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1

Basic Theoretical Methods in Microwave Plasma Polarimetry: Quasi-Isotropic Approximation, Stokes Vector Formalism and Complex Polarization Angle Method  

NASA Astrophysics Data System (ADS)

Three different theoretical approaches are presented: quasi-isotropic approximation (QIA), Stokes vector formalism and complex polarization angle method, which allow describing polarization of electromagnetic waves in weakly anisotropic plasma. QIA stems directly from the Maxwell equations under assumption of weak anisotropy and has a form of coupled differential equations for the transverse components of the electromagnetic wave field. Being applied to high frequency (microwave or IR) electromagnetic waves in magnetized plasma, QIA describes combined action of Faraday and Cotton-Mouton phenomena. QIA takes into account curvature and torsion of the ray, describes normal modes conversion in the inhomogeneous plasma and allows specifying area of applicability of the method. In distinction to QIA, Stokes vector formalism (SVF) deals with quantities, quadratic in a wave field. It is shown (and this is the main result of the paper) that equation for Stokes vector evolution can be derived directly from QIA. This evidences deep unity of two seemingly different approaches. In fact QIA suggests somewhat more information than SVF; in particular, it describes the phases of both transverse components of the electromagnetic field, whereas SVF operates only with the phase difference. At last, the coupled equations of the quasi-isotropic approximation can be reduced to a single equation for complex polarization angle (CPA), which describes both the shape and orientation of the polarization ellipse. In turn, equation for CPA allows obtaining equations for traditional parameters of polarization ellipse, which in fact are equivalent to the equation for Stokes vector evolution. It is pointed out that every method under discussion has its own advantages plasma polarimetry.

Kravtsov, Yu. A.; Bieg, B.; Bliokh, K. Yu.; Hirsch, M.

2008-03-01

2

Evolution of the polarization of electromagnetic waves in weakly anisotropic inhomogeneous media — a comparison of quasi-isotropic approximations of the geometrical optics method and the Stokes vector formalism  

NASA Astrophysics Data System (ADS)

The main methods describing polarization of electromagnetic waves in weakly anisotropic inhomogeneous media are reviewed: the quasi-isotropic approximation (QIA) of geometrical optics method that deals with coupled equations for electromagnetic field components, and the Stokes vector formalism (SVF), dealing with Stokes vector components, which are quadratic in electromagnetic field intensity. The equation for the Stokes vector evolution is shown to be derived directly from QIA, whereas the inverse cannot be true. Derivation of SVF from QIA establishes a deep unity of these two approaches, which happen to be equivalent up to total phase. It is pointed out that in contrast to QIA, the Stokes vector cannot be applied for a polarization analysis of the superposition of coherent electromagnetic beams. Additionally, the ability of QIA to describe a normal modes conversion in inhomogeneous media is emphasized.

Kravtsov, Yury A.; Bieg, Bohdan

2008-09-01

3

Flexural Stiffnesses of and Dimensional Stability in Circular Quasi-isotropic Laminate Mirrors  

E-print Network

buffer layers on composite mirrors for high surface smoothness. In this dissertation document, radial stiffness associated with stacking sequence effects in quasi-isotropic laminates (pi/n, where n=3, 4, and 6) and dimensional stability in the composite...

Kim, Kyungpyo

2009-01-01

4

A quasi-isotropic reflecting boundary condition for the TIBERE heterogeneous leakage model  

SciTech Connect

The influence of assembly or cell heterogeneity on neutron leakage has been consistently taken into account in the TIBERE simplified heterogeneous B{sub 1} model. The assumption adopted within the TIBERE model that neutrons are specularly reflected on the boundary introduces two problems. Calculations with this model may become rather time consuming and even unnecessarily long in the case of a Canada deuterium uranium reactor cell, and the peripheral or total coolant voiding of a pressurized water reactor assembly leads to infinite leakage coefficients. These problems have been overcome by the development of another simplified heterogeneous B{sub 1} leakage model, TIBERE-2, which has quasi-isotropic reflecting boundary conditions. The TIBERE-2 model uses similar approximations as the TIBERE model and yields an iterative scheme to simultaneously compute multigroup scalar fluxes and directional currents in a heterogeneous geometry. These values enable the evaluation of directional space-dependent leakage coefficients. This new model requires the classical and directional escape and transmission probabilities in addition to the classical and directional first-flight collision probabilities calculated for an open assembly. The TIBERE-2 model has been introduced for general two-dimensional geometry into the DRAGON multigroup transport code. The numerical results obtained by DRAGON show that the TIBERE-2 model represents leakages much better than the homogeneous B{sub 1} leakage model. Moreover, the TIBERE-2 model yields results that are extremely close to those obtained by the TIBERE model with considerably shorter computing times.

Petrovic, I.; Marleau, G. [Ecole Polytechnique de Montreal, Quebec, Montreal (Canada). Institut de Genie Nucleaire; Benoist, P.

1996-02-01

5

Construction of a polarization insensitive lens from a quasi-isotropic metamaterial slab  

Microsoft Academic Search

We propose to employ the quasi-isotropic metamaterial (QIMM) slab to construct a polarization insensitive lens, in which both E - and H -polarized waves exhibit the same refocusing effect. For shallow incident angles, the QIMM slab will provide some degree of refocusing in the same manner as an isotropic negative index material. The refocusing effect allows us to introduce the

Hailu Luo; Zhongzhou Ren; Weixing Shu; Fei Li

2007-01-01

6

Quasi-isotropic VHF antenna array design study for the International Ultraviolet Explorer satellite  

NASA Technical Reports Server (NTRS)

Results of a study to design a quasi-isotropic VHF antenna array for the IUE satellite are presented. A free space configuration was obtained that has no nulls deeper than -6.4 dbi in each of two orthogonal polarizations. A computer program named SOAP that analyzes the electromagnetic interaction between antennas and complicated conducting bodies, such as satellites was developed.

Raines, J. K.

1975-01-01

7

Large deflection behavior of quasi-isotropic laminates under low-velocity impact type point loading  

NASA Technical Reports Server (NTRS)

Eight-ply quasi-isotropic circular composite plates of Thornel 300 graphite in Narmco 5208 epoxy resin (T300/5208) were analyzed to obtain the large deformation behavior under low-velocity impact type point loads. A simple plate-membrane coupling model was developed. The impact type point loads were replaced by equivalent quasi-static point loads. The plate-membrane coupling model was used to obtain the large deformation shapes for the thin circular composite laminates. The analyses indicated that the large deformation shapes of the composite plates under point loads vary with the center point displacements, and hence are different for different load levels. Quasi-isotropic plates were analyzed by replacing anisotropic bending stiffness components with the equivalent flexural stiffness for the isotropic plates. The plate-membrane coupling model was verified by conducting a series of tests on clamped circular quasi-isotropic laminates. Deflected shapes for the thin composite plates were experimentally obtained. These shapes agreed well with the analytically predicted shapes.

Kelkar, A.; Elber, W.; Raju, I. S.

1985-01-01

8

Delamination behavior of quasi-isotropic graphite epoxy laminates subjected to tension and torsion loads  

NASA Technical Reports Server (NTRS)

Sixteen and thirty-two ply quasi-isotropic laminates fabricated from AS4/3501-6 were subjected to pure tension, simultaneous tension and torsion, and torsion fatigue. Layups tested were (45 sub n/-45 sub n/O sub n/90 sub n) sub s, with n = 2 or 4. A torsion damage pattern consisting of a localized matrix crack and delaminations was characterized, and the measured torsional stiffnesses were compared with calculated values. It was found that a combination of tension and torsion led to failure at smaller loads than either type of deformation acting alone. Further work is required to determine the exact form of the failure criterion.

Hinkley, J. A.; Obrien, T. K.

1992-01-01

9

Elastic properties and fracture strength of quasi-isotropic graphite/epoxy composites  

NASA Technical Reports Server (NTRS)

A research program is described which was devised to determine experimentally the elastic properties in tension and bending of quasi-isotropic laminates made from high-modulus graphite fiber and epoxy. Four laminate configurations were investigated, and determinations were made of the tensile modulus, Poisson's ratio, bending stiffness, fracture strength, and fracture strain. The measured properties are compared with those predicted by laminate theory, reasons for scatter in the experimental data are discussed, and the effect of fiber misalignment on predicted elastic tensile properties is examined. The results strongly suggest that fiber misalignment in combination with variation in fiber volume content is responsible for the scatter in both elastic constants and fracture strength.

Sullivan, T. L.

1977-01-01

10

Buckling Behavior of Compression-Loaded Quasi-Isotropic Curved Panels with a Circular Cutout  

NASA Technical Reports Server (NTRS)

Results from a numerical and experimental study of the response of compression-loaded quasi-isotropic curved panels with a centrally located circular cutout are presented. The numerical results were obtained by using a geometrically nonlinear finite element analysis code. The effects of cutout size, panel curvature and initial geo- metric imperfections on the overall response of compression-loaded panels are described. In addition, results are presented from a numerical parametric study that indicate the effects of elastic circumferential edge restraints on the prebuckling and buckling response of a selected panel and these numerical results are compared to experimentally measured results. These restraints are used to identify the effects of circumferential edge restraints that are introduced by the test fixture that was used in the present study. It is shown that circumferential edge restraints can introduce substantial nonlinear prebuckling deformations into shallow compression-loaded curved panels that can results in a significant increase in buckling load.

Hilburger, Mark W.; Britt, Vicki O.; Nemeth, Michael P.

1999-01-01

11

Study of the dynamical behaviour of the polarization of a quasi-isotropic laser in the earth magnetic field  

Microsoft Academic Search

High-gain quasi-isotropic lasers are shown to be very sensitive probes of the earth magnetic field. The rate of rotation of the polarization is shown to exhibit an Adler-type evolution with the azimuth of the laser propagation axis, with a locking region depending on the controlled loss-anisotropies introduced in the cavity. The evolution of this rotation rate with the excitation and

J. C. Cotteverte; Fabien Bretenaker; Albert Le Floch

1990-01-01

12

Active deformation and engineering analysis of CFRP mirror of various lay-up sequences within quasi-isotropic laminates  

NASA Astrophysics Data System (ADS)

A regularization stiffness coefficient method was verified further to optimize lay-up sequences of quasi-isotropic laminates for carbon fiber reinforced polymer (CFRP) composite mirrors. Firstly, the deformation due to gravity of 1G and temperature difference of 20-100°C and the modal were analyzed by finite element method (FEM). Secondly, the influence of angle error of ply stacking on quasi-isotropic of bending stiffness was evaluated. Finally, an active support system of 49 actuators in circular arrangement is designed for a 500mm CFRP mirror, and its goal is to deform the spherical CFRP mirror to a parabolic. Therefore, the response functions of the actuators were gotten, and the surface form errors and stresses were calculated and analyzed. The results show that the CFRP mirrors designed by the method have a better symmetrical bending deformation under gravity and thermal load and a higher fundamental frequency, and the larger n the better symmetry (for ?/n quasi-isotropic laminates); the method reduces the sensitivity to misalignment of ply orientation for symmetric bending, and the mirror's maximum von Mises stress and maximum shear stress are less compared to those laminates not optimized in lay-up sequence.

Zeng, Chunmei; Yu, Xia; Guo, Peiji

2014-08-01

13

The structural behavior of a graphite-polymide honeycomb sandwich panel with quasi-isotropic face sheets and an orthotropic core  

NASA Technical Reports Server (NTRS)

The results of a series of tests of graphite-polyimide honeycomb sandwich panels are presented. The panels were 1.22 m long, 0.508 m wide, and approximately 13.3 m thick. The face sheets were a T-300/PMR-15 fabric in a quasi-isotropic layup and were 0.279 mm thick. The core was Hexcel HRH 327-3/16 - 4.0 glass reinforced polyimide honeycomb, 12.7 mm thick. Three panels were used in the test: one was cut into smaller pieces for testing as beam, compression, and shear specimens; a second panel was used for plate bending tests; the third panel was used for in-plane stability tests. Presented are the experimental results of four point bending tests, short block compression tests, core transverse shear modulus, three point bending tests, vibration tests, plate bending tests, and panel stability tests. The results of the first three tests are used to predict the results of some of the other tests. The predictions and experimental results are compared, and the agreement is quite good.

Hyer, M. W.; Hagaman, J. A.

1979-01-01

14

Fabrication of Nanometer Silicon Pillars for Buried-Gate-Type Surrounding Gate Transistor by Silicon Quasi-Isotropic Etching  

NASA Astrophysics Data System (ADS)

A fabrication process for nanometer silicon pillars by silicon quasi-isotropic etching for a buried-gate-type surrounding gate transistor (BG-SGT) is proposed. In a normal SGT structure, the diameter of a channel region is defined using a silicon pillar whose diameter is equal to a minimum feature size. However, in a BG-SGT structure, the channel region is located within a buried region and hence is defined using a silicon pillar whose diameter is smaller than the minimum feature size. By electron beam (EB) lithography with a minimum feature size of 65 nm, we were able to fabricate successfully an entire silicon pillar with a buried region whose diameter was about 40 nm. In addition, the dependence of the etching rate of the silicon sidewall on the crystallographic orientation was investigated.

Kitagawa, Takeyuki; Hidaka, Takeshi; Ohba, Takuya; Amikawa, Hiroyuki; Izumida, Takashi; Ohtsu, Syuuhei; Nakamura, Hiroki; Sakuraba, Hiroshi; Masuoka, Fujio

2006-01-01

15

Variations of Fatigue Damage Growth in Cross-Ply and Quasi-Isotropic laminates Under High-Cycle Fatigue Loading  

NASA Astrophysics Data System (ADS)

The behavior of transverse crack growth and delamination growth under high-cycle fatigue loadings was investigated with cross-ply CFRP laminates, [0/902]s and [0/906]s, and quasi-isotropic CFRP laminates, [45/0/-45/90]s. As a result, it was observed that the behavior of damage growth was different depending on the applied stress level. The growth of local or edge delamination was exacerbated under the test conditions of a low applied stress level and high-cycle loadings, because the areas of stress concentration were applied with high-cyclic loadings. On the other hand, when the fatigue tests were conducted under the applied stress level of 40% of the transverse crack initiation, the growth of transverse cracks was hardly observed until 108 cycles with [0/902]s, [0/906]s and [45/0/-45/90]s laminates.

Hosoi, Atsushi; Shi, Jiadi; Sato, Narumichi; Kawada, Hiroyuki

16

Approximation Theory Approximation Practice  

E-print Network

. Orthogonal polynomials, 123 18. Polynomial roots and colleague matrices, 132 19. Clenshaw­Curtis and Gauss-squares, 219 27. Pad´e approximation, 232 28. Analytic continuation and convergence acceleration, 247 Appendix. Everything is practical and fast, so we will routinely compute polynomial interpolants or Gauss quadrature

Morrow, James A.

17

An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program  

NASA Technical Reports Server (NTRS)

An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.

Rose, Cheryl A.; Herakovich, Carl T.

1992-01-01

18

Approximate schedule  

E-print Network

Oct 8, 2014 ... Binomial theorem (1), definition of probability (2.3) , properties of probability, examples ... Distribution function of random variables (4.10). Sep 25 ... Poisson random variables, Poisson approximation to binomial distribution ...

Alex Misiats

2014-08-25

19

Approximating pi  

NSDL National Science Digital Library

This web page features mathematical information about Archimedes' successful approach to finding an approximation to pi and an interactive manipulative that replicates the approach. The user can approximate pi as a number between the lengths of the perimeters of two polygons, one inscribed inside a circle and one circumscribed around the circle. The number of sides for the polygons may be increased to 96 with the value for pi always being between the two approximations. Similarities and differences between Archimedes' approach and the manipulative's approach are noted. The page is part of a NOVA web site that describes the discovery of the Archimedes palimpsest and examines the mathematical and philosophical meanings of infinity. Copyright 2005 Eisenhower National Clearinghouse

British Broadcasting Corporation (BBC)

2003-01-01

20

Approximate (Euclidean)  

E-print Network

Approximate Nearest Neighbor in High Dimensions via Hashing Aris Gionis Piotr Indyk Rajeev Motwani­tree Guttman '84 LSD­tree Henrich, Six, Widmayer '89 R \\Lambda ­tree Beckmann, Kriegel et al '90 hB­tree Lomet #12; The curse of dimensionality ``Theorem:'' For dimensionality ``high enough'', any data structure

21

Introduction Approximating  

E-print Network

to predict forward model output from WRF grids 4 In real time, input WRF to NN, obtain satellite visible a Satellite Visible Image from Model Output Visualizing Model Data Using a Fast Approximation of a Radiative Transfer Model Valliappa Lakshmanan1,2 Robert Rabin2 Jason Otkin3 John Kain2 1Cooperative Institute

Lakshmanan, Valliappa

22

Wissenschaftliches Approximation  

E-print Network

' am Digitalcomputer Archimedes und die Berechnung von = 3.14159 . . . Das leidige Integral Das Einleitung: `Alles ist Zahl' am Digitalcomputer Archimedes und die Berechnung von = 3.14159 . . . Das Approximation als SparmaÃ?nahme Anhang Ã?berblick Einleitung: `Alles ist Zahl' am Digitalcomputer Archimedes und

Auzinger, Winfried

23

Stresses in a quasi-isotropic pin loaded connector using photoelasticity  

NASA Technical Reports Server (NTRS)

Birefringent glass-epoxy and a numerical stress separation scheme are used to compute the stresses in the vicinity of a pin-loaded hole. The radial and circumferential stresses at the hole edge, and the net section and shear-out stresses are computed. The numerical and experimental results are compared with the computed stresses. The fixture used to load the connector is discussed and typical isochromatic and isoclinic fringe patterns are presented. The stress-separation scheme is briefly discussed.

Hyer, M. W.; Liu, D. H.

1983-01-01

24

Elastic properties and fracture strength of quasi-isotropic graphite/epoxy composites  

NASA Technical Reports Server (NTRS)

The layups of the studied laminates are (0, + or - 60) sub s, (0, + or - 45, 90) sub s, (0, + or - 30, + or - 60, 90) sub s (0, + or - 22 1/2, + or - 45, + or - 67 1/2, 90) sub s. The properties determined were tensile modulus, Poisson's ratio, bending stiffness, fracture strength and fracture strain. Measured properties and properties predicted using laminate theory were found to be in reasonable agreement. Reasons for data scatter were determined.

Sullivan, T. L.

1977-01-01

25

Fast Approximate Convex Decomposition  

E-print Network

Approximate convex decomposition (ACD) is a technique that partitions an input object into "approximately convex" components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can...

Ghosh, Mukulika

2012-10-19

26

Approximation Via Value Unification  

Microsoft Academic Search

Numerical function approximation over a Boolean domain is a classical problem with wide application to data modeling tasks and various forms of learning. A great many function approximation algorithms have been devised over the years. Because the goal is to produce an approximating function that has low expected error, algorithms are typically guided by error reduction. This guiding force, to

Paul E. Utgoff; David J. Stracuzzi

1999-01-01

27

Quasi-isotropic Surface Plasmon Polariton Generation through Near-Field Coupling to a Penrose Pattern of Silver Nanoparticles.  

PubMed

Quasicrystals are structures that possess long-range order without being periodic. We investigate the unique characteristics of a photonic quasicrystal that consists of plasmonic Ag nanodisks arranged in a Penrose pattern. The quasicrystal scatters light in a complex but spectacular diffraction pattern that can be directly imaged in the back focal plane of an optical microscope, allowing us to assess the excitation efficiency of the various diffraction modes. Furthermore, surface plasmon polaritons can be launched almost isotropically through near-field grating coupling when the quasicrystal is positioned close to a homogeneous silver surface. We characterize the dispersion relation of the different excited plasmon modes by reflection measurements and simulations. It is demonstrated that the quasicrystal in-coupling efficiency is strongly enhanced compared to a nanoparticle array with the same particle density but only short-range lateral order. We envision that the system can be useful for a number of advanced light harvesting and optoelectronic applications. PMID:25182843

Verre, Ruggero; Antosiewicz, Tomasz J; Svedendahl, Mikael; Lodewijks, Kristof; Shegai, Timur; Käll, Mikael

2014-09-23

28

Two-Dimensional Imaging of Selected Ply Orientations in Quasi-Isotropic Composite Laminates Using Polar Backscattering  

Microsoft Academic Search

The polar backscatter technique of Bar-Cohen and Crane offers the potential of selectively interrogating plies of a single orientation in composite material composed of lamina exhibiting multiple orientations. In this work we report an application of this novel measurement technique to quantitative two-dimensional imaging of impact and fatigue damage in graphite epoxy composite materials. For each composite investigated, 4 images

Eric I. Madaras; J. G. Miller

1982-01-01

29

Compound Poisson process approximation  

Microsoft Academic Search

Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications are

A. D. Barbour; Marianne Månsson

2002-01-01

30

Approximation of Hopf bifurcation  

Microsoft Academic Search

Summary We make several assumptions on a nonlinear evolution problem, ensuring the existence of a Hopf bifurcation. Under a fairly general approximation condition, we define a discrete problem which retains the bifurcation property and we prove an error estimate between the branches of exact and approximate periodic solutions.

C. Bernardi; M. Curie

1982-01-01

31

Constructive Function Approximation1  

Microsoft Academic Search

The problem of automatically constructing features for use in a learned evaluation function is visited. Issues of feature overlap, independence, and coverage are addressed. Three algorithms are applied to two tasks, measuring the error in the approximated function as learning proceeds. The issues are discussed in the context of their apparent effects on the function approximation pro cess.

Paul E. Utgoff; Doina Precup

32

Approximate spatial reasoning  

NASA Technical Reports Server (NTRS)

A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning.

Dutta, Soumitra

1988-01-01

33

APPROXIMATE CHEMISTRY 113  

E-print Network

APPROXIMATE CHEMISTRY 113 Spring 2014 Forensic Science Professors James T. Spencer (jtspence SKILLS: Chemistry 113, Forensic Science, is focused upon the application of scientific methods specifically relevant to crime detection and analysis will be presented. No prior chemistry instruction

Doyle, Robert

34

Tsunami Travel Time Approximation  

NSDL National Science Digital Library

Eric Grosfils, Pomona College Summary Students are asked to calculate approximate tsunami travel times across the Pacific basin. The assignment builds off of a lab introducing students to Spatial Analyst, and ...

Grosfils, Eric

35

Relative Value Function Approximation  

Microsoft Academic Search

A form of temporal difference learning is presented that learns the relative utility of states,instead of the absolute utility. This formulation backs up decisions instead of values, makingit possible to learn a simpler function for defining a decision-making policy. A nonlinearrelative value function can be learned without increasing the dimensionality of the inputs.Contents1 Introduction 12 Approximating Absolute Utility 13 Approximating

Doina Precup; Paul E. Utgoff

1997-01-01

36

Covariant approximation averaging  

E-print Network

We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.

Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph

2014-01-01

37

Approximate programmable quantum processors  

E-print Network

A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor to approximate a set of unitary operators to a specified level of precision. We measure how well an operation is performed by the process fidelity between the desired operation and the operation produced by the processor. We show how to find the program for a given processor that produces the best approximation of a particular unitary operation. We also place bounds on the dimension of the program space that is necessary to approximate a set of unitary operators to a specified level of precision.

Mark Hillery; Mario Ziman; Vladimir Buzek

2005-10-20

38

Covariant approximation averaging  

E-print Network

We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.

Eigo Shintani; Rudy Arthur; Thomas Blum; Taku Izubuchi; Chulwoo Jung; Christoph Lehner

2014-02-02

39

On Stochastic Approximation.  

ERIC Educational Resources Information Center

This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic…

Wolff, Hans

40

Multicriteria approximation through decomposition  

SciTech Connect

The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.

Burch, C. [Carnegie Mellon Univ., Pittsburgh, PA (United States). School of Computer Sciences]|[Sandia National Labs., Albuquerque, NM (United States); Krumke, S. [Univ. of Wuerzburg (Germany). Dept. of Computer Science; Marathe, M. [Los Alamos National Lab., NM (United States); Phillips, C. [Sandia National Labs., Albuquerque, NM (United States). Applied Mathematics Dept.; Sundberg, E. [Rutgers Univ., NJ (United States). Dept. of Computer Science]|[Sandia National Labs., Albuquerque, NM (United States)

1997-12-01

41

Extended Abstract Approximating Visibility  

E-print Network

for Figure 4 June 1, 2000, 21:3 #12;Franklin Approximating Visibility 7 Figure 6: Lake Champlain W Cell 2.2 Lake Champlain West The second test case was the £¥¤§¦¨£T©U£¥¤§¦A£ Lake Champlain West level-1 DEM from

Franklin, W. Randolph

42

Multicriteria approximation through decomposition  

SciTech Connect

The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of their technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. Their method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) the authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing; (2) they also show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.

Burch, C. [Carnegie Mellon Univ., Pittsburgh, PA (United States). School of Computer Science; Krumke, S. [Univ. of Wuerzburg (Germany). Dept. of Computer Science; Marathe, M. [Los Alamos National Lab., NM (United States); Phillips, C. [Sandia National Labs., Albuquerque, NM (United States). Applied Mathematics Dept.; Sundberg, E. [Rutgers Univ., NJ (United States). Dept. of Computer Science

1998-06-01

43

Optimizing the Zeldovich approximation  

NASA Technical Reports Server (NTRS)

We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment of phases in the nonlinear regime. We also report on the accuracy of particle positions and velocities produced by TZA.

Melott, Adrian L.; Pellman, Todd F.; Shandarin, Sergei F.

1994-01-01

44

Approximate strip packing  

SciTech Connect

We present an approximation scheme for strip-packing, or packing rectangles into a rectangle of fixed width and minimum height, a classical NP-hard cutting-stock problem. The algorithm finds a packing of n rectangles whose total height is within a factor of (1 + {epsilon}) of optimal, and has running time polynomial both in n and in 1/{epsilon}. It is based on a reduction to fractional bin-packing, and can be performed by 5 stages of guillotine cuts.

Kenyon, C. [CNRS, Lyon (France); Remila, E. [LASPI, Roanne (France)

1996-12-31

45

l ?Approximation via Subdominants  

Microsoft Academic Search

Given a vector u and a certain subset K of a real vector space E, the problem of l?-approximation involves determining an element u in K nearest to u in the sense of the l?-error norm. The subdominant u? of u is the upper bound (if it exists) of the set {x?K:x?u} (we let x?y if all coordinates of x

Victor Chepoi; Bernard Fichet

2000-01-01

46

Approximate option pricing  

SciTech Connect

As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.

Chalasani, P.; Saias, I. [Los Alamos National Lab., NM (United States); Jha, S. [Carnegie Mellon Univ., Pittsburgh, PA (United States)

1996-04-08

47

Exploring Machin's Approximation of Exploring Machin's Approximation of  

E-print Network

#12;Exploring Machin's Approximation of Precursors Method of Exhaustion `a la Archimedes Archimedes of Precursors Method of Exhaustion `a la Archimedes Archimedes of Syracuse ( 287­212 BC) approximated la Archimedes Archimedes of Syracuse ( 287­212 BC) approximated by the Method of Exhaustion: 3

Knaust, Helmut

48

Forms of Approximate Radiation Transport  

SciTech Connect

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.

BRUNNER, THOMAS A.

2002-06-01

49

Noncommutative lattices as finite approximations  

Microsoft Academic Search

Lattice discretizations of continuous manifolds are common tools used in a variety of physical contexts. Conventional discrete approximations, however, cannot capture all aspects of the original manifold, notably its topology. In this paper we discuss an approximation scheme due to Sorkin (1991) which correctly reproduces important topological aspects of continuum physics. The approximating topological spaces are partially ordered sets (posets),

A. P. Balachandran; G. Bimonte; E. Ercolessi; G. Landi; F. Lizzi; G. Sparano; P. Teotonio-Sobrinho

1996-01-01

50

Approximations of fractional Brownian motion  

E-print Network

Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.

Li, Yuqiang; 10.3150/10-BEJ319

2012-01-01

51

Networks for approximation and learning  

Microsoft Academic Search

The problem of the approximation of nonlinear mapping, (especially continuous mappings) is considered. Regularization theory and a theoretical framework for approximation (based on regularization techniques) that leads to a class of three-layer networks called regularization networks are discussed. Regularization networks are mathematically related to the radial basis functions, mainly used for strict interpolation tasks. Learning as approximation and learning as

T. Poggio; F. Girosi

1990-01-01

52

Approximate equivalence and approximate synchronization of metric transition systems  

Microsoft Academic Search

In this paper, we consider metric transition systems which are transition systems equipped with metrics for observation and synchronization labels. The existence of metrics leads to the introduction of two new concepts, (i) (epsi, delta)-approximate (bi)simulation of transition systems and (ii) approximate synchronization of transition systems. We show that the notion of (epsi, delta)-approximate (bi)simulation can be thought of as

A. Agung Julius; George J. Pappas

2006-01-01

53

Supporting Text Approximation of the Multinomial. Using Stirling's approximation  

E-print Network

Supporting Text Approximation of the Multinomial. Using Stirling's approximation n! (n/e)n 2n! . [S12] To calculate B L (^n) limN BN L (^n), we apply Stirling's formula to N!, n0!, and n1!, which that r Stirling's formula

Peterson, Carsten

54

Computer Science Approximately Uniform Random  

E-print Network

. Byers and Jeffrey Considine #12;Computer Science Motivation Data aggregation Approximations to COUNT sketches (Considine et al. 2004) Randomized algorithms e.g. randomized routing #12;Computer Science

Massachusetts at Amherst, University of

55

Fuzzy systems as universal approximators  

Microsoft Academic Search

The author shows that an additive fuzzy system can approximate any continuous function on a compact domain to any degree of accuracy. Fuzzy systems are dense in the space of continuous functions. The fuzzy system approximates the function by covering its graph with fuzzy patches in the input-output state space. Each fuzzy rule defines a fuzzy patch and connects commonsense

Bart Kosko

1992-01-01

56

) Hermite approximation for conic sections  

E-print Network

An O(h 2n ) Hermite approximation for conic sections Michael Floater SINTEF P.O. Box 124, Blindern 0314 Oslo, NORWAY November 1994, Revised March 1996 Abstract. Given a segment of a conic section order approximation, conic sections, splines §1. Introduction It was described in a recent paper [6

Floater, Michael S.

57

Fuzzy systems are universal approximators  

Microsoft Academic Search

The author proves that fuzzy systems are universal approximators. The Stone-Weierstrass theorem is used to prove that fuzzy systems with product inference, centroid defuzzification, and a Gaussian membership function are capable of approximating any real continuous function on a compact set to arbitrary accuracy. This result can be viewed as an existence theorem of an optimal fuzzy system for a

Li-Xin Wang

1992-01-01

58

Quasiclassical Born–Oppenheimer Approximations  

Microsoft Academic Search

We discuss several problems in quasiclassical physics for which approximate solutions were recently obtained by a new method, and which can also be solved by novel versions of the Born–Oppenheimer approximation. These cases include the so-called bouncing ball modes, low angular momentum states in perturbed circular billiards, resonant states in perturbed rectangular billiards, and whispering gallery modes. Some rare, special

Oleg Zaitsev; R. Narevich; R. E. Prange

2001-01-01

59

Approximate Correspondences in High Dimensions  

E-print Network

Pyramid intersection is an efficient method for computing an approximate partial matching between two sets of feature vectors. We introduce a novel pyramid embedding based on a hierarchy of non-uniformly shaped bins that ...

Grauman, Kristen

2006-06-15

60

Greedy approximation in convex optimization  

E-print Network

Jun 2, 2012 ... continuous functions. One more important argument that motivates us to ... In optimization theory an energy function E(x) is given and we should find an approximate ..... of matrices with nuclear norm not exceeding 1. We are ...

2012-06-02

61

method and approximate sparse inverses  

Microsoft Academic Search

Application of algebraic multigrid method and approximate sparse inverses are applied as preconditioners for large algebraic systems arising in approximation of diusion-reaction problems in 3-dimensional complex domains. Here we report the results of numerical experiments when using highly graded and locally rened meshes for problems with non-homogeneous and anisotropic coecien ts that have small features and almost singular solutions. For

Veselin Dobrev; Richard Ewing; Raytcho Lazarov; Joseph Pasciak

62

Fuzzy Systems as Universal Approximators  

Microsoft Academic Search

An additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. An additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input-output state space and averaging patches that overlap. The fuzzy system computes a conditional expectation E|Y|X| if we view the fuzzy sets as random

Bart Kosko

1994-01-01

63

Approximate Data Structures with Applications  

E-print Network

. INSERT(~) inserts i recursively into the appropriate Sk. If Sk was previously empty, it creates the data structure for Sk and recursively inserts k into T. DELETE(N) recursively deletes the element from the appropriate Sk. If Sk becomes empty... the same dynamic operations as the standard van Emde Boas data structure [28, 201, except that answers to queries are approximate. The variants support all operations in constant time provided the error of approximation is l/polylog(n), and in O...

