�bius transformation, not even the continuity of the transformation is assumed. The text is at the level of advanced undergr...

  9. LHC Report: 2 inverse femtobarns!

    CERN Multimedia

    Mike Lamont for the LHC Team

    2011-01-01

    The LHC is enjoying a confluence of twos. This morning (Friday 5 August) we passed 2 inverse femtobarns delivered in 2011; the peak luminosity is now just over 2 x1033 cm-2s-1; and recently fill 2000 was in for nearly 22 hours and delivered around 90 inverse picobarns, almost twice 2010's total.   In order to increase the luminosity we can increase of number of bunches, increase the number of particles per bunch, or decrease the transverse beam size at the interaction point. The beam size can be tackled in two ways: either reduce the size of the injected bunches or squeeze harder with the quadrupole magnets situated on either side of the experiments. Having increased the number of bunches to 1380, the maximum possible with a 50 ns bunch spacing, a one day meeting in Crozet decided to explore the other possibilities. The size of the beams coming from the injectors has been reduced to the minimum possible. This has brought an increase in the peak luminosity of about 50% and the 2 x 1033 cm...

  10. Instrument developments for inverse photoemission

    International Nuclear Information System (INIS)

    Brenac, A.

    1987-02-01

    Experimental developments principally concerning electron sources for inverse photoemission are presented. The specifications of the electron beam are derived from experiment requirements, taking into account the limitations encountered (space charge divergence). For a wave vector resolution of 0.2 A -1 , the maximum current is 25 microA at 20 eV. The design of a gun providing such a beam in the range 5 to 50 eV is presented. Angle-resolved inverse photoemission experiments show angular effects at 30 eV. For an energy of 10 eV, angular effects should be stronger, but the low efficiency of the spectrometer in this range makes the experiments difficult. The total energy resolution of 0.3 eV is the result mainly of electron energy spread, as expected. The electron sources are based on field effect electron emission from a cathode consisting of a large number of microtips. The emission arises from a few atomic cells for each tip. The ultimate theoretical energy spread is 0.1 eV. This value is not attained because of an interface resistance problem. A partial solution of this problem allows measurement of an energy spread of 0.9 eV for a current of 100 microA emitted at 60 eV. These cathodes have a further advantage in that emission can occur at a low temperature [fr

  11. Tracking time-varying parameters with local regression

    DEFF Research Database (Denmark)

    Joensen, Alfred Karsten; Nielsen, Henrik Aalborg; Nielsen, Torben Skov

    2000-01-01

    This paper shows that the recursive least-squares (RLS) algorithm with forgetting factor is a special case of a varying-coe\\$cient model, and a model which can easily be estimated via simple local regression. This observation allows us to formulate a new method which retains the RLS algorithm, bu......, but extends the algorithm by including polynomial approximations. Simulation results are provided, which indicates that this new method is superior to the classical RLS method, if the parameter variations are smooth....

  12. Weakly Coupled Oscillators in a Slowly Varying World

    OpenAIRE

    Park, Youngmin; Ermentrout, Bard

    2016-01-01

    We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a pair of oscillators. We apply this to the simple Hopf oscillator and then to a biophysical model. The latter represents the behavior of a neuron that is subject to slow modulation of a muscarinic current such as would occur during transient attention through ...

  13. Inverse problems and inverse scattering of plane waves

    CERN Document Server

    Ghosh Roy, Dilip N

    2001-01-01

    The purpose of this text is to present the theory and mathematics of inverse scattering, in a simple way, to the many researchers and professionals who use it in their everyday research. While applications range across a broad spectrum of disciplines, examples in this text will focus primarly, but not exclusively, on acoustics. The text will be especially valuable for those applied workers who would like to delve more deeply into the fundamentally mathematical character of the subject matter.Practitioners in this field comprise applied physicists, engineers, and technologists, whereas the theory is almost entirely in the domain of abstract mathematics. This gulf between the two, if bridged, can only lead to improvement in the level of scholarship in this highly important discipline. This is the book''s primary focus.

  14. Diagonal Pade approximations for initial value problems

    International Nuclear Information System (INIS)

    Reusch, M.F.; Ratzan, L.; Pomphrey, N.; Park, W.

    1987-06-01

    Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab

  15. Approximation properties of fine hyperbolic graphs

    Indian Academy of Sciences (India)

    2016-08-26

    Aug 26, 2016 ... In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use ... Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, People's Republic of China ...

  16. Approximation properties of fine hyperbolic graphs

    Indian Academy of Sciences (India)

    2010 Mathematics Subject Classification. 46L07. 1. Introduction. Given a countable discrete group G, some nice approximation properties for the reduced. C∗-algebras C∗ r (G) can give us the approximation properties of G. For example, Lance. [7] proved that the nuclearity of C∗ r (G) is equivalent to the amenability of G; ...

  17. Non-Linear Approximation of Bayesian Update

    KAUST Repository

    Litvinenko, Alexander

    2016-01-01

    We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

  18. Simultaneous approximation in scales of Banach spaces

    International Nuclear Information System (INIS)

    Bramble, J.H.; Scott, R.

    1978-01-01

    The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods

  19. Approximation algorithms for guarding holey polygons ...

    African Journals Online (AJOL)

    Guarding edges of polygons is a version of art gallery problem.The goal is finding the minimum number of guards to cover the edges of a polygon. This problem is NP-hard, and to our knowledge there are approximation algorithms just for simple polygons. In this paper we present two approximation algorithms for guarding ...

  20. Efficient automata constructions and approximate automata

    NARCIS (Netherlands)

    Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.

    2008-01-01

    In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern

  1. Efficient automata constructions and approximate automata

    NARCIS (Netherlands)

    Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.; Holub, J.; Zdárek, J.

    2006-01-01

    In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern

  2. Spline approximation, Part 1: Basic methodology

    Science.gov (United States)

    Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar

    2018-04-01

    In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

  3. Nonlinear approximation with general wave packets

    DEFF Research Database (Denmark)

    Borup, Lasse; Nielsen, Morten

    2005-01-01

    We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...

  4. Quirks of Stirling's Approximation

    Science.gov (United States)

    Macrae, Roderick M.; Allgeier, Benjamin M.

    2013-01-01

    Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…

  5. Non-Linear Approximation of Bayesian Update

    KAUST Repository

    Litvinenko, Alexander

    2016-06-23

    We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

  6. Approximations for stop-loss reinsurance premiums

    NARCIS (Netherlands)

    Reijnen, Rajko; Albers, Willem/Wim; Kallenberg, W.C.M.

    2005-01-01

    Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are

  7. Improved Dutch Roll Approximation for Hypersonic Vehicle

    Directory of Open Access Journals (Sweden)

    Liang-Liang Yin

    2014-06-01

    Full Text Available An improved dutch roll approximation for hypersonic vehicle is presented. From the new approximations, the dutch roll frequency is shown to be a function of the stability axis yaw stability and the dutch roll damping is mainly effected by the roll damping ratio. In additional, an important parameter called roll-to-yaw ratio is obtained to describe the dutch roll mode. Solution shows that large-roll-to-yaw ratio is the generate character of hypersonic vehicle, which results the large error for the practical approximation. Predictions from the literal approximations derived in this paper are compared with actual numerical values for s example hypersonic vehicle, results show the approximations work well and the error is below 10 %.

  8. Approximate error conjugation gradient minimization methods

    Science.gov (United States)

    Kallman, Jeffrey S

    2013-05-21

    In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.

  9. A new parameterization for waveform inversion in acoustic orthorhombic media

    KAUST Repository

    Masmoudi, Nabil

    2016-05-26

    Orthorhombic anisotropic model inversion is extra challenging because of the multiple parameter nature of the inversion problem. The high number of parameters required to describe the medium exerts considerable trade-off and additional nonlinearity to a full-waveform inversion (FWI) application. Choosing a suitable set of parameters to describe the model and designing an effective inversion strategy can help in mitigating this problem. Using the Born approximation, which is the central ingredient of the FWI update process, we have derived radiation patterns for the different acoustic orthorhombic parameterizations. Analyzing the angular dependence of scattering (radiation patterns) of the parameters of different parameterizations starting with the often used Thomsen-Tsvankin parameterization, we have assessed the potential trade-off between the parameters and the resolution in describing the data and inverting for the parameters. The analysis led us to introduce new parameters ϵd, δd, and ηd, which have azimuthally dependent radiation patterns, but keep the scattering potential of the transversely isotropic parameters stationary with azimuth (azimuth independent). The novel parameters ϵd, δd, and ηd are dimensionless and represent a measure of deviation between the vertical planes in orthorhombic anisotropy. Therefore, these deviation parameters offer a new parameterization style for an acoustic orthorhombic medium described by six parameters: three vertical transversely isotropic (VTI) parameters, two deviation parameters, and one parameter describing the anisotropy in the horizontal symmetry plane. The main feature of any parameterization based on the deviation parameters, is the azimuthal independency of the modeled data with respect to the VTI parameters, which allowed us to propose practical inversion strategies based on our experience with the VTI parameters. This feature of the new parameterization style holds for even the long-wavelength components of

  10. Inverse scattering theory foundations of tomography with diffracting wavefields

    International Nuclear Information System (INIS)

    Devaney, A.J.