Matias, Yossi; Vitter, Jeffrey Scott; Young, Neal E.

1994-01-01

64

Exponential approximations in optimal design  

NASA Technical Reports Server (NTRS)

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.

1990-01-01

65

Approximating random quantum optimization problems  

NASA Astrophysics Data System (ADS)

We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem k-body quantum satisfiability (k-QSAT) on large random graphs. As an approximation strategy, we optimize the solution space over “classical” product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are (i) the derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment; (ii) a demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects the structure of the solution space of random k-QSAT. Simulated annealing exhibits metastability in similar “hard” regions of parameter space; and (iii) a generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy “landscape” of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random k-QSAT in a two-dimensional energy-density-clause-density space.

Hsu, B.; Laumann, C. R.; Läuchli, A. M.; Moessner, R.; Sondhi, S. L.

2013-06-01

66

Heat pipe transient response approximation.  

SciTech Connect

A simple and concise routine that approximates the response of an alkali metal heat pipe to changes in evaporator heat transfer rate is described. This analytically based routine is compared with data from a cylindrical heat pipe with a crescent-annular wick that undergoes gradual (quasi-steady) transitions through the viscous and condenser boundary heat transfer limits. The sonic heat transfer limit can also be incorporated into this routine for heat pipes with more closely coupled condensers. The advantages and obvious limitations of this approach are discussed. For reference, a source code listing for the approximation appears at the end of this paper.

Reid, R. S. (Robert Stowers)

2001-01-01

67

An evaluation of the effects of stacking sequence and thickness on the fatigue life of quasi-isotropic graphite/epoxy laminates  

NASA Technical Reports Server (NTRS)

Notched and unnotched geometries at 16, 32, and 64-ply thicknesses of a 90/45/0-45 (ns) laminate and a 45/0/-45/90 (ns) laminate were tested in compression-compression fatigue. The fatigue life and the initiation, type, and progression of damage were determined. Interlaminar stresses generated at straight, free edges of axially loaded laminates were used to interpret the test results. The fatigue lives of the notched specimens did not appear to be a strong function of laminate stacking sequence or specimen thickness. The stress concentration at the hole dominated over the interlaminar stresses at the straight free edge. The unnotched specimens of the 90/45/0/-45 (ns) laminate with tensile interlaminar normal stresses delaminated more readily than did the 45/0/-45/90 (ns) laminate with compressive interlaminar normal stress. The life of the 16-ply unnotched specimens was lower than the 32- and 64-ply specimens. Delaminations were located at the interface where the maximum shear stress occurred regardless of the sense or magnitude of the interlaminar normal stress. An antibuckling fixture was effective in preventing out-of-plane motion without overconstraining the specimen.

Harris, C. E.; Morris, D. H.

1983-01-01

68

Approximate Parameterized Matching Carmit Hazay  

E-print Network

was a postdoctoral student at Bar-Ilan University; partially supported by the Israel Science Foun- dation Grant 282 applications in image processing and computational biology. For example, approximate parameterized matching,moshe}@cs.biu.ac.il The second author was partially supported by an IBM faculty award grant. § Brooklyn College of the City

Lewenstein, Moshe

69

Conic approximation of planar curves  

Microsoft Academic Search

An upper bound of the Hausdorff distance between planar curve and conic section can be expressed by the maximum norm of error function from the conic section to the planar curve (Comput. Aided Geomet. Design, 14 (1997) 135–151). With respect to the maximum norm we characterize the necessary and sufficient condition for the conic section to be optimal approximation of

Young Joon Ahn

2001-01-01

70

The WKB Approximation without Divergences  

E-print Network

In this paper, the WKB approximation to the scattering problem is developed without the divergences which usually appear at the classical turning points. A detailed procedure of complexification is shown to generate results identical to the usual WKB prescription but without the cumbersome connection formulas.

D. Cocolicchio; M. Viggiano

1997-10-01

71

Approximation Algorithms for Combinatorial Problems  

Microsoft Academic Search

Simple, polynomial-time, heuristic algorithms for finding approximate solutions to various polynomial complete optimization problems are analyzed with respect to their worst case behavior, measured by the ratio of the worst solution value that can be chosen by the algorithm to the optimal value. For certain problems, such as a simple form of the knapsack problem and an optimization problem based

David S. Johnson

1973-01-01

72

Approximation Algorithms for Combinatorial Problems  

Microsoft Academic Search

Simple, polynomial-time, heuristic algorithms for finding approximate solutions to various polynomial complete optimization problems are analyzed with respect to their worst case behavior, measured by the ratio of the worst solution value that can be chosen by the algorithm to the optimal value. For certain problems, such as a simple form of the knapsack problem and an optimization problem based

David S. Johnson

1974-01-01

73

Pythagorean Approximations and Continued Fractions  

ERIC Educational Resources Information Center

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…

Peralta, Javier

2008-01-01

74

Some issues of linguistic approximation  

Microsoft Academic Search

Summary form only given. Two of the most exemplary capabilities of the human mind are the capability of using perceptions in purposeful ways and the capability of approximating perceptions by statements in natural language. Understanding these capabilities and emulating them by machines is the crux of intelligent systems. To construct intelligent systems, we need to develop appropriate methodological tools for

George J. Klir

2004-01-01

75

Quantized mean-field approximation  

Microsoft Academic Search

An extension of the quantum–classical mean-field (MF) approximation is developed by application of quantized Hamilton dynamics (QHD) to the classical subsystem. The resulting quantized MF (QMF) approach supplements the classical position and momentum variables with higher order moments. In the limit of all moments exact quantum dynamics is achieved. Already with second order variables, QMF properly treats zero point energy

Craig Brooksby; Oleg V. Prezhdo

2001-01-01

76

Approximate dynamic programming for management  

E-print Network

Approximate dynamic programming for management of high-value spare parts Hugo Simao and Warren Jersey, USA Abstract Purpose ­ An aircraft manufacturer faces the problem of allocating inventory interest in managing high value, low volume spare parts which must be available to respond to low

Powell, Warren B.

77

Normal Approximation to Poisson Distribution  

NSDL National Science Digital Library

This applet, created by Ivo Dinov of the University of California, Los Angeles, demonstrates the normal approximation to the Poisson distribution. Users can set the rate, lambda, and the number of trials, n, and observe how the shape of the distribution changes. The Poisson distribution is shown in blue, and the Normal distribution is shown in red.

Dinov, Ivo

2009-01-14

78

APPROXIMATION CLASSES FOR ADAPTIVE METHODS  

Microsoft Academic Search

Adaptive Finite Element Methods (AFEM) are numerical proce- dures that approximate the solution to a partial differential equation (PDE) by piecewise polynomials on adaptively generated triangulations. Only re- cently has any analysis of the convergence of these methods (10, 13) or their rates of convergence (2) become available. In the latter paper it is shown that a certain AFEM for

Peter Binev; Wolfgang Dahmen; Ronald DeVore; Pencho Petrushev

2002-01-01

79

Linear approximations of nonlinear systems  

NASA Technical Reports Server (NTRS)

A method for designing an automatic flight controller for short and vertical takeoff aircraft is presently being developed at NASA Ames Research Center. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system, called the modified tangent model, was recently introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this an approximation of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x(0) yields the same modified tangent model.

Hunt, L. R.; Su, R.

1983-01-01

80

One sign ion mobile approximation  

NASA Astrophysics Data System (ADS)

The electrical response of an electrolytic cell to an external excitation is discussed in the simple case where only one group of positive and negative ions is present. The particular case where the diffusion coefficients of the negative ions, Dm, is very small with respect to that of the positive ions, Dp, is considered. In this framework, it is discussed under what conditions the one mobile approximation, in which the negative ions are assumed fixed, works well. The analysis is performed by assuming that the external excitation is sinusoidal with circular frequency ?, as that used in the impedance spectroscopy technique. In this framework, we show that there exists a circular frequency, ?*, such that for ? > ?*, the one mobile ion approximation works well. We also show that for Dm << Dp, ?* is independent of Dm.

Barbero, G.

2011-12-01

81

Simulating bioterrorism through epidemiology approximation  

Microsoft Academic Search

Bioterrorism represents a significant threat to society. The lack of successful attacks that have resulted in true epidemics have created a need for data that can be generated from existing known factors. We have taken the popular susceptible-infected-recovery model and created a hybridized model that balances the simplicity of the original with an approximation of what more complex agent-based models

Ryan Layfield; Murat Kantarcioglu; Bhavani M. Thuraisingham

2008-01-01

82

Finite approximations in fluid mechanics  

Microsoft Academic Search

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

Hirschel

1986-01-01

83

Simultaneous approximation by greedy algorithms  

Microsoft Academic Search

We study nonlinear m-term approximation with regard to a redundant dictionary D in a Hilbert space H. It is known that the Pure Greedy Algorithm (or, more generally, the Weak Greedy Algorithm) provides for each f 2 H and any dictionary D an expansion into a series f = 1 X j=1 cj(f)'j(f); 'j(f) 2 D; j = 1;2;::: with

Dany Leviatan; Vladimir N. Temlyakov

2006-01-01

84

Approximate calculations for heat exchangers  

Microsoft Academic Search

Estimates were developed for the total heat transfer coefficient for various types of heat exchangers. These estimates were not meant to replace more accurate calculations for individual heat exchangers, but to provide quick approximations for situations in which great accuracy was not required. The heat transfer coefficients k (in kcal\\/m²\\/hr\\/°C) were calculated based on assumed average values for input and

Matz

2008-01-01

85

Best Approximation with Walsh Atoms  

Microsoft Academic Search

.    We consider the approximation in L\\u000a \\u000a 2\\u000a \\u000a R of a given function using finite linear combinations of Walsh atoms, which are Walsh functions localized to dyadic intervals,\\u000a also called Haar—Walsh wavelet packets. It is shown that up to a constant factor, a linear combination of K atoms can be represented to relative error ? by a linear combination

L. F. Villemoes

1997-01-01

86

Computer Experiments for Function Approximations  

SciTech Connect

This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.

Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C

2007-10-15

87

Approximate reasoning using terminological models  

NASA Technical Reports Server (NTRS)

Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved.

Yen, John; Vaidya, Nitin

1992-01-01

88

Rotating wave approximation and entropy  

E-print Network

This paper studies composite quantum systems, like atom-cavity systems and coupled optical resonators, in the absence of external driving by resorting to methods from quantum field theory. Going beyond the rotating wave approximation, it is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the entropy operator and generates an irreversible time evolution. The vacuum state of the system is shown to evolve into a generalized coherent state exhibiting entanglement of the modes in which the counter-rotating terms are expressed. Possible consequences at observational level in quantum optics experiments are currently under study.

Andreas Kurcz; Antonio Capolupo; Almut Beige; Emilio Del Giudice; Giuseppe Vitiello

2010-01-22

89

Approximating distributions in stochastic learning.  

PubMed

On-line machine learning algorithms, many biological spike-timing-dependent plasticity (STDP) learning rules, and stochastic neural dynamics evolve by Markov processes. A complete description of such systems gives the probability densities for the variables. The evolution and equilibrium state of these densities are given by a Chapman-Kolmogorov equation in discrete time, or a master equation in continuous time. These formulations are analytically intractable for most cases of interest, and to make progress a nonlinear Fokker-Planck equation (FPE) is often used in their place. The FPE is limited, and some argue that its application to describe jump processes (such as in these problems) is fundamentally flawed. We develop a well-grounded perturbation expansion that provides approximations for both the density and its moments. The approach is based on the system size expansion in statistical physics (which does not give approximations for the density), but our simple development makes the methods accessible and invites application to diverse problems. We apply the method to calculate the equilibrium distributions for two biologically-observed STDP learning rules and for a simple nonlinear machine-learning problem. In all three examples, we show that our perturbation series provides good agreement with Monte-Carlo simulations in regimes where the FPE breaks down. PMID:22418034

Leen, Todd K; Friel, Robert; Nielsen, David

2012-08-01

90

Approximate simulation of quantum channels  

NASA Astrophysics Data System (ADS)

Earlier, we proved a duality between two optimizations problems [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.104.120501 104, 120501 (2010)]. The primary one is, given two quantum channels M and N, to find a quantum channel R such that R?N is optimally close to M as measured by the worst-case entanglement fidelity. The dual problem involves the information obtained by the environment through the so-called complementary channels M? and N?, and consists in finding a quantum channel R' such that R'?M? is optimally close to N?. It turns out to be easier to find an approximate solution to the dual problem in certain important situations, notably when M is the identity channel—the problem of quantum error correction—yielding a good near-optimal worst-case entanglement fidelity as well as the corresponding near-optimal correcting channel. Here we provide more detailed proofs of these results. In addition, we generalize the main theorem to the case where there are certain constraints on the implementation of R, namely, on the number of Kraus operators. We also offer a simple algebraic form for the near-optimal correction channel in the case M=id. For approximate error correction, we show that any ?-correctable channel is, up to appending an ancilla, ?-close to an exactly correctable one. We also demonstrate an application of our theorem to the problem of minimax state discrimination.

Bény, Cédric; Oreshkov, Ognyan

2011-08-01

91

Linear approximations of nonlinear systems  

NASA Technical Reports Server (NTRS)

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

Hunt, L. R.; Su, R.

1983-01-01

92

Communication: The distinguishable cluster approximation.  

PubMed

We present a method that accurately describes strongly correlated states and captures dynamical correlation. It is derived as a modification of coupled-cluster theory with single and double excitations (CCSD) through consideration of particle distinguishability between dissociated fragments, whilst retaining the key desirable properties of particle-hole symmetry, size extensivity, invariance to rotations within the occupied and virtual spaces, and exactness for two-electron subsystems. The resulting method, called the distinguishable cluster approximation, smoothly dissociates difficult cases such as the nitrogen molecule, with the modest N(6) computational cost of CCSD. Even for molecules near their equilibrium geometries, the new model outperforms CCSD. It also accurately describes the massively correlated states encountered when dissociating hydrogen lattices, a proxy for the metal-insulator transition, and the fully dissociated system is treated exactly. PMID:23862916

Kats, Daniel; Manby, Frederick R

2013-07-14

93

Wavelets and distributed approximating functionals  

NASA Astrophysics Data System (ADS)

A general procedure is proposed for constructing father and mother wavelets that have excellent time-frequency localization and can be used to generate entire wavelet families for use as wavelet transforms. One interesting feature of our father wavelets (scaling functions) is that they belong to a class of generalized delta sequences, which we refer to as distributed approximating functionals (DAFs). We indicate this by the notation wavelet-DAFs. Correspondingly, the mother wavelets generated from these wavelet-DAFs are appropriately called DAF-wavelets. Wavelet-DAFs can be regarded as providing a pointwise (localized) spectral method, which furnishes a bridge between the traditional global methods and local methods for solving partial differential equations. They are shown to provide extremely accurate numerical solutions for a number of nonlinear partial differential equations, including the Korteweg-de Vries (KdV) equation, for which a previous method has encountered difficulties (J. Comput. Phys. 132 (1997) 233).

Wei, G. W.; Kouri, D. J.; Hoffman, D. K.

1998-07-01

94

IONIS: Approximate atomic photoionization intensities  

NASA Astrophysics Data System (ADS)

A program to compute relative atomic photoionization cross sections is presented. The code applies the output of the multiconfiguration Dirac-Fock method for atoms in the single active electron scheme, by computing the overlap of the bound electron states in the initial and final states. The contribution from the single-particle ionization matrix elements is assumed to be the same for each final state. This method gives rather accurate relative ionization probabilities provided the single-electron ionization matrix elements do not depend strongly on energy in the region considered. The method is especially suited for open shell atoms where electronic correlation in the ionic states is large. Program summaryProgram title: IONIS Catalogue identifier: AEKK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1149 No. of bytes in distributed program, including test data, etc.: 12 877 Distribution format: tar.gz Programming language: Fortran 95 Computer: Workstations Operating system: GNU/Linux, Unix Classification: 2.2, 2.5 Nature of problem: Photoionization intensities for atoms. Solution method: The code applies the output of the multiconfiguration Dirac-Fock codes Grasp92 [1] or Grasp2K [2], to compute approximate photoionization intensities. The intensity is computed within the one-electron transition approximation and by assuming that the sum of the single-particle ionization probabilities is the same for all final ionic states. Restrictions: The program gives nonzero intensities for those transitions where only one electron is removed from the initial configuration(s). Shake-type many-electron transitions are not computed. The ionized shell must be closed in the initial state. Running time: Few seconds for a large problem with a few thousand configurations.

Heinäsmäki, Sami

2012-02-01

95

Approximate analytic solutions to the NPDD: Short exposure approximations  

NASA Astrophysics Data System (ADS)

There have been many attempts to accurately describe the photochemical processes that take places in photopolymer materials. As the models have become more accurate, solving them has become more numerically intensive and more 'opaque'. Recent models incorporate the major photochemical reactions taking place as well as the diffusion effects resulting from the photo-polymerisation process, and have accurately described these processes in a number of different materials. It is our aim to develop accessible mathematical expressions which provide physical insights and simple quantitative predictions of practical value to material designers and users. In this paper, starting with the Non-Local Photo-Polymerisation Driven Diffusion (NPDD) model coupled integro-differential equations, we first simplify these equations and validate the accuracy of the resulting approximate model. This new set of governing equations are then used to produce accurate analytic solutions (polynomials) describing the evolution of the monomer and polymer concentrations, and the grating refractive index modulation, in the case of short low intensity sinusoidal exposures. The physical significance of the results and their consequences for holographic data storage (HDS) are then discussed.

Close, Ciara E.; Sheridan, John T.

2014-04-01

96

Approximation techniques in strongly correlated electron systems  

Microsoft Academic Search

This dissertation details the study and application of three approximation techniques for strongly correlated electron systems. These techniques are the dynamical mean field approximation (DMFA), dynamical cluster approximation (DCA) and cellular dynamical mean field theory (CDMFT). The DMFA is a local approximation in which electron-electron correlations are only dynamical in time and all non-local correlations in space are suppressed. This

Karan Aryanpour

2003-01-01

97

Adiabatic approximations to internal rotation  

NASA Astrophysics Data System (ADS)

A number of subtle and confusing issues are addressed concerning large amplitude motion (LAM) coordinates (?) for internal molecular motions, using the methyl rotation in acetaldehyde (CH3CHO) as a model problem. If the LAM coordinate is chosen to be one of the H-C-C-O dihedral angles ?1, ?2, or ?3, it lacks the required 2?/3 periodicity, and its use is thus undesirable. An excellent local internal coordinate for this model problem is ?3=1/3(?1+?2+?3-2?). A similarly good but nonlocal coordinate for the adiabatic approximation of internal rotation is provided by the intrinsic reaction coordinate s. Comparison of the mass-independent V0(?3) and the mass-dependent V0(s) internal rotation curves shows that the two are virtually identical for the parent isotopolog of acetaldehyde. A unified internal coordinate projection scheme for determining complementary vibrational frequencies and subsequently VZPVE(?) along a path for LAM has been formulated, where VZPVE(?) is the zero-point vibrational energy correction to the internal rotation curve. In addition to its simplicity, the projection scheme developed for a distinguished reaction path generated by constrained optimizations is appealing because the vibrational frequencies along the LAM path are invariant to chemically meaningful choices of the internal coordinates for the complementary modes.

Allen, Wesley D.; Bodi, Andras; Szalay, Viktor; Császár, Attila G.

2006-06-01

98

Femtolensing: Beyond the semiclassical approximation  

NASA Technical Reports Server (NTRS)

Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths.

Ulmer, Andrew; Goodman, Jeremy

1995-01-01

99

SPECTRALLY INVARIANT APPROXIMATIONS WITHIN ATMOSPHERIC RADIATIVE TRANSFER  

E-print Network

SPECTRALLY INVARIANT APPROXIMATIONS WITHIN ATMOSPHERIC RADIATIVE TRANSFER Alexander Marshak, NASA "spectrally invariant relationships" and are the consequence of wavelength independence of the extinction invariant approximation can accurately describe the extinction and scattering properties of cloudy

100

Approximate Uniqueness Estimates for Singular Correlation Matrices.  

ERIC Educational Resources Information Center

The residual variance is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is presented for the case when the correlation matrix is singular. (Author/JKS)

Finkbeiner, C. T.; Tucker, L. R.

1982-01-01

101

Comparison of two Pareto frontier approximations  

NASA Astrophysics Data System (ADS)

A method for comparing two approximations to the multidimensional Pareto frontier in nonconvex nonlinear multicriteria optimization problems, namely, the inclusion functions method is described. A feature of the method is that Pareto frontier approximations are compared by computing and comparing inclusion functions that show which fraction of points of one Pareto frontier approximation is contained in the neighborhood of the Edgeworth-Pareto hull approximation for the other Pareto frontier.

Berezkin, V. E.; Lotov, A. V.

2014-09-01

102

NURBS Curve Approximation Using Particle Swarm Optimization  

Microsoft Academic Search

This paper presents curve approximation problem using Particle Swarm Optimization (PSO). The proposed algorithm will be used to develop a skinning surface with PSO to keep the number of surface control points minimum. The experiments are conducted on various parameterization methods for approximating the curves. By implementing PSO on NURBS curve approximation, the weights of the curve can be adjusted

D. I. S. Adi; S. M. b. Shamsuddin; Siti Zaiton Mohd Hashim

2010-01-01

103

On Approximation of Distribution and Density Functions.  

ERIC Educational Resources Information Center

Stochastic approximation algorithms for least square error approximation to density and distribution functions are considered. The main results are necessary and sufficient parameter conditions for the convergence of the approximation processes and a generalization to some time-dependent density and distribution functions. (Author)

Wolff, Hans

104

Efficient Analytic Approximation of American Option Values  

Microsoft Academic Search

This paper provides simple analytic approximations for pricing exchange-traded American call and put options written on commodities and commodity futures contracts. These approximations are accurate and considerably more computationally efficient than finite- difference, binomial, or compound-option approximation methods. Copyright 1987 by American Finance Association.

Giovanni Barone-Adesi; Robert E. Whaley

1987-01-01

105

DISTRIBUTED VERIFICATION AND HARDNESS OF DISTRIBUTED APPROXIMATION  

E-print Network

DISTRIBUTED VERIFICATION AND HARDNESS OF DISTRIBUTED APPROXIMATION ATISH DAS SARMA, STEPHAN HOLZER on the hardness of distributed approximation for many classical optimization problems including minimum spanning the previous hardness of approximation bound of Elkin [STOC 2004] as well as the lower bound for (exact) MST

106

On the hardness of approximating minimization problems  

Microsoft Academic Search

We prove results indicating that it is hard to compute efficiently good approximate solutions to the Graph Coloring, Set Covering and other related minimization problems. Specifi- cally, there is an E > 0 such that Graph Coloring cannot be approximated with ratio n' unless P = NP. Set Covering cannot be approximated with ratio c log n for any c

Carsten Lund; Mihalis Yannakakis

1993-01-01

107

Approximating Tail Areas of Probability Distributions  

Microsoft Academic Search

A general method for approximating tail areas is developed through an extension of the methodology of Andrews. This extension is applied to both continuous and discrete distributions. Examples of the approximations are given for the standard normal, $t$, and chi-square distributions in the continuous case and for the Poisson and binomial distributions in the discrete case. Errors of the approximations

Alan J. Gross; David W. Hosmer

1978-01-01

108

Planar curve offset based on circle approximation  

Microsoft Academic Search

An algorithm is presented to approximate planar offset curves within an arbitrary tolerance ?> 0. Given a planar parametric curve C(t) and an offset radius r, the circle of radius r is first approximated by piecewise quadratic Bezier curve segments within the tolerance ? . The exact offset curve Cr(t) is then approximated by the convolution of C(t) with the

In-kwon Lee; Myung-soo Kim; Gershon Elber

1996-01-01

109

More on approximations of Poisson probabilities  

SciTech Connect

Calculation of Poisson probabilities frequently involves calculating high factorials, which becomes tedious and time-consuming with regular calculators. The usual way to overcome this difficulty has been to find approximations by making use of the table of the standard normal distribution. A new transformation proposed by Kao in 1978 appears to perform better for this purpose than traditional transformations. In the present paper several approximation methods are stated and compared numerically, including an approximation method that utilizes a modified version of Kao's transformation. An approximation based on a power transformation was found to outperform those based on the square-root type transformations as proposed in literature. The traditional Wilson-Hilferty approximation and Makabe-Morimura approximation are extremely poor compared with this approximation. 4 tables. (RWR)

Kao, C

1980-05-01

110

Motivation Approximations Shift-Resolve Parsing Ambiguity Detection Conclusion Approximating Context-Free  

E-print Network

Motivation Approximations Shift-Resolve Parsing Ambiguity Detection Conclusion Approximating Context-Free Grammars for Parsing and Verification Sylvain Schmitz LORIA, INRIA Nancy - Grand Est October 18, 2007 #12;Motivation Approximations Shift-Resolve Parsing Ambiguity Detection Conclusion A Syntax

Paris-Sud XI, Université de

111

Practical VTI approximations: a systematic anatomy  

NASA Astrophysics Data System (ADS)

Transverse isotropy (TI) with a vertical symmetry axis (VTI) often provides an appropriate earth model for prestack imaging of steep-dip reflection seismic data. Exact P-wave and SV-wave phase velocities in VTI media are described by complicated equations requiring four independent parameters. Estimating appropriate multiparameter earth models can be difficult and time-consuming, so it is often useful to replace the exact VTI equations with simpler approximations requiring fewer parameters. The accuracy limits of different previously published VTI approximations are not always clear, nor is it always obvious how these different approximations relate to each other. Here I present a systematic framework for deriving a variety of useful VTI approximations. I develop first a sequence of well-defined approximations to the exact P-wave and SV-wave phase velocities. In doing so, I show how the useful but physically questionable heuristic of setting shear velocities identically to zero can be replaced with a more precise and quantifiable approximation. The key here to deriving accurate approximations is to replace the stiffness a13 with an appropriate factorization in terms of velocity parameters. Two different specific parameter choices lead to the P-wave approximations of Alkhalifah (Geophysics 63 (1998) 623) and Schoenberg and de Hoop (Geophysics 65 (2000) 919), but there are actually an infinite number of reasonable parametrizations possible. Further approximations then lead to a variety of other useful phase velocity expressions, including those of Thomsen (Geophysics 51 (1986) 1954), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Harlan (Stanford Exploration Project Report 89 (1995) 145), and Stopin (Stopin, A., 2001. Comparison of v(?) equations in TI medium. 9th International Workshop on Seismic Anisotropy). Each P-wave phase velocity approximation derived this way can be paired naturally with a corresponding SV-wave approximation. Each P-wave or SV-wave phase velocity approximation can then be converted into an equivalent dispersion relation in terms of horizontal and vertical slownesses. A simple heuristic substitution also allows each phase velocity approximation to be converted into an explicit group velocity approximation. From these, in turn, travel time or moveout approximations can also be derived. The group velocity and travel time approximations derived this way include ones previously used by Byun et al. (Geophysics 54 (1989) 1564), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Tsvankin and Thomsen (Geophysics 59 (1994) 1290), Harlan (89 (1995) 145), and Zhang and Uren (Zhang, F. and Uren, N., 2001. Approximate explicit ray velocity functions and travel times for P-waves in TI media. 71st Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 106-109).

Fowler, Paul J.

2003-12-01

112

A greedy algorithm for yield surface approximation  

NASA Astrophysics Data System (ADS)

This Note presents an approximation method for convex yield surfaces in the framework of yield design theory. The proposed algorithm constructs an approximation using a convex hull of ellipsoids such that the approximate criterion can be formulated in terms of second-order conic constraints. The algorithm can treat bounded as well as unbounded yield surfaces. Its efficiency is illustrated on two yield surfaces obtained using up-scaling procedures.

Bleyer, Jérémy; de Buhan, Patrick

113

Application of the GW Approximation to Trans -  

Microsoft Academic Search

The emphasis of the work described in this dissertation is the application of a many-body Greens function technique called the GW approximation. Pilot calculations have been performed implementing this technique on the quasi-one -dimensional system, trans-polyacetylene. Until recently, standard procedures for band structure calculations have been limited to approximations such as the Hartree-Fock or local density approximation in which electrons

Elana Chris Ethridge

1993-01-01

114

Approximation algorithms for directed Steiner problems  

Microsoft Academic Search

We give the first non-trivial approximation algorithms for the Steiner tree problem andthe generalized Steiner network problem on general directed graphs. These problems haveseveral applications in network design and multicast routing. For both problems, the bestratios known before our work were the trivial O(k)-approximations. For the directed Steinertree problem, we design a family of algorithms that achieves an approximation ratio

Moses Charikart Chandra Chekurit; Chandra Chekuri; To-yat Cheung; Zuo Dai; Ashish Goel; Sudipto Guha; Ming Li

1998-01-01

115

Approximate dynamic model of a turbojet engine  

NASA Technical Reports Server (NTRS)

An approximate dynamic nonlinear model of a turbojet engine is elaborated on as a tool in studying the aircraft control loop, with the turbojet engine treated as an actuating component. Approximate relationships linking the basic engine parameters and shaft speed are derived to simplify the problem, and to aid in constructing an approximate nonlinear dynamic model of turbojet engine performance useful for predicting aircraft motion.

Artemov, O. A.

1978-01-01

116

Discrete conformal approximation of complex earthquake maps.  

E-print Network

??Using the techniques of circle packing, we construct discrete conformal approximations for complex earthquake maps on the Teichmüller spaces of compact, hyperbolic Riemann surfaces developed… (more)

Murphy, Eric Michael

2005-01-01

117

Bent approximations to synchrotron radiation optics  

SciTech Connect

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.

Heald, S.

1981-01-01

118

Diffusion approximation of neuronal models revisited.  

PubMed

Leaky integrate-and-fire neuronal models with reversal potentials have a number of different diffusion approximations, each depending on the form of the amplitudes of the postsynaptic potentials. Probability distributions of the first-passage times of the membrane potential in the original model and its diffusion approximations are numerically compared in order to find which of the approximations is the most suitable one. The properties of the random amplitudes of postsynaptic potentials are discussed. It is shown on a simple example that the quality of the approximation depends directly on them. PMID:24245676

Cupera, Jakub

2014-02-01

119

Product Operation of Grade Upper Approximation Operator and Grade Lower Approximation Operator Based on Two Parameters  

Microsoft Academic Search

Grade is an important quantitative index, and graded rough set model is an important improved rough set model. The purpose of this paper is to explore product operation of grade approximation operators. Based on logical product operation of grade approximation operators, this paper proposes product operation of grade upper approximation operator and grade lower approximation operator based on two parameters.

Xianyong Zhang; Zhiwen Mo; Fang Xiong

2009-01-01

120

Approximate quantum data storage and teleportation  

Microsoft Academic Search

In this paper we present an optimal protocol by which an unknown state on a Hilbert space of dimension N can be approximately stored in an M-dimensional quantum system or be approximately teleported via an M-dimensional quantum channel. The fidelity of our procedure is determined for pure states as well as for mixed states and states that are entangled with

Thomas Laustsen; Klaus Mølmer

2002-01-01

121

Analytical long-wavelength approximation for parallelepipeds  

NASA Astrophysics Data System (ADS)

We suggest a new analytical long-wavelength approximation for rectangular parallelepipeds based on replacement of the internal field with a uniform one. The approximation is not quite accurate (the typical accuracy is of the order of about 10%) but is extremely simple and works in a sufficiently wide region of parameter values.

Farafonov, Victor G.; Il'in, Vladimir B.