    1987-01-01

    The underlying mathematical models employed in reflection and transmission computed tomography using diffracting wavefields (called diffraction tomography) are reviewed and shown to have a rigorous basis in inverse scattering theory. In transmission diffraction tomography the underlying wave model is shown to be the Rytov approximation to the complex phase of the wavefield transmitted by the object being probed while in reflection diffraction tomography the underlying wave model is shown to be the Born approximation to the backscattered wavefield from the object. In both cases the goal of the reconstruction process is the determination of the objects's complex index of refraction as a function of position r/sup →/ and, possibly, the frequency ω of the probing wavefield. By use of these approximations the reconstruction problem for both transmission and reflection diffraction tomography can be cast into the simple and elegant form of linearized inverse scattering theory. Linearized inverse scattering theory is shown to lead directly to generalized projection-slice theorems for both reflection and transmission diffraction tomography that provide a simple mathematical relationship between the object's complex index of refraction (the unknown) and the data (the complex phase of the transmitted wave or the complex amplitude of the reflected wave). The conventional projection-slice theorem of X-ray CT is shown to result from the generalized projection-slice theorem for transmission diffraction tomography in the limit of vanishing wavelength (in the absence of wave effects). Fourier based and back-projection type reconstruction algorithms are shown to be directly derivable from the generalized projection-slice theorems

  11. Intensity-based hierarchical elastic registration using approximating splines.

    Science.gov (United States)

    Serifovic-Trbalic, Amira; Demirovic, Damir; Cattin, Philippe C

    2014-01-01

    We introduce a new hierarchical approach for elastic medical image registration using approximating splines. In order to obtain the dense deformation field, we employ Gaussian elastic body splines (GEBS) that incorporate anisotropic landmark errors and rotation information. Since the GEBS approach is based on a physical model in form of analytical solutions of the Navier equation, it can very well cope with the local as well as global deformations present in the images by varying the standard deviation of the Gaussian forces. The proposed GEBS approximating model is integrated into the elastic hierarchical image registration framework, which decomposes a nonrigid registration problem into numerous local rigid transformations. The approximating GEBS registration scheme incorporates anisotropic landmark errors as well as rotation information. The anisotropic landmark localization uncertainties can be estimated directly from the image data, and in this case, they represent the minimal stochastic localization error, i.e., the Cramér-Rao bound. The rotation information of each landmark obtained from the hierarchical procedure is transposed in an additional angular landmark, doubling the number of landmarks in the GEBS model. The modified hierarchical registration using the approximating GEBS model is applied to register 161 image pairs from a digital mammogram database. The obtained results are very encouraging, and the proposed approach significantly improved all registrations comparing the mean-square error in relation to approximating TPS with the rotation information. On artificially deformed breast images, the newly proposed method performed better than the state-of-the-art registration algorithm introduced by Rueckert et al. (IEEE Trans Med Imaging 18:712-721, 1999). The average error per breast tissue pixel was less than 2.23 pixels compared to 2.46 pixels for Rueckert's method. The proposed hierarchical elastic image registration approach incorporates the GEBS

  12. Wake Vortex Inverse Model User's Guide

    Science.gov (United States)

    Lai, David; Delisi, Donald

    2008-01-01

    NorthWest Research Associates (NWRA) has developed an inverse model for inverting landing aircraft vortex data. The data used for the inversion are the time evolution of the lateral transport position and vertical position of both the port and starboard vortices. The inverse model performs iterative forward model runs using various estimates of vortex parameters, vertical crosswind profiles, and vortex circulation as a function of wake age. Forward model predictions of lateral transport and altitude are then compared with the observed data. Differences between the data and model predictions guide the choice of vortex parameter values, crosswind profile and circulation evolution in the next iteration. Iterations are performed until a user-defined criterion is satisfied. Currently, the inverse model is set to stop when the improvement in the rms deviation between the data and model predictions is less than 1 percent for two consecutive iterations. The forward model used in this inverse model is a modified version of the Shear-APA model. A detailed description of this forward model, the inverse model, and its validation are presented in a different report (Lai, Mellman, Robins, and Delisi, 2007). This document is a User's Guide for the Wake Vortex Inverse Model. Section 2 presents an overview of the inverse model program. Execution of the inverse model is described in Section 3. When executing the inverse model, a user is requested to provide the name of an input file which contains the inverse model parameters, the various datasets, and directories needed for the inversion. A detailed description of the list of parameters in the inversion input file is presented in Section 4. A user has an option to save the inversion results of each lidar track in a mat-file (a condensed data file in Matlab format). These saved mat-files can be used for post-inversion analysis. A description of the contents of the saved files is given in Section 5. An example of an inversion input