2014-10-01

122

Approximate Bayesian Computation in Population Genetics  

Microsoft Academic Search

We propose a new method for approximate Bayesian statistical inference on the basis of summary statistics. The method is suited to complex problems that arise in population genetics, extending ideas developed in this setting by earlier authors. Properties of the posterior distribution of a parameter, such as its mean or density curve, are approximated without explicit likelihood calculations. This is

Mark A. Beaumont; Wenyang Zhang; David J. Balding

2002-01-01

123

SEMIMARTINGALE STOCHASTIC APPROXIMATION PROCEDURE AND RECURSIVE ESTIMATION  

Microsoft Academic Search

The semimartingale stochastic approximation procedure, na- mely, the Robbins-Monro type SDE is introduced which naturally includes both generalized stochastic approximation algorithms with martingale no- ises and recursive parameter estimation procedures for statistical models associated with semimartingales. General results concerning the asymp- totic behaviour of the solution are presented. In particular, the conditions ensuring the convergence, rate of convergence and asymptotic

N. LAZRIEVA; T. SHARIA; T. TORONJADZE

2007-01-01

124

Semimartingale Stochastic Approximation Procedures and Recursive Estimation  

Microsoft Academic Search

The semimartingale stochastic approximation procedure, namely, the Robbins-Monro type SDE is introduced which naturally includes both generalized stochastic approximation algorithms with martingale noises and recursive parameter estimation procedures for statistical models associated with semimartingales. General results concerning the asymptotic behaviour of the solution are presented. In particular, the conditions ensuring the convergence, rate of convergence and asymptotic expansion are established.

N. Lazrieva; T. Sharia; T. Toronjadze

2007-01-01

125

Semimartingale stochastic approximation procedure and recursive estimation  

Microsoft Academic Search

UDC 519.2 Abstract. The semimartingale stochastic approximation procedure, precisely, the Robbins-Monro type SDE, is introduced, which naturally includes both generalized stochastic approximation algorithms with martingale noises and recursive parameter estimation procedures for statistical models associated with semimartingales. General results concerning the asymptotic behavior of the solution are presented. In particular, the conditions ensuring the convergence, the rate of convergence, and

N. Lazrieva; T. Sharia; T. Toronjadze

2008-01-01

126

Computing Functions by Approximating the Input  

ERIC Educational Resources Information Center

In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…

Goldberg, Mayer

2012-01-01

127

Improved Distributed Approximate Matching Department of Communication  

E-print Network

@umich.edu ABSTRACT We present improved algorithms for finding approximately optimal matchings in both weighted. In the context of weighted graphs, we give another algorithm which provides (1 2 - ) approximation in general intrinsic posi- tive "weights," and matching of the largest possible weight is sought. For example

Patt-Shamir, Boaz

128

APPROXIMATION OF HUNT PROCESSES BY MULTIVARIATE  

E-print Network

APPROXIMATION OF HUNT PROCESSES BY MULTIVARIATE POISSON PROCESSES Zhi­Ming Ma 1); 2) Michael R¨ ockner 2) Wei Sun 1) Abstract We prove that arbitrary Hunt processes on a general state space can. Running Title: Approximation of Hunt processes Key words: Hunt process, multivariate Poisson process, weak

Bielefeld, University of

129

A contamination model for approximate stochastic order.  

E-print Network

satisfy the stochastic ordering. The minimal level of contam- ination that makes this approximate modelA contamination model for approximate stochastic order. Pedro C. ´Alvarez-Esteban1 , E. del Barrio1 to believe that a certain variable is somehow smaller than other. Instead of considering this rigid model

Cuesta, Juan Antonio

130

Approximately J ? -homomorphisms: A fixed point approach  

Microsoft Academic Search

The functional equation (?) is stable if any function g satisfying the equation (?)approximately is near to the true solution of (?). A functional equation is superstable if every solution satisfying the equation approximately is an exact solution of it. Using fixed point methods, we prove the stability and superstability of J?-homomorphisms between J?-algebras for the generalized Jensen-type functional equation

M. Eshaghi Gordji; A. Najati

2010-01-01

131

Gutzwiller approximation in strongly correlated electron systems  

Microsoft Academic Search

Gutzwiller wave function is an important theoretical technique for treating local electron-electron correlations nonperturbatively in condensed matter and materials physics. It is concerned with calculating variationally the ground state wave function by projecting out multi-occupation configurations that are energetically costly. The projection can be carried out analytically in the Gutzwiller approximation that offers an approximate way of calculating expectation values

Chunhua Li

2009-01-01

132

Normal Approximation to the Binomial Distribution  

NSDL National Science Digital Library

This demonstration, by David M. Lane of Rice University, allows you to view the binomial distribution and the normal approximation to it as a function of the probability of a success on a given trial and the number of trials. It can be used to compute binomial probabilities and normal approximations of those probabilities.

Lane, David M.

2009-07-07

133

A General Greedy Approximation Algorithm with Applications  

E-print Network

A General Greedy Approximation Algorithm with Applications Tong Zhang IBM T.J. Watson Research Center Yorktown Heights, NY 10598 tzhang@watson.ibm.com Abstract Greedy approximation algorithms have a general greedy algorithm for solving a class of convex optimization problems. We derive a bound

Zhang, Tong

134

Greedy Algorithm and m Term Trigonometric Approximation  

Microsoft Academic Search

.    We study the following nonlinear method of approximation by trigonometric polynomials in this paper. For a periodic function\\u000a f we take as an approximant a trigonometric polynomial of the form , where is a set of cardinality m containing the indices of the m biggest (in absolute value) Fourier coefficients of function f . We compare the efficiency

V. N. Temlyakov

1998-01-01

135

Approximation algorithms for facility location (Extended Abstract)  

E-print Network

Approximation algorithms for facility location problems (Extended Abstract) David B. Shmoys # â?? Eva facility location problems. In each facility location problem that we study, there is a set of locations approximation algorithms for a variety of facility location problems. One of the most well­studied problems

Tardos, Ã?va

136

Approximation algorithms for facility location problems  

E-print Network

Approximation algorithms for facility location problems David B. Shmoys \\Lambda ' Eva Tardos y. In each facility location problem that we study, there is a set of locations at which we may build approximation algorithms for a variety of facility location problems. One of the most well­studied problems

Utrecht, Universiteit

137

Notion of p-value Parametric Approximations  

E-print Network

Power of a test ROC and AUC Example with GWAS G. NUEL Significance of an Observation in Post with GWAS G. NUEL Significance of an Observation in Post-Genomics #12;Notion of p-value Parametric Approximations Gumbel Approximations 3 Power Power of a test ROC and AUC Example with GWAS G. NUEL Significance

Nuel, Gregory

138

Approximative solutions of best choice Andreas Faller  

E-print Network

probability v was identified as optimal choice probability in an associated plane Poisson process on [0, 1 processes in the plane to a Poisson process we establish that the optimal choice problem can be approximated by the optimal choice problem in the limiting Poisson process. This allows to derive approximations

Rüschendorf, Ludger

139

On the Approximability of Dense Steiner Problems  

E-print Network

On the Approximability of Dense Steiner Problems M. Hauptmann #3; February 15, 2008 Abstract The #15;-Dense Steiner Tree Problem was de#12;ned by Karpinski and Zelikovsky [11] who proved of various Steiner Tree problems. In particular, we give polynomial time approximation schemes for the #15

Eckmiller, Rolf

140

Approximate Confidence Computation in Probabilistic Databases  

E-print Network

Approximate Confidence Computation in Probabilistic Databases Dan Olteanu1 , Jiewen Huang1 be effectively used to compute approximate confidence values of answer tuples to positive relational algebra tune our algorithm so as to capture all known tractable conjunctive queries without self- joins

Oxford, University of

141

Approximate error conjugation gradient minimization methods  

DOEpatents

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.

Kallman, Jeffrey S

2013-05-21

142

Frankenstein's Glue: Transition functions for approximate solutions  

E-print Network

Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate solutions together. In particular, we propose certain sufficient conditions on these functions and proof that these conditions guarantee that the joined solution still satisfies the Einstein equations to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the proposed conditions, the joined solution does not contain any violations to the Einstein equations larger than those already inherent in the approximations. We further show that if these functions violate the proposed conditions, then the matter content of the spacetime is modified by the introduction of a matter-shell, whose stress-energy tensor depends on derivatives of these functions.

Nicolas Yunes

2006-11-23

143

Wave-mechanics and the adhesion approximation  

E-print Network

The dynamical equations describing the evolution of a self-gravitating fluid of cold dark matter (CDM) can be written in the form of a Schrodinger equation coupled to a Poisson equation describing Newtonian gravity. It has recently been shown that, in the quasi-linear regime, the Schrodinger equation can be reduced to the exactly solvable free-particle Schrodinger equation. The free-particle Schrodinger equation forms the basis of a new approximation scheme -the free-particle approximation - that is capable of evolving cosmological density perturbations into the quasi-linear regime. The free-particle approximation is essentially an alternative to the adhesion model in which the artificial viscosity term in Burgers' equation is replaced by a non-linear term known as the quantum pressure. Simple one-dimensional tests of the free-particle method have yielded encouraging results. In this paper we comprehensively test the free-particle approximation in a more cosmologically relevant scenario by appealing to an N-body simulation. We compare our results with those obtained from two established methods: the linearized fluid approach and the Zeldovich approximation. We find that the free-particle approximation comprehensively out-performs both of these approximation schemes in all tests carried out and thus provides another useful analytical tool for studying structure formation on cosmological scales.

C. J. Short; P. Coles

2006-04-29

144

Wave mechanics and the adhesion approximation  

NASA Astrophysics Data System (ADS)

The dynamical equations describing the evolution of a self-gravitating fluid of cold dark matter (CDM) can be written in the form of a Schrödinger equation coupled to a Poisson equation describing Newtonian gravity. It has recently been shown that, in the quasi-linear regime, the Schrödinger equation can be reduced to the exactly solvable free-particle Schrödinger equation. The free-particle Schrödinger equation forms the basis of a new approximation scheme—the free-particle approximation—that is capable of evolving cosmological density perturbations into the quasi-linear regime. The free-particle approximation is essentially an alternative to the adhesion model in which the artificial viscosity term in Burgers' equation is replaced by a non-linear term known as the quantum pressure. Simple one-dimensional tests of the free-particle method have yielded encouraging results. In this paper we comprehensively test the free-particle approximation in a more cosmologically relevant scenario by appealing to an N-body simulation. We compare our results with those obtained from two established methods: the linearized fluid approach and the Zeldovich approximation. We find that the free-particle approximation comprehensively out-performs both of these approximation schemes in all tests carried out and thus provides another useful analytical tool for studying structure formation on cosmological scales.

Short, C. J.; Coles, P.

2006-12-01

145

Approximate knowledge compilation: The first order case  

SciTech Connect

Knowledge compilation procedures make a knowledge base more explicit so as make inference with respect to the compiled knowledge base tractable or at least more efficient. Most work to date in this area has been restricted to the propositional case, despite the importance of first order theories for expressing knowledge concisely. Focusing on (LUB) approximate compilation, our contribution is twofold: (1) We present a new ground algorithm for approximate compilation which can produce exponential savings with respect to the previously known algorithm. (2) We show that both ground algorithms can be lifted to the first order case preserving their correctness for approximate compilation.

Val, A. del [Universidad Autonoma de Madrid (Spain)

1996-12-31

146

Learning Approximate Sequential Patterns for Classification  

E-print Network

In this paper, we present an automated approach to discover patterns that can distinguish between sequences belonging to different labeled groups. Our method searches for approximately conserved motifs that occur with ...

Syed, Zeeshan

147

Local graph partitions for approximation and testing  

E-print Network

We introduce a new tool for approximation and testing algorithms called partitioning oracles. We develop methods for constructing them for any class of bounded-degree graphs with an excluded minor, and in general, for any ...

Hassidim, Avinatan

148

Approximating the Permanent with Fractional Belief Propagation  

E-print Network

We discuss schemes for exact and approximate computations of permanents, and compare them with each other. Specifically, we analyze the belief propagation (BP) approach and its fractional belief propagation (FBP) generalization ...

Yedidia, Adam B.

149

Shape Approximation in Kinematic Systems Ernest Davis #  

E-print Network

, Philip Davis, Drew McDermott, Bud Mishra, Igor Najfeld, Chee Yap, and Ken Yip. 1 #12; calculations basedShape Approximation in Kinematic Systems Ernest Davis # New York University 251 Mercer St. New York

Davis, Ernest

150

Linear Approximation SAR Azimuth Processing Study  

NASA Technical Reports Server (NTRS)

A segmented linear approximation of the quadratic phase function that is used to focus the synthetic antenna of a SAR was studied. Ideal focusing, using a quadratic varying phase focusing function during the time radar target histories are gathered, requires a large number of complex multiplications. These can be largely eliminated by using linear approximation techniques. The result is a reduced processor size and chip count relative to ideally focussed processing and a correspondingly increased feasibility for spaceworthy implementation. A preliminary design and sizing for a spaceworthy linear approximation SAR azimuth processor meeting requirements similar to those of the SEASAT-A SAR was developed. The study resulted in a design with approximately 1500 IC's, 1.2 cubic feet of volume, and 350 watts of power for a single look, 4000 range cell azimuth processor with 25 meters resolution.

Lindquist, R. B.; Masnaghetti, R. K.; Belland, E.; Hance, H. V.; Weis, W. G.

1979-01-01

151

Moment approximations for set-semidefinite polynomials  

E-print Network

Jun 1, 2012 ... can provide a new outer approximation hierarchy based on the completely positive moment matrices, .... In this section we recall basic definitions and concepts from the moment theory. .... For this we will first need to recall.

Peter J.C. Dickinson

2012-06-01

152

Computational aspects of pseudospectral Laguerre approximations  

NASA Technical Reports Server (NTRS)

Pseudospectral approximations in unbounded domains by Laguerre polynomials lead to ill-conditioned algorithms. Introduced are a scaling function and appropriate numerical procedures in order to limit these unpleasant phenomena.

Funaro, Daniele

1989-01-01

153

Approximate analytical solution of Blasius' equation  

NASA Astrophysics Data System (ADS)

The Blasius' equation, with boundary conditions, is studied in this paper. An approximate analytical solution is obtained via the variational iteration method. The comparison with Howarth's numerical solution reveals that the proposed method is of high accuracy.

He, Jihuan

1999-03-01

154

NEW APPROXIMATIONS FOR THE CONE OF COPOSITIVE ...  

E-print Network

inner and outer approximations have a very simple interpretation. Finally, ... degree at most d, which forms a vector space of dimension s(d) = (n+d d. ) ..... ness and optimization, Ph.D. Dissertation, California Institute of Technology, 2000.

2010-12-12

155

The Hardness of Approximation: Gap Location  

Microsoft Academic Search

. We refine the complexity analysis of approximation problems by relating it to a new parameter called gap location. Many of the results obtained so far for approximations yield satisfactory analysis with respect to this refined parameter, but some known results (e.g., maxk-colorability, max 3-dimensional matching and max not-allequal 3sat) fall short of doing so. As a second contribution, our

Erez Petrank

1994-01-01

156

Transient queueing approximations for computer networks  

E-print Network

for just the mean. Rothkopf/Oren's and Chang/Wang's methods obtained mean and variance values, and Clark's method produced several quantities which were used to find mean and variance statistics. For the M/M/1 case, the approximations by Gark and Chang... were very ac- curate over a wide range of input patterns and initial conditions. Rothkopf's was accurate over sll conditions but never as accurate as Chang or Clark. Johnston's and Rider's approximations performed acceptably only over some...

Baker, William A.

2012-06-07

157

Semimartingale Stochastic Approximation Procedures and Recursive Estimation  

E-print Network

The semimartingale stochastic approximation procedure, namely, the Robbins-Monro type SDE is introduced which naturally includes both generalized stochastic approximation algorithms with martingale noises and recursive parameter estimation procedures for statistical models associated with semimartingales. General results concerning the asymptotic behaviour of the solution are presented. In particular, the conditions ensuring the convergence, rate of convergence and asymptotic expansion are established. The results concerning the Polyak weighted averaging procedure are also presented.

Lazrieva, N; Toronjadze, T

2007-01-01

158

On the approximation of invariant measures  

Microsoft Academic Search

Given a discrete dynamical system defined by the map t:X ?X, the density of the absolutely continuous (a.c.) invariant measure (if it exists) is the fixed point of the Frobenius-Perron operator defined on L1(X). Ulam proposed a numerical method for approximating such densities based on the computation of a fixed point of a matrix approximation of the operator. T. Y.

Fern Y. Hunt; Walter M. Miller

1992-01-01

159

A Ballistic Monte Carlo Approximation of {\\pi}  

E-print Network

We compute a Monte Carlo approximation of {\\pi} using importance sampling with shots coming out of a Mossberg 500 pump-action shotgun as the proposal distribution. An approximated value of 3.136 is obtained, corresponding to a 0.17% error on the exact value of {\\pi}. To our knowledge, this represents the first attempt at estimating {\\pi} using such method, thus opening up new perspectives towards computing mathematical constants using everyday tools.

Dumoulin, Vincent

2014-01-01

160

An improved proximity force approximation for electrostatics  

SciTech Connect

A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated with their shapes. Indeed, in the so called 'proximity force approximation' the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contributions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip-sample electrostatic interaction in atomic force microscopes. - Highlights: Black-Right-Pointing-Pointer The proximity force approximation (PFA) has been widely used in different areas. Black-Right-Pointing-Pointer The PFA can be improved using a derivative expansion in the shape of the surfaces. Black-Right-Pointing-Pointer We use the improved PFA to compute electrostatic forces between conductors. Black-Right-Pointing-Pointer The results can be used as an analytic benchmark for numerical calculations in AFM. Black-Right-Pointing-Pointer Insight is provided for people who use the PFA to compute nuclear and Casimir forces.

Fosco, Cesar D. [Centro Atomico Bariloche, Comision Nacional de Energia Atomica, R8402AGP Bariloche (Argentina) [Centro Atomico Bariloche, Comision Nacional de Energia Atomica, R8402AGP Bariloche (Argentina); Instituto Balseiro, Universidad Nacional de Cuyo, R8402AGP Bariloche (Argentina); Lombardo, Fernando C. [Departamento de Fisica Juan Jose Giambiagi, FCEyN UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina) [Departamento de Fisica Juan Jose Giambiagi, FCEyN UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina); IFIBA (Argentina)] [Argentina; Mazzitelli, Francisco D., E-mail: fdmazzi@cab.cnea.gov.ar [Centro Atomico Bariloche, Comision Nacional de Energia Atomica, R8402AGP Bariloche (Argentina); Departamento de Fisica Juan Jose Giambiagi, FCEyN UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina)

2012-08-15

161

Logical difference model of grade upper approximation operator and grade lower approximation operator  

Microsoft Academic Search

Grade is an important quantitative index, and graded rough set model is an important improved rough set model. This paper is to explore new improved rough set model. Based on logical difference operation of grade approximation operators, it proposes logical difference model of grade upper approximation operator and grade lower approximation operator. In the new model, basic structure and properties

Xianyong Zhang

2010-01-01

162

Minimal entropy approximation for cellular automata  

NASA Astrophysics Data System (ADS)

We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim.

Fuk?, Henryk

2014-02-01

163

Exponential Approximations Using Fourier Series Partial Sums  

NASA Technical Reports Server (NTRS)

The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.

Banerjee, Nana S.; Geer, James F.

1997-01-01

164

Approximate initial data for binary black holes  

SciTech Connect

We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the transverse-traceless decomposition and consider perturbations of Schwarzschild black holes caused by boosts and the presence of a binary companion. A superposition of these two perturbations then yields approximate, but fully analytic binary black hole initial data that are accurate to first order in the inverse of the binary separation and the square of the black holes' momenta.

Dennison, Kenneth A.; Baumgarte, Thomas W.; Pfeiffer, Harald P. [Department of Physics and Astronomy, Bowdoin College, Brunswick, Maine 04011 (United States); Theoretical Astrophysics, California Institute of Technology, Pasadena, California 91125 (United States)

2006-09-15

165

Approximate quantum data storage and teleportation  

E-print Network

In this paper we present an optimal protocol by which an unknown state on a Hilbert space of dimension $N$ can be approximately stored in an $M$-dimensional quantum system or be approximately teleported via an $M$-dimensional quantum channel. The fidelity of our procedure is determined for pure states as well as for mixed states and states which are entangled with auxiliary quantum systems of varying Hilbert space dimension, and it is compared with theoretical results for the maximally achievable fidelity.

Thomas Laustsen; Klaus Molmer

2002-01-08

166

Approximate quantum data storage and teleportation  

NASA Astrophysics Data System (ADS)

In this paper we present an optimal protocol by which an unknown state on a Hilbert space of dimension N can be approximately stored in an M-dimensional quantum system or be approximately teleported via an M-dimensional quantum channel. The fidelity of our procedure is determined for pure states as well as for mixed states and states that are entangled with auxiliary quantum systems of varying Hilbert-space dimension, and it is compared with theoretical results for the maximally achievable fidelity.

Laustsen, Thomas; Mølmer, Klaus

2002-06-01

167

Congruence Approximations for Entrophy Endowed Hyperbolic Systems  

NASA Technical Reports Server (NTRS)

Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

Barth, Timothy J.; Saini, Subhash (Technical Monitor)

1998-01-01

168

Approximate initial data for binary black holes  

E-print Network

We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the transverse-traceless decomposition and consider perturbations of Schwarzschild black holes caused by boosts and the presence of a binary companion. A superposition of these two perturbations then yields approximate, but fully analytic binary black hole initial data that are accurate to first order in the inverse of the binary separation and the square of the black holes' momenta.

Kenneth A. Dennison; Thomas W. Baumgarte; Harald P. Pfeiffer

2006-06-08

169

On the approximation of protein threading  

SciTech Connect

In this paper, we study the protein threading problem, which was proposed for finding a folded 3D protein structure from an amino acid sequence. Since this problem was already proved to be NP-hard by Lathrop, we study polynomial time approximation algorithms. First we show that the protein threading problem is MAX SNP-hard. Next we show that the protein threading problem can be approximated within a factor 4 for a special case in which a graph representing interaction between residues (amino acids) is planar. This case corresponds to a {beta}-sheet substructure, which appears in most protein structures. 14 refs., 9 figs.

Akutsu, Tatsuya; Miyano, Satoru [Univ. of Tokyo (Japan)

1997-12-01

170

Truncated Stochastic Approximation with Moving Bounds: Convergence  

E-print Network

In this paper we propose a wide class of truncated stochastic approximation procedures with moving random bounds. While we believe that the proposed class of procedures will find its way to a wider range of applications, the main motivation is to accommodate applications to parametric statistical estimation theory. Our class of stochastic approximation procedures has three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and dynamically changing random regression function. We establish convergence and consider several examples to illustrate the results.

Sharia, Teo

2011-01-01

171

Approximation Algorithms for Extensible Bin Packing  

E-print Network

In a variation of bin packing called extensible bin packing, the number of bins to use is specified as part of the input, and bins may be extended to hold more than the usual unit capacity. The cost of a bin is one if it is not extended, and the size if it is extended. The goal is to pack a set of items of given sizes with minimum cost. Adapting ideas in [6, 7, 3], we give a fully polynomial asymptotic approximation scheme for this extensible bin packing. We also show that the additive constant in the approximation bound cannot be eliminated unless P = NP .

E. G. Coffman, Jr.; George S. Lueker

172

Realizing Physical Approximation of the Partial Transpose  

E-print Network

The partial transpose by which a subsystem's quantum state is solely transposed is of unique importance in quantum information processing from both fundamental and practical point of view. In this work, we present a practical scheme to realize a physical approximation to the partial transpose using local measurements on individual quantum systems and classical communication. We then report its linear optical realization and show that the scheme works with no dependence on local basis of given quantum states. A proof-of-principle demonstration of entanglement detection using the physical approximation of the partial transpose is also reported.

Hyang-Tag Lim; Yong-Su Kim; Young-Sik Ra; Joonwoo Bae; Yoon-Ho Kim

2011-04-15

173

The Velocity of Compressional Waves in Rocks to 10 Kilobars, Part 2  

Microsoft Academic Search

The measurements of the velocity of compressional waves up to 10 kilobars for some 250 specimens of rock, reported in part 1, are discussed with respect to the effects of porosity, alteration, anisotropy, and composition. The relations of isotropic elasticity are shown to be approximately valid for a number of examples. Reasonable agreement with theoretical values for quasi-isotropic aggregates is

Francis Birch

1961-01-01

174

Nonlinear approximation by sums of nonincreasing exponentials  

E-print Network

Prony method (APM) which is based on [2]. In contrast to [2], we apply perturbation theory as regularization parameter. The first part of APM recovers the exponents. The second part computes the co­ e words and phrases: nonlinear approximation, exponential sum, approxi­ mate Prony method, singular value

Potts, Daniel

175

Adaptive Finite Element Approximation of Hyperbolic Problems  

E-print Network

prob- lems. The error bounds stem from an error representation formula which equates the error of elliptic type, while for hyperbolic partial di#11;erential equations the theory of a posteriori error: the mechanisms of error propagation in #12;nite element approximations of hyperbolic PDEs are more ? Paul Houston

Jensen, Max

176

Rough Set Approximations in Formal Concept Analysis  

E-print Network

different from that of rough set theory [16], [17]. A comparative examination of rough set theory and formal is based on an equivalence relation on the set of objects. With respect to the formal context, a pair are then used to define a pair of lower and upper approximations of formal concepts. Saquer and Deogun studied

Yao, Yiyu

177

Rough Set Approximations in Formal Concept Analysis  

E-print Network

[38]. A comparative examination of rough set analysis and formal con- cept analysis shows that each analysis is developed based on a formal context given by a binary relation between a set of objectsRough Set Approximations in Formal Concept Analysis Yiyu Yao and Yaohua Chen Department of Computer

Yao, Yiyu

178

ON THE LANDAU APPROXIMATION IN PLASMA PHYSICS  

E-print Network

ON THE LANDAU APPROXIMATION IN PLASMA PHYSICS R. ALEXANDRE AND C. VILLANI Abstract. This paper of his important works in plasma physics, established the kinetic equation which is now called after him interacting through binary collisions. Since then, this equation has been widely in use in plasma physics, see

Villani, Cédric

179

On the Landau approximation in plasma physics  

Microsoft Academic Search

This paper studies the approximation of the Boltzmann equation by the Landau equation in a regime when grazing collisions prevail. While all previous results in the subject were limited to the spatially homogeneous case, here we manage to cover the general, space-dependent situation, assuming only basic physical estimates of finite mass, energy, entropy and entropy production. The proofs are based

R. ALEXANDRE; C. VILLANI

2004-01-01

180

Approximations to the Distributed Activation Energy Model  

E-print Network

Approximations to the Distributed Activation Energy Model for Pyrolysis C.P. Please, 1 M.J. Mc, then resubmitted after minor revisions in September 2002. Abstract The Distributed Activation Energy Model (DAEM effective method for estimating kinetic parameters and the distribution of activation energies. Comparison

McGuinness, Mark

181

Polyhedral Approximation of Ellipsoidal Uncertainty Sets via ...  

E-print Network

Feb 21, 2014 ... power of modern integer programming solvers such as CPLEX and Gurobi. ...... as row-wise uncertainties by projecting the uncertainty set to the space ..... estimated or measured values in contrast to coefficients determining the ..... For the approximate method, the first value states the number of simplex.

Andreas Bärmann, Christoph Thurner, Andreas Heidt, Sebastian Pokutta, Alexander Martin

2014-02-21

182

Can Distributional Approximations Give Exact Answers?  

ERIC Educational Resources Information Center

Some mathematical activities and investigations for the classroom or the lecture theatre can appear rather contrived. This cannot, however, be levelled at the idea given here, since it is based on a perfectly sensible question concerning distributional approximations that was posed by an undergraduate student. Out of this simple question, and…

Griffiths, Martin

2013-01-01

183

An approximate model for artificial chiral material  

Microsoft Academic Search

This paper presents an approximate, but simple, theoretical model for computing the constitutive parameters of artificial chiral materials made by embedding small conducting helices in a lossy isotropic achiral host material. The model explicitly includes helix resonance and the first-order effects of reradiation from the helix, near-field losses, and mutual coupling. Computations made using the model are compared with published

Alfred J. Bahr; K. R. Clausing

1994-01-01

184

Revisiting Twomey's approximation for peak supersaturation  

NASA Astrophysics Data System (ADS)

Twomey's seminal 1959 paper provided lower and upper bound approximations to the estimation of peak supersaturation within an updraft and thus provides the first closed expression for the number of nucleated cloud droplets. The form of this approximation is simple, but provides a surprisingly good estimate and has subsequently been employed in more sophisticated treatments of nucleation parametrization. In the current paper, we revisit the lower bound approximation of Twomey and make a small adjustment which can be used to obtain a more accurate calculation of peak supersaturation under all potential aerosol loadings and thermodynamic conditions. In order to make full use of this improved approximation, the underlying integro-differential equation for supersaturation evolution and the condition for calculating peak supersaturation are examined. A simple rearrangement of the algebra allows for an expression to be written down which can then be solved with a single lookup table with only one independent variable for an underlying lognormal aerosol population. Multimode aerosol with only N different dispersion characteristics require only N of these one-dimensional lookup tables. No additional information is required in the lookup table to deal with additional chemical, physical or thermodynamic properties. The resulting implementation provides a relatively simple, yet computationally cheap and very accurate physically-based parametrization of droplet nucleation for use in climate and NWP models.

Shipway, B. J.

2014-10-01

185

Approximating Border Length for DNA Microarray Synthesis  

E-print Network

Approximating Border Length for DNA Microarray Synthesis Cindy Y. Li1 Prudence W.H. Wong1 Qin Xin2. The borders between the masked and unmasked regions are represented by bold lines. DNA microarray synthesis arises in microarray synthesis to place and embed probes in the array. The synthesis is based on a light

Wong, Prudence W.H.

186

Moment problems and polynomial approximation Christian Berg  

E-print Network

introduction In Stieltjes famous 1894­memoir [38, n ffi 24] he writes: Nous appellerons probl`eme des momentsMoment problems and polynomial approximation Christian Berg February 4, 1997 1 Historical le probl`eme suivant: Trouver une distribution de masse positive sur une droite (0; 1), les moments d

Berg, Christian

187

Moment problems and polynomial approximation Christian Berg  

E-print Network

Moment problems and polynomial approximation Christian Berg: Nous appellerons probl`eme des moments le probl`eme suivant: Trouver une distribution de masse and for Stieltjes, a positive measure is given by an increasing function, cf. [* *38, nO 37]): Le probl`eme

Berg, Christian

188

Approximate Frequency Counts over Data Streams  

Microsoft Academic Search

We present algorithms for computing frequency counts exceeding a user-specified threshold over data streams. Our algorithms are simple and have provably small memory footprints. Although the output is approximate, the error is guaranteed not to exceed a user-specified parameter. Our algo- rithms can easily be deployed for streams of single- ton items like those found in IP network monitor- ing.

Gurmeet Singh Manku; Rajeev Motwani

2002-01-01

189

ORDERING FOR FACTORED APPROXIMATE INVERSE PRECONDITIONERS \\Lambda  

E-print Network

preconditioner we need a more accurate approximation to the true inverse factors. However, sparsity constraints, the Infor­ mation Technology Research Centre (which is funded by the Province of Ontario), and RIACS/NASA of guaranteeing that that the preconditioner is non­ singular, and more importantly it seems that the factored

190

ORDERING FOR FACTORED APPROXIMATE INVERSE PRECONDITIONERS  

E-print Network

need a more accurate approximation to the true inverse factors. However, sparsity constraints do- mation Technology Research Centre (which is funded by the Province of Ontario), and RIACS/NASA Ames NAS 2 of guaranteeing that that the preconditioner is non- singular, and more importantly it seems that the factored

Bridson, Robert

191

Symbolic Test Selection Based on Approximate Analysis  

E-print Network

Symbolic Test Selection Based on Approximate Analysis Bertrand Jeannet, Thierry J´eron, Vlad Rusu}@irisa.fr Abstract. This paper addresses the problem of generating symbolic test cases for testing the conformance. The challenge we consider is the selection of test cases according to a test purpose, which is here a set

Paris-Sud XI, Université de

192

Finite eigenfuction approximations for continuous spectrum operators  

Microsoft Academic Search

In this paper, we introduce a new formulation of the theory of continuous spectrum eigenfunction expansions for self-adjoint operators and analyze the question of when operators may be approximated in an operator norm by finite sums of multiples of eigenprojections of multiplicity one. The theory is designed for application to ordinary and partial differential equations; relationships between the abstract theory

Robert M. Kauffman

1993-01-01

193

Approximation of Agent Dynamics Using Reinforcement Learning  

E-print Network

a lot of attention has been the control of cooperative multi- agent systems through the use of Q-learning-based algorithms. Learning to control multiple agents for the purpose of cooperatively achieving a specified goalApproximation of Agent Dynamics Using Reinforcement Learning Kenton Kirkpatrick and John Valasek

Valasek, John

194

Uniform approximation by Mc Callig rationals  

Microsoft Academic Search

Mc Callig considered ordinary rational functionsp\\/q on [0,?] or a finite subset with the denominatorq satisfying a normalization condition and having a lower bound. Existence of best uniform approximations and behavior of discretization are major topics of this paper. Characterization, uniqueness and denisty are also examined.