  13. Inverse diffusion theory of photoacoustics

    International Nuclear Information System (INIS)

    Bal, Guillaume; Uhlmann, Gunther

    2010-01-01

    This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photoacoustics, the internal data are the amount of thermal energy deposited by high frequency radiation propagating inside a domain of interest. These data are obtained by solving an inverse wave equation, which is well studied in the literature. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determines two constitutive parameters in diffusion and Schrödinger equations. Stability of the reconstruction is guaranteed under additional geometric constraints of strict convexity. No geometric constraints are necessary when 2n internal data for well-chosen boundary conditions are available, where n is spatial dimension. The set of well-chosen boundary conditions is characterized in terms of appropriate complex geometrical optics solutions

  14. Optimization and inverse problems in electromagnetism

    CERN Document Server

    Wiak, Sławomir

    2003-01-01

    From 12 to 14 September 2002, the Academy of Humanities and Economics (AHE) hosted the workshop "Optimization and Inverse Problems in Electromagnetism". After this bi-annual event, a large number of papers were assembled and combined in this book. During the workshop recent developments and applications in optimization and inverse methodologies for electromagnetic fields were discussed. The contributions selected for the present volume cover a wide spectrum of inverse and optimal electromagnetic methodologies, ranging from theoretical to practical applications. A number of new optimal and inverse methodologies were proposed. There are contributions related to dedicated software. Optimization and Inverse Problems in Electromagnetism consists of three thematic chapters, covering: -General papers (survey of specific aspects of optimization and inverse problems in electromagnetism), -Methodologies, -Industrial Applications. The book can be useful to students of electrical and electronics engineering, computer sci...

  15. Reverse Universal Resolving Algorithm and inverse driving

    DEFF Research Database (Denmark)

    Pécseli, Thomas

    2012-01-01

    Inverse interpretation is a semantics based, non-standard interpretation of programs. Given a program and a value, an inverse interpreter finds all or one of the inputs, that would yield the given value as output with normal forward evaluation. The Reverse Universal Resolving Algorithm is a new...... variant of the Universal Resolving Algorithm for inverse interpretation. The new variant outperforms the original algorithm in several cases, e.g., when unpacking a list using inverse interpretation of a pack program. It uses inverse driving as its main technique, which has not been described in detail...... before. Inverse driving may find application with, e.g., supercompilation, thus suggesting a new kind of program inverter....

  16. Solution to the inversely stated transient source-receptor problem

    International Nuclear Information System (INIS)

    Sajo, E.; Sheff, J.R.

    1995-01-01

    Transient source-receptor problems are traditionally handled via the Boltzmann equation or through one of its variants. In the atmospheric transport of pollutants, meteorological uncertainties in the planetary boundary layer render only a few approximations to the Boltzmann equation useful. Often, due to the high number of unknowns, the atmospheric source-receptor problem is ill-posed. Moreover, models to estimate downwind concentration invariably assume that the source term is known. In this paper, an inverse methodology is developed, based on downwind measurement of concentration and that of meterological parameters to estimate the source term

  17. Regression with Sparse Approximations of Data

    DEFF Research Database (Denmark)

    Noorzad, Pardis; Sturm, Bob L.

    2012-01-01

    We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...

  18. Conditional Density Approximations with Mixtures of Polynomials

    DEFF Research Database (Denmark)

    Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre

    2015-01-01

    Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities...

  19. Hardness and Approximation for Network Flow Interdiction

    OpenAIRE

    Chestnut, Stephen R.; Zenklusen, Rico

    2015-01-01

    In the Network Flow Interdiction problem an adversary attacks a network in order to minimize the maximum s-t-flow. Very little is known about the approximatibility of this problem despite decades of interest in it. We present the first approximation hardness, showing that Network Flow Interdiction and several of its variants cannot be much easier to approximate than Densest k-Subgraph. In particular, any $n^{o(1)}$-approximation algorithm for Network Flow Interdiction would imply an $n^{o(1)}...

  20. Approximation of the semi-infinite interval

    Directory of Open Access Journals (Sweden)

    A. McD. Mercer

    1980-01-01

    Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.

  1. Mathematical analysis, approximation theory and their applications

    CERN Document Server

    Gupta, Vijay

    2016-01-01

    Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

  2. Inverse kinematics of OWI-535 robotic arm

    OpenAIRE

    DEBENEC, PRIMOŽ

    2015-01-01

    The thesis aims to calculate the inverse kinematics for the OWI-535 robotic arm. The calculation of the inverse kinematics determines the joint parameters that provide the right pose of the end effector. The pose consists of the position and orientation, however, we will focus only on the second one. Due to arm limitations, we have created our own type of the calculation of the inverse kinematics. At first we have derived it only theoretically, and then we have transferred the derivation into...

  3. Automatic Flight Controller With Model Inversion

    Science.gov (United States)

    Meyer, George; Smith, G. Allan

    1992-01-01

    Automatic digital electronic control system based on inverse-model-follower concept being developed for proposed vertical-attitude-takeoff-and-landing airplane. Inverse-model-follower control places inverse mathematical model of dynamics of controlled plant in series with control actuators of controlled plant so response of combination of model and plant to command is unity. System includes feedback to compensate for uncertainties in mathematical model and disturbances imposed from without.

  4. Lectures on the inverse scattering method

    International Nuclear Information System (INIS)

    Zakharov, V.E.

    1983-06-01

    In a series of six lectures an elementary introduction to the theory of inverse scattering is given. The first four lectures contain a detailed theory of solitons in the framework of the KdV equation, together with the inverse scattering theory of the one-dimensional Schroedinger equation. In the fifth lecture the dressing method is described, while the sixth lecture gives a brief review of the equations soluble by the inverse scattering method. (author)

  5. Time-reversal and Bayesian inversion

    Science.gov (United States)

    Debski, Wojciech

    2017-04-01

    Probabilistic inversion technique is superior to the classical optimization-based approach in all but one aspects. It requires quite exhaustive computations which prohibit its use in huge size inverse problems like global seismic tomography or waveform inversion to name a few. The advantages of the approach are, however, so appealing that there is an ongoing continuous afford to make the large inverse task as mentioned above manageable with the probabilistic inverse approach. One of the perspective possibility to achieve this goal relays on exploring the internal symmetry of the seismological modeling problems in hand - a time reversal and reciprocity invariance. This two basic properties of the elastic wave equation when incorporating into the probabilistic inversion schemata open a new horizons for Bayesian inversion. In this presentation we discuss the time reversal symmetry property, its mathematical aspects and propose how to combine it with the probabilistic inverse theory into a compact, fast inversion algorithm. We illustrate the proposed idea with the newly developed location algorithm TRMLOC and discuss its efficiency when applied to mining induced seismic data.

  6. Inverse Kinematics of a Serial Robot

    Directory of Open Access Journals (Sweden)

    Amici Cinzia

    2016-01-01

    Full Text Available This work describes a technique to treat the inverse kinematics of a serial manipulator. The inverse kinematics is obtained through the numerical inversion of the Jacobian matrix, that represents the equation of motion of the manipulator. The inversion is affected by numerical errors and, in different conditions, due to the numerical nature of the solver, it does not converge to a reasonable solution. Thus a soft computing approach is adopted to mix different traditional methods to obtain an increment of algorithmic convergence.

  7. Multilevel weighted least squares polynomial approximation

    KAUST Repository

    Haji-Ali, Abdul-Lateef; Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren

    2017-01-01

    , obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose

  8. Low Rank Approximation Algorithms, Implementation, Applications

    CERN Document Server

    Markovsky, Ivan

    2012-01-01

    Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...

  9. Nonlinear Ritz approximation for Fredholm functionals

    Directory of Open Access Journals (Sweden)

    Mudhir A. Abdul Hussain

    2015-11-01

    Full Text Available In this article we use the modify Lyapunov-Schmidt reduction to find nonlinear Ritz approximation for a Fredholm functional. This functional corresponds to a nonlinear Fredholm operator defined by a nonlinear fourth-order differential equation.

  10. Euclidean shortest paths exact or approximate algorithms

    CERN Document Server

    Li, Fajie

    2014-01-01

    This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.

  11. Square well approximation to the optical potential

    International Nuclear Information System (INIS)

    Jain, A.K.; Gupta, M.C.; Marwadi, P.R.