Charles B. Dunham

1994-01-01

195

Searching for approximate description of decision classes  

Microsoft Academic Search

We discuss a searching method for synthesis of approximate description of decision classes in large data tables (decision tables). The method consists of the following stages: (i) searching for basic templates which are next used as elementary building blocks for decision classes description; (ii) performing templates grouping as a pre-processing for generalisation and contraction; (iii) generalisation and contraction operations performed

S. H. Nguyen; L. Polkowski; A. Skowron; P. Synak; J. Wróblewski

1996-01-01

196

Approximate clustering via the mountain method  

Microsoft Academic Search

We develop a simple and effective approach for approximate estimation of the cluster centers on the basis of the concept of a mountain function. We call the procedure the mountain method. It can be useful for obtaining the initial values of the clusters that are required by more complex cluster algorithms. It also can be used as a stand alone

R. R. Yager; D. P. Filev

1994-01-01

197

Approximate risk assessment prioritizes remedial decisions  

Microsoft Academic Search

Approximate risk assessment (ARA) is a management tool that prioritizes cost\\/benefit options for risk reduction decisions. Management needs a method that quantifies how much control is satisfactory for each level of risk reduction. Two risk matrices develop a scheme that estimates the necessary control a unit should implement with its present probability and severity of consequences\\/disaster. A second risk assessment

1993-01-01

198

Approximation and learning by greedy algorithms  

Microsoft Academic Search

We consider the problem of approximating a given element f from a Hilbert space $\\\\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the existing theory of convergence rates for both the orthogonal greedy algorithm and the relaxed greedy algorithm, as well as for the forward

Andrew R. Barron; Albert Cohen; Wolfgang Dahmen; Ronald A. DeVore

2008-01-01

199

APPROXIMATION ALGORITHMS FOR FACILITY LOCATION PROBLEMS  

E-print Network

APPROXIMATION ALGORITHMS FOR FACILITY LOCATION PROBLEMS a dissertation submitted to the department distance. The facility location problem and its variant the k­median problem, which minimizes upper bound. We also prove a lower bound of factor 1:36. ffl The Facility Location Problem: We present

Pratt, Vaughan

200

Approximation algorithms for facility location problems  

E-print Network

Approximation algorithms for facility location problems David B. Shmoys Eva Tardosy Karen Aardalz location problem that we study, there is a set of locations at which we may build a facility of facility location problems. One of the most well-studied problems in the Operations Research literature

Utrecht, Universiteit

201

Approximation Algorithms for Facility Location Problems  

E-print Network

Approximation Algorithms for Facility Location Problems (Lecture Notes) Jens Vygen Research . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 The Uncapacitated Facility Location Problem 13 3.1 Relation to Set Covering the demand (of customers, users etc.) best. Facility location problems, which occur also in less obvious

Vygen, Jens

202

A New Approximation Of ECM Frequencies  

E-print Network

We investigate wave amplification through the Electron Cyclotron Maser mechanism. We derive a semi-analytic approximation formula giving the frequencies at which the absorption coefficient is negative. The coefficients still need to be computed to obtain the largest, and therefore the dominant, coefficient.

Amnon Stupp

1998-10-25

203

Alternative approximation concepts for space frame synthesis  

NASA Technical Reports Server (NTRS)

A structural synthesis methodology for the minimum mass design of 3-dimensionall frame-truss structures under multiple static loading conditions and subject to limits on displacements, rotations, stresses, local buckling, and element cross-sectional dimensions is presented. A variety of approximation concept options are employed to yield near optimum designs after no more than 10 structural analyses. Available options include: (A) formulation of the nonlinear mathematcal programming problem in either reciprocal section property (RSP) or cross-sectional dimension (CSD) space; (B) two alternative approximate problem structures in each design space; and (C) three distinct assumptions about element end-force variations. Fixed element, design element linking, and temporary constraint deletion features are also included. The solution of each approximate problem, in either its primal or dual form, is obtained using CONMIN, a feasible directions program. The frame-truss synthesis methodology is implemented in the COMPASS computer program and is used to solve a variety of problems. These problems were chosen so that, in addition to exercising the various approximation concepts options, the results could be compared with previously published work.

Lust, R. V.; Schmit, L. A.

1985-01-01

204

Generalized Nonnegative Matrix Approximations with Bregman Divergences  

Microsoft Academic Search

Nonnegative matrix approximation (NNMA) is a recent technique for di- mensionality reduction and data analysis that yields a part s based, sparse nonnegative representation for nonnegative input data. NNMA has found a wide variety of applications, including text analysis, do cument cluster- ing, face\\/image recognition, language modeling, speech processing and many others. Despite these numerous applications, the algorithmic de- velopment

Inderjit S. Dhillon; Suvrit Sra

2005-01-01

205

Kravchuk functions for the finite oscillator approximation  

NASA Technical Reports Server (NTRS)

Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.

Atakishiyev, Natig M.; Wolf, Kurt Bernardo

1995-01-01

206

Dynamical friction in a mean field approximation  

Microsoft Academic Search

An exact formula is derived for the average frictional force acting upon a ‘test’ star which moves along a prescribed trajectory amongst a collection of ‘field’ stars which are characterized by a Maxwellian distribution of velocities. In the limit that the actual stellar trajectories may be approximated by their average forms, as determined by the mean gravitational field, one obtains

Henry E. Kandrup

1983-01-01

207

Galerkin discontinuous approximation of the MHD equations  

E-print Network

Galerkin discontinuous approximation of the MHD equations Altmann, Belat, Gutnic, Helluy, Mathis, Sonnendr¨ucker Contents 1 Some properties of the MHD system 2 1.1 Equations . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.4 Symmetric form of the MHD system . . . . . . . . . . . . 7 2 Numerical resolution

Paris-Sud XI, Université de

208

Approximation algorithms for planning and control  

NASA Technical Reports Server (NTRS)

A control system operating in a complex environment will encounter a variety of different situations, with varying amounts of time available to respond to critical events. Ideally, such a control system will do the best possible with the time available. In other words, its responses should approximate those that would result from having unlimited time for computation, where the degree of the approximation depends on the amount of time it actually has. There exist approximation algorithms for a wide variety of problems. Unfortunately, the solution to any reasonably complex control problem will require solving several computationally intensive problems. Algorithms for successive approximation are a subclass of the class of anytime algorithms, algorithms that return answers for any amount of computation time, where the answers improve as more time is allotted. An architecture is described for allocating computation time to a set of anytime algorithms, based on expectations regarding the value of the answers they return. The architecture described is quite general, producing optimal schedules for a set of algorithms under widely varying conditions.

Boddy, Mark; Dean, Thomas

1989-01-01

209

Approximate analytical solution of Blasius' equation  

NASA Astrophysics Data System (ADS)

The Blasius' equation f?' + ff?/2=0 , with boundary conditions f(0) = f'(0)0, f'(+?)=1 is studied in this paper. An approximate analytical solution is obtained via the variational iteration method. The comparison with Howarth's numerical solution reveals that the proposed method is of high accuracy.

He, Jihuan

1998-12-01

210

Feature Function Learning for Value Function Approximation  

Microsoft Academic Search

To represent and learn a value function, one needs a set of features that facilitates the processby describing sets of states that share intrinsic properties. We visit existing approachesto automatic feature construction for value function approximation, and note importantstrengths and weakness of each. We offer an alternative approach that addresses some ofthese known weaknesses. Finally, we observe that searching for

Paul E. Utgoff

1996-01-01

211

A finite element approximation of grazing collisions #  

E-print Network

A finite element approximation of grazing collisions # B. Lucquin­Desreux, S.Mancini Laboratoire element discretization of the Boltzmann­ Lorentz operator for which it is possible to define a grazing#cient, which is independent on the grazing collision parameter. Finally, the focaliza­ tion of a beam

Mancini, Simona

212

Anatomy of relativistic mean-field approximations  

SciTech Connect

In this paper, the authors set up a scheme to treat field theoretical Lagrangians in the same bases of the well known non-relativistic many-body techniques. The authors show here that fermions and bosons can be treated quantum mechanically in a symmetric way and obtain results for the mean field approximation.

Barrios, S.C.; Nemes, M.C. (Inst. di Fisica, Dept. di Fisica Mathematica, Univ. de Sao Paulo, C.P. 20516, Sao Paulo (BR))

1992-07-10

213

Approximating polyhedral objects with deformable smooth surfaces  

Microsoft Academic Search

We propose a method to approximate a polyhedral object with a deformable smooth surface, namely the t-skin defined by Edelsbrunner for all 0 0. This construction makes it possible for fully automatic, smooth and robust deformation between two polyhedral objects with different topologies. En

Ho-lun Cheng; Tony Tan

2008-01-01

214

Approximating Polygonal Objects by Deformable Smooth Surfaces  

Microsoft Academic Search

We propose a method to approximate a polygonal object by a deformable smooth surface, namely the t-skin dened by Edelsbrunner (5) for all 0 < t < 1. We guarantee that they are homeomorphic and their Hausdor distance is at most > 0. This construction make it possible for fully automatic, smooth and robust deformation between two polygonal objects with

Ho-lun Cheng; Tony Tan

2005-01-01

215

Approximate Lifted Belief Propagation Parag Singla  

E-print Network

Approximate Lifted Belief Propagation Parag Singla Department of Computer Science University}@cs.washington.edu Abstract Lifting can greatly reduce the cost of inference on first- order probabilistic models, but constructing the lifted network can itself be quite costly. In addition, the mini- mal lifted network is often

Singla, Parag

216

Mathematical Analysis of BornOppenheimer Approximations  

E-print Network

of their much smaller masses, electrons typically move very rapidly compared to the nuclei. So, the electrons­dependent approximation to accommodate electron energy level crossings. Finally, in Section 5, we discuss the analogous and the masses of electrons. The protons and neutrons that make up nuclei have masses that 1991 Mathematics

Joye, Alain

217

Approximation Algorithms for NP-Hard Problems  

Microsoft Academic Search

Approximation algorithms have developed in response to the impossibility of solving a great variety of important optimization problems. Too frequently, when attempting to get a solution for a problem, one is confronted with the fact that the problem is NP-hard. This, in the words of Garey and Johnson, means \\

1997-01-01

218

Distributed Verification and Hardness of Distributed Approximation  

E-print Network

Distributed Verification and Hardness of Distributed Approximation Atish Das Sarma Google Foundation (BSF). Permission to make digital or hard copies of all or part of this work for personal on the hardness of distributed approxi- mation for many classical optimization problems including minimum spanning

219

Markovian approximation of classical open systems  

NASA Astrophysics Data System (ADS)

We discuss exponential convergence to equilibrium for dissipative Markovian systems generated by hypoelliptic non-selfadjoint operators and we present a method to determine the exact rate of convergence to equilibrium. The main example that we will consider is a class of Markovian approximations of the Generalized Langevin equation (GLE).

Ottobre, M.

2012-09-01

220

Quickly Approximating the Distance Between Two Objects  

NASA Technical Reports Server (NTRS)

A method of quickly approximating the distance between two objects (one smaller, regarded as a point; the other larger and complexly shaped) has been devised for use in computationally simulating motions of the objects for the purpose of planning the motions to prevent collisions.

Hammen, David

2009-01-01

221

A simple, approximate model of parachute inflation  

Microsoft Academic Search

A simple, approximate model of parachute inflation is described. The model is based on the traditional, practical treatment of the fluid resistance of rigid bodies in nonsteady flow, with appropriate extensions to accommodate the change in canopy inflated shape. Correlations for the steady drag and steady radial force as functions of the inflated radius are required as input to the

Macha

1992-01-01

222

Generalized approximation to seniority shell model  

Microsoft Academic Search

A generalized approximation to seniority shell model, based on the number conserving quasiparticle theory, is presented which includes the cases where both neutrons and protons are present in the valance shells. The numerical calculations are carried out for even Zr isotopes. The results obtained compare well with the corresponding exact shell model results, demonstrating thereby the validity of the present

Y. K. Gambhir; S. Haq; J. K. Suri

1979-01-01

223

Generalized approximation to seniority shell model  

Microsoft Academic Search

A generalized approximation to seniority shell model, based on the number conserving quasiparticle theory, is presented which includes the cases where both neutrons and protons are present in the valence shells. The numerical calculations are carried out for even Zr isotopes. The results obtained compare well with the corresponding exact shell model results, demonstrating thereby the validity of the present

Y. K. Gambhir; S. Haq; J. K. Suri

1979-01-01

224

Numerical Approximation of the M1-model  

Microsoft Academic Search

In this paper, we introduce the M1 model and derive several appropriate solvers. The robust- ness of the numerical approximation will be one of the main focus as well as the conservation of the important physical properties. Particular attention will be paid to preserve the energy positiveness, the flux limitation, the total energy conservation. Moreover, we carefully check that the

C. Berthon; J. Dubois; R. Turpault

225

Capacity Approximations for a Deterministic MIMO Channel.  

National Technical Information Service (NTIS)

In this paper, we derive closed form approximations for the capacity of a point-to-point, deterministic Gaussian MIMO communication channel. We focus on the behavior of the inverse eigenvalues of the Gram matrix associated with the gain matrix of the MIMO...

I. S. Moskowitz, M. H. Kang, P. Cotae, P. N. Safier

2011-01-01

226

Numerical approximation of SDE with explosions.  

E-print Network

Numerical approximation of SDE with explosions. Joint work with Ju´an D´avila, U. de Chile Juli of the largest crack. The explosion time corresponds to the time of ultimate damage or fatigue failure in the material. #12;The Feller Test for Explosions provides a precise criteria to de- termine, in terms of b

Groisman, Pablo

227

Approximating Probability Distributions Using Small Sample Spaces  

E-print Network

variables distributed uniformly and independently over the range f0; : : : ; d \\Gamma 1g, we provide the approximate distribution as it does under the uniform distribution over f0; : : : ; d \\Gamma 1g. Our construc for any positive integers d and n. We measure the distance between two distributions over G

Motwani, Rajeev

228

Approximating Rooted Steiner Networks Joseph Cheriyan  

E-print Network

Vetta § Abstract The Directed Steiner Tree (DST) problem is a corner- stone problem in network design as the directed Steiner forest problem, and the latter is well known to be as hard to approximate as the label, the Steiner tree problem, and the directed Steiner tree (DST) problem. In the latter problem, we are given

Cheriyan, Joseph

229

Approximating Rooted Steiner Networks Joseph Cheriyan  

E-print Network

Vetta § September 23, 2011 Abstract The Directed Steiner Tree (DST) problem is a cornerstone problem as the directed Steiner forest problem, and the latter is well known to be as hard to approximate as the label examples include the minimum spanning tree (MST) problem, the Steiner tree problem, and the directed

Paris-Sud XI, Université de

230

Improved approximations for the Steiner tree problem  

Microsoft Academic Search

For a set S contained in a metric space, a Steiner tree of S is a tree that connects the points in S. Finding a minimum cost Steiner tree is an NP-hard problem in euclidean and rectilinear metrics as well as in graphs. We give an approximation algorithm and show that the worst-case ratio of the cost of our solutions

Piotr Berman; Viswanathan Ramaiyer

1992-01-01

231

THE MATRIX CUBE PROBLEM: Approximations and Applications  

E-print Network

THE MATRIX CUBE PROBLEM: Approximations and Applications Arkadi Nemirovski, Stieltjes Visiting with A. Ben-Tal 1. Matrix Cube � The problem: formulation and moti- vation � Main result � Back to applications � Sketch of the proof 2. From Matrix Cube to Computing Ma- trix Norms � The problem � Main result

Nemirovski, Arkadi

232

352 Chapter 4 Homotopy Theory CW Approximation  

E-print Network

352 Chapter 4 Homotopy Theory CW Approximation A map f : XY is called a weak homotopy equivalence's theorem can be restated as saying that a weak homotopy equivalence between CW complexes is a homotopy equivalence. It follows easily that this holds also for spaces homotopy equivalent to CW complexes. In general

Hatcher, Allen

233

Block Addressing Indices for Approximate Text Retrieval.  

ERIC Educational Resources Information Center

Discusses indexing in large text databases, approximate text searching, and space-time tradeoffs for indexed text searching. Studies the space overhead and retrieval times as functions of the text block size, concludes that an index can be sublinear in space overhead and query time, and applies the analysis to the Web. (Author/LRW)

Baeza-Yates, Ricardo; Navarro, Gonzalo

2000-01-01

234

Relativistic point interactions: Approximation by smooth potentials  

NASA Astrophysics Data System (ADS)

We show that the four-parameter family of one-dimensional relativistic point interactions studied by Benvegnu and D?browski may be approximated in the strong resolvent sense by smooth, local, short-range perturbations of the Dirac Hamiltonian. In addition, we prove that the nonrelativistic limits correspond to the Schrödinger point interactions studied extensively by the author and Paul Chernoff.

Hughes, Rhonda J.

1997-06-01

235

APRICODD: Approximate Policy Construction Using Decision Diagrams  

Microsoft Academic Search

We propose a method of approximate dynamic programming for Markov decision processes (MDPs) using algebraic decision diagrams (ADDs). We produce near-optimal value functions and policies with much lower time and space requirements than exact dynamic programming. Our method reduces the sizes of the intermediate value functions generated during value iteration by replacing the values at the terminals of the ADD

Robert St-aubin; Jesse Hoey; Craig Boutilier

2000-01-01

236

FRACTAL APPROXIMATION AND COMPRESSION USING PROJECTED IFS  

E-print Network

FRACTAL APPROXIMATION AND COMPRESSION USING PROJECTED IFS �ric Guérin, �ric Tosan and Atilla, or images) with fractal models is an important center of interest for research. The general inverse problem.The most known of them is the fractal image compression method introduced by Jacquin. Generally speaking

Baskurt, Atilla

237

6D SLAM with approximate data association  

Microsoft Academic Search

This paper provides a new solution to the simultaneous localization and mapping (SLAM) problem with six degrees of freedom. A fast variant of the iterative closest points (ICP) algorithm registers 3D scans taken by a mobile robot into a common coordinate system and thus provides relocalization. Hereby, data association is reduced to the problem of searching for closest points. Approximation

A. Nuchter; Kai Lingemann; Joachim Hertzberg; Hartmut Surmann

2005-01-01

238

Approximately Strategy-Proof Voting Eleanor Birrell  

E-print Network

are strategy- proof; under any other voting rule, players have an incentive to lie about their true preferences these previous negative results: approximately strategy-proof voting rules. This approach is motivated by the observation that previous work assumes that people w

Keinan, Alon

239

Approximately Strategy-Proof Voting Eleanor Birrell  

E-print Network

, players have an incentive to lie about their true preferences. We consider a new approach these previous negative results: approximately strategy-proof voting rules. This approach is motivated by the observation that previous work assumes that people will deviate from the honest strategy even

Keinan, Alon

240

Two algorithms for fast approximate subspace tracking  

Microsoft Academic Search

New fast algorithms are presented for tracking singular values, singular vectors, and the dimension of a signal subspace through an overlapping sequence of data matrices. The basic algorithm is called fast approximate subspace tracking (FAST). The algorithm is derived for the special case in which the matrix is changed by deleting the oldest column, shifting the remaining columns to the

Edward C. Real; Donald W. Tufts; James W. Cooley

1999-01-01

241

Generalizing the finite element method: Diffuse approximation and diffuse elements  

Microsoft Academic Search

This paper describes the new “diffuse approximation” method, which may be presented as a generalization of the widely used “finite element approximation” method. It removes some of the limitations of the finite element approximation related to the regularity of approximated functions, and to mesh generation requirements. The diffuse approximation method may be used for generating smooth approximations of functions known

B. Nayroles; G. Touzot; P. Villon

1992-01-01

242

Validity of the energy sudden approximation  

SciTech Connect

This paper contains an examination of the conditions under which the energy sudden (ES) approximation may be expected to be valid. Our approach involves using dimensional analysis to identify (dimensionless) quantities which control energy suddenness and in this fashion three sets of ES criteria emerge. One involves the relative kinetic energy between collision partners and the energy spacing of the internal states of interest; another the strength of the coupling interaction and the same spacing; and a third involves the masses of the colliding molecules and component atoms. We discuss the relationship between these conditions and the justifications given by earlier workers for adopting the ES approximation and then the mass conditions in particular are used as the basis for certain broad statements concerning the applicability of the ES method within nonreactive diatom--diatom and reactive atom--diatom collisions. Finally, a number of avenues for further development of this work are discussed.

Chang, B.; Eno, L.; Rabitz, H.

1983-03-15

243

Comparison of quasilinear and WKB approximations  

SciTech Connect

It is shown that the quasilinearization method (QLM) sums the WKB series. The method approaches solution of the Riccati equation (obtained by casting the Schroedinger equation in a nonlinear form) by approximating the nonlinear terms by a sequence of the linear ones, and is not based on the existence of a smallness parameter. Each pth QLM iterate is expressible in a closed integral form. Its expansion in powers of h reproduces the structure of the WKB series generating an infinite number of the WKB terms. Coefficients of the first 2 {sup p} terms of the expansion are exact while coefficients of a similar number of the next terms are approximate. The quantization condition in any QLM iteration, including the first, leads to exact energies for many well known physical potentials such as the Coulomb, harmonic oscillator, Poeschl-Teller, Hulthen, Hyleraas, Morse, Eckart, etc.

Mandelzweig, V.B. [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)]. E-mail: victor@phys.huji.ac.il

2006-12-15

244

Discrete-dipole approximation for scattering calculations  

Microsoft Academic Search

The discrete-dipole approximation (DDA) for scattering calculations, including the relationship between the DDA and other methods, is reviewed. Computational considerations, i.e., the use of complex-conjugate gradient algorithms and fast-Fourier-transform methods, are discussed. We test the accuracy of the DDA by using the DDA to compute scattering and absorption by isolated, homogeneous spheres as well as by targets consisting of two

Bruce T. Draine; Piotr J. Flatau

1994-01-01

245

Approximate symmetry groups of inhomogeneous metrics  

Microsoft Academic Search

A useful step toward understanding inhomogeneous space-times would be to classify them, perhaps in a fashion analogous to that used for spatially homogeneous space-times. To that end, a technique for determining an approximate simply-transitive three-parameter symmetry group of a three-dimensional positive-definite Riemannian metric is developed. The technique employs a variational principle to find a set of three orthonormal vectors whose

Alan Spero; Ralph Baierlein

1977-01-01

246

Approximate symmetry groups of inhomogeneous metrics: Examples  

Microsoft Academic Search

By definition, an N-dimensional positive-definite inhomogeneous metric is not invariant under any N-parameter, simply-transitive continuous group of motions. Nonetheless, it is possible to construct a group (simply-transitive and of N parameters) that comes closest to leaving the given metric invariant. We call this group the approximate symmetry group of the metric. In an earlier paper, we described a technique for

Alan Spero; Ralph Baierlein

1978-01-01

247

Approximations to the plasma dispersion function  

NASA Technical Reports Server (NTRS)

Linear wave propagation in hot collisionless plasmas is described by the linearized Vlasov and Maxwell equations. In uniform media, the utilization of spatial and temporal transforms of those equations leads to the consideration of integrals of the Hilbert transform type. Analysis and comparison of two simple approximations are provided based on the utilization of resonance velocity distributions. Application is then made to the Landau and whistler waves, along with a discussion of the results, and commentary on possible improvements.

Brinca, A. L.

1972-01-01

248

Approximation techniques for average completion time scheduling  

SciTech Connect

We consider the problem of nonpreemptive scheduling to minimize average (weighted) completion time, allowing for release dates, parallel machines, and precedence constraints. Recent work has led to constant-factor approximations for this problem, based on solving a preemptive or linear programming relaxation and then using the solution to get an ordering on the jobs. We introduce several new techniques which generalize this basic paradigm. We use these ideas to obtain improved approximation algorithms for one-machine scheduling to minimize average completion time with release dates. In the process, we obtain an optimal randomized on-line algorithm for the same problem that beats a lower bound for deterministic on-line algorithms. We consider extensions to the case of parallel machine scheduling, and for this we introduce two new ideas: first, we show that a preemptive one-machine relaxation is a powerful tool for designing parallel machine scheduling algorithms that simultaneously produce good approximations and have small running times; second, we show that a non-greedy {open_quotes}rounding{close_quotes} of the relaxation yields better approximations than a greedy one. We also prove a general theorem relating the value of one-machine relaxations to that of the schedules obtained for the original m-machine problems. This theorem applies even when there are precedence constraints on the jobs. We apply this result to precedence graphs such as in-trees, out-trees, and series- parallel graphs; these are of particular interest in compiler applications that partly motivated our work.

Chekuri, C.; Motwani, R. [Stanford Univ., CA (United States); Natarajan, B. [Hewlett Packard Labs., Palo Alto, CA (United States); Stein, C. [Dartmouth College, Hannover, NH (United States)

1997-06-01

249

Approximation algorithms for facility location problems  

Microsoft Academic Search

We present new approximation algorithms for several facility location prob-\\u000alems. In each facility location problem that we study, there is a set of locations\\u000aat which we may build a facility (such asawarehouse), where the cost of build-\\u000aing at location i is fi; furthermore, there is a set of client locations (such as\\u000astores) that require to be

David B. Shmoys; K. I. Aardal

1997-01-01

250

Approximation algorithms for facility location problems  

Microsoft Academic Search

One of the most flourishing areas of research in the design and analysis of approximation algorithms has been for facility\\u000a location problems. In particular, for the metric case of two simple models, the uncapacitated facility location and the k-median problems, there are now a variety of techniques that yield constant performance guarantees. These methods include\\u000a LP rounding, primal-dual algorithms, and

David B. Shmoys

2000-01-01

251

An Approximation for the Zakai Equation  

SciTech Connect

In this article we consider a polygonal approximation to the unnormalized conditional measure of a filtering problem, which is the solution of the Zakai stochastic differential equation on measure space. An estimate of the convergence rate based on a distance which is equivalent to the weak convergence topology is derived. We also study the density of the unnormalized conditional measure, which is the solution of the Zakai stochastic partial differential equation. An estimate of the convergence rate is also given in this case.

Hu, Y. [Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS 66045-2142 (United States)], E-mail: hu@math.ukans.edu; Kallianpur, G. [Department of Statistics, University of North Carolina, Chapel Hill, NC 27599-3260 (United States)], E-mail: gk@stat.unc.edu; Xiong, J. [Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300 (United States)], E-mail: jxiong@math.utk.edu

2002-07-01

252

Application Limits for the Kinematic Wave Approximation  

Microsoft Academic Search

Flows with predominate flow direction are governed by the de Saint Venant flow equations. The kinematic wave approach retains the mass balance but considers pseudo-uniform flow conditions instead of the full momentum ba- lance. This approximation is particularly well-suited for overland runoff pro- cesses. The zero-inertia approach may be regarded as an intermediate formula- tion which retains the effect of

Willi H. Hager; Kurt Hager

1985-01-01

253

Hessian approximation algorithms for hybrid optimization methods  

Microsoft Academic Search

This article introduces Hessian approximation algorithms to estimate the search direction of the quasi-Newton methods for solving optimization problems of continuous parameters. The proposed algorithms are quite different from other well-known quasi-Newton methods, such as symmetric rank-one, Davidon–Fletcher–Powell, and Broyden–Fletcher–Goldfarb–Shanno, in that the Hessian matrix is not calculated from the gradient information, rather directly from the function values. The proposed

Min-Jea Tahk; Moon-Su Park; Hyun-Wook Woo; Hyoun-Jin Kim

2009-01-01

254

Capacitor-Chain Successive-Approximation ADC  

NASA Technical Reports Server (NTRS)

A proposed successive-approximation analog-to-digital converter (ADC) would contain a capacitively terminated chain of identical capacitor cells. Like a conventional successive-approximation ADC containing a bank of binary-scaled capacitors, the proposed ADC would store an input voltage on a sample-and-hold capacitor and would digitize the stored input voltage by finding the closest match between this voltage and a capacitively generated sum of binary fractions of a reference voltage (Vref). However, the proposed capacitor-chain ADC would offer two major advantages over a conventional binary-scaled-capacitor ADC: (1) In a conventional ADC that digitizes to n bits, the largest capacitor (representing the most significant bit) must have 2(exp n-1) times as much capacitance, and hence, approximately 2(exp n-1) times as much area as does the smallest capacitor (representing the least significant bit), so that the total capacitor area must be 2(exp n) times that of the smallest capacitor. In the proposed capacitor-chain ADC, there would be three capacitors per cell, each approximately equal to the smallest capacitor in the conventional ADC, and there would be one cell per bit. Therefore, the total capacitor area would be only about 3(exp n) times that of the smallest capacitor. The net result would be that the proposed ADC could be considerably smaller than the conventional ADC. (2) Because of edge effects, parasitic capacitances, and manufacturing tolerances, it is difficult to make capacitor banks in which the values of capacitance are scaled by powers of 2 to the required precision. In contrast, because all the capacitors in the proposed ADC would be identical, the problem of precise binary scaling would not arise.

Cunningham, Thomas

2003-01-01

255

Sparse greedy matrix approximation for machine learning  

Microsoft Academic Search

In kernel based methods such as RegularizationNetworks large datasets pose signi-cant problems since the number of basis functionsrequired for an optimal solution equalsthe number of samples. We present a sparsegreedy approximation technique to constructa compressed representation of the designmatrix. Experimental results are given andconnections to Kernel-PCA, Sparse KernelFeature Analysis, and Matching Pursuit arepointed out.1. IntroductionMany recent advances in...

Alex J. Smola; B. Scholkopf

2000-01-01

256

WKB approximation to the power wall  

NASA Astrophysics Data System (ADS)

We present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply monotonically rising potential. The models studied in detail have potentials proportional to x? for x > 0; the limit ? ? ? would reproduce a perfectly reflecting boundary, but at present we concentrate on the cases ? = 1 and 2, for which exact solutions in terms of well known functions are available for comparison. We classify the classical paths in this system by their qualitative nature and calculate the contributions of the various classes to the leading-order semiclassical approximation: for each classical path we find the action S, the amplitude function A and the Laplacian of A. (The Laplacian is of interest because it gives an estimate of the error in the approximation and is needed for computing higher-order approximations.) The resulting semiclassical propagator can be used to rewrite the exact problem as a Volterra integral equation, whose formal solution by iteration (Neumann series) is a semiclassical, not perturbative, expansion. We thereby test, in the context of a concrete problem, the validity of the two technical hypotheses in a previous proof of the convergence of such a Neumann series in the more abstract setting of an arbitrary smooth potential. Not surprisingly, we find that the hypotheses are violated when caustics develop in the classical dynamics; this opens up the interesting future project of extending the methods to momentum space.

Mera, F. D.; Fulling, S. A.; Bouas, J. D.; Thapa, K.

2013-05-01

257

Radiance modelling using the P3 approximation  

NASA Astrophysics Data System (ADS)

Light dosimetry is an essential component of effective photodynamic therapy (PDT) of tumours. Present PDT light dosimetry techniques rely on fluence-based models and measurements. However, in a previous paper by Barajas et al, radiance-based light dosimetry was explored as an alternative approach. Although successful in demonstrating the use of Monte Carlo (MC) simulations of radiance in tissue optical characterization, the MC proved time consuming and impractical for clinical applications. It was proposed that an analytical solution to the transport equation for radiance would be desirable as this would facilitate and increase the speed of tissue characterization. It has been found that the P3 approximation is one such potential solution. Radiance and fluence expressions based on the P3 approximation were used to optically characterize an Intralipid-based tissue phantom of varying concentration of scatterer (Intralipid) and absorber (methylene blue) using a plane wave illuminated, semi-infinite medium geometry. The results obtained compare favourably with the Grosjean approximation of fluence (a modified diffusion theory) using the same optical parameters . The results illustrate that radiance-based light dosimetry is a viable alternative approach to tissue characterization and dosimetry. It is potentially useful for clinical applications because of the limited number of invasive measurements needed and the speed at which the tissue can be characterized.

Dickey, Dwayne; Barajas, Oscar; Brown, Kevin; Tulip, John; Moore, Ronald B.

1998-12-01

258

Strong washout approximation to resonant leptogenesis  

NASA Astrophysics Data System (ADS)

We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ?=Xsin(2varphi)/(X2+sin2varphi), where X=8??/(|Y1|2+|Y2|2), ?=4(M1-M2)/(M1+M2), varphi=arg(Y2/Y1), and M1,2, Y1,2 are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y1,2|2gg ?, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to the case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.

Garbrecht, Björn; Gautier, Florian; Klaric, Juraj

2014-09-01

259

Fast algorithms for approximate circular string matching  

PubMed Central

Background Circular string matching is a problem which naturally arises in many biological contexts. It consists in finding all occurrences of the rotations of a pattern of length m in a text of length n. There exist optimal average-case algorithms for exact circular string matching. Approximate circular string matching is a rather undeveloped area. Results In this article, we present a suboptimal average-case algorithm for exact circular string matching requiring time O ( n ) . Based on our solution for the exact case, we present two fast average-case algorithms for approximate circular string matching with k-mismatches, under the Hamming distance model, requiring time O ( n ) for moderate values of k, that is k = O ( m / log m ) . We show how the same results can be easily obtained under the edit distance model. The presented algorithms are also implemented as library functions. Experimental results demonstrate that the functions provided in this library accelerate the computations by more than three orders of magnitude compared to a naïve approach. Conclusions We present two fast average-case algorithms for approximate circular string matching with k-mismatches; and show that they also perform very well in practice. The importance of our contribution is underlined by the fact that the provided functions may be seamlessly integrated into any biological pipeline. The source code of the library is freely available at http://www.inf.kcl.ac.uk/research/projects/asmf/. PMID:24656145

2014-01-01

260

Approximation abilities of neuro-fuzzy networks  

NASA Astrophysics Data System (ADS)

The paper presents the operation of two neuro-fuzzy systems of an adaptive type, intended for solving problems of the approximation of multi-variable functions in the domain of real numbers. Neuro-fuzzy systems being a combination of the methodology of artificial neural networks and fuzzy sets operate on the basis of a set of fuzzy rules "if-then", generated by means of the self-organization of data grouping and the estimation of relations between fuzzy experiment results. The article includes a description of neuro-fuzzy systems by Takaga-Sugeno-Kang (TSK) and Wang-Mendel (WM), and in order to complement the problem in question, a hierarchical structural self-organizing method of teaching a fuzzy network. A multi-layer structure of the systems is a structure analogous to the structure of "classic" neural networks. In its final part the article presents selected areas of application of neuro-fuzzy systems in the field of geodesy and surveying engineering. Numerical examples showing how the systems work concerned: the approximation of functions of several variables to be used as algorithms in the Geographic Information Systems (the approximation of a terrain model), the transformation of coordinates, and the prediction of a time series. The accuracy characteristics of the results obtained have been taken into consideration.

Mrówczy?ska, Maria

2010-01-01

261

Using Approximations to Accelerate Engineering Design Optimization  

NASA Technical Reports Server (NTRS)

Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the current approximation to the objective during the course of the optimization. We define and experiment with the use of merit functions chosen to simultaneously improve both the solution to the optimization problem (the objective) and the quality of the approximation. Our goal is to further improve the effectiveness of our general approach without sacrificing any of its rigor.

Torczon, Virginia; Trosset, Michael W.

1998-01-01

262

Fuzzy systems with defuzzification are universal approximators.  

PubMed

In this paper, we consider a fundamental theoretical question: Is it always possible to design a fuzzy system capable of approximating any real continuous function on a compact set with arbitrary accuracy? Moreover, we research whether the answer to the above question is positive when we restrict to a fixed (but arbitrary) type of fuzzy reasoning and to a subclass of fuzzy relations. This result can be viewed as an existence theorem of an optimal fuzzy system for a wide variety of problems. PMID:18263015

Castro, J L; Delgado, M

1996-01-01

263

Probabilistic Approximations of Signaling Pathway Dynamics  

NASA Astrophysics Data System (ADS)

Systems of ordinary differential equations (ODEs) are often used to model the dynamics of complex biological pathways. We construct a discrete state model as a probabilistic approximation of the ODE dynamics by discretizing the value space and the time domain. We then sample a representative set of trajectories and exploit the discretization and the structure of the signaling pathway to encode these trajectories compactly as a dynamic Bayesian network. As a result, many interesting pathway properties can be analyzed efficiently through standard Bayesian inference techniques. We have tested our method on a model of EGF-NGF signaling pathway [1] and the results are very promising in terms of both accuracy and efficiency.

Liu, Bing; Thiagarajan, P. S.; Hsu, David

264

The monoenergetic approximation in stellarator neoclassical calculations  

E-print Network

In the standard "monoenergetic" approach to numerical calculation of stellarator neoclassical transport, to expedite computation, ad-hoc changes are made to the kinetic equation so speed enters only as a parameter. Here we examine the validity of this approach by considering the effective particle trajectories in a model magnetic field. We find monoenergetic codes systematically under-predict the true trapped particle fraction, with the error in the trapped ion fraction being of order unity when the electric field is large, suggesting some results of these codes may be unreliable in this regime. This inaccuracy is independent of any errors introduced by approximation of the collision operator.

Landreman, Matt

2011-01-01

265

On asymptotic approximations to entire functions  

NASA Astrophysics Data System (ADS)

A way of circumventing the obstacles in the realization of original ideas by von Neumann and Gabor that are posed by the Balian-Low theorem on localization is shown, by using a special entire function with a strong exponential localization property. A square-integrable, doubly periodic and exponentially localized basis in Hilbert space of functions on C is used to solve the problem of asymptotic approximations to entire functions, in Hilbert space metrics. A new technique is suggested for numerical methods in phase-space quantum mechanics and signal processing.

Avanesyan, Gagik T.

2008-07-01

266

Structural design utilizing updated, approximate sensitivity derivatives  

NASA Technical Reports Server (NTRS)

A method to improve the computational efficiency of structural optimization algorithms is investigated. In this method, the calculations of 'exact' sensitivity derivatives of constraint functions are performed only at selected iterations during the optimization process. The sensitivity derivatives utilized within other iterations are approximate derivatives which are calculated using an inexpensive derivative update formula. Optimization results are presented for an analytic optimization problem (i.e., one having simple polynomial expressions for the objective and constraint functions) and for two structural optimization problems. The structural optimization results indicate that up to a factor of three improvement in computation time is possible when using the updated sensitivity derivatives.

Scotti, Stephen J.

1993-01-01

267

Exact and approximate time-shift operators  

NASA Astrophysics Data System (ADS)

A novel fractional time-shift operator is presented in this paper. It is based on performing a phase shift in the frequency domain, which, of course, corresponds to the desired time shift in the time domain. The operations of transforming to the frequency domain, multiplying by the phase shift, and transforming back to the time domain can be accomplished efficiently using one matrix. This matrix is Toeplitz with terms away from the shift number near zero. By approximating the near zero terms as zero, a banded or truncated Toeplitz matrix results. This reduces the computational load and allows an FIR filter realization for the fractional time shift.

Piper, John E.

2009-05-01

268

Approximation concepts for numerical airfoil optimization  

NASA Technical Reports Server (NTRS)

An efficient algorithm for airfoil optimization is presented. The algorithm utilizes approximation concepts to reduce the number of aerodynamic analyses required to reach the optimum design. Examples are presented and compared with previous results. Optimization efficiency improvements of more than a factor of 2 are demonstrated. Improvements in efficiency are demonstrated when analysis data obtained in previous designs are utilized. The method is a general optimization procedure and is not limited to this application. The method is intended for application to a wide range of engineering design problems.

Vanderplaats, G. N.

1979-01-01

269

Modeling error in Approximate Deconvolution Models  

E-print Network

We investigate the assymptotic behaviour of the modeling error in approximate deconvolution model in the 3D periodic case, when the order $N$ of deconvolution goes to $\\infty$. We consider successively the generalised Helmholz filters of order $p$ and the Gaussian filter. For Helmholz filters, we estimate the rate of convergence to zero thanks to energy budgets, Gronwall's Lemma and sharp inequalities about Fouriers coefficients of the residual stress. We next show why the same analysis does not allow to conclude convergence to zero of the error modeling in the case of Gaussian filter, leaving open issues.

Adrian Dunca; Roger Lewandowski

2011-11-28

270

Asphericity and approximation properties of crossed modules  

SciTech Connect

This paper is devoted to the study of the Baer invariants and approximation properties of crossed modules and cat{sup 1}-groups. Conditions are considered under which the kernels of crossed modules coincide with the intersection of the lower central series. An algebraic criterion for asphericity is produced for two-dimensional complexes having aspherical plus-construction. As a consequence it is shown that a subcomplex of an aspherical two-dimensional complex is aspherical if and only if its fundamental cat{sup 1}-group is residually soluble. Thus, a new formulation in group-theoretic terms is given to the Whitehead asphericity conjecture. Bibliography: 25 titles.

Mikhailov, R V [Steklov Mathematical Institute, Russian Academy of Sciences (Russian Federation)

2007-04-30

271

Wavelet-Based Signal approximation with Genetic Algorithms  

Microsoft Academic Search

In this paper, the usability of genetic algorithms for signa l approximation is discussed. Due to recent developments in the field of signal approximation by wavelets, this work concentrates on signal approximation by wavelet-like functions. Signals are approximated by a finite linear combination of elementary functions and a genetic algorithm is employed to find the coefficients to such an approximation.

Marc M. Lankhorst; Marten D. Van Der Laan

1995-01-01

272

Analytic approximations to Kelvin functions with applications to electromagnetics  

Microsoft Academic Search

We present analytical approximations for the real Kelvin function ber x and the imaginary Kelvin function bei x, using the two-point quasi-fractional approximation procedure. We have applied these approximations to the calculation of the current distribution within a cylindrical conductor. Our approximations are simple and accurate. An infinite number of roots is also obtained with the approximation and precision increases

L. Brualla; P. Martin

2001-01-01

273

Approximability and in-approximability results for no-wait shop scheduling  

Microsoft Academic Search

We investigate the approximability of no-wait shop scheduling problems under the makespan criterion. In a flow shop, all jobs pass through the machines in the same ordering. In the more general job shop, the routes of the jobs are job-dependent. We present a polynomial time approximation scheme (PTAS) for the no-wait flow shop problem on any fixed number of machines.

Maxim Sviridenko; Gerhard J. Woeginger

2000-01-01

274

Bethe approximation for a semiflexible polymer chain  

NASA Astrophysics Data System (ADS)

We present a Bethe approximation to study lattice models of linear polymers. The approach is variational in nature and based on the cluster variation method. We focus on a model with (i) a nearest-neighbor attractive energy ?v between a pair of nonbonded monomers, (ii) a bending energy ?h for each pair of successive chain segments that are not collinear. We determine the phase diagram of the system as a function of the reduced temperature t=T/?v and of the parameter x=?h/?v. We find two different qualitative behaviors, on varying t. For small values of x the system undergoes a ? collapse from an extended coil to a compact globule; subsequently, on decreasing further t, there is a first order transition to an anisotropic phase, characterized by global orientational order. For sufficiently large values of x, instead, there is directly a first order transition from the coil to the orientational ordered phase. Our results are in good agreement with previous Monte Carlo simulations and contradict in some aspects mean-field theory. In the limit of Hamiltonian walks, our approximation recovers results of the Flory-Huggins theory for polymer melting.

Lise, Stefano; Maritan, Amos; Pelizzola, Alessandro

1998-11-01

275

Quantum algorithm for approximating partition functions  

NASA Astrophysics Data System (ADS)

We present a quantum algorithm based on classical fully polynomial randomized approximation schemes (FPRASs) for estimating partition functions that combine simulated annealing with the Monte Carlo Markov chain method and use nonadaptive cooling schedules. We achieve a twofold polynomial improvement in time complexity: a quadratic reduction with respect to the spectral gap of the underlying Markov chains and a quadratic reduction with respect to the parameter characterizing the desired accuracy of the estimate output by the FPRAS. Both reductions are intimately related and cannot be achieved separately. First, we use Grover’s fixed-point search, quantum walks, and phase estimation to efficiently prepare approximate coherent encodings of stationary distributions of the Markov chains. The speed up we obtain in this way is due to the quadratic relation between the spectral and phase gaps of classical and quantum walks. The second speed up with respect to accuracy comes from generalized quantum counting used instead of classical sampling to estimate expected values of quantum observables.

Wocjan, Pawel; Chiang, Chen-Fu; Nagaj, Daniel; Abeyesinghe, Anura

2009-08-01

276

Spectrally Invariant Approximation within Atmospheric Radiative Transfer  

NASA Technical Reports Server (NTRS)

Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These spectrally invariant relationships are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

Marshak, A.; Knyazikhin, Y.; Chiu, J. C.; Wiscombe, W. J.

2011-01-01

277

Revisiting approximate dynamic programming and its convergence.  

PubMed

Value iteration-based approximate/adaptive dynamic programming (ADP) as an approximate solution to infinite-horizon optimal control problems with deterministic dynamics and continuous state and action spaces is investigated. The learning iterations are decomposed into an outer loop and an inner loop. A relatively simple proof for the convergence of the outer-loop iterations to the optimal solution is provided using a novel idea with some new features. It presents an analogy between the value function during the iterations and the value function of a fixed-final-time optimal control problem. The inner loop is utilized to avoid the need for solving a set of nonlinear equations or a nonlinear optimization problem numerically, at each iteration of ADP for the policy update. Sufficient conditions for the uniqueness of the solution to the policy update equation and for the convergence of the inner-loop iterations to the solution are obtained. Afterwards, the results are formed as a learning algorithm for training a neurocontroller or creating a look-up table to be used for optimal control of nonlinear systems with different initial conditions. Finally, some of the features of the investigated method are numerically analyzed. PMID:24846687

Heydari, Ali

2014-12-01

278

Approximation of Failure Probability Using Conditional Sampling  

NASA Technical Reports Server (NTRS)

In analyzing systems which depend on uncertain parameters, one technique is to partition the uncertain parameter domain into a failure set and its complement, and judge the quality of the system by estimating the probability of failure. If this is done by a sampling technique such as Monte Carlo and the probability of failure is small, accurate approximation can require so many sample points that the computational expense is prohibitive. Previous work of the authors has shown how to bound the failure event by sets of such simple geometry that their probabilities can be calculated analytically. In this paper, it is shown how to make use of these failure bounding sets and conditional sampling within them to substantially reduce the computational burden of approximating failure probability. It is also shown how the use of these sampling techniques improves the confidence intervals for the failure probability estimate for a given number of sample points and how they reduce the number of sample point analyses needed to achieve a given level of confidence.

Giesy. Daniel P.; Crespo, Luis G.; Kenney, Sean P.

2008-01-01

279

Optimal Approximation of Quadratic Interval Functions  

NASA Technical Reports Server (NTRS)

Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.

Koshelev, Misha; Taillibert, Patrick

1997-01-01

280

Function approximation using adaptive and overlapping intervals  

SciTech Connect

A problem common to many disciplines is to approximate a function given only the values of the function at various points in input variable space. A method is proposed for approximating a function of several to one variable. The model takes the form of weighted averaging of overlapping basis functions defined over intervals. The number of such basis functions and their parameters (widths and centers) are automatically determined using given training data and a learning algorithm. The proposed algorithm can be seen as placing a nonuniform multidimensional grid in the input domain with overlapping cells. The non-uniformity and overlap of the cells is achieved by a learning algorithm to optimize a given objective function. This approach is motivated by the fuzzy modeling approach and a learning algorithms used for clustering and classification in pattern recognition. The basics of why and how the approach works are given. Few examples of nonlinear regression and classification are modeled. The relationship between the proposed technique, radial basis neural networks, kernel regression, probabilistic neural networks, and fuzzy modeling is explained. Finally advantages and disadvantages are discussed.

Patil, R.B.

1995-05-01

281

WKB approximation for abruptly varying potential wells  

NASA Astrophysics Data System (ADS)

We present an approach to obtain eigenfunctions and eigenenergies for abruptly varying potentials in the framework of the Wentzel-Kramers-Brillouin (WKB) approximation. To illustrate it, two examples of the potentials are studied. The first one is the combination of a step barrier and a harmonic oscillator potential, and the second one consists of a step barrier and a linear potential. The formulation of a WKB quantization rule is proposed. Our approach shows that WKB energies and those from numerical calculation are in good agreement. According to matching conditions used, WKB wavefunctions in this present work are violated at only one classical turning point, but they behave well at another point where the potentials are discontinuous.

Amthong, Attapon

2014-11-01

282

The random phase approximation applied to ice  

E-print Network

Standard density functionals without van der Waals interactions yield an unsatisfactory description of ice phases, specifically, high density phases occurring under pressure are too unstable compared to the common low density phase I$_h$ observed at ambient conditions. Although the description is improved by using functionals that include van der Waals interactions, the errors in relative volumes remain sizable. Here we assess the random phase approximation (RPA) for the correlation energy and compare our results to experimental data as well as diffusion Monte Carlo data for ice. The RPA yields a very balanced description for all considered phases, approaching the accuracy of diffusion Monte Carlo in relative energies and volumes. This opens a route towards a concise description of molecular water phases on surfaces and in cavities.

Macher, Markus; Franchini, Cesare; Kresse, Georg

2014-01-01

283

Sivers function in the quasiclassical approximation  

NASA Astrophysics Data System (ADS)

We calculate the Sivers function in semi-inclusive deep inelastic scattering (SIDIS) and in the Drell-Yan process (DY) by employing the quasiclassical Glauber-Mueller/McLerran-Venugopalan approximation. Modeling the hadron as a large "nucleus" with nonzero orbital angular momentum (OAM), we find that its Sivers function receives two dominant contributions: one contribution is due to the OAM, while another one is due to the local Sivers function density in the nucleus. While the latter mechanism, being due to the "lensing" interactions, dominates at large transverse momentum of the produced hadron in SIDIS or of the dilepton pair in DY, the former (OAM) mechanism is leading in saturation power counting and dominates when the above transverse momenta become of the order of the saturation scale. We show that the OAM channel allows for a particularly simple and intuitive interpretation of the celebrated sign flip between the Sivers functions in SIDIS and DY.

Kovchegov, Yuri V.; Sievert, Matthew D.

2014-03-01

284

Generic sequential sampling for metamodel approximations  

SciTech Connect

Metamodels approximate complex multivariate data sets from simulations and experiments. These data sets often are not based on an explicitly defined function. The resulting metamodel represents a complex system's behavior for subsequent analysis or optimization. Often an exhaustive data search to obtain the data for the metalnodel is impossible, so an intelligent sampling strategy is necessary. While inultiple approaches have been advocated, the majority of these approaches were developed in support of a particular class of metamodel, known as a Kriging. A more generic, cotninonsense approach to this problem allows sequential sampling techniques to be applied to other types of metamodeis. This research compares recent search techniques for Kriging inetamodels with a generic, inulti-criteria approach combined with a new type of B-spline metamodel. This B-spline metamodel is competitive with prior results obtained with a Kriging metamodel. Furthermore, the results of this research highlight several important features necessary for these techniques to be extended to more complex domains.

Turner, C. J. (Cameron J.); Campbell, M. I. (Matthew I.)

2003-01-01

285

Approximate Stokes Drift Profiles in Deep Water  

E-print Network

A deep-water approximation to the Stokes drift velocity profile is explored as an alternative to the monochromatic profile. The alternative profile investigated relies on the same two quantities required for the monochromatic profile, viz the Stokes transport and the surface Stokes drift velocity. Comparisons with parametric spectra and profiles under wave spectra from the ERA-Interim reanalysis and buoy observations reveal much better agreement than the monochromatic profile even for complex sea states. That the profile gives a closer match and a more correct shear has implications for ocean circulation models since the Coriolis-Stokes force depends on the magnitude and direction of the Stokes drift profile and Langmuir turbulence parameterizations depend sensitively on the shear of the profile. The alternative profile comes at no added numerical cost compared to the monochromatic profile.

Breivik, Øyvind; Bidlot, Jean-Raymond

2014-01-01

286

Approximate maximum likelihood decoding of block codes  

NASA Technical Reports Server (NTRS)

Approximate maximum likelihood decoding algorithms, based upon selecting a small set of candidate code words with the aid of the estimated probability of error of each received symbol, can give performance close to optimum with a reasonable amount of computation. By combining the best features of various algorithms and taking care to perform each step as efficiently as possible, a decoding scheme was developed which can decode codes which have better performance than those presently in use and yet not require an unreasonable amount of computation. The discussion of the details and tradeoffs of presently known efficient optimum and near optimum decoding algorithms leads, naturally, to the one which embodies the best features of all of them.

Greenberger, H. J.

1979-01-01

287

Hunting resonance poles with Rational Approximants  

E-print Network

Based on the mathematically well defined Pad\\'e Theory, a theoretically safe new procedure for the extraction of the pole mass and width of resonances is proposed. In particular, thanks to the Montessus de Ballore's theorem we are able to unfold the Second Riemann sheet of an amplitude to search the position of the resonant pole in the complex plane. The method is systematic and provides a model-independent treatment of the prediction and the corresponding errors of the approximation. This letter partially covers the material presented by the author at the 15th International QCD Conference: QCD 10 (25th anniversary), Montpellier, France, 28 Jun - 3 Jul 2010 and at the Quark Confinement and the Hadron Spectrum IX, 30 August - 3 September 2010, Madrid, Spain.

Pere Masjuan

2010-12-13

288

An approximate CPHD filter for superpositional sensors  

NASA Astrophysics Data System (ADS)

Most multitarget tracking algorithms, such as JPDA, MHT, and the PHD and CPHD filters, presume the following measurement model: (a) targets are point targets, (b) every target generates at most a single measurement, and (c) any measurement is generated by at most a single target. However, the most familiar sensors, such as surveillance and imaging radars, violate assumption (c). This is because they are actually superpositional-that is, any measurement is a sum of signals generated by all of the targets in the scene. At this conference in 2009, the first author derived exact formulas for PHD and CPHD filters that presume general superpositional measurement models. Unfortunately, these formulas are computationally intractable. In this paper, we modify and generalize a Gaussian approximation technique due to Thouin, Nannuru, and Coates to derive a computationally tractable superpositional-CPHD filter. Implementation requires sequential Monte Carlo (particle filter) techniques.

Mahler, Ronald; El-Fallah, Adel

2012-06-01

289

Architecture-independent approximation of functions.  

PubMed

We show that minimizing the expected error of a feedforward network over a distribution of weights results in an approximation that tends to be independent of network size as the number of hidden units grows. This minimization can be easily performed, and the complexity of the resulting function implemented by the network is regulated by the variance of the weight distribution. For a fixed variance, there is a number of hidden units above which either the implemented function does not change or the change is slight and tends to zero as the size of the network grows. In sum, the control of the complexity depends on only the variance, not the architecture, provided it is large enough. PMID:11359647

Ruiz De Angulo, V; Torras, C

2001-05-01

290

Accelerated convergence for synchronous approximate agreement  

NASA Technical Reports Server (NTRS)

The protocol for synchronous approximate agreement presented by Dolev et. al. exhibits the undesirable property that a faulty processor, by the dissemination of a value arbitrarily far removed from the values held by good processors, may delay the termination of the protocol by an arbitrary amount of time. Such behavior is clearly undesirable in a fault tolerant dynamic system subject to hard real-time constraints. A mechanism is presented by which editing data suspected of being from Byzantine-failed processors can lead to quicker, predictable, convergence to an agreement value. Under specific assumptions about the nature of values transmitted by failed processors relative to those transmitted by good processors, a Monte Carlo simulation is presented whose qualitative results illustrate the trade-off between accelerated convergence and the accuracy of the value agreed upon.

Kearns, J. P.; Park, S. K.; Sjogren, J. A.

1988-01-01

291

Approximate Acoustic Cloaking in Inhomogeneous Isotropic Space  

E-print Network

In this paper, we consider the approximate acoustic cloaking in inhomogeneous isotropic background space. By employing transformation media, together with the use of a sound-soft layer lining right outside the cloaked region, we show that one can achieve the near-invisibility by the `blow-up-a-small-region' construction. This is based on novel scattering estimates corresponding to small sound-soft obstacles located in isotropic space. One of the major novelties of our scattering estimates is that one cannot make use of the scaling argument in the setting of current study due to the simultaneous presence of asymptotically small obstacle components and regularly sized obstacle components, and one has to decouple the nonlinear scattering interaction between the small obstacle components and, the regular obstacle components together with the background medium.

Hongyu Liu

2010-10-27

292

Approximate Bayesian computation with functional statistics.  

PubMed

Functional statistics are commonly used to characterize spatial patterns in general and spatial genetic structures in population genetics in particular. Such functional statistics also enable the estimation of parameters of spatially explicit (and genetic) models. Recently, Approximate Bayesian Computation (ABC) has been proposed to estimate model parameters from functional statistics. However, applying ABC with functional statistics may be cumbersome because of the high dimension of the set of statistics and the dependences among them. To tackle this difficulty, we propose an ABC procedure which relies on an optimized weighted distance between observed and simulated functional statistics. We applied this procedure to a simple step model, a spatial point process characterized by its pair correlation function and a pollen dispersal model characterized by genetic differentiation as a function of distance. These applications showed how the optimized weighted distance improved estimation accuracy. In the discussion, we consider the application of the proposed ABC procedure to functional statistics characterizing non-spatial processes. PMID:23446870

Soubeyrand, Samuel; Carpentier, Florence; Guiton, François; Klein, Etienne K

2013-03-01

293

Approximation Preserving Reductions among Item Pricing Problems  

NASA Astrophysics Data System (ADS)

When a store sells items to customers, the store wishes to determine the prices of the items to maximize its profit. Intuitively, if the store sells the items with low (resp. high) prices, the customers buy more (resp. less) items, which provides less profit to the store. So it would be hard for the store to decide the prices of items. Assume that the store has a set V of n items and there is a set E of m customers who wish to buy those items, and also assume that each item i ? V has the production cost di and each customer ej ? E has the valuation vj on the bundle ej ? V of items. When the store sells an item i ? V at the price ri, the profit for the item i is pi = ri - di. The goal of the store is to decide the price of each item to maximize its total profit. We refer to this maximization problem as the item pricing problem. In most of the previous works, the item pricing problem was considered under the assumption that pi ? 0 for each i ? V, however, Balcan, et al. [In Proc. of WINE, LNCS 4858, 2007] introduced the notion of “loss-leader, ” and showed that the seller can get more total profit in the case that pi < 0 is allowed than in the case that pi < 0 is not allowed. In this paper, we derive approximation preserving reductions among several item pricing problems and show that all of them have algorithms with good approximation ratio.

Hamane, Ryoso; Itoh, Toshiya; Tomita, Kouhei

294

ON NUMBERS BADLY APPROXIMABLE BY Q-ADIC RATIONALS  

E-print Network

Approximable Numbers collected in this thesis are based upon the four papers, P1. J. Nilsson. On Numbers Badly Approximable by Dyadic Rationals. P2. J. Nilsson. On Numbers Badly Approximable Via the -shift. P3. J. Nilsson. The Fine Structure of Dyadically Badly Approximable Numbers. P4. J. Nilsson. The Fine Structure of q

Paris-Sud XI, Université de

295

A comparison of approximate interval estimators for the Bernoulli parameter  

NASA Technical Reports Server (NTRS)

The goal of this paper is to compare the accuracy of two approximate confidence interval estimators for the Bernoulli parameter p. The approximate confidence intervals are based on the normal and Poisson approximations to the binomial distribution. Charts are given to indicate which approximation is appropriate for certain sample sizes and point estimators.

Leemis, Lawrence; Trivedi, Kishor S.

1993-01-01

296

Approximation of high-degree and procedural curves  

Microsoft Academic Search

The objective of this paper is to present an efficient adaptive algorithm to approximate high-degree and procedural continuous parametric curves by integral B-splines. This approximation algorithm covers nonperiodic and periodic curves. The approximation algorithm is motivated and accompanied by an extensive discussion on approximation errors for position and derivatives accuracies. This discussion includes the derivation of local error bounds for

Franz-Erich Wolter; Séamus T. Tuohy

1992-01-01

297

Shock wave profiles in the burnett approximation  

PubMed

This paper is devoted to a discussion of the profiles of shock waves using the full nonlinear Burnett equations of hydrodynamics as they appear from the Chapman-Enskog solution to the Boltzmann equation. The system considered is a dilute gas composed of rigid spheres. The numerical analysis is carried out by transforming the hydrodynamic equations into a set of four first-order equations in four dimensions. We compare the numerical solutions of the Burnett equations, obtained using Adam's method, with the well known direct simulation Monte Carlo method for different Mach numbers. An exhaustive mathematical analysis of the results offered here has been done mainly in connection with the existence of heteroclinic trajectories between the two stationary points located upflow and downflow. The main result of this study is that such a trajectory exists for the Burnett equations for Mach numbers greater than 1. Our numerical calculations suggest that heteroclinic trajectories exist up to a critical Mach number ( approximately 2.69) where local mathematical analysis and numerical computations reveal a saddle-node-Hopf bifurcation. This upper limit for the existence of heteroclinic trajectories deserves further clarification. PMID:11102002

Uribe; Velasco; Garcia-Colin; Diaz-Herrera

2000-11-01

298

Network histograms and universality of blockmodel approximation.  

PubMed

In this paper we introduce the network histogram, a statistical summary of network interactions to be used as a tool for exploratory data analysis. A network histogram is obtained by fitting a stochastic blockmodel to a single observation of a network dataset. Blocks of edges play the role of histogram bins and community sizes that of histogram bandwidths or bin sizes. Just as standard histograms allow for varying bandwidths, different blockmodel estimates can all be considered valid representations of an underlying probability model, subject to bandwidth constraints. Here we provide methods for automatic bandwidth selection, by which the network histogram approximates the generating mechanism that gives rise to exchangeable random graphs. This makes the blockmodel a universal network representation for unlabeled graphs. With this insight, we discuss the interpretation of network communities in light of the fact that many different community assignments can all give an equally valid representation of such a network. To demonstrate the fidelity-versus-interpretability tradeoff inherent in considering different numbers and sizes of communities, we analyze two publicly available networks-political weblogs and student friendships-and discuss how to interpret the network histogram when additional information related to node and edge labeling is present. PMID:25275010

Olhede, Sofia C; Wolfe, Patrick J

2014-10-14

299

Adaptive approximation of higher order posterior statistics  

NASA Astrophysics Data System (ADS)

Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively.

Lee, Wonjung

2014-02-01

300

Configuring Airspace Sectors with Approximate Dynamic Programming  

NASA Technical Reports Server (NTRS)

In response to changing traffic and staffing conditions, supervisors dynamically configure airspace sectors by assigning them to control positions. A finite horizon airspace sector configuration problem models this supervisor decision. The problem is to select an airspace configuration at each time step while considering a workload cost, a reconfiguration cost, and a constraint on the number of control positions at each time step. Three algorithms for this problem are proposed and evaluated: a myopic heuristic, an exact dynamic programming algorithm, and a rollouts approximate dynamic programming algorithm. On problem instances from current operations with only dozens of possible configurations, an exact dynamic programming solution gives the optimal cost value. The rollouts algorithm achieves costs within 2% of optimal for these instances, on average. For larger problem instances that are representative of future operations and have thousands of possible configurations, excessive computation time prohibits the use of exact dynamic programming. On such problem instances, the rollouts algorithm reduces the cost achieved by the heuristic by more than 15% on average with an acceptable computation time.

Bloem, Michael; Gupta, Pramod

2010-01-01

301

Rainbows: Mie computations and the Airy approximation.  

PubMed

Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution f rom the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work. PMID:20581954

Wang, R T; van de Hulst, H C

1991-01-01

302

Network histograms and universality of blockmodel approximation  

PubMed Central

In this paper we introduce the network histogram, a statistical summary of network interactions to be used as a tool for exploratory data analysis. A network histogram is obtained by fitting a stochastic blockmodel to a single observation of a network dataset. Blocks of edges play the role of histogram bins and community sizes that of histogram bandwidths or bin sizes. Just as standard histograms allow for varying bandwidths, different blockmodel estimates can all be considered valid representations of an underlying probability model, subject to bandwidth constraints. Here we provide methods for automatic bandwidth selection, by which the network histogram approximates the generating mechanism that gives rise to exchangeable random graphs. This makes the blockmodel a universal network representation for unlabeled graphs. With this insight, we discuss the interpretation of network communities in light of the fact that many different community assignments can all give an equally valid representation of such a network. To demonstrate the fidelity-versus-interpretability tradeoff inherent in considering different numbers and sizes of communities, we analyze two publicly available networks—political weblogs and student friendships—and discuss how to interpret the network histogram when additional information related to node and edge labeling is present. PMID:25275010

Olhede, Sofia C.; Wolfe, Patrick J.