    1976-01-01

    Approximations for obtaining T-matrix elements for a sum of several potentials in terms of T-matrices for individual potentials are studied. Based on model calculations for S-wave for a sum of two separable non-local potentials of Yukawa type form factors and a sum of two delta function potentials, it is shown that the T-matrix for a sum of several potentials can be approximated satisfactorily over all the energy regions by the sum of T-matrices for individual potentials. Based on this, an approximate method for finding T-matrix for any local potential by approximating it by a sum of suitable number of square wells is presented. This provides an interesting way to calculate the T-matrix for any arbitary potential in terms of Bessel functions to a good degree of accuracy. The method is applied to the Saxon-Wood potentials and good agreement with exact results is found. (author)

  12. Approximation for the adjoint neutron spectrum

    International Nuclear Information System (INIS)

    Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

    2002-01-01

    The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)

  13. Saddlepoint approximation methods in financial engineering

    CERN Document Server

    Kwok, Yue Kuen

    2018-01-01

    This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables.  The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quanti...

  14. Methods of Fourier analysis and approximation theory

    CERN Document Server

    Tikhonov, Sergey

    2016-01-01

    Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

  15. Pion-nucleus cross sections approximation

    International Nuclear Information System (INIS)

    Barashenkov, V.S.; Polanski, A.; Sosnin, A.N.

    1990-01-01

    Analytical approximation of pion-nucleus elastic and inelastic interaction cross-section is suggested, with could be applied in the energy range exceeding several dozens of MeV for nuclei heavier than beryllium. 3 refs.; 4 tabs

  16. APPROXIMATE DEVELOPMENTS FOR SURFACES OF REVOLUTION

    Directory of Open Access Journals (Sweden)

    Mădălina Roxana Buneci

    2016-12-01

    Full Text Available The purpose of this paper is provide a set of Maple procedures to construct approximate developments of a general surface of revolution generalizing the well-known gore method for sphere

  17. Steepest descent approximations for accretive operator equations

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1993-03-01

    A necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi-accretive operators defined on a uniformly smooth Banach space. (author). 49 refs

  18. Seismic wave extrapolation using lowrank symbol approximation

    KAUST Repository

    Fomel, Sergey

    2012-04-30

    We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.

  19. An overview on Approximate Bayesian computation*

    Directory of Open Access Journals (Sweden)

    Baragatti Meïli

    2014-01-01

    Full Text Available Approximate Bayesian computation techniques, also called likelihood-free methods, are one of the most satisfactory approach to intractable likelihood problems. This overview presents recent results since its introduction about ten years ago in population genetics.

  20. Approximate Computing Techniques for Iterative Graph Algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram

    2017-12-18

    Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.

  1. Validation and genotyping of multiple human polymorphic inversions mediated by inverted repeats reveals a high degree of recurrence.

    Directory of Open Access Journals (Sweden)

    Cristina Aguado

    2014-03-01

    Full Text Available In recent years different types of structural variants (SVs have been discovered in the human genome and their functional impact has become increasingly clear. Inversions, however, are poorly characterized and more difficult to study, especially those mediated by inverted repeats or segmental duplications. Here, we describe the results of a simple and fast inverse PCR (iPCR protocol for high-throughput genotyping of a wide variety of inversions using a small amount of DNA. In particular, we analyzed 22 inversions predicted in humans ranging from 5.1 kb to 226 kb and mediated by inverted repeat sequences of 1.6-24 kb. First, we validated 17 of the 22 inversions in a panel of nine HapMap individuals from different populations, and we genotyped them in 68 additional individuals of European origin, with correct genetic transmission in ∼ 12 mother-father-child trios. Global inversion minor allele frequency varied between 1% and 49% and inversion genotypes were consistent with Hardy-Weinberg equilibrium. By analyzing the nucleotide variation and the haplotypes in these regions, we found that only four inversions have linked tag-SNPs and that in many cases there are multiple shared SNPs between standard and inverted chromosomes, suggesting an unexpected high degree of inversion recurrence during human evolution. iPCR was also used to check 16 of these inversions in four chimpanzees and two gorillas, and 10 showed both orientations either within or between species, providing additional support for their multiple origin. Finally, we have identified several inversions that include genes in the inverted or breakpoint regions, and at least one disrupts a potential coding gene. Thus, these results represent a significant advance in our understanding of inversion polymorphism in human populations and challenge the common view of a single origin of inversions, with important implications for inversion analysis in SNP-based studies.