2014-01-01

303

Approximate algorithms for partitioning and assignment problems  

NASA Technical Reports Server (NTRS)

The problem of optimally assigning the modules of a parallel/pipelined program over the processors of a multiple computer system under certain restrictions on the interconnection structure of the program as well as the multiple computer system was considered. For a variety of such programs it is possible to find linear time if a partition of the program exists in which the load on any processor is within a certain bound. This method, when combined with a binary search over a finite range, provides an approximate solution to the partitioning problem. The specific problems considered were: a chain structured parallel program over a chain-like computer system, multiple chain-like programs over a host-satellite system, and a tree structured parallel program over a host-satellite system. For a problem with m modules and n processors, the complexity of the algorithm is no worse than O(mnlog(W sub T/epsilon)), where W sub T is the cost of assigning all modules to one processor and epsilon the desired accuracy.

Iqbal, M. A.

1986-01-01

304

On Approximation of Functions on the Sphere  

NASA Astrophysics Data System (ADS)

Let S^n be the unit sphere in \\mathbf{R}^{n+1} ( n \\geqslant 1) with center at the origin of coordinates, and let \\Vert\\cdot\\Vert_p be the norm in the space L_p(S^n), 1\\leqslant p\\leqslant\\infty ( L_\\infty(S^n)\\equiv C(S^n)). Problems posed by Butzer, Johnen [4], and Wehrens (Appróximationstheorie auf der Einheitskugel in R^3. Legendre-Transformationsmethoden und Anwendungen, Forschungsberichte Landes Nordrhein-Westfalen No. 3090, 1981) are solved; namely, a direct theorem on best approximation is proved for the modulus of smoothness of arbitrary (fractional) order r ( r > 0) \\displaystyle \\omega_r(f;\\tau)_p := \\sup_{0 < t\\leqslant\\tau}\\Vert (E-\\operatorname{sh}_t)^{r/2}f\\Vert_p,\\qquad0 < \\tau < \\pi, where \\operatorname{sh}_t is the shift operator on the sphere, \\displaystyle (\\operatorname{sh}_tf)(\\theta)=\\frac{\\Gamma(n/2)}{2\\pi^{n/2}(\\sin t)^{n-1}}\\int_{\\theta\\cdot\\mu=\\cos t} f(\\mu)\\,dt(\\mu),\\qquad 0 < t < \\pi, and its equivalence to the K-functional is proved. Special cases of the results established were known from work of Kushnirenko, Butzer, and Johnen, Löfström and Peetre, Pawelke, Lizorkin and Nikol'skii, Kalyabin, and others.

Rustamov, Kh P.

1994-04-01

305

Improved Discrete Approximation of Laplacian of Gaussian  

NASA Technical Reports Server (NTRS)

An improved method of computing a discrete approximation of the Laplacian of a Gaussian convolution of an image has been devised. The primary advantage of the method is that without substantially degrading the accuracy of the end result, it reduces the amount of information that must be processed and thus reduces the amount of circuitry needed to perform the Laplacian-of- Gaussian (LOG) operation. Some background information is necessary to place the method in context. The method is intended for application to the LOG part of a process of real-time digital filtering of digitized video data that represent brightnesses in pixels in a square array. The particular filtering process of interest is one that converts pixel brightnesses to binary form, thereby reducing the amount of information that must be performed in subsequent correlation processing (e.g., correlations between images in a stereoscopic pair for determining distances or correlations between successive frames of the same image for detecting motions). The Laplacian is often included in the filtering process because it emphasizes edges and textures, while the Gaussian is often included because it smooths out noise that might not be consistent between left and right images or between successive frames of the same image.

Shuler, Robert L., Jr.

2004-01-01

306

A simple, approximate model of parachute inflation  

SciTech Connect

A simple, approximate model of parachute inflation is described. The model is based on the traditional, practical treatment of the fluid resistance of rigid bodies in nonsteady flow, with appropriate extensions to accommodate the change in canopy inflated shape. Correlations for the steady drag and steady radial force as functions of the inflated radius are required as input to the dynamic model. In a novel approach, the radial force is expressed in terms of easily obtainable drag and reefing fine tension measurements. A series of wind tunnel experiments provides the needed correlations. Coefficients associated with the added mass of fluid are evaluated by calibrating the model against an extensive and reliable set of flight data. A parameter is introduced which appears to universally govern the strong dependence of the axial added mass coefficient on motion history. Through comparisons with flight data, the model is shown to realistically predict inflation forces for ribbon and ringslot canopies over a wide range of sizes and deployment conditions.

Macha, J.M.

1992-01-01

307

A simple, approximate model of parachute inflation  

SciTech Connect

A simple, approximate model of parachute inflation is described. The model is based on the traditional, practical treatment of the fluid resistance of rigid bodies in nonsteady flow, with appropriate extensions to accommodate the change in canopy inflated shape. Correlations for the steady drag and steady radial force as functions of the inflated radius are required as input to the dynamic model. In a novel approach, the radial force is expressed in terms of easily obtainable drag and reefing fine tension measurements. A series of wind tunnel experiments provides the needed correlations. Coefficients associated with the added mass of fluid are evaluated by calibrating the model against an extensive and reliable set of flight data. A parameter is introduced which appears to universally govern the strong dependence of the axial added mass coefficient on motion history. Through comparisons with flight data, the model is shown to realistically predict inflation forces for ribbon and ringslot canopies over a wide range of sizes and deployment conditions.

Macha, J.M.

1992-11-01

308

An approximate treatment of gravitational collapse  

NASA Astrophysics Data System (ADS)

This work studies a simplified model of the gravitational instability of an initially homogeneous infinite medium, represented by Td, based on the approximation that the mean fluid velocity is always proportional to the local acceleration. It is shown that, mathematically, this assumption leads to the restricted Patlak-Keller-Segel model considered by Jäger and Luckhaus or, equivalently, the Smoluchowski equation describing the motion of self-gravitating Brownian particles, coupled to the modified Newtonian potential that is appropriate for an infinite mass distribution. We discuss some of the fundamental properties of a non-local generalization of this model where the effective pressure force is given by a fractional Laplacian with 0

Ascasibar, Yago; Granero-Belinchón, Rafael; Moreno, José Manuel

2013-11-01

309

Magnetic reconnection under anisotropic magnetohydrodynamic approximation  

SciTech Connect

We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless MHD codes based on the double adiabatic approximation and the Landau closure model. We bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observations. Our results showed that once magnetic reconnection takes place, a firehose-sense (p{sub ?}>p{sub ?}) pressure anisotropy arises in the downstream region, and the generated slow shocks are quite weak comparing with those in an isotropic MHD. In spite of the weakness of the shocks, however, the resultant reconnection rate is 10%–30% higher than that in an isotropic case. This result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere.

Hirabayashi, K.; Hoshino, M. [Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo (Japan)] [Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo (Japan)

2013-11-15

310

Approximation Schemes for Scheduling with Availability Constraints  

NASA Astrophysics Data System (ADS)

We investigate the problems of scheduling n weighted jobs to m identical machines with availability constraints. We consider two different models of availability constraints: the preventive model where the unavailability is due to preventive machine maintenance, and the fixed job model where the unavailability is due to a priori assignment of some of the n jobs to certain machines at certain times. Both models have applications such as turnaround scheduling or overlay computing. In both models, the objective is to minimize the total weighted completion time. We assume that m is a constant, and the jobs are non-resumable. For the preventive model, it has been shown that there is no approximation algorithm if all machines have unavailable intervals even when w i = p i for all jobs. In this paper, we assume there is one machine permanently available and the processing time of each job is equal to its weight for all jobs. We develop the first PTAS when there are constant number of unavailable intervals. One main feature of our algorithm is that the classification of large and small jobs is with respect to each individual interval, thus not fixed. This classification allows us (1) to enumerate the assignments of large jobs efficiently; (2) and to move small jobs around without increasing the objective value too much, and thus derive our PTAS. Then we show that there is no FPTAS in this case unless P = NP.

Fu, Bin; Huo, Yumei; Zhao, Hairong

311

Approximate Inference in Stochastic Processes and Dynamical Systems Approximate Bayesian Computation: a simulation based  

E-print Network

of an acceptance rate. In this talk I shall introduce a group of Monte Carlo methods that can be used to perform Carlo techniques usually go under the name of Approx- imate Bayesian Computation (ABC) [1], and although distribution. Approximate likelihood-free Markov Chain Monte Carlo algorithms [2] and approx- imate sequential

Rattray, Magnus

312

Interpretation of approximate entropy: analysis of intracranial pressure approximate entropy during acute intracranial hypertension  

Microsoft Academic Search

We studied changes in intracranial pressure (ICP) complexity, estimated by the approximate entropy (ApEn) of the ICP signal, as subjects progressed from a state of normal ICP (25 mmHg for ? 5 min). We hypothesized that the measures of intracranial pressure (ICP) complexity and irregularity would decrease during acute elevations in ICP. To test this hypothesis we studied ICP spikes

Roberto Hornero; Mateo Aboy; Daniel Abásolo; James McNames; Brahm Goldstein

2005-01-01

313

Guillotine subdivisions approximate polygonal subdivisions: Part III --Faster polynomialtime approximation schemes for  

E-print Network

­time approximation schemes for geometric network optimization \\Lambda Joseph S. B. Mitchell y April 19, 1997; Last=ffl) time algorithms of Arora [1] and Mitchell [10]. Arora [2] has recently obtained even better of an ``m­guillotine subdivision'', which were introduced by Mitchell [9, 10]. Roughly speaking, an ``m

Mitchell, Joseph S.B.

314

Bond selective chemistry beyond the adiabatic approximation  

SciTech Connect

One of the most important challenges in chemistry is to develop predictive ability for the branching between energetically allowed chemical reaction pathways. Such predictive capability, coupled with a fundamental understanding of the important molecular interactions, is essential to the development and utilization of new fuels and the design of efficient combustion processes. Existing transition state and exact quantum theories successfully predict the branching between available product channels for systems in which each reaction coordinate can be adequately described by different paths along a single adiabatic potential energy surface. In particular, unimolecular dissociation following thermal, infrared multiphoton, or overtone excitation in the ground state yields a branching between energetically allowed product channels which can be successfully predicted by the application of statistical theories, i.e. the weakest bond breaks. (The predictions are particularly good for competing reactions in which when there is no saddle point along the reaction coordinates, as in simple bond fission reactions.) The predicted lack of bond selectivity results from the assumption of rapid internal vibrational energy redistribution and the implicit use of a single adiabatic Born-Oppenheimer potential energy surface for the reaction. However, the adiabatic approximation is not valid for the reaction of a wide variety of energetic materials and organic fuels; coupling between the electronic states of the reacting species play a a key role in determining the selectivity of the chemical reactions induced. The work described below investigated the central role played by coupling between electronic states in polyatomic molecules in determining the selective branching between energetically allowed fragmentation pathways in two key systems.

Butler, L.J. [Univ. of Chicago, IL (United States)

1993-12-01

315

Differential equation based method for accurate approximations in optimization  

NASA Technical Reports Server (NTRS)

A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

316

Analytic approximations to Kelvin functions with applications to electromagnetics  

NASA Astrophysics Data System (ADS)

We present analytical approximations for the real Kelvin function ber x and the imaginary Kelvin function bei x, using the two-point quasi-fractional approximation procedure. We have applied these approximations to the calculation of the current distribution within a cylindrical conductor. Our approximations are simple and accurate. An infinite number of roots is also obtained with the approximation and precision increases with the value of the root. Our results could find useful applications in problems where analytical approximations of the Kelvin functions are needed.

Brualla, L.; Martin, P.

2001-11-01

317

Three fast computational approximation methods in hypersonic aerothermodynamics  

E-print Network

Three fast computational approximation methods in hypersonic aerothermodynamics V.V. Riabov* Rivier analyzed to study nonequilibrium hypersonic viscous flows near blunt bodies. These approximations allow; Nonequilibrium hypersonic flows 1. Introduction Numerous methods [1,2] that require significant computational

Riabov, Vladimir V.

318

UNIFORM RECTIFIABILITY, CARLESON MEASURE ESTIMATES, AND APPROXIMATION OF HARMONIC FUNCTIONS  

E-print Network

UNIFORM RECTIFIABILITY, CARLESON MEASURE ESTIMATES, AND APPROXIMATION OF HARMONIC FUNCTIONS STEVE rectifiable set of dimension n. Then bounded harmonic functions in := Rn+1 \\ E satisfy Carleson measure25, 42B37. Key words and phrases. Carleson measures, -approximability, uniform rectifiability

Mayboroda, Svitlana

319

A short proof of the Approximation Conjecture for amenable groups  

Microsoft Academic Search

We give a short proof of the Approximation Conjecture with complex coefficients for amenable groups [G. Elek, The Strong Approximation Conjecture holds for amenable groups, J. Funct. Anal. 239 (1) (2006) 345–355].

Daniel Pape

2008-01-01

320

New Approximation Algorithms for the Unsplittable Capacitated Facility Location  

E-print Network

New Approximation Algorithms for the Unsplittable Capacitated Facility Location Problem Babak (hard) Capaci- tated Facility Location Problem (UCFLP) with uniform capacities and present some new approximation algorithms for it. This problem is a generalization of the classical facility location problem

Salavatipour, Mohammad R.

321

Logic Systems for Approximate Reasoning via Rough Sets and Topology  

E-print Network

toward the formalization of what Hao Wang called ``approximate proof '' three decades ago. 1 Introduction as a small step toward a formalization of what Hao Wang called ``approximate proof'' [17]. 2 Neighborhood

Lin, Tsau Young

322

Approximation Algorithms and Heuristics for a Heterogeneous Traveling Salesman Problem  

E-print Network

minimum spanning tree algorithm. We use 3 different approaches to solve the sequencing problem; namely, the 2 approximation algorithm, Christofide's algorithm and the Lin - Kernighan Heuristic (LKH). The approximation algorithms were implemented in MATLAB...

Rangarajan, Rahul

2011-08-08

323

On the Consistency of the Ladder Approximation and the Rainbow Approximation of Dyson-Schwinger Equation of QCD  

E-print Network

We study the consistency of the ladder approximation and the rainbow approximation of the Dyson-Schwinger equation of QCD. By considering the non-Abelian property of QCD, we show that the QED-type Ward-Takahashi identity is not required for the rainbow-ladder approximation of QCD. It indicates that there does not exists any internal inconsistency in the usual rainbow-ladder approximation of QCD. In addition, we propose an modified ladder approximation which guarantees the Slavnov-Taylor identity for the quark-gluon vertex omitting the ghost effect in the approximation.

Lei Chang; Yu-xin Liu

2006-10-14

324

Pawlak algebra and approximate structure on fuzzy lattice.  

PubMed

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties. PMID:25152922

Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai

2014-01-01

325

Approximability of identifying codes and locating-dominating codes  

Microsoft Academic Search

We study the approximability and inapproximability of finding identifying codes and locating-dominating codes of the minimum size. In general graphs, we show that it is possible to approximate both problems within a logarithmic factor, but sublog- arithmic approximation ratios are intractable. In bounded-degree graphs, there is a trivial constant-factor approximation algorithm, but arbitrarily low approxima- tion ratios remain intractable. In

Jukka Suomela

2007-01-01

326

A unified approach to the Darwin approximation Todd B. Krause  

E-print Network

's theory are not. We present here action principles for the Darwin approximation in the Vlasov contextA unified approach to the Darwin approximation Todd B. Krause Institute for Fusion Studies to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge

Morrison, Philip J.,

327

Pitch Contour Stylization Using an Optimal Piecewise Polynomial Approximation  

Microsoft Academic Search

We propose a dynamic programming (DP) based piecewise polynomial approximation of discrete data such that the L 2 norm of the approximation error is minimized. We apply this technique for the stylization of speech pitch contour. Objective evaluation verifies that the DP based technique indeed yields minimum mean square error (MSE) compared to other approximation methods. Subjective evaluation reveals that

Prasanta Kumar Ghosh; Shrikanth S. Narayanan

2009-01-01

328

Radial basis approximation and its application to biharmonic equation  

Microsoft Academic Search

Order of approximating functions and their derivatives by radial bases on arbitrarily scattered data is derived. And then\\u000a radial bases are used to construct solutions of biharmonic equations that approximate potential integrals for the exact solutions\\u000a with the order of approximation derived.

Xin Li

2010-01-01

329

Modulated power-law behaviour in Stirling's approximation  

E-print Network

Modulated power-law behaviour in Stirling's approximation Les Hatton CISM, University of Kingston. This argument used Stirling's approximation which limits its relevance to larger component sizes. Although power to broaden Stirling's approximation to see if it corresponds with the departures from power-law observed

Hatton, Les

330

Accurate Approximations for Posterior Moments and Marginal Densities  

Microsoft Academic Search

This article describes approximations to the posterior means and variances of positive functions of a real or vector-valued parameter, and to the marginal posterior densities of arbitrary (i.e., not necessarily positive) parameters. These approximations can also be used to compute approximate predictive densities. To apply the proposed method, one only needs to be able to maximize slightly modified likelihood functions

Luke Tierney; Joseph B. Kadane

1986-01-01

331

Invariant approximations of robustly positively invariant sets for constrained  

E-print Network

Invariant approximations of robustly positively invariant sets for constrained linear discrete/F-INFENG/TR.473 8 January 2004 #12;Invariant approximations of robustly positively invariant sets for constrained of Cambridge, UK 8 January 2004 Abstract This paper provides results on invariant approximations of robustly

Cambridge, University of

332

Smoluchowski-Kramers approximation in the case of variable friction  

E-print Network

We consider the small mass asymptotics (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The limit of the solution in the classical sense does not exist in this case. We study a modification of the Smoluchowski-Kramers approximation. Some applications of the Smoluchowski-Kramers approximation to problems with fast oscillating or discontinuous coefficients are considered.

Mark Freidlin; Wenqing Hu

2012-03-03

333

High order approximation of conic sections by quadratic splines  

E-print Network

High order approximation of conic sections by quadratic splines Michael Floater SINTEF P.O. Box 124, Blindern 0314 Oslo Norway December 1993. Revised, October 1994 Abstract. Given a segment of a conic section and cylinder. Keywords. approximation, conic sections, quadratic splines §1. Introduction The approximate

Floater, Michael S.

334

Fast and Precise Regular Approximation of Logic Programs  

Microsoft Academic Search

A practical procedure for computing a regular approximation of a logic program is given. The algorithm shown here incorporates optimisations taken from deductive database fixpoint algorithms and efficient abstract interpretation techniques. Regular approximations can be applied to a variety of tasks in debugging and program specialisation. Frameworks for defining regular approximations have been put forward in the past, but previously

J. P. Gallagher; D. A. de Waal

1993-01-01

335

The Use of Approximations in a High School Chemistry Course  

ERIC Educational Resources Information Center

While approximations are used frequently in science, high school students may be unaware of the use of approximations in science, the motivation for their use, and the limitations of their use. In the article, we consider the use of approximations in a high school chemistry class as opportunities to increase student understanding of the use of…

Matsumoto, Paul S.; Tong, Gary; Lee, Stephanie; Kam, Bonita

2009-01-01

336

ON NUMBERS BADLY APPROXIMABLE BY Q-ADIC RATIONALS  

E-print Network

collected in this thesis are based upon the four papers, P1. J. Nilsson. On Numbers Badly Approximable by Dyadic Rationals. P2. J. Nilsson. On Numbers Badly Approximable Via the -shift. P3. J. Nilsson. The Fine Structure of Dyadically Badly Approximable Numbers. P4. J. Nilsson. The Fine Structure of q-adically Badly

Nilsson, Johan

337

Accurate Period Approximation for Any Simple Pendulum Amplitude  

Microsoft Academic Search

Accurate approximate analytical formulae of the pendulum period composed of a few elementary functions for any amplitude are constructed. Based on an approximation of the elliptic integral, two new logarithmic formulae for large amplitude close to 180° are obtained. Considering the trigonometric function modulation results from the dependence of relative error on the amplitude, we realize accurate approximation period expressions

Xue De-Sheng; Zhou Zhao; Gao Mei-Zhen

2012-01-01

338

-FINE APPROXIMATION OF FUNCTIONS ON BANACH SPACES WITH UNCONDITIONAL BASIS  

E-print Network

C1 -FINE APPROXIMATION OF FUNCTIONS ON BANACH SPACES WITH UNCONDITIONAL BASIS by DANIEL AZAGRA of Ck-fine approximation when k > 0 is much less understood and not generally amenable to a solution when the identity map is concerned!) a fine approximation by E-mail: daniel azagra@mat.ucm.es E

Azagra Rueda, Daniel

339

Approximate exchange perturbation study of intermolecular interactions in molecular complexes  

Microsoft Academic Search

In an attempt to rationalize and improve an approximate exchange perturbation scheme related to the model of Murrell et al., more accurate approximations are introduced eliminating the use of empirical parameters. The total interaction energy was evaluated as the sum of additive electrostatic, exchange, charge transfer, and dispersion contributions. It is proven that the assumption of intramolecular ZDO approximation is

W. Andrzej Sokalski; Henryk Chojnacki

1978-01-01

340

Approximation Algorithms for Facility Location Problems Adriana Bumb  

E-print Network

Approximation Algorithms for Facility Location Problems Adriana Bumb 2002 Ph.D. thesis University.tup.utwente.nl/tupress/catalogue/book/index.jsp?isbn=9036517877 Twente University Press #12;Approximation Algorithms For Facility Location Problems #12;Publisher;APPROXIMATION ALGORITHMS FOR FACILITY LOCATION PROBLEMS PROEFSCHRIFT ter verkrijging van de graad van doctor aan

Gabor, Adriana

341

Local RBF Approximation for Scattered Data Fitting with Bivariate Splines  

E-print Network

Local RBF Approximation for Scattered Data Fitting with Bivariate Splines Oleg Davydov, Alessandra at developing efficient meth- ods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used

Davydov, Oleg

342

The hard pulse approximation for the AKNS 2 2-system  

E-print Network

scattering transform for this hard pulse approximation converge to the expected continuum potential pointwiseThe hard pulse approximation for the AKNS 2 Ã? 2-system Charles L. Epstein and Jeremy Magland LSNI, 2005 Abstract In the hard pulse approximation, commonly used in nuclear magnetic reso- nance, one

343

A MODICA-MORTOLA APPROXIMATION FOR THE STEINER PROBLEM  

E-print Network

A MODICA-MORTOLA APPROXIMATION FOR THE STEINER PROBLEM ANTOINE LEMENANT AND FILIPPO SANTAMBROGIO Abstract. In this note we present a way to approximate the Steiner problem by a family of elliptic energies : Une approximation `a la Modica-Mortola pour le probl`eme de Steiner. Version franc¸aise abr´eg´ee Le

Paris-Sud XI, Université de

344

Approximation Hardness of the (1; 2)-Steiner Tree Problem  

E-print Network

Approximation Hardness of the (1; 2)- Steiner Tree Problem Mathias Hauptmann #3; Abstract We give a survey on the approximation hardness of the Steiner Tree Problem. While for the general metric case to the (1,2)-Steiner Tree Problem due to Bern and Plassmann [BP89] with approximation hardness results

Eckmiller, Rolf

345

Dierential approximation results for the Steiner tree problem Marc Demange  

E-print Network

Dierential approximation results for the Steiner tree problem Marc Demange ESSEC, Dept. SID demange,paschos}@lamsade.dauphine.fr Abstract We study the approximability of three versions of the Steiner tree problem. For the rst one where approximable within 0.82. Also, we extend the result of (M. Bern and P. Plassmann The Steiner problem with edge

Paris-Sud XI, Université de

346

Mappings and accuracy for Chebyshev pseudo-spectral approximations  

NASA Technical Reports Server (NTRS)

The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials which can be accurately approximated by Chebyshev polynomial expansions. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in approximations. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than in physical space or where mappings constructed from other strategies are employed.

Bayliss, Alvin; Turkel, Eli

1990-01-01

347

Complex angular momentum approximation to hard-core scattering  

NASA Technical Reports Server (NTRS)

The complex angular momentum (CAM) approximation for nonrelativistic quantum scattering by a hard sphere - a union of the recently developed CAM uniform approximation with a semiclassical WKB-like approximation valid at large angles - is shown to be remarkably accurate over the complete range of scattering angles and down to size parameters (circumference to de Broglie wavelength ratios) of order unity. The best approximations previously derivable (Fock-type) cannot reach large scattering angles where semiclassical approximations are useful; even at angles where Fock-type approximations are valid, they are typically two or more orders of magnitude less accurate than CAM. The crucial new feature responsible for the high accuracy of the CAM approximation is the treatment of large-angle diffraction associated with (1) tunneling near the edge of the scatterer, and (2) anomalous reflection.

Nussenzveig, H. M.; Wiscombe, W. J.

1991-01-01

348

A Posteriori Error Estimation for Finite Volume and Finite Element Approximations Using Broken Space Approximation  

NASA Technical Reports Server (NTRS)

We consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.

Barth, Timothy J.; Larson, Mats G.

2000-01-01

349

Approximation Set of the Interval Set in Pawlak's Space  

PubMed Central

The interval set is a special set, which describes uncertainty of an uncertain concept or set Z with its two crisp boundaries named upper-bound set and lower-bound set. In this paper, the concept of similarity degree between two interval sets is defined at first, and then the similarity degrees between an interval set and its two approximations (i.e., upper approximation set R¯(Z) and lower approximation set R_(Z)) are presented, respectively. The disadvantages of using upper-approximation set R¯(Z) or lower-approximation set R_(Z) as approximation sets of the uncertain set (uncertain concept) Z are analyzed, and a new method for looking for a better approximation set of the interval set Z is proposed. The conclusion that the approximation set R 0.5(Z) is an optimal approximation set of interval set Z is drawn and proved successfully. The change rules of R 0.5(Z) with different binary relations are analyzed in detail. Finally, a kind of crisp approximation set of the interval set Z is constructed. We hope this research work will promote the development of both the interval set model and granular computing theory. PMID:25177721

Wang, Jin; Wang, Guoyin

2014-01-01

350

A Lattice-Theoretic Approach to Multigranulation Approximation Space  

PubMed Central

In this paper, we mainly investigate the equivalence between multigranulation approximation space and single-granulation approximation space from the lattice-theoretic viewpoint. It is proved that multigranulation approximation space is equivalent to single-granulation approximation space if and only if the pair of multigranulation rough approximation operators (?i=1nRi¯,?i=1nRi_) forms an order-preserving Galois connection, if and only if the collection of lower (resp., upper) definable sets forms an (resp., union) intersection structure, if and only if the collection of multigranulation upper (lower) definable sets forms a distributive lattice when n = 2, and if and only if ?X?U,???i=1nRi_(X)=?i=1nRi_(X). The obtained results help us gain more insights into the mathematical structure of multigranulation approximation spaces. PMID:25243226

He, Xiaoli

2014-01-01

351

Energetics of a fluid under the Boussinesq approximation  

E-print Network

This paper presents a theory describing the energy budget of a fluid under the Boussinesq approximation: the theory is developed in a manner consistent with the conservation law of mass. It shows that no potential energy is available under the Boussinesq approximation, and also reveals that the work done by the buoyancy force due to changes in temperature corresponds to the conversion between kinetic and internal energy. This energy conversion, however, makes only an ignorable contribution to the distribution of temperature under the approximation. The Boussinesq approximation is, in physical oceanography, extended so that the motion of seawater can be studied. This paper considers this extended approximation as well. Under the extended approximation, the work done by the buoyancy force due to changes in salinity corresponds to the conversion between kinetic and potential energy. It also turns out that the conservation law of mass does not allow the condition $\

Maruyama, Kiyoshi

2014-01-01

352

Error Estimates for Approximate Optimization by the Extended Ritz Method  

Microsoft Academic Search

An alternative to the classical Ritz method for approximate optimization is investi- gated. In the extended Ritz method, sets of admissible solutions are approximated by their intersec- tions with sets of linear combinations of all n-tuples of functions from a given basis. This alternative scheme, called variable-basis approximation, includes functions computable by trigonometric poly- nomials with free frequencies, free-node splines,

Vera Kurková; Marcello Sanguineti

2005-01-01

353

Approximate equivalence and synchronization of metric transition systems  

Microsoft Academic Search

In this paper, we consider metric transition systems which are transition systems equipped with metrics for observation and synchronization labels. The existence of metrics leads to the introduction of two new concepts, (i) (?,?)-approximate (bi)simulation of transition systems and (ii) approximate synchronization of transition systems.We show that the notion of (?,?)-approximate (bi)simulation can be thought of as a generalization or

A. Agung Julius; Alessandro D’Innocenzo; Maria Domenica Di Benedetto; George J. Pappas

2009-01-01

354

Multijet final states: exact results and the leading pole approximation  

SciTech Connect

Exact results for the process gg ..-->.. ggg are compared with those obtained using the leading pole approximation. Regions of phase space where the approximation breaks down are discussed. A specific example relevant for background estimates to W boson production is presented. It is concluded that in this instance the leading pole approximation may underestimate the standard QCD background by more than a factor of two in certain kinematic regions of physical interest.

Ellis, R.K.; Owens, J.F.

1984-09-01

355

Analysis of a Force-Based Quasicontinuum Approximation  

Microsoft Academic Search

We analyze a force-based quasicontinuum approximation to a one-dimensional system of atoms that interact by a classical atomistic potential. This force-based quasicontinuum approximation is derived as the modification of an energy-based quasicontinuum approximation by the addition of nonconservative forces to correct nonphysical ``ghost'' forces that occur in the atomistic to continuum interface. We prove that the force-based quasicontinuum equations have

Matthew Dobson; Mitchell Luskin

2006-01-01

356

Approximation forte et topologie des varits sur un corps valu  

E-print Network

Approximation forte et topologie des variétés sur un corps valué Laurent Moret-Bailly IRMAR-Bailly (IRMAR) Approximation et topologie Laumon, 25/06/2012 1 / 29 #12;Notations (pour tout l'exposé) R : un) Approximation et topologie Laumon, 25/06/2012 2 / 29 #12;Notations (pour tout l'exposé) R : un anneau de

Moret-Bailly, Laurent

357

Approximation forte et topologie des varits sur un corps valu  

E-print Network

Approximation forte et topologie des variétés sur un corps valué Laurent Moret-Bailly IRMAR-Bailly (IRMAR) Approximation et topologie Laumon, 25/06/2012 1 / 29 #12;Notations (pour tout l'exposé) R : un) Approximation et topologie Laumon, 25/06/2012 2 / 29 #12;La topologie de la valuation Le corps valué K est un

Moret-Bailly, Laurent

358

Optimal initial approximations for the Newton-Raphson division algorithm  

Microsoft Academic Search

Newton-Raphson iteration provides a high-speed method for performing division. The Newton-Raphson division algorithm begins with an initial approximation to the reciprocal of the divisor. This value is iteratively refined until a specified accuracy is achieved. In this paper, we develop methods for selecting constant and linear approximations which minimize the maximum absolute error of the final result. These approximations are

Michael J. Schulte; J. Omar; Earl E. Swartzlander Jr.