  2. A varying-α brane world cosmology

    International Nuclear Information System (INIS)

    Youm, Donam

    2001-08-01

    We study the brane world cosmology in the RS2 model where the electric charge varies with time in the manner described by the varying fine-structure constant theory of Bekenstein. We map such varying electric charge cosmology to the dual variable-speed-of-light cosmology by changing system of units. We comment on cosmological implications for such cosmological models. (author)

  3. Semiclassical approximation of the Wheeler-DeWitt equation: arbitrary orders and the question of unitarity

    Science.gov (United States)

    Kiefer, Claus; Wichmann, David

    2018-06-01

    We extend the Born-Oppenheimer type of approximation scheme for the Wheeler-DeWitt equation of canonical quantum gravity to arbitrary orders in the inverse Planck mass squared. We discuss in detail the origin of unitarity violation in this scheme and show that unitarity can be restored by an appropriate modification which requires back reaction from matter onto the gravitational sector. In our analysis, we heavily rely on the gauge aspects of the standard Born-Oppenheimer scheme in molecular physics.

  4. Approximative solutions of stochastic optimization problem

    Czech Academy of Sciences Publication Activity Database

    Lachout, Petr

    2010-01-01

    Roč. 46, č. 3 (2010), s. 513-523 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic optimization problem * sensitivity * approximative solution Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/lachout-approximative solutions of stochastic optimization problem.pdf

  5. Lattice quantum chromodynamics with approximately chiral fermions

    Energy Technology Data Exchange (ETDEWEB)

    Hierl, Dieter

    2008-05-15

    In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

  6. An approximate analytical approach to resampling averages

    DEFF Research Database (Denmark)

    Malzahn, Dorthe; Opper, M.

    2004-01-01

    Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for appr...... for approximate Bayesian inference. We demonstrate our approach on regression with Gaussian processes. A comparison with averages obtained by Monte-Carlo sampling shows that our method achieves good accuracy....

  7. Stochastic quantization and mean field approximation

    International Nuclear Information System (INIS)

    Jengo, R.; Parga, N.

    1983-09-01

    In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)

  8. Polynomial approximation of functions in Sobolev spaces

    International Nuclear Information System (INIS)

    Dupont, T.; Scott, R.

    1980-01-01

    Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces

  9. Magnus approximation in the adiabatic picture

    International Nuclear Information System (INIS)

    Klarsfeld, S.; Oteo, J.A.

    1991-01-01

    A simple approximate nonperturbative method is described for treating time-dependent problems that works well in the intermediate regime far from both the sudden and the adiabatic limits. The method consists of applying the Magnus expansion after transforming to the adiabatic basis defined by the eigenstates of the instantaneous Hamiltonian. A few exactly soluble examples are considered in order to assess the domain of validity of the approximation. (author) 32 refs., 4 figs

  10. Lattice quantum chromodynamics with approximately chiral fermions

    International Nuclear Information System (INIS)

    Hierl, Dieter

    2008-05-01

    In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the Θ + pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

  11. A pericentric inversion of chromosome X disrupting F8 and resulting in haemophilia A.

    Science.gov (United States)

    Xin, Yu; Zhou, Jingyi; Ding, Qiulan; Chen, Changming; Wu, Xi; Wang, Xuefeng; Wang, Hongli; Jiang, Xiaofeng

    2017-08-01

    The frequency of X chromosome pericentric inversion is much less than that of autosome chromosome. We hereby characterise a pericentric inversion of X chromosome associated with severe factor VIII (FVIII) deficiency in a sporadic haemophilia A (HA) pedigree. PCR primer walking and genome walking strategies were adopted to identify the exact breakpoints of the inversion. Copy number variations (CNVs) of the F8 and the whole chromosomes were detected by AccuCopy and Affymetrix CytoScan High Definition (HD) assays, respectively. A karyotype analysis was performed by cytogenetic G banding technique. We identified a previously undescribed type of pericentric inversion of the X chromosome [inv(X)(p11.21q28)] in the proband with FVIII:C inversion segment was approximately 64.4% of the total chromosomal length. The karyotype analysis of the X chromosome confirmed the pericentric inversion of the X chromosome in the proband and his mother. A haplotype analysis traced the inversion to his maternal grandfather, who was not a somatic mosaic of the inversion. This finding indicated that the causative mutation may originate from his germ cells or a rare possibility of germ-cell mosaicism. The characterisation of pericentric inversion involving F8 extended the molecular mechanisms causing HA. The pericentric inversion rearrangement involves F8 by non-homologous end joining is responsible for pathogensis of severe HA. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.