1994-01-01

359

Number-Conserving Approximation to the Shell Model  

Microsoft Academic Search

The broken-pair-approximation (BPA) formalism is presented in this paper in complete form for the description of the nuclear properties of medium and heavy spherical nuclei. Starting from an approximate ground state of even nuclei having BCS-type pair distribution in the valence shells, the model Hilbert space is constructed by replacing one, two,... pairs in the assumed approximate ground state by

Y. K. Gambhir; A. Rimini; T. Weber

1969-01-01

360

Orthogonal polynomial approximation in higher dimensions: Applications in astrodynamics  

NASA Astrophysics Data System (ADS)

We propose novel methods to utilize orthogonal polynomial approximation in higher dimension spaces, which enable us to modify classical differential equation solvers to perform high precision, long-term orbit propagation. These methods have immediate application to efficient propagation of catalogs of Resident Space Objects (RSOs) and improved accounting for the uncertainty in the ephemeris of these objects. More fundamentally, the methodology promises to be of broad utility in solving initial and two point boundary value problems from a wide class of mathematical representations of problems arising in engineering, optimal control, physical sciences and applied mathematics. We unify and extend classical results from function approximation theory and consider their utility in astrodynamics. Least square approximation, using the classical Chebyshev polynomials as basis functions, is reviewed for discrete samples of the to-be-approximated function. We extend the orthogonal approximation ideas to n-dimensions in a novel way, through the use of array algebra and Kronecker operations. Approximation of test functions illustrates the resulting algorithms and provides insight into the errors of approximation, as well as the associated errors arising when the approximations are differentiated or integrated. Two sets of applications are considered that are challenges in astrodynamics. The first application addresses local approximation of high degree and order geopotential models, replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. A method is introduced which adapts the approximation degree radially, compatible with the truth that the highest degree approximations (to ensure maximum acceleration error < 10-9 ms-2, globally) are required near the Earths surface, whereas lower degree approximations are required as radius increases. We show that a four order of magnitude speedup is feasible, with both speed and storage efficiency op- timized using radial adaptation. The second class of problems addressed includes orbit propagation and solution of associated boundary value problems. The successive Chebyshev-Picard path approximation method is shown well-suited to solving these problems with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. Used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss.

Bani Younes, Ahmad Hani Abd Alqader

361

Monotonically improving approximate answers to relational algebra queries  

NASA Technical Reports Server (NTRS)

We present here a query processing method that produces approximate answers to queries posed in standard relational algebra. This method is monotone in the sense that the accuracy of the approximate result improves with the amount of time spent producing the result. This strategy enables us to trade the time to produce the result for the accuracy of the result. An approximate relational model that characterizes appromimate relations and a partial order for comparing them is developed. Relational operators which operate on and return approximate relations are defined.

Smith, Kenneth P.; Liu, J. W. S.

1989-01-01

362

An approximation based global optimization strategy for structural synthesis  

NASA Technical Reports Server (NTRS)

A global optimization strategy for structural synthesis based on approximation concepts is presented. The methodology involves the solution of a sequence of highly accurate approximate problems using a global optimization algorithm. The global optimization algorithm implemented consists of a branch and bound strategy based on the interval evaluation of the objective function and constraint functions, combined with a local feasible directions algorithm. The approximate design optimization problems are constructed using first order approximations of selected intermediate response quantities in terms of intermediate design variables. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure setforth.

Sepulveda, A. E.; Schmit, L. A.

1991-01-01

363

Master's Thesis Approximation and analysis of confluent hypergeometric differential  

E-print Network

the calculation cost of computer loaded at missile, we will find simple approximation of solution of confluent to air missile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Missile

Kim, Yong Jung

364

Legendre-Tau approximations for functional differential equations  

NASA Technical Reports Server (NTRS)

The numerical approximation of solutions to linear 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 approximations is made.

Ito, K.; Teglas, R.

1983-01-01

365

Accurate Period Approximation for Any Simple Pendulum Amplitude  

NASA Astrophysics Data System (ADS)

Accurate approximate analytical formulae of the pendulum period composed of a few elementary functions for any amplitude are constructed. Based on an approximation of the elliptic integral, two new logarithmic formulae for large amplitude close to 180° are obtained. Considering the trigonometric function modulation results from the dependence of relative error on the amplitude, we realize accurate approximation period expressions for any amplitude between 0 and 180°. A relative error less than 0.02% is achieved for any amplitude. This kind of modulation is also effective for other large-amplitude logarithmic approximation expressions.

Xue, De-Sheng; Zhou, Zhao; Gao, Mei-Zhen

2012-04-01

366

Approximating the physical inner product of Loop Quantum Cosmology  

E-print Network

In this article, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: Firstly, we compute it analytically via a trick, secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We will find that the approximation is able to recover the analytic solution of the problem, which solidifies hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity.

Benjamin Bahr; Thomas Thiemann

2006-07-19

367

Bethe free-energy approximations for disordered quantum systems.  

PubMed

Given a locally consistent set of reduced density matrices, we construct approximate density matrices which are globally consistent with the local density matrices we started from when the trial density matrix has a tree structure. We employ the cavity method of statistical physics to find the optimal density matrix representation by slowly decreasing the temperature in an annealing algorithm, or by minimizing an approximate Bethe free energy depending on the reduced density matrices and some cavity messages originated from the Bethe approximation of the entropy. We obtain the classical Bethe expression for the entropy within a naive (mean-field) approximation of the cavity messages, which is expected to work well at high temperatures. In the next order of the approximation, we obtain another expression for the Bethe entropy depending only on the diagonal elements of the reduced density matrices. In principle, we can improve the entropy approximation by considering more accurate cavity messages in the Bethe approximation of the entropy. We compare the annealing algorithm and the naive approximation of the Bethe entropy with exact and approximate numerical simulations for small and large samples of the random transverse Ising model on random regular graphs. PMID:25019754

Biazzo, I; Ramezanpour, A

2014-06-01

368

Sensitivity analysis and approximation methods for general eigenvalue problems  

NASA Technical Reports Server (NTRS)

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.; Haftka, R. T.

1986-01-01

369

Approximations based on the adiabatic treatment of rotation for resonances  

SciTech Connect

In the adiabatic treatment of overall rotational motion, the rotational energy is obtained by diagonalization of the inertia tensor at each nuclear configuration, and subsequent insertion of the rotation constants into the standard formalism for the energy for a symmetric or asymmetric top. We have tested this approximation previously for bound states and resonances in HCO, and found it to be quite accurate. This adiabatic approximation is justified here by deriving an approximation very similar to it (but less accurate) for a triatomic molecule. We then consider further approximations to the adiabatic rotation approximation. In one we assume that rotation constants for each resonance are independent of the angular momentum state J. This approximation requires a minimum of two calculations of resonance positions and widths for nonzero J in addition to the one for J=0. The second approximation we consider is standard first-order perturbarion theory. The adiabatic rotational energy is the perturbation relative to the J=0 Hamiltonian, and the complex L{sup 2} eigenfunctions of this Hamiltonian are the zero-order states. These two approximations are tested for HCO bound states and resonances, where those obtained from the full adiabatic rotation approximation are assumed to be the benchmark calculations. {copyright} {ital 1997 American Institute of Physics.}

Qi, J.; Bowman, J.M. [Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322 (United States)] [Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322 (United States)

1997-12-01

370

Adiabatic approximation in PT-symmetric quantum mechanics  

NASA Astrophysics Data System (ADS)

In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics, which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.

Guo, ZhiHua; Cao, HuaiXin; Lu, Ling

2014-10-01

371

Embedding impedance approximations in the analysis of SIS mixers  

NASA Technical Reports Server (NTRS)

Future millimeter-wave radio astronomy instruments will use arrays of many SIS receivers, either as focal plane arrays on individual radio telescopes, or as individual receivers on the many antennas of radio interferometers. Such applications will require broadband integrated mixers without mechanical tuners. To produce such mixers, it will be necessary to improve present mixer design techniques, most of which use the three-frequency approximation to Tucker's quantum mixer theory. This paper examines the adequacy of three approximations to Tucker's theory: (1) the usual three-frequency approximation which assumes a sinusoidal LO voltage at the junction, and a short-circuit at all frequencies above the upper sideband; (2) a five-frequency approximation which allows two LO voltage harmonics and five small-signal sidebands; and (3) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker's equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omega R(sub N)C for the SIS junctions used. For large omega R(sub N)C, all three approximations approach the eight-harmonic solution. For omega R(sub N)C values in the range 0.5 to 10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, and should be suitable for much design work. For the realistic SIS mixers considered here, the five-frequency approximation gives results very close to those of the eight-harmonic solution. Use of these approximations, where appropriate, considerably reduces the computational effort needed to analyze an SIS mixer, and allows the design and optimization of mixers using a personal computer.

Kerr, A. R.; Pan, S.-K.; Withington, S.

1992-01-01

372

Approximate off-line receding horizon control of constrained nonlinear discrete-time systems: Smooth approximation of the control law  

Microsoft Academic Search

In this work, the off-line approximation of state-feedback nonlinear model predictive control laws by means of smooth functions of the state is addressed. The idea is to investigate how the approximation errors affect the stability of the closed-loop system, in order to derive suitable bounds which have to be fulfilled by the approximating function. This analysis allows to conveniently set

Gilberto Pin; Marco Filippo; Felice Andrea Pellegrino; Gianfranco Fenu; Thomas Parisini

2010-01-01

373

On the Approximation of Markov Processes by Compound Poisson Processes  

E-print Network

On the Approximation of Markov Processes by Compound Poisson Processes P.J. Fitzsimmons My process by ``compound Poisson'' (or ``pure jump'') processes. Such approximations have been discussed­step transition kernel Kn . Let \\Pi n = (\\Pi n (t)) tâ??0 be a Poisson process of rate n, independent of Y n

Fitzsimmons, Patrick J.

374

On the Approximation of Markov Processes by Compound Poisson Processes  

E-print Network

On the Approximation of Markov Processes by Compound Poisson Processes P.J. Fitzsimmons My process by \\compound Poisson" (or \\pure jump") processes. Such approximations have been discussed recently with one-step transition kernel Kn. Let n = ( n(t))t 0 be a Poisson process of rate n, independent of Yn

Fitzsimmons, Patrick J.

375

An Exponential Approximation to the Hockey Stick Function  

E-print Network

An Exponential Approximation to the Hockey Stick Function Ian Iscoe Ken Jackson Alex Kreinin§ Xiaofang Ma¶ March 19, 2010 Abstract The hockey stick (HS) function plays an important role in pricing and Monz´on is used to determine the parameters of the exponential approximation to the hockey stick

Toronto, University of

376

On Exponential Approximation to the Hockey Stick Ken Jackson  

E-print Network

On Exponential Approximation to the Hockey Stick Function Ian Iscoe Ken Jackson Alex Kreinin§ Xiaofang Ma¶ January 24, 2007 Abstract The hockey stick function is a basic function in pricing and risk management of many financial derivatives. This paper considers approximating the hockey stick function

Toronto, University of

377

Error propagation in approximations to reaction-diffusion-advection equations  

Microsoft Academic Search

The quasi steady state approximation (QSSA) is one of the most used approximations in chemical dynamics, in which certain reactions from a large scheme are taken to have reached dynamical equilibrium, thus leading to a reduced system. In spatially distributed systems, error propagation can be important, and in this paper some a priori bounds for the error of the QSSA

A. N. Yannacopoulos; A. S. Tomlin; J. Brindley; J. H. Merkin; M. J. Pilling

1996-01-01

378

B-Splines Approximation Industrial and Systems Engineering  

E-print Network

1 B-Splines Approximation Yuan Yuan Industrial and Systems Engineering University of Wisconsin Madison Apr.27, 2010 #12;Outline · B-splines and their properties ­ Subspace $k,t · B-splines approximation ­ Distance from continuous functions to $k,t · Knots placement · Questions? 2 #12;B

Recht, Ben

379

Data reduction by an approximate thermal diffusion solution  

Microsoft Academic Search

A solution of the differential equations for a one dimensional time dependent heat conduction problem is used to generate approximate transfer functions for the response for the geometry defined by the boundary conditions, The resulting approximate transfer functions are used to develop a method for calculating the transient surface conditions of simulated nuclear fuel rods from known transient internal conditions.

J. M. Kendall

1975-01-01

380

Critical heat flux function approximation using genetic algorithms  

Microsoft Academic Search

Function approximation is the problem of finding a system that best explains the relationship between input variables and an output variable. We propose two hybrid genetic algorithms (GAs) of parametric and nonparametric models for function approximation. The former GA is a genetic nonlinear Levenberg-Marquardt algorithm of parametric model. We designed the chromosomes in a way that geographically exploits the relationships

Yung-Keun Kwon; Byung-Ro Moon; Sung-Deok Hong

2005-01-01

381

ARGUMENTWISE INVARIANT KERNELS FOR THE APPROXIMATION OF INVARIANT FUNCTIONS  

E-print Network

ARGUMENTWISE INVARIANT KERNELS FOR THE APPROXIMATION OF INVARIANT FUNCTIONS DAVID GINSBOURGER algebraic invariances of the function to be approximated, it is clearly unreasonable not trying to use- integrable processes have their paths invariant under the action of a finite group. We then give examples

Paris-Sud XI, Université de

382

ARGUMENTWISE INVARIANT KERNELS FOR THE APPROXIMATION OF INVARIANT FUNCTIONS  

E-print Network

ARGUMENTWISE INVARIANT KERNELS FOR THE APPROXIMATION OF INVARIANT FUNCTIONS DAVID GINSBOURGER kernels for approximating functions invariant under a known finite group action. We introduce the class of argumentwise invariant kernels, and show that they characterize centered square-integrable random fields

Paris-Sud XI, Université de

383

APPROXIMATION OF SOLUTIONS OF RICCATI EQUATIONS PAVEL BUB  

E-print Network

APPROXIMATION OF SOLUTIONS OF RICCATI EQUATIONS PAVEL BUB â?? AK # , CORNELIS V. M. VAN DER MEE subspace approach to finding solutions for the algebraic Riccati equation for a class of infinite dimensional systems. The second is approximation of the solution of the algebraic Riccati equation by finite

Ran, André

384

An approximate analytic solution of the nonlinear Riccati differential equation  

Microsoft Academic Search

In this paper, a hybrid method which combines the Adomian decomposition method (ADM), the Laplace transform algorithm and the Padé approximant is introduced to solve the approximate analytic solutions of the nonlinear Riccati differential equations. This hybrid method demonstrates accurate and reliable results, and has a great improvement in the ADM truncated series solution which diverges rapidly as the applicable

Pa-Yee Tsai; Cha’o-Kuang Chen

2010-01-01

385

SIGNAL APPROXIMATION VIA THE GOPHER FAST FOURIER TRANSFORM  

E-print Network

SIGNAL APPROXIMATION VIA THE GOPHER FAST FOURIER TRANSFORM By I. Ben Segal and M.A. Iwen IMA-626-7370 URL: http://www.ima.umn.edu #12;Signal Approximation via the Gopher Fast Fourier Transform I. Ben this problem [1, 2]. These methods were implemented as the Ann Arbor Fast Fourier Transform (AAFFT

386

Perturbation approximation for orbits in axially symmetric funnels  

NASA Astrophysics Data System (ADS)

A perturbation method that can be traced back to Isaac Newton is applied to obtain approximate analytic solutions for objects sliding in axially symmetric funnels in near circular orbits. Some experimental observations are presented for balls rolling in inverted cones with different opening angles, and in a funnel with a hyperbolic surface that approximately simulates the gravitational force.

Nauenberg, Michael

2014-11-01

387

Learning theory viewpoint of approximation by positive linear operators  

Microsoft Academic Search

We follow a learning theory viewpoint to study a family of learning schemes for regression related to positive linear operators in approximation theory. Such a learning scheme is generated from a random sample by a kernel function parameterized by a scaling parameter. The essential difference between this algorithm and the classical approximation schemes is the randomness of the sampling points,

Shaogao Lv; Lei Shi

2010-01-01

388

Finding the Best Quadratic Approximation of a Function  

ERIC Educational Resources Information Center

This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

Yang, Yajun; Gordon, Sheldon P.

2011-01-01

389

Small-scale magnetic fields in turbulence - Saffman's approximation revisited  

Microsoft Academic Search

The approximation developed by Saffman (1963) to describe the small-scale structure of a magnetic field in a turbulent conducting medium and its evolution in time is examined with a view to placing sharper limits on the numerical parameters that appear in the approximate correlation functions. It is shown that if magnetic dissipation is ignored entirely, then results for a magnetic

Ralph Baierlein

1980-01-01

390

Single-frequency approximation of the coupling ray theory  

E-print Network

Single-frequency approximation of the coupling ray theory Ludek Klimes & Petr Bulant Department­ray­theory Green tensor is frequency dependent, and is usually calculated for many frequencies. This frequency this frequency dependence. In the vicinity of a given prevailing frequency, we approximate the frequency­ domain

Cerveny, Vlastislav

391

Approximations for the Entropy Rate of a Hidden Markov Process  

E-print Network

rise to a deterministic algorithm for approximating the entropy rate, achieving the best knownApproximations for the Entropy Rate of a Hidden Markov Process Erik Ordentlich and Tsachy Weissman1 memoryless channel. We present an approach to bound- ing the entropy rate of {Zt} by the construction

Weissman, Tsachy

392

PASS Approximation: A Framework for Analyzing and Designing Heuristics  

Microsoft Academic Search

We introduce a new framework for designing and analyzing algorithms. Our framework applies best to problems that are inapproximable according to the standard worst-case analysis. We circumvent such negative results by designing guarantees for classes of instances, parameterized according to properties of the optimal solution. Given our parameterized approximation, called PArametrized by the Signature of the Solution (PASS) approximation, we

Uriel Feige; Nicole Immorlica; Vahab S. Mirrokni; Hamid Nazerzadeh

2009-01-01

393

The weighted curvature approximation in scattering from sea surfaces  

NASA Astrophysics Data System (ADS)

A family of unified models in scattering from rough surfaces is based on local corrections of the tangent plane approximation through higher-order derivatives of the surface. We revisit these methods in a common framework when the correction is limited to the curvature, that is essentially the second-order derivative. The resulting expression is formally identical to the weighted curvature approximation, with several admissible kernels, however. For sea surfaces under the Gaussian assumption, we show that the weighted curvature approximation reduces to a universal and simple expression for the off-specular normalized radar cross-section (NRCS), regardless of the chosen kernel. The formula involves merely the sum of the NRCS in the classical Kirchhoff approximation and the NRCS in the small perturbation method, except that the Bragg kernel in the latter has to be replaced by the difference of a Bragg and a Kirchhoff kernel. This result is consistently compared with the resonant curvature approximation. Some numerical comparisons with the method of moments and other classical approximate methods are performed at various bands and sea states. For the copolarized components, the weighted curvature approximation is found numerically very close to the cut-off invariant two-scale model, while bringing substantial improvement to both the Kirchhoff and small-slope approximation. However, the model is unable to predict cross-polarization in the plane of incidence. The simplicity of the formulation opens new perspectives in sea state inversion from remote sensing data.

Guérin, Charles-Antoine; Soriano, Gabriel; Chapron, Bertrand

2010-07-01

394

Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?  

ERIC Educational Resources Information Center

This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…

Oud, Johan H. L.; Folmer, Henk

2011-01-01

395

HOMOGENEOUS APPROXIMATION RECURSIVE OBSERVER DESIGN AND OUTPUT FEEDBACK  

E-print Network

HOMOGENEOUS APPROXIMATION RECURSIVE OBSERVER DESIGN AND OUTPUT FEEDBACK VINCENT ANDRIEU, LAURENT observer and output feedback design. The first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting

Paris-Sud XI, Université de

396

On Approximation of Max-Vertex-Cover Qiaoming Han y  

E-print Network

, The University of Iowa. 1 #12; Abstract We consider the Max-Vertex-Cover (MVC) problem, i.e., #12;nd k vertices that the existence of a (1 #15;)- approximation algorithm for MVC implies P=NP for some #15; > 0. There is a 3=4-approximation algorithm for MVC, based on a linear programming (LP) relaxation. We illustrate

Ye, Yinyu

397

Reaching Approximate Agreement in the Presence of Faults  

Microsoft Academic Search

This paper considers a variant of the Byzantine Generals problem, in which processes start with arbitrary real values rather than Boolean values or values from some bounded range, and in which approximate, rather than exact, agreement is the desired goal. Algorithms are presented to reach approximate agreement in asynchronous, as well as synchronous systems. The asynchronous agreement algorithm is an

Danny Dolev; Nancy A. Lynch; Shlomit S. Pinter; Eugene W. Stark; William E. Weihl

1983-01-01

398

ALGORITHMS FOR SIMULTANEOUS SPARSE APPROXIMATION PART I: GREEDY PURSUIT  

E-print Network

ALGORITHMS FOR SIMULTANEOUS SPARSE APPROXIMATION PART I: GREEDY PURSUIT JOEL A. TROPP, ANNA C of this paper proposes a greedy pursuit algorithm, called Simultaneous Orthogonal Matching Pursuit sparse approximation. Date: Typeset on March 17, 2005. Key words and phrases. Greedy algorithms

Eustice, Ryan

399

Approximation algorithms for facility location problems (Extended Abstract)  

E-print Network

Approximation algorithms for facility location problems (Extended Abstract) David B. Shmoys \\Lambda­ cation problems. In each facility location problem that we study, there is a set of locations at which we approximation algorithms for a variety of facility location problems. One of the most well­studied problems

Keinan, Alon

400

Improved Approximation Algorithms for Multilevel Facility Location Problems  

Microsoft Academic Search

We show that the metric multilevel facility location problem is polynomial-time reducible within a factor of 3 to the metric uncapacitated facility location problem. This leads to a combinatorial 4.83-approximation algorithm for the metric multilevel facility location problem and to a 9-approximation algorithm for a capacitated version of it.

Alexander A. Ageev

2002-01-01

401

A new approximation algorithm for the multilevel facility location problem  

E-print Network

A new approximation algorithm for the multilevel facility location problem Adriana F. Gabor a In this paper we propose a new integer programming formulation for the multi- level facility location problem- proximation algorithms for this type of problems. Key words: facility location, approximation algorithms

Boucherie, Richard J.

402

Approximation Algorithms for Facility Location David B. Shmoys  

E-print Network

Approximation Algorithms for Facility Location Problems David B. Shmoys Cornell University, Ithaca of approximation algorithms has been for facility location problems. In particular, for the metric case of two simple models, the uncapacitated facility location and the k­median problems, there are now a variety

Shmoys, David B.

403

Fast approximate calculation of multiply scattered lidar returns  

E-print Network

Fast approximate calculation of multiply scattered lidar returns Robin J. Hogan An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides or fourth order in retrieval algorithms. For typical cloud profiles and a wide range of lidar fields of view

Hogan, Robin

404

Integrating DCT and DWT for approximating cube streams  

Microsoft Academic Search

For time-relevant multi-dimensional data sets (MDS), users usually pose a huge amount of data due to the large dimensionality, and approximating query processing has emerged as a viable solution. Specifically, the cube streams handle MDSs in a continuous manner. Traditional cube approximation focuses on generating single snapshots rather than continuous ones. To address this issue, the application of generating snapshots

Ming-Jyh Hsieh; Ming-Syan Chen; Philip S. Yu

2005-01-01

405

A provably efficient computational model for approximate spatiotemporal retrieval  

Microsoft Academic Search

The paper is concerned with the effective and efficient processing of spatiotemporal selection queries under varying degrees of approximation. Such queries may employ operators like overlaps, north, during, etc., and their result is a set of entities standing approximately in some spatiotemporal relation with respect to a query object X. The contribution of our work is twofold: i) First we

Delis Vasilis; Makris Christos; Sioutas Spiros

1999-01-01

406

Approximate Fault-Tree Analysis with Prescribed Accuracy  

Microsoft Academic Search

Unavailability or Unreliability of a system can be found with a given error-bound by a proper approximate fault-tree analysis. In essence: Using a given maximum error, the set of mincuts is reduced, and the rest of the mincuts are processed such that at the end an approximate value of system unavailability or unreliability is found, which is too high by

W. Schneeweiss

1987-01-01

407

Semidefinite relaxations for approximate inference on graphs with cycles  

E-print Network

on a Gaussian entropy bound combined with a semidefinite outer bound on the marginal polytope. This combination for calculating approximate marginals for probability distributions defined by graphs with cycles, based of this problem can be taken as approximations to the exact marginals. In contrast to Bethe/Kikuchi approaches

Jordan, Michael I.

408

Optimization by Max-Propagation Using Kikuchi Approximations  

Microsoft Academic Search

In this paper we address the problem of using region-based approximations to find the optimal points of a given function. Our approach combines the use of Kikuchi approximations with the application of generalized belief propagation (GBP) using maximization instead of marginalization. The relationship between the fixed points of maximum GBP and the free energy is elucidated. A straightforward connection between

Robin Hons; Roberto Santana; Pedro Larranaga; Jose A. Lozano

409

Hand Tracking Using Kernel Density Approximation Aras Dargazany1  

E-print Network

Hand Tracking Using Kernel Density Approximation Aras Dargazany1 , Ali Soleimani2 1,2 Department.dargazany@gmail.com ali_solimani@shahroodut.ac.ir Abstract-In this paper, a new method is proposed for hand tracking based an approximator to recognize hands from its background. This procedure is done by extracting feature vector

Berns, Karsten

410

Nucleon Properties from Approximating Chiral Quark Sigma Model  

E-print Network

We apply the approximating chiral quark model. This chiral quark model is based on an effective Lagrangian which the interactions between quarks via sigma and pions mesons. The field equations have been solved in the mean field approximation for the hedgehog baryon state. Good results are obtained for nucleon properties in comparison with original model.

M. Abu-Shady

2009-12-18

411

Bohmian Quantum Gravity in the Linear Field Approximation  

E-print Network

In this paper we have applied Bohmian quantum theory to the linear field approximation of gravity and present a self--consistent quantum gravity theory in the linear field approximation. The theory is then applied to some specific problems, the Newtonian limit, and the static spherically symmetric solution. Some observable effects of the theory are investigated.

Ali Shojai; Fatimah Shojai

2003-06-22

412

A new approximate iteration solution of Blasius equation  

NASA Astrophysics Data System (ADS)

An approximate analytical solution of Blasius equation is obtained by the parameter iteration method. The comparison with Howarth's numerical solution shows that the accuracy of the proposed method is higher than other approximate analytical solutions. Further, we provide also a numerical iteration scheme which is simple, efficient and practical.

Lin, Jianguo

1999-06-01

413

Reaching Approximate Agreement in the Presence of Faults  

Microsoft Academic Search

This paper considers a variant on the Byzantine Generals problem, in which processes start with arbitrary real values rather than Boolean values or values from some bounded range, and in which approximate, rather than exact, agreement is the desired goal. Algorithms are presented to reach approximate agreement in asynchronous, as well as synchronous systems. The asynchronous agreement algorithm is an

Danny Dolev; Nancy A. Lynch

1985-01-01

414

A Lie Bracket Approximation for Extremum Seeking Vehicles  

E-print Network

A Lie Bracket Approximation for Extremum Seeking Vehicles Hans-Bernd D¨urr Milos S. Stankovi as input-affine systems with periodic excitations and by using the methodology of Lie brackets, we existing methods. By examining this approximate Lie bracket system, we are able to directly derive

Johansson, Karl Henrik

415

Approximation Algorithms for Clustering to Minimize the Sum of Diameters  

Microsoft Academic Search

. We consider the problem of partitioning the nodes of a completeedge weighted graph into k clusters so as to minimize the sumof the diameters of the clusters. Since the problem is NP-complete, ourfocus is on the development of good approximation algorithms. Whenedge weights satisfy the triangle inequality, we present the first approximationalgorithm for the problem. The approximation algorithm yieldsa

Srinivas R. Doddi; Madhav V. Marathe; S. S. Ravi; David Scot Taylor; Peter Widmayer

2000-01-01

416

Approximate distance queries and compact routing in sparse graphs  

Microsoft Academic Search

An approximate distance query data structure is a compact representation of a graph, and can be queried to approximate shortest paths between any pair of vertices. Any such data structure that retrieves stretch 2k? 1 paths must require space (n 1+1=k ) for graphs of n nodes. The hard cases that enforce this lower bound are, however, rather dense graphs

Rachit Agarwal; P. Brighten Godfrey; Sariel Har-Peled

2011-01-01

417

The blind leading the blind: Mutual refinement of approximate theories  

NASA Technical Reports Server (NTRS)

The mutual refinement theory, a method for refining world models in a reactive system, is described. The method detects failures, explains their causes, and repairs the approximate models which cause the failures. The approach focuses on using one approximate model to refine another.

Kedar, Smadar T.; Bresina, John L.; Dent, C. Lisa

1991-01-01

418

E cient Approximation and Optimization Algorithms for Computational Metrology  

E-print Network

E cient Approximation and Optimization Algorithms for Computational Metrology Christian A. Duncan in computational metrology, focusing on the fun- damental issues of \\ atness" and \\roundness." Speci c- ally, we-dimensional point set, which corresponds to the metrology notion of \\ atness," giv- ing an approximation method

Goodrich, Michael T.

419

Stein's method, Palm theory and Poisson process approximation  

Microsoft Academic Search

The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem \\\\refimportantproposition) in Poisson process approximation is proved by taking the local approach. It is obtained without reference to any particular metric, thereby allowing wider applicability. A

Louis H. Y. Chen; Aihua Xia

2004-01-01

420

Thickness-shear approximation for piezoelectric ceramic plates  

Microsoft Academic Search

The thickness-shear mode in piezoelectric ceramic plates has been analysed theoretically with the approximate two-dimensional plate theory. The theoretical dispersion for a fully electroded infinite plate has been compared with experimental results on rectangular plate resonators. Limits of the application of the thickness-shear approximation related to the plate geometry have been established.

V. L. STRASHILOV; M. M. NADOLIISKI

1989-01-01

421

An Approximate Image-Space Approach for Interactive  

E-print Network

interfaces ­ For additional refractions ­ For total internal reflection #12;1) Use data at front surfaces ReflectRefract (alter angle) #12;ImplementationImplementation · Split these 6 steps into two online passesAn Approximate Image-Space Approach for Interactive Refraction An Approximate Image-Space Approach

Wyman, Chris

422

Approximation Methods for the Item Parameters of Mental Test Models.  

ERIC Educational Resources Information Center

Equations are derived to enable the graphic approximation of the item parameters of the stochastic mental test models, i.e., the generalized normal ogive and logistic models. The item parameters for the models are discriminatory power, difficulty, and probability of chance success. Suggested uses for the approximations were to provide a basis for…

Urry, Vern W.

423

Fast Polygonal Approximation of Terrains and Height Fields  

Microsoft Academic Search

Several algorithms for approximating terrains and other height fields using polygonal meshes aredescribed, compared, and optimized. These algorithms take a height field as input, typically arectangular grid of elevation data H(x; y), and approximate it with a mesh of triangles, also knownas a triangulated irregular network, or TIN. The algorithms attempt to minimize both the errorand the number of triangles

Michael Garland; Paul S. Heckbert

1995-01-01

424

A Study of Approximate Data Management Techniques for Sensor Networks  

E-print Network

for different types of approximate queries, including aggregate and non-aggregate queries (e.g. time the monitoring operation of sensor nodes by efficiently using their limited energy, bandwidth and computation resources are aggregation and approximation. In-network aggregation reduces the load of data propagated

Martin, Ralph R.

425

Using Datacube Aggregates for Approximate Querying and Deviation Detection  

E-print Network

Using Datacube Aggregates for Approximate Querying and Deviation Detection Themis Palpanas, Nick to the efficient computation of relational aggregations and, specifically, the efficient execution of the datacube about it. We then show how approximate queries on the data from which the aggregates were derived can

Palpanas, Themis

426

Using Rational B-Spline Neural Networks for Curve Approximation  

Microsoft Academic Search

Rational B-spline neural network (RBNN) is a neural network can be used for curves and surfaces approximation using rational B-spline model. The approximation is solved by learning process of rational B-spline neural networks from observation data points. A hybrid genetic based algorithm for optimizing knots, control points and weights of RBNN

TANG VAN TO

427

Approximation Algorithms for Directed Steiner Problems \\Lambda Moses Charikar y  

E-print Network

Approximation Algorithms for Directed Steiner Problems \\Lambda Moses Charikar y Stanford University for the Steiner tree problem and the generalized Steiner network problem on general directed graphs ratios known before our work were the trivial O(k)­approximations. For the directed Steiner tree problem

Chekuri, Chandra

428

Approximation Algorithms for Directed Steiner Problems Moses Charikar y  

E-print Network

Approximation Algorithms for Directed Steiner Problems #3; Moses Charikar y Stanford University problem and the generalized Steiner network problem on general directed graphs. These problems have before our work were the trivial O(k)-approximations. For the directed Steiner tree problem, we design

Charikar, Moses

429

Hardness and Approximation Results for Packing Steiner Trees Joseph Cheriyan  

E-print Network

of approximation for several versions of the problem of packing Steiner trees. For packing edge-disjoint Steiner algorithms and hardness of approximation for several versions of the problem of packing Steiner trees. Given, are optional). The basic problem of packing edge-disjoint undirected Steiner trees is to #12;nd as many edge

Salavatipour, Mohammad R.