  12. Approximating centrality in evolving graphs: toward sublinearity

    Science.gov (United States)

    Priest, Benjamin W.; Cybenko, George

    2017-05-01

    The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.

  13. Minimum mean square error estimation and approximation of the Bayesian update

    KAUST Repository

    Litvinenko, Alexander; Matthies, Hermann G.; Zander, Elmar

    2015-01-01

    Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(w), a measurement operator Y (u(q); q), where u(q; w) uncertain solution. Aim: to identify q(w). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(w) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a functional approximation, e.g. polynomial chaos expansion (PCE). New: We derive linear, quadratic etc approximation of full Bayesian update.

  14. Minimum mean square error estimation and approximation of the Bayesian update

    KAUST Repository

    Litvinenko, Alexander

    2015-01-07

    Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(w), a measurement operator Y (u(q); q), where u(q; w) uncertain solution. Aim: to identify q(w). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(w) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a functional approximation, e.g. polynomial chaos expansion (PCE). New: We derive linear, quadratic etc approximation of full Bayesian update.

  15. Background velocity inversion by phase along reflection wave paths

    KAUST Repository

    Yu, Han; Guo, Bowen; Schuster, Gerard T.

    2014-01-01

    A background velocity model containing the correct lowwavenumber information is desired for both the quality of the migration image and the success of waveform inversion. We propose to invert for the low-wavenumber part of the velocity model by minimizing the phase difference between predicted and observed reflections. The velocity update is exclusively along the reflection wavepaths and, unlike conventional FWI, not along the reflection ellipses. This allows for reconstructing the smoothly varying parts of the background velocity model. Tests with synthetic data show both the benefits and limitations of this method.

  16. Interferometric full-waveform inversion of time-lapse data

    KAUST Repository

    Sinha, Mrinal

    2017-08-17

    One of the key challenges associated with time-lapse surveys is ensuring the repeatability between the baseline and monitor surveys. Non-repeatability between the surveys is caused by varying environmental conditions over the course of different surveys. To overcome this challenge, we propose the use of interferometric full waveform inversion (IFWI) for inverting the velocity model from data recorded by baseline and monitor surveys. A known reflector is used as the reference reflector for IFWI, and the data are naturally redatumed to this reference reflector using natural reflections as the redatuming operator. This natural redatuming mitigates the artifacts introduced by the repeatability errors that originate above the reference reflector.

  17. Background velocity inversion by phase along reflection wave paths

    KAUST Repository

    Yu, Han

    2014-08-05

    A background velocity model containing the correct lowwavenumber information is desired for both the quality of the migration image and the success of waveform inversion. We propose to invert for the low-wavenumber part of the velocity model by minimizing the phase difference between predicted and observed reflections. The velocity update is exclusively along the reflection wavepaths and, unlike conventional FWI, not along the reflection ellipses. This allows for reconstructing the smoothly varying parts of the background velocity model. Tests with synthetic data show both the benefits and limitations of this method.

  18. Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

    Directory of Open Access Journals (Sweden)

    Xiao-Ying Qin

    2014-01-01

    Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.

  19. Analytical approximations to the Hotelling trace for digital x-ray detectors

    Science.gov (United States)

    Clarkson, Eric; Pineda, Angel R.; Barrett, Harrison H.

    2001-06-01

    The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

  20. ɛ-connectedness, finite approximations, shape theory and coarse graining in hyperspaces

    Science.gov (United States)

    Alonso-Morón, Manuel; Cuchillo-Ibanez, Eduardo; Luzón, Ana

    2008-12-01

    We use upper semifinite hyperspaces of compacta to describe ε-connectedness and to compute homology from finite approximations. We find a new connection between ε-connectedness and the so-called Shape Theory. We construct a geodesically complete R-tree, by means of ε-components at different resolutions, whose behavior at infinite captures the topological structure of the space of components of a given compact metric space. We also construct inverse sequences of finite spaces using internal finite approximations of compact metric spaces. These sequences can be converted into inverse sequences of polyhedra and simplicial maps by means of what we call the Alexandroff-McCord correspondence. This correspondence allows us to relate upper semifinite hyperspaces of finite approximation with the Vietoris-Rips complexes of such approximations at different resolutions. Two motivating examples are included in the introduction. We propose this procedure as a different mathematical foundation for problems on data analysis. This process is intrinsically related to the methodology of shape theory. This paper reinforces Robins’s idea of using methods from shape theory to compute homology from finite approximations.