430

New Approximation Algorithms for the Steiner Tree Problems  

Microsoft Academic Search

The Steiner tree problem asks for the shortest tree connecting a given set of terminal points ina metric space. We design new approximation algorithms for the Steiner tree problems usinga novel technique of choosing Steiner points in dependence on the possible deviation from theoptimal solutions. We achieve the best up to now approximation ratios of 1.644 in arbitrarymetric and 1.267

Marek Karpinski; Alexander Zelikovsky

1995-01-01

431

New Approximation Algorithms for the Steiner Tree Problems  

E-print Network

New Approximation Algorithms for the Steiner Tree Problems Marek Karpinski \\Lambda Alexander Zelikovsky y Abstract The Steiner tree problem asks for the shortest tree connecting a given set of terminal points in a metric space. We design new approximation algorithms for the Steiner tree problems using

Karpinski, Marek

432

Stochastic Shear Thickening Fluids: Strong Convergence of the Galerkin Approximation  

E-print Network

Stochastic Shear Thickening Fluids: Strong Convergence of the Galerkin Approximation and the Energy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 The stochastic shear thickening fluids 4 2.1 Strong convergence of the Galerkin approximation.1) where div = (d j=1 jij )d i=1 . The fluid is said shear thinning if p shear

Yoshida, Nobuo

433

Sensitivity analysis of kinematic approximations in dynamic medusan swimming models  

Microsoft Academic Search

Models of medusan swimming typically rely on kinematic approximations to observed animal morphology to make such investigations tractable. The effect of these simplifications on the accuracy of predicted dynamics has not been examined in detail. We conduct a case study of the scyphozoan jellyfish Chrysaora fuscescens to isolate and quantify the sensitivity of dynamic models to common kinematic approximations. It

John O. Dabiri; Morteza Gharib

2003-01-01

434

Index-Based Approximate XML Joins Sudipto Guha  

E-print Network

of such operations. We propose novel search and join algorithms for R-trees adopted to index XML document collections, we propose R-tree based search and join algorithms for the approximate XML join problem. Our completeIndex-Based Approximate XML Joins Sudipto Guha University of Pennsylvania sudipto

Yu, Ting

435

An approximation theory for the identification of linear thermoelastic systems  

NASA Technical Reports Server (NTRS)

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

436

Recent advances in approximation concepts for optimum structural design  

NASA Technical Reports Server (NTRS)

The basic approximation concepts used in structural optimization are reviewed. Some of the most recent developments in that area since the introduction of the concept in the mid-seventies are discussed. The paper distinguishes between local, medium-range, and global approximations; it covers functions approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It also appears that some new methodologies are emerging which could greatly benefit from the introduction of new computer architecture.

Barthelemy, Jean-Francois M.; Haftka, Raphael T.

1991-01-01

437

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering  

NASA Technical Reports Server (NTRS)

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

Melott, Adrian L.

1994-01-01

438

Production-Passage-Time Approximation: A New Approximation Method to Accelerate the Simulation Process of Enzymatic Reactions  

Microsoft Academic Search

Given the substantial computational requirements of stochas- tic simulation, approximation is essential for efficient analysis of any re- alistic biochemical system. This paper introduces a new approximation method to reduce the computational cost of stochastic simulations of an enzymatic reaction scheme which in biochemical systems often includes rapidly changing fast reactions with enzyme and enzyme-substrate com- plex molecules present in

Hiroyuki Kuwahara; Chris J. Myers

2007-01-01

439

Mapping biological entities using the longest approximately common prefix method  

PubMed Central

Background The significant growth in the volume of electronic biomedical data in recent decades has pointed to the need for approximate string matching algorithms that can expedite tasks such as named entity recognition, duplicate detection, terminology integration, and spelling correction. The task of source integration in the Unified Medical Language System (UMLS) requires considerable expert effort despite the presence of various computational tools. This problem warrants the search for a new method for approximate string matching and its UMLS-based evaluation. Results This paper introduces the Longest Approximately Common Prefix (LACP) method as an algorithm for approximate string matching that runs in linear time. We compare the LACP method for performance, precision and speed to nine other well-known string matching algorithms. As test data, we use two multiple-source samples from the Unified Medical Language System (UMLS) and two SNOMED Clinical Terms-based samples. In addition, we present a spell checker based on the LACP method. Conclusions The Longest Approximately Common Prefix method completes its string similarity evaluations in less time than all nine string similarity methods used for comparison. The Longest Approximately Common Prefix outperforms these nine approximate string matching methods in its Maximum F1 measure when evaluated on three out of the four datasets, and in its average precision on two of the four datasets. PMID:24928653

2014-01-01

440

A test of the adhesion approximation for gravitational clustering  

NASA Technical Reports Server (NTRS)

We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.

1993-01-01

441

Title: Quadrupole collective inertia in nuclear fission: cranking approximation  

E-print Network

Collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian Overlap Approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in 256Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and perturbative cranking approximations to ATDHFB, and within GOA, are discussed.

A. Baran; J. A. Sheikh; J. Dobaczewski; W. Nazarewicz

2010-07-21

442

Evaluation of fault-tolerant system performance by approximate techniques  

NASA Technical Reports Server (NTRS)

An approximate method for calculating the statistics of the performance of a fault-tolerant system is developed. An approximate method is necessary because the statistical model of the system behavior is large-scale and the time horizon of interest encompasses many cycles of the Redundancy Management logic. In the development, a compact representation of the necessary information called the v-transform is introduced and discussed. Based upon this representation, an approximation that leads to a very efficient computational procedure is suggested and numerically analyzed. A very brief discussion of other related work is also presented.

Walker, B. K.; Gerber, D. K.

1985-01-01

443

The Space Complexity of Approximating the Frequency Moments  

Microsoft Academic Search

The frequency moments of a sequence containingmielements of typei, 1?i?n, are the numbersFk=?ni=1mki. We consider the space complexity of randomized algorithms that approximate the numbersFk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, it turns out that the numbersF0,F1, andF2can be approximated in logarithmic space, whereas the approximation ofFkfork?6 requiresn?(1)space. Applications to

Noga Alon; Yossi Matias; Mario Szegedy

1999-01-01

444

Approximating the magnetic recording step response using a Voigt function  

NASA Astrophysics Data System (ADS)

A simple, closed-form expression for the step response or pulse shape of a magnetic recording channel is described. The step responses of inductive and magnetoresistive heads with thin-film media are shown to be well approximated by a Voigt function (the convolution of a Lorentzian and a Gaussian function). For convenience, an accurate approximation to the Voigt function (the linear superposition of a Lorentzian and a Gaussian function with appropriate weighting) was fit to the step responses using one adjustable parameter. The improved accuracy of this approximation to the step response has a strong impact on channel performance analysis and modeling.

Stupp, Steven E.

2000-05-01

445

Effective Hamiltonian approach to adiabatic approximation in open systems  

E-print Network

The adiabatic approximation in open systems is formulated through the effective Hamiltonian approach. By introducing an ancilla, we embed the open system dynamics into a non-Hermitian quantum dynamics of a composite system, the adiabatic evolution of the open system is then defined as the adiabatic dynamics of the composite system. Validity and invalidity conditions for this approximation are established and discussed. A High-order adiabatic approximation for open systems is introduced. As an example, the adiabatic condition for an open spin-$\\frac 1 2$ particle in time-dependent magnetic fields is analyzed.

X. X. Yi; D. M. Tong; L. C. Kwek; C. H. OH

2006-06-24

446

Numerical approximation strategies for product-form network performance  

SciTech Connect

Product-form queueing network models are an effective tool in the modeling of computer and communications systems. Compared with other models of comparable expressive power, these models offer comparable accuracy and the advantages of robustness, simplicity, and low computational cost. Several trends in performance evaluation make the approximate solution of queueing models increasingly important. A new technique for the approximation of closed product-form single-class and multiclass queueing networks is presented. Based on the extrapolation of rational polynomial functions, this approximation has important advantages over existing methods when performance behavior over a population range is desired. It is especially applicable to the study of hierarchical models, thresholding, and elasticity.

Hooper, W.H.

1988-01-01

447

Approximate Controllability of Fractional Neutral Stochastic System with Infinite Delay  

NASA Astrophysics Data System (ADS)

The concept of controllability plays an important role in analysis and design of linear and nonlinear control systems. Further, fractional differential equations have wide applications in engineering and science. In this paper, the approximate controllability of neutral stochastic fractional integro-differential equation with infinite delay in a Hilbert space is studied. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of nonlinear fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.

Sakthivel, R.; Ganesh, R.; Suganya, S.

2012-12-01

448

On the Approximation of Markov Processes by Compound Poisson Processes  

E-print Network

On the Approximation of Markov Processes by Compound Poisson Processes P.J. Fitzsimmons My intention in this note is to present a simple approach to the approximat* *ion of a continuous time Markov process by "compound

Fitzsimmons, Patrick J.

449

Approximate inference : decomposition methods with applications to networks  

E-print Network

Markov random field (MRF) model provides an elegant probabilistic framework to formulate inter-dependency between a large number of random variables. In this thesis, we present a new approximation algorithm for computing ...

Jung, Kyomin

2009-01-01

450

Approximation algorithms for stochastic scheduling on unrelated machines  

E-print Network

Motivated by problems in distributed computing, this thesis presents the first nontrivial polynomial time approximation algorithms for an important class of machine scheduling problems. We study the family of preemptive ...

Scott, Jacob (Jacob Healy)

2008-01-01

451

An Outer-Inner Approximation for separable MINLPs  

E-print Network

Outer approximation consists in building a mixed-integer linear ... and constraints can be cast into that form by introducing an extra variable and moving the objective ...... On the implementation of a primal-dual interior point filter line search.

2011-06-03

452

Real-time creased approximate subdivision surfaces with displacements.  

PubMed

We present an extension of Loop and Schaefer's approximation of Catmull-Clark surfaces (ACC) for surfaces with creases and corners. We discuss the integration of ACC into Valve's Source game engine and analyze performance of our implementation. PMID:20616390

Kovacs, Denis; Mitchell, Jason; Drone, Shanon; Zorin, Denis

2010-01-01

453

A Binomial Approximation Method for the Ising Model  

NASA Astrophysics Data System (ADS)

A large portion of the computation required for the partition function of the Ising model can be captured with a simple formula. In this work, we support this claim by defining an approximation to the partition function and other thermodynamic quantities of the Ising model that requires no algorithm at all. This approximation, which uses the high temperature expansion, is solely based on the binomial distribution, and performs very well at low temperatures. At high temperatures, we provide an alternative approximation, which also serves as a lower bound on the partition function and is trivial to compute. We provide theoretical evidence and the results of numerical experiments to support the strength of these approximations.

Streib, Noah; Streib, Amanda; Beichl, Isabel; Sullivan, Francis

2014-08-01

454

Approximate Solution Techniques for Factored Firstorder MDPs Scott Sanner  

E-print Network

Approximate Solution Techniques for Factored First­order MDPs Scott Sanner Department of Computer on grounding the prob­ lem w.r.t. specific domain instantiations, thereby incur­ ring a combinatorial blowup

Sanner, Scott

455

Approximation Algorithms for Data Placement Problems Rajmohan Rajaraman  

E-print Network

. (Cooperation is of course likely to be the default mode under centralized control, where all the network nodes§ Abstract We develop approximation algorithms for the problem of placing replicated data in arbitrary net

Swamy, Chaitanya

456

Tractability through approximation : a study of two discrete optimization problems  

E-print Network

(cont.) algorithm, at one extreme, and complete enumeration, at the other extreme. We derive worst-case approximation guarantees on the solution produced by such an algorithm for matroids. We then define a continuous ...

Farahat, Amr, 1973-

2004-01-01

457

Vacancy-rearrangement theory in the first Magnus approximation  

SciTech Connect

In the present paper we employ the first Magnus approximation (M1A), a unitarized Born approximation, in semiclassical collision theory. We have found previously that the M1A gives a substantial improvement over the first Born approximation (B1A) and can give a good approximation to a full coupled channels calculation of the mean L-shell vacancy probability per electron, p/sub L/, when the L-vacancies are accompanied by a K-shell vacancy (p/sub L/ is obtained experimentally from measurements of K/sub ..cap alpha../-satellite intensities). For sufficiently strong projectile-electron interactions (sufficiently large Z/sub p/ or small v) the M1A ceases to reproduce the coupled channels results, but it is accurate over a much wider range of Z/sub p/ and v than the B1A. 27 references.

Becker, R.L.

1984-01-01

458

Variational approach versus accessible soliton approximation in nonlocal, nonlinear media  

NASA Astrophysics Data System (ADS)

We discuss differences between the variational approach to solitons and the accessible soliton approximaion in a highly nonlocal, nonlinear medium. We compare results of both approximations by considering the same system of equations in the same spatial region, under the same boundary conditions. We also compare these approximations with the numerical solution of the equations. We find that the variational highly nonlocal approximation provides more accurate results and, as such, is a more appropriate solution than the accessible soliton approximation. The accessible soliton model offers a radical simplification in the treatment of highly nonlocal, nonlinear media, with easy comprehension and convenient parallels to a quantum harmonic oscillator, however, with a hefty price tag: a systematic numerical discrepancy of up to 100% with the numerical results.

Aleksi?, Branislav N.; Aleksi?, Najdan B.; Petrovi?, Milan S.; Strini?, Aleksandra I.; Beli?, Milivoj R.

2014-09-01

459

Improved Approximation Bounds for Planar Point Pattern Matching  

E-print Network

. This is a well studied problem in computational geometry. Goodrich, Mitchell, and Orletsky [GMO94] presented, and Orletsky [GMO94]. They presented a very simple approximation algorithm for a number of pattern matching

Mount, David

460

Provably Good Approximation Algorithms for Optimal Kinodynamic Planning: Robots with  

E-print Network

Provably Good Approximation Algorithms for Optimal Kinodynamic Planning: Robots with Decoupled-7501 Patrick Xavier Sandia National Laboratories, Albuquerque NM 87185-0951 Keywords: robot motion planning, kinodynamics, polyhedral obstacles Abstract: We consider the following problem: given a robot system, nd

Richardson, David

461

Approximating the Helium Wavefunction in Positronium-Helium Scattering  

NASA Technical Reports Server (NTRS)

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

DiRienzi, Joseph; Drachman, Richard J.

2003-01-01

462

Non-ideal boson system in the Gaussian approximation  

SciTech Connect

We investigate ground-state and thermal properties of a system of non-relativistic bosons interacting through repulsive, two-body interactions in a self-consistent Gaussian mean-field approximation which consists in writing the variationally determined density operator as the most general Gaussian functional of the quantized field operators. Finite temperature results are obtained in a grand canonical framework. Contact is made with the results of Lee, Yang, and Huang in terms of particular truncations of the Gaussian approximation. The full Gaussian approximation supports a free phase or a thermodynamically unstable phase when contact forces and a standard renormalization scheme are used. When applied to a Hamiltonian with zero range forces interpreted as an effective theory with a high momentum cutoff, the full Gaussian approximation generates a quasi-particle spectrum having an energy gap, in conflict with perturbation theory results. {copyright} 1997 Academic Press, Inc.

Tommasini, P.R. [Institute for Theoretical Atomic and Molecular Physics, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138 (United States)] [Institute for Theoretical Atomic and Molecular Physics, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138 (United States); de Toledo Piza, A.F. [Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05389-970 Sao Paulo, SP, (Brasil)] [Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05389-970 Sao Paulo, SP, (Brasil)

1997-01-01

463

Low-complexity approximations to maximum likelihood MPSK modulation classification  

NASA Technical Reports Server (NTRS)

We present a new approximation to the maximum likelihood classifier to discriminate between M-ary and M'-ary phase-shift-keying transmitted on an additive white Gaussian noise (AWGN) channel and received noncoherentl, partially coherently, or coherently.

Hamkins, Jon

2004-01-01

464

On the Accuracy of Uniform Polyhedral Approximations of the ...  

E-print Network

Jul 18, 2009 ... For quadratic optimization over the unit simplex (also known as standard ..... Theorem 4.1 establishes that the rate of convergence of the sequence {µr u ?µr ..... Figure 1 illustrates the distribution of the approximation ratios µr.

2009-07-18

465

The Sobolev approximation for line formation with partial frequency redistribution  

NASA Technical Reports Server (NTRS)

Attention is given to the formation of a spectral line in a uniformly expanding infinite medium in the Sobolev approximation, with emphasis on the various mechanisms for frequency redistribution. Numerical and analytic solutions of the transfer equation are presented of a number of redistribution functions and their approximations, including type I and type II partial redistribution, coherent scattering and complete redistribution, and the Fokker-Planck and uncorrelated approximation to the R sub II function. The solutions for the mean intensity are shown to depend very much on the type of redistribution mechanism, while for the frequency-weighted mean intensity, which enters the rate equations, this dependence is weak. It is inferred that use of Sobolev escape probabilities based on complete redistribution can be an adequate approximation for many calculations for which only the radiative excitation rates are needed.

Hummer, D. G.; Rybicki, G. B.

1992-01-01

466

A stochastic approximation algorithm for estimating mixture proportions  

NASA Technical Reports Server (NTRS)

A stochastic approximation algorithm for estimating the proportions in a mixture of normal densities is presented. The algorithm is shown to converge to the true proportions in the case of a mixture of two normal densities.

Sparra, J.

1976-01-01

467

PLASMA Approximate Dynamic Programming finally cracks the locomotive optimization problem  

E-print Network

PLASMA ­ Approximate Dynamic Programming finally cracks the locomotive optimization problem schedules and new operating policies. PLASMA is currently running at Norfolk Southern for strategic of PLASMA: Each locomotive is modeled individually, making it possible to capture both horsepower

Powell, Warren B.

468

Approximation algorithms for grammar-based data compression  

E-print Network

This thesis considers the smallest grammar problem: find the smallest context-free grammar that generates exactly one given string. We show that this problem is intractable, and so our objective is to find approximation ...

Lehman, Eric (Eric Allen), 1970-

2002-01-01

469

Faster approximate multicommodity flow using quadratically coupled flows  

E-print Network

The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a 1-? approximation to the multicommodity flow problem on graphs is a well-studied ...

Miller, Gary L.

470

Orthogonal Polynomial Approximation in Higher Dimensions: Applications in Astrodynamics  

E-print Network

ensure maximum acceleration error ms^?2, globally) are required near the Earths surface, whereas lower degree approximations are required as radius increases. We show that a four order of magnitude speedup is feasible, with both speed and storage...

Bani Younes, Ahmad H.

2013-08-05

471

Approximation of Matrix Rank Function and Its Application to Matrix ...  

E-print Network

minimization problem within any level of accuracy. Furthermore, the monotonicity and ... On this basis, we design a new method, which is called as successive projected ... the stationary point of a series of approximation problems. Finally, the.

2012-08-20

472

8. BUILDING 223 INTERIOR, EASTERN MAIN STOREROOM, FROM APPROXIMATE CENTER, ...  

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

8. BUILDING 223 INTERIOR, EASTERN MAIN STOREROOM, FROM APPROXIMATE CENTER, LOOKING SOUTHEAST, WITH VALUABLES CAGE AT LEFT BEHIND FORKLIFT. - Oakland Naval Supply Center, Pier Transit Sheds, North Marginal Wharf, between First & Third Streets, Oakland, Alameda County, CA

473

Approximate dynamic programming with applications in multi-agent systems  

E-print Network

This thesis presents the development and implementation of approximate dynamic programming methods used to manage multi-agent systems. The purpose of this thesis is to develop an architectural framework and theoretical ...

Valenti, Mario J. (Mario James), 1976-

2007-01-01

474

6. BUILDING 522, INTERIOR, STOREROOM, FROM APPROXIMATELY TWOTHIRDS OF DISTANCE ...  

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

6. BUILDING 522, INTERIOR, STOREROOM, FROM APPROXIMATELY TWO-THIRDS OF DISTANCE FROM EAST END, LOOKING WEST. - Oakland Naval Supply Center, Aeronautical Materials Storehouses, Between E & G Streets, between Fourth & Sixth Streets, Oakland, Alameda County, CA

475

4. BUILDING 422, WEST SIDE, FROM APPROXIMATELY 25 FEET SOUTHWEST ...  

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

4. BUILDING 422, WEST SIDE, FROM APPROXIMATELY 25 FEET SOUTHWEST OF SOUTHWEST CORNER, LOOKING NORTHEAST. - Oakland Naval Supply Center, Aeronautical Materials Storehouses, Between E & G Streets, between Fourth & Sixth Streets, Oakland, Alameda County, CA

476

5. BUILDING 522, INTERIOR, STOREROOM, FROM APPROXIMATELY 50 FEET SOUTHEAST ...  

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

5. BUILDING 522, INTERIOR, STOREROOM, FROM APPROXIMATELY 50 FEET SOUTHEAST OF NORTHWEST CORNER, LOOKING EAST. - Oakland Naval Supply Center, Aeronautical Materials Storehouses, Between E & G Streets, between Fourth & Sixth Streets, Oakland, Alameda County, CA

477

Robust Approximate Aggregation in Sensor Data Management Systems  

E-print Network

Robust Approximate Aggregation in Sensor Data Management Systems Jeffrey Considine Boston, and computation ACM Transactions on Database Systems, Vol. V, No. N, Month 20YY, Pages 1­0??. #12;2 · J. Considine

Kollios, George

478

A quantum relaxation-time approximation for finite fermion systems  

E-print Network

We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensi...

Reinhard, P -G

2014-01-01

479

Efficient Approximation of Optimization Queries Under Parametric Aggregation Constraints  

E-print Network

Efficient Approximation of Optimization Queries Under Parametric Aggregation Constraints Sudipto of queries that we refer to as OPAC (optimization under parametric aggregation constraints) queries indices to efficiently provide answers to OPAC queries. The answers returned by our indices

Pennsylvania, University of

480

Large-aperture approximation for not-so-large apertures  

E-print Network

angles, the LAA consistently underestimates the time-averaged Strehl ratio, so the LAA should be used of the optical wavefronts. A different approximation for computing time-averaged Strehl ratios is proposed

Gordeyev, Stanislav

481

Second post-Newtonian approximation of Einstein-aether theory  

SciTech Connect

In this paper, second post-Newtonian approximation of Einstein-aether theory is obtained by Chandrasekhar's approach. Five parametrized post-Newtonian parameters in first post-Newtonian approximation are presented after a time transformation and they are identical with previous works, in which {gamma}=1, {beta}=1, and two preferred-frame parameters remain. Meanwhile, in second post-Newtonian approximation, a parameter, which represents third order nonlinearity for gravity, is zero--the same as in general relativity. For an application for future deep space laser ranging missions, we reduce the metric coefficients for light propagation in a case of N point masses as a simplified model of the Solar System. The resulting light deflection angle in second post-Newtonian approximation poses another constraint on the Einstein-aether theory.

Xie Yi [Department of Astronomy, Nanjing University, Nanjing 210093 (China); Huang Tianyi [Department of Astronomy, Nanjing University, Nanjing 210093 (China); Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 20030 (China)

2008-06-15

482

Approximate translation : media, narrative, and experience in urban design  

E-print Network

Approximate translation is developed as a design process through which the place-embedded history of an urban environment can be understood, allowing for better design and intervention in that urban environment. Generally, ...

Crisman, Jonathan

2013-01-01

483

15. Looking north from east bank of ditch, approximately halfway ...  

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

15. Looking north from east bank of ditch, approximately halfway between cement pipe to north and burned irrigation pump station to south - Natomas Ditch System, Blue Ravine Segment, Juncture of Blue Ravine & Green Valley Roads, Folsom, Sacramento County, CA

484

Nested Taylor decomposition of univariate functions under fluctuationlessness approximation  

NASA Astrophysics Data System (ADS)

Taylor decomposition of an analytic function and the use of the remainder part of this decomposition expressed in integral form on which Fluctuationlessness theorem is applied was already known in the litterature, but application of Fluctuationlessness approximation twice on the remainder part adds up an amelioration to the approximation. Organisation of the decomposition in such a way that this is made possible is explained in detail in this work.

Gürvit, Ercan; Baykara, N. A.

2014-10-01

485

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques  

NASA Technical Reports Server (NTRS)

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Banks, H. T.; Wang, C.

1989-01-01

486

On Rosenau-Type Approximations to Fractional Diffusion Equations  

E-print Network

Owing to the Rosenau argument in Physical Review A, 46 (1992), pag. 12-15, originally proposed to obtain a regularized version of the Chapman-Enskog expansion of hydrodynamics, we introduce a non-local linear kinetic equation which approximates a fractional diffusion equation. We then show that the solution to this approximation, apart of a rapidly vanishing in time perturbation, approaches the fundamental solution of the fractional diffusion (a L\\'evy stable law) at large times.

Giulia Furioli; Ada Pulvirenti; Elide Terraneo; Giuseppe Toscani

2014-03-13

487

High-order approximation of conic sections by quadratic splines  

Microsoft Academic Search

Given a segment of a conic section in the form of a rational Bezier curve, a quadratic spline approximation is constructed and an explicit error bound is derived. The convergence order of the error bound is shown to be O(h4) which is optimal, and the spline curve is both C1 and G2. The approximation method is very efficient as it

Michael Floater

1995-01-01

488

Interior, building 810, view to west from approximately midhangar. Area ...  

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Interior, building 810, view to west from approximately mid-hangar. Area of photo encompasses approximately 1/4 of the interior space, with the KC-10 tanker aircraft and the figures beneath it giving an idea of scale, 90mm lens plus electronic flash fill lightening. - Travis Air Force Base, B-36 Hangar, Between Woodskill Avenue & Ellis, adjacent to Taxiway V & W, Fairfield, Solano County, CA

489

Finite-State Approximation of Phrase Structure Grammars  

Microsoft Academic Search

Phrase-structure grammars are an effective representation for important syntactic and semantic aspects of natural languages, but are computationally too demanding for use as language models in real-time speech recognition. An algorithm is described that computes finite-state approximations for context-free grammars and equivalent augmented phrase-structure grammar formalisms. The approximation is exact for certain context-free grammars generating regular languages, including all left-linear

Fernando C. N. Pereira; Rebecca N. Wright

1991-01-01

490

An expression for an approximation of the Voigt profile I  

NASA Astrophysics Data System (ADS)

An expression for an approximation of the deconvolution of the Voigt integral is presented. The results derived from this approach are discussed. It is found that the expressions proposed here give better results in the range of 2 < ? < ? than those approximations published previously. The FWHMs of the Lorentzian ?L and Gaussian ?G profiles are estimated whenever the Gaussian contribution to the Voigt profile be small, i.e. ? > 2.

Flores-Llamas, H.; Cabral-Prieto, A.; Jiménez-Domínguez, H.; Torres-Valderrama, M.

1991-01-01

491

Approximately J?-homomorphisms: A fixed point approach  

NASA Astrophysics Data System (ADS)

The functional equation (?) is stable if any function g satisfying the equation (?)approximately is near to the true solution of (?). A functional equation is superstable if every solution satisfying the equation approximately is an exact solution of it. Using fixed point methods, we prove the stability and superstability of J?-homomorphisms between J?-algebras for the generalized Jensen-type functional equation f({x+y}/{2})+f({x-y}/{2})=f(x).

Eshaghi Gordji, M.; Najati, A.

2010-05-01

492

Spectra of absolute instruments from the WKB approximation  

NASA Astrophysics Data System (ADS)

We calculate the frequency spectra of absolute optical instruments using the Wentzel-Kramers-Brillouin (WKB) approximation. The resulting eigenfrequencies approximate the actual values very accurately; in some cases they even give the exact values. Our calculations confirm the results obtained previously by a completely different method. In particular, the eigenfrequencies of absolute instruments form tight groups that are almost equidistantly spaced. We demonstrate our method and its results applied to several examples.

Tyc, Tomáš

2013-06-01

493

Approximations of the Wiener sausage and its curvature measures  

E-print Network

A parallel neighborhood of a path of a Brownian motion is sometimes called the Wiener sausage. We consider almost sure approximations of this random set by a sequence of random polyconvex sets and show that the convergence of the corresponding mean curvature measures holds under certain conditions in two and three dimensions. Based on these convergence results, the mean curvature measures of the Wiener sausage are calculated numerically by Monte Carlo simulations in two dimensions. The corresponding approximation formulae are given.

Rataj, Jan; Meschenmoser, Daniel; 10.1214/09-AAP596

2009-01-01

494

Spectrum in spontaneous emission: Beyond the Weisskopf-Wigner approximation  

SciTech Connect

The theory of spontaneous emission presented by Weisskopf and Wigner [V. Weisskopf and E. Wigner, Z. Phys. 63, 54 (1930)] provides an excellent approximation of the actual decay that atoms undergo on optically allowed transitions. However, the theory cannot be rigorously correct since it leads to a Lorentzian spectrum that extends to negative frequencies. Within the rotating-wave approximation, we derive a closed-form expression for the spectrum that is valid for all frequencies.

Berman, P. R.; Ford, G. W. [Michigan Center for Theoretical Physics and Physics Department, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040 (United States)

2010-08-15

495

Superdeformation in the mass A {approximately} 80 region  

SciTech Connect

A new island of superdeformed nuclei with major-to-minor axis ratio of 2:1 has recently been discovered in the A {approximately} 80 medium-mass region, confirming the predictions for the existence of a large SD gap at particle number N,Z {approximately} 44. The general properties of more than 20 bands observed so far will be reviewed here, and compared with those of the superdeformed bands in the heavier nuclei.

Baktash, C. [Oak Ridge National Lab., TN (United States). Physics Div.

1996-12-31

496

The Complexity of Approximating the Class Steiner Tree Problem  

Microsoft Academic Search

Given a connected, undirected distance graph with required classesof nodes and optional Steiner nodes, find a shortest tree containingat least one node of each required class. This problem called ClassSteiner Tree is NP-hard and therefore we are dependent on approximation.In this paper, we investigate various restrictions of the problemcomparing their complexities with respect to approximability. A mainresult is that for

Edmund Ihler

1991-01-01

497

Approximating steady states in equilibrium and nonequilibrium condensates  

NASA Astrophysics Data System (ADS)

We obtain approximations for the time-independent Gross-Pitaevskii (GP) and complex GP equation in two and three spatial dimensions by generalizing the divergence-free WKB method. The results include an explicit expression of a uniformly valid approximation for the condensate density of an ultracold Bose gas confined in a harmonic trap that extends into the classically forbidden region. This provides an accurate approximation of the condensate density that includes healing effects at leading order that are missing in the widely adopted Thomas-Fermi approximation. The results presented herein allow us to formulate useful approximations to a range of experimental systems including the equilibrium properties of a finite-temperature Bose gas and the steady-state properties of a two-dimensional nonequilibrium condensate. Comparisons between our asymptotic and numerical results for the conservative and forced-dissipative forms of the GP equations as applied to these systems show excellent agreement between the two sets of solutions, thereby illustrating the accuracy of these approximations.

Salman, Hayder

2012-06-01

498

An intermediate level of approximation for computing the dual descriptor.  

PubMed

At present, there are two levels of approximation to compute the dual descriptor (DD). The first uses the total electronic density of the original system along with the electronic densities of the system with one more electron and one less electron, but this procedure is time consuming and normal termination of computation of total electronic densities is not guaranteed. The second level of approximation uses only the electronic densities of frontier molecular orbitals, HOMO and LUMO, to avoid the former approximation; however, the orbital relaxation implicitly included in the first level of approximation is absent in the second, thus risking an incorrect interpretation of local reactivity. Between the lowest occupied molecular orbital (LOMO) and the highest unoccupied molecular orbital (HUMO), a framework to provide an expression of the DD in terms of the electronic densities of all molecular orbitals (except HUMO and LOMO) has been proposed to be implemented by programmers as a computational code. This methodology implies another level of approximation located between the conventional approximation methods mentioned above. In this study, working equations have been oriented toward molecular closed- and open-shell systems. In addition, the mathematical expression for a closed-shell system was applied to acetylene in order to assess the capability of this approach to generate the DD. PMID:23229228

Martínez-Araya, Jorge Ignacio

2013-07-01

499

Structural Reliability Analysis and Optimization: Use of Approximations  

NASA Technical Reports Server (NTRS)

This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.

Grandhi, Ramana V.; Wang, Liping

1999-01-01

500

On the dynamics of approximating schemes for dissipative nonlinear equations  

NASA Technical Reports Server (NTRS)

Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

Jones, Donald A.

1993-01-